## Main.HomePage History

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[[http://www.math.ucsb.edu/home | Return to Department of Mathematics Homepage]]

to:

[[http://www.math.ucsb.edu/home | Return to the Department of Mathematics Homepage]]

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[[http://www.math.ucsb.edu/home | Return to ~~Mathematics ~~Department Homepage]]

to:

[[http://www.math.ucsb.edu/home | Return to Department of Mathematics Homepage]]

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''' ''Prospective Graduate Students: '' ''' The applied mathematics group welcomes you to apply to the graduate program. Applied mathematics offers many opportunities for ~~exciting ~~graduate research ~~making~~ connections between core areas of mathematics and important problems arising in applications. At UCSB there are also many exciting research opportunities to conduct interdisciplinary research at the interface of mathematics with fields from the sciences, engineering, and computation. To learn more about individual research areas please see the above faculty webpages.

to:

''' ''Prospective Graduate Students: '' ''' The applied mathematics group welcomes you to apply to the graduate program. Applied mathematics offers many exciting opportunities for graduate research that makes connections between core areas of mathematics and important problems arising in applications. At UCSB there are also many exciting research opportunities to conduct interdisciplinary research at the interface of mathematics with fields from the sciences, engineering, and computation. To learn more about individual research areas please see the above faculty webpages.

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%width=300px% Attach:George_Danny.jpg %width=300px% Attach:Ed.jpg %width=300px% Attach:REUgroup.jpg

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''' ''Apply for graduate studies in applied mathematics. '' '''~~ :~~ [[{$Group}.HomePage?skin=applmathLayout1#graduate_students | [more information here] ]] \\

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''' ''Apply for graduate studies in applied mathematics. '' ''' [[{$Group}.HomePage?skin=applmathLayout1#graduate_students | [more information here] ]] \\

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''' ''Apply for graduate studies in ~~Applied Mathematics~~. '' ''' : [[{$Group}.HomePage?skin=applmathLayout1#graduate_students | [more information here] ]] \\

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''' ''Apply for graduate studies in applied mathematics. '' ''' : [[{$Group}.HomePage?skin=applmathLayout1#graduate_students | [more information here] ]] \\

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''' ''Apply for graduate studies in Applied Mathematics '' ''' : [[{$Group}.HomePage?skin=applmathLayout1#graduate_students | [more information here] ]] \\

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''' ''Apply for graduate studies in Applied Mathematics. '' ''' : [[{$Group}.HomePage?skin=applmathLayout1#graduate_students | [more information here] ]] \\

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''' ''Apply for ~~Graduate Studies~~ in Applied Mathematics '' ''' : [[{$Group}.HomePage?skin=applmathLayout1#graduate_students | [more information here] ]] \\

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''' ''Apply for graduate studies in Applied Mathematics '' ''' : [[{$Group}.HomePage?skin=applmathLayout1#graduate_students | [more information here] ]] \\

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[[http://www.math.ucsb.edu/home | Return to Mathematics Department Homepage]]

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''' ''Apply for Graduate Studies in Applied Mathematics '' ''' : [[{$Group}.~~TestPage7~~?skin=applmathLayout1#graduate_students | [more information here] ]] \\

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''' ''Apply for Graduate Studies in Applied Mathematics '' ''' : [[{$Group}.HomePage?skin=applmathLayout1#graduate_students | [more information here] ]] \\

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\\

\\

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''' ''Apply for Graduate Studies in Applied Mathematics '' ''' : [[{$Group}.TestPage7?skin=applmathLayout1#graduate_students | [more information here] ]] \\

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Applied mathematics integrates the development of core areas of mathematics with

the solution of~~specific ~~problems arising in ~~applications, often in~~ the ~~basic~~ sciences

~~or~~ engineering~~. Faculty of the Applied Mathematics Group~~ are active in ~~diverse~~ areas

~~and participate in collaborations with many faculty on campus. Research areas include: ~~

* Complex Fluids and Soft-Condensed Matter Physics.

~~* Crystalline Solids and Liquid Crystals~~.

~~* Computational Fluid Dynamics.~~

*~~ Density Functional Theory.~~

* ~~Analysis of Non-linear Evolutionary PDE's (existence results ~~/~~ finite time singularities)~~.

* Applied Harmonic Analysis.

* Stochastic Analysis.

Here you will find information about our program in Applied Mathematics, current activities,

~~upcoming seminar talks, and highlights from recent research.~~

-~~---~~

!!News

----

'+%color555555%Paul J.~~ Atzberger Wins NSF Faculty Early Career Development Award (NSF CAREER)+'~~

%lfloat text-align=left margin-top=5px margin-right=5px margin-bottom=10px margin-left=5px width=100px% Attach:atzbergerPhoto_board.jpg

Professor Paul J.~~ Atzberger awarded NSF CAREER Award "Emergent Biological Mechanics of Cellular Microstructures~~.~~" His proposed research aims to develop new methods combining approaches from stochastic analysis, statistical mechanics, and scientific computing to study fundamental problems related to the mechanics of biological materials. This $435K, five year grant "recognizes and supports the early career development activities~~ of ~~those faculty members who are most likely to become the academic leaders of the 21st century.” Significantly, this proposal will be funded by three NSF agencies: Mathematical Biology, Applied Mathematics, and the Office of Cyberinfrastructure. ~~

the solution of

* Complex Fluids and Soft-Condensed Matter Physics

* Applied Harmonic Analysis

* Stochastic Analysis

Here you will find information about our program in Applied Mathematics, current activities,

!!News

----

'+%color555555%Paul J

%lfloat text-align=left margin-top=5px margin-right=5px margin-bottom=10px margin-left=5px width=100px% Attach:atzbergerPhoto_board.jpg

Professor Paul J

to:

Applied mathematics integrates the development of core areas of mathematics with the solution of problems arising in diverse application areas including the natural sciences, engineering, and computation. Faculty of applied mathematics are active in many areas. More information on the specific research interests of individual faculty can be found below.

!! Associated Faculty:

* Paul J. Atzberger

**[[http://atzberger.org/ | [webpage] ]].

* Bjorn Birnir

**[[http://www.math.ucsb.edu/~birnir | [webpage] ]]

* Hector Ceniceros

**[[http://www.math.ucsb.edu/~hdc | [webpage] ]]

* Katy C. Craig

**[[http://www.math.ucsb.edu/~kcraig/math/home.html | [webpage] ]].

* Carlos Garcia-Cervera

**[[http://www.math.ucsb.edu/~cgarcia | [webpage] ]]

* Davit Harutyunyan

**[[http://web.math.ucsb.edu/~harutyunyan/ | [webpage] ]].

* Maria Isabel Bueno Cachadina

** [[http://www.math.ucsb.edu/~mbueno | [webpage] ]].

* Christopher Ograin

** [[http://www.math.ucsb.edu/~ograin/ | [webpage] ]].

* Gustavo Ponce

** [[http://www.math.ucsb.edu/~ponce/ | [webpage] ]].

* Thomas Sideris

** [[http://www.math.ucsb.edu/~sideris/Home_Page.html | [webpage] ]].

* Xu Yang

** [[http://www.math.ucsb.edu/~xuyang | [webpage] ]].

* Hanming Zhou

** [[http://web.math.ucsb.edu/~hzhou/ | [webpage] ]].

''' ''Applied Mathematics Seminar:'' '''

A seminar is held on topics in applied mathematics and analysis. For more information on the schedule of upcoming talks, please see the calendar on the Department of Mathematics [[http://www.math.ucsb.edu/home | homepage]]. \\

!! Associated Faculty:

* Paul J. Atzberger

**[[http://atzberger.org/ | [webpage] ]].

* Bjorn Birnir

**[[http://www.math.ucsb.edu/~birnir | [webpage] ]]

* Hector Ceniceros

**[[http://www.math.ucsb.edu/~hdc | [webpage] ]]

* Katy C. Craig

**[[http://www.math.ucsb.edu/~kcraig/math/home.html | [webpage] ]].

* Carlos Garcia-Cervera

**[[http://www.math.ucsb.edu/~cgarcia | [webpage] ]]

* Davit Harutyunyan

**[[http://web.math.ucsb.edu/~harutyunyan/ | [webpage] ]].

* Maria Isabel Bueno Cachadina

** [[http://www.math.ucsb.edu/~mbueno | [webpage] ]].

* Christopher Ograin

** [[http://www.math.ucsb.edu/~ograin/ | [webpage] ]].

* Gustavo Ponce

** [[http://www.math.ucsb.edu/~ponce/ | [webpage] ]].

* Thomas Sideris

** [[http://www.math.ucsb.edu/~sideris/Home_Page.html | [webpage] ]].

* Xu Yang

** [[http://www.math.ucsb.edu/~xuyang | [webpage] ]].

* Hanming Zhou

** [[http://web.math.ucsb.edu/~hzhou/ | [webpage] ]].

''' ''Applied Mathematics Seminar:'' '''

A seminar is held on topics in applied mathematics and analysis. For more information on the schedule of upcoming talks, please see the calendar on the Department of Mathematics [[http://www.math.ucsb.edu/home | homepage]]. \\

Added lines 42-46:

[[#graduate_students]]

''' ''Prospective Graduate Students: '' ''' The applied mathematics group welcomes you to apply to the graduate program. Applied mathematics offers many opportunities for exciting graduate research making connections between core areas of mathematics and important problems arising in applications. At UCSB there are also many exciting research opportunities to conduct interdisciplinary research at the interface of mathematics with fields from the sciences, engineering, and computation. To learn more about individual research areas please see the above faculty webpages.

Please feel free to reach out to the faculty and staff with any questions you may have about the graduate program. General information about the Mathematics Program at UCSB and important deadlines can be found on the Department of Mathematics [[http://www.math.ucsb.edu/home | homepage]].

Deleted line 47:

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----

'+%color555555%Carlos Garcia-Cervera Wins NSF Faculty Early Career Development Award (NSF CAREER)+'

%lfloat text-align=left margin-top=5px margin-right=5px margin-bottom=10px margin-left=5px width=100px% Attach:carlosSmiles.jpg

Professor Carlos Garcia-Cervera receives the prestigious NSF Career Award for his proposal "Multilevel Physics in the Study of Solids: Modeling, Analysis and Simulations".

The Faculty Early Career Development (CAREER) Program offers the NSF’s most prestigious awards in support of early career development activities of those teacher-scholars who are most likely to become the academic leaders of the 21st century.

The awards are for a minimum of $400,000 and support his research for five years providing funding

for postdoctoral researchers and graduate students. The proposed research program has the potential

to impact fundamental computational approaches used in studying solid materials. This is the first

NSF CAREER award given to a faculty member of the department of mathematics.\\

[[http://www.ia.ucsb.edu/93106/2007/November19/math.html | Full Article]]

\\

\\

More information about Professor Garcia-Cervera's research be found on his [[http://www.math.ucsb.edu/~cgarcia/index.html | website]]. \\

\\

\\

----

'+%color555555%Math Circle Started at UCSB+'

%lfloat text-align=left margin-top=5px margin-right=5px margin-bottom=10px margin-left=5px width=100px% Attach:mathCircleLogo.gif

A Math Circle has been started at UCSB for outreach to the local community. The Math Circle engages in mathematics pre-college

students from local high schools. The UCSB Math Circle offers a forum for the discussion of mathematical topics, mathematics education,

and careers involving mathematics. From the Applied Mathematics Group, [[http://www.math.ucsb.edu/~mbueno/index.html | Maribel Bueno Cachadina]] is playing a leading role in organizing the UCSB Math Circle. For more information see the Math Circle Website:\\

[[http://www.math.ucsb.edu/~mbueno/mathcircle/index.html | UCSB Math Circle Website]].\\

\\

----

[[#ResearchHighlights]]

!!Research Highlights

----

'+Fluid-Structure Interactions : Immersed Boundary Methods and Boundary Integral Methods+'

The mechanics of many physical systems depends importantly on the interaction of flexible elastic

structures with a fluid flow. Examples of macroscopic systems include the pumping of the heart in which blood flow interacts with valves, lift general in insect flight, and wave propagation in the cochlea of the inner ear. Examples of microscopic systems include the rheology of complex fluids and soft-matter which depends importantly on microstructures (such as colloids, lipids, polymers, vesicles) which interact with shear and extensional fluid flows serving through small-scale deformations to elastically store or dissipate energy. These microscopic processes often result macroscopically in material properties exhibiting interesting counter-intuitive phenomena and features hard to predict a priori. Immersed Boundary Methods (IBM) and Boundary Integral Methods (BIM) are numerical approaches for studying the mechanics of elastic structures which interact with a fluid.

%width=300px% Attach:SIB_Schematic.png

In the IBM formalism the hydrodynamic interactions of the composite system are handled by an approximate treatment of the fluid-structure stresses in which a Lagrangian representation of the immersed structures is coupled to an Eulerian representation of the fluid. In the BIM formalism the hydrodynamic equations are reduced to a description on the surface of an immersed structure usually taking the form of integral equations (possibly non-linear). The fluid-structure interaction problem and these underlying formulations present many interesting mathematical problems both for analysis and numerics.

Faculty members working in this area include:

* [[http://www.math.ucsb.edu/~atzberg/index.html | Dr. Atzberger]] : Prof. Atzberger has done work on utilizing immersed boundary methods to study properties of soft condensed matter. To account consistently for microstructure mechanics, hydrodynamic coupling, and thermal fluctuations he has extended the IBM formalism to incorporate stochastic driving fields consistent with statistical mechanics. The resulting stochastic partial differential equations (SPDEs) present many interesting challenges both for analysis and the development of numerical methods. A paper on the methodology can be found here : [[http://www.math.ucsb.edu/~atzberg/publications/preprintStochIB.pdf | A Stochastic Immersed Boundary Method for Fluid-Structure Dynamics at Microscopic Length Scales]]. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method and applications can be found here [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | [Video of IMA Talk]]].

* [[http://www.math.ucsb.edu/~hdc | Dr. Ceniceros]] : Prof. Ceniceros in joint work with UCSB grad student Jordan Fisher and [[http://www.ime.usp.br/~roma/index-1.html |Prof. Alexandre Roma]] (USP) has recently designed efficient implicit methods for the IBM formalisms significantly advancing the time-scales accessible in simulations of systems with stiff elastic structures. A soon to appear manuscript of the work can be found most likely here: [[http://www.math.ucsb.edu/~hdc/public/IBM_Implicit.pdf | Efficient solutions to robust, semi-implicit discretizations of the Immersed Boundary Method]].

----

'+Local and Global Wellposedness of Nonlinear Evolutionary Equations +'

Provide conditions on initial data which ensure the existence, uniqueness, and continuous dependence of solutions to the initial value problem for nonlinear

evolutionary partial differential equations.

Determine whether solutions exist globally in time or develop singularities in finite time. Explore the regularity and asymptotic behavior of solutions.

Applications to nonlinear dispersive equations, hydro- and elasto-dynamics.

Faculty members working in this area include:

* Dr. Sideris : [[http://www.math.ucsb.edu/~sideris/index.html | Research Website]].

* Dr. Ponce : [[http://www.math.ucsb.edu/~ponce/index.html | Research Website]].

----

!!Research Gallery \\

%width=200px% [[http://www.math.ucsb.edu/~atzberg/pmwiki_intranet/index.php?n=AtzbergerHomePage.HomePage?setskin=atzbergerHomepage1#ResearchSummaries | Attach:montage_sib.png]] %width=100px% [[http://www.math.ucsb.edu/~cgarcia/index.html | Attach:carlosImage.png]] %width=100px% [[http://www.math.ucsb.edu/~hdc/index.html | Attach:fingers.jpg]] %width=100px% [[http://www.math.ucsb.edu/~hdc/index.html | Attach:strings.jpg]] %width=125px% [[http://www.math.ucsb.edu/~atzberg/pmwiki_intranet/index.php?n=AtzbergerHomePage.HomePage?setskin=atzbergerHomepage1#ResearchSummaries | Attach:montage_osmosis.png]] %width=100px% [[http://www.math.ucsb.edu/~hdc/index.html | Attach:rolls.jpg]] %width=100px% [[http://www.math.ucsb.edu/~atzberg/pmwiki_intranet/index.php?n=AtzbergerHomePage.HomePage?setskin=atzbergerHomepage1#ResearchSummaries | Attach:atzbergerImage.png]] %width=200px% [[http://www.math.ucsb.edu/~atzberg/pmwiki_intranet/index.php?n=AtzbergerHomePage.HomePage?setskin=atzbergerHomepage1#ResearchSummaries | Attach:montage_molBio.png]]

----

Changed lines 22-32 from:

!! Applied Mathematics and PDE Seminar

For more information, please see the above faculty webpages.

to:

Here you will find information about our program in Applied Mathematics, current activities,

upcoming seminar talks, and highlights from recent research.

----

!!News

----

'+%color555555%Paul J. Atzberger Wins NSF Faculty Early Career Development Award (NSF CAREER)+'

%lfloat text-align=left margin-top=5px margin-right=5px margin-bottom=10px margin-left=5px width=100px% Attach:atzbergerPhoto_board.jpg

Professor Paul J. Atzberger awarded NSF CAREER Award "Emergent Biological Mechanics of Cellular Microstructures." His proposed research aims to develop new methods combining approaches from stochastic analysis, statistical mechanics, and scientific computing to study fundamental problems related to the mechanics of biological materials. This $435K, five year grant "recognizes and supports the early career development activities of those faculty members who are most likely to become the academic leaders of the 21st century.” Significantly, this proposal will be funded by three NSF agencies: Mathematical Biology, Applied Mathematics, and the Office of Cyberinfrastructure.

\\

\\

More information about Professor Atzberger's research be found on his [[http://www.math.ucsb.edu/~atzberg/index.html | website]]. \\

\\

\\

----

'+%color555555%Carlos Garcia-Cervera Wins NSF Faculty Early Career Development Award (NSF CAREER)+'

%lfloat text-align=left margin-top=5px margin-right=5px margin-bottom=10px margin-left=5px width=100px% Attach:carlosSmiles.jpg

Professor Carlos Garcia-Cervera receives the prestigious NSF Career Award for his proposal "Multilevel Physics in the Study of Solids: Modeling, Analysis and Simulations".

The Faculty Early Career Development (CAREER) Program offers the NSF’s most prestigious awards in support of early career development activities of those teacher-scholars who are most likely to become the academic leaders of the 21st century.

The awards are for a minimum of $400,000 and support his research for five years providing funding

for postdoctoral researchers and graduate students. The proposed research program has the potential

to impact fundamental computational approaches used in studying solid materials. This is the first

NSF CAREER award given to a faculty member of the department of mathematics.\\

[[http://www.ia.ucsb.edu/93106/2007/November19/math.html | Full Article]]

\\

\\

More information about Professor Garcia-Cervera's research be found on his [[http://www.math.ucsb.edu/~cgarcia/index.html | website]]. \\

\\

\\

----

'+%color555555%Math Circle Started at UCSB+'

%lfloat text-align=left margin-top=5px margin-right=5px margin-bottom=10px margin-left=5px width=100px% Attach:mathCircleLogo.gif

A Math Circle has been started at UCSB for outreach to the local community. The Math Circle engages in mathematics pre-college

students from local high schools. The UCSB Math Circle offers a forum for the discussion of mathematical topics, mathematics education,

and careers involving mathematics. From the Applied Mathematics Group, [[http://www.math.ucsb.edu/~mbueno/index.html | Maribel Bueno Cachadina]] is playing a leading role in organizing the UCSB Math Circle. For more information see the Math Circle Website:\\

[[http://www.math.ucsb.edu/~mbueno/mathcircle/index.html | UCSB Math Circle Website]].\\

\\

----

[[#ResearchHighlights]]

!!Research Highlights

----

'+Fluid-Structure Interactions : Immersed Boundary Methods and Boundary Integral Methods+'

The mechanics of many physical systems depends importantly on the interaction of flexible elastic

structures with a fluid flow. Examples of macroscopic systems include the pumping of the heart in which blood flow interacts with valves, lift general in insect flight, and wave propagation in the cochlea of the inner ear. Examples of microscopic systems include the rheology of complex fluids and soft-matter which depends importantly on microstructures (such as colloids, lipids, polymers, vesicles) which interact with shear and extensional fluid flows serving through small-scale deformations to elastically store or dissipate energy. These microscopic processes often result macroscopically in material properties exhibiting interesting counter-intuitive phenomena and features hard to predict a priori. Immersed Boundary Methods (IBM) and Boundary Integral Methods (BIM) are numerical approaches for studying the mechanics of elastic structures which interact with a fluid.

%width=300px% Attach:SIB_Schematic.png

In the IBM formalism the hydrodynamic interactions of the composite system are handled by an approximate treatment of the fluid-structure stresses in which a Lagrangian representation of the immersed structures is coupled to an Eulerian representation of the fluid. In the BIM formalism the hydrodynamic equations are reduced to a description on the surface of an immersed structure usually taking the form of integral equations (possibly non-linear). The fluid-structure interaction problem and these underlying formulations present many interesting mathematical problems both for analysis and numerics.

Faculty members working in this area include:

* [[http://www.math.ucsb.edu/~atzberg/index.html | Dr. Atzberger]] : Prof. Atzberger has done work on utilizing immersed boundary methods to study properties of soft condensed matter. To account consistently for microstructure mechanics, hydrodynamic coupling, and thermal fluctuations he has extended the IBM formalism to incorporate stochastic driving fields consistent with statistical mechanics. The resulting stochastic partial differential equations (SPDEs) present many interesting challenges both for analysis and the development of numerical methods. A paper on the methodology can be found here : [[http://www.math.ucsb.edu/~atzberg/publications/preprintStochIB.pdf | A Stochastic Immersed Boundary Method for Fluid-Structure Dynamics at Microscopic Length Scales]]. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method and applications can be found here [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | [Video of IMA Talk]]].

* [[http://www.math.ucsb.edu/~hdc | Dr. Ceniceros]] : Prof. Ceniceros in joint work with UCSB grad student Jordan Fisher and [[http://www.ime.usp.br/~roma/index-1.html |Prof. Alexandre Roma]] (USP) has recently designed efficient implicit methods for the IBM formalisms significantly advancing the time-scales accessible in simulations of systems with stiff elastic structures. A soon to appear manuscript of the work can be found most likely here: [[http://www.math.ucsb.edu/~hdc/public/IBM_Implicit.pdf | Efficient solutions to robust, semi-implicit discretizations of the Immersed Boundary Method]].

----

'+Local and Global Wellposedness of Nonlinear Evolutionary Equations +'

Provide conditions on initial data which ensure the existence, uniqueness, and continuous dependence of solutions to the initial value problem for nonlinear

evolutionary partial differential equations.

Determine whether solutions exist globally in time or develop singularities in finite time. Explore the regularity and asymptotic behavior of solutions.

Applications to nonlinear dispersive equations, hydro- and elasto-dynamics.

Faculty members working in this area include:

* Dr. Sideris : [[http://www.math.ucsb.edu/~sideris/index.html | Research Website]].

* Dr. Ponce : [[http://www.math.ucsb.edu/~ponce/index.html | Research Website]].

----

!!Research Gallery \\

%width=200px% [[http://www.math.ucsb.edu/~atzberg/pmwiki_intranet/index.php?n=AtzbergerHomePage.HomePage?setskin=atzbergerHomepage1#ResearchSummaries | Attach:montage_sib.png]] %width=100px% [[http://www.math.ucsb.edu/~cgarcia/index.html | Attach:carlosImage.png]] %width=100px% [[http://www.math.ucsb.edu/~hdc/index.html | Attach:fingers.jpg]] %width=100px% [[http://www.math.ucsb.edu/~hdc/index.html | Attach:strings.jpg]] %width=125px% [[http://www.math.ucsb.edu/~atzberg/pmwiki_intranet/index.php?n=AtzbergerHomePage.HomePage?setskin=atzbergerHomepage1#ResearchSummaries | Attach:montage_osmosis.png]] %width=100px% [[http://www.math.ucsb.edu/~hdc/index.html | Attach:rolls.jpg]] %width=100px% [[http://www.math.ucsb.edu/~atzberg/pmwiki_intranet/index.php?n=AtzbergerHomePage.HomePage?setskin=atzbergerHomepage1#ResearchSummaries | Attach:atzbergerImage.png]] %width=200px% [[http://www.math.ucsb.edu/~atzberg/pmwiki_intranet/index.php?n=AtzbergerHomePage.HomePage?setskin=atzbergerHomepage1#ResearchSummaries | Attach:montage_molBio.png]]

----

upcoming seminar talks, and highlights from recent research.

----

!!News

----

'+%color555555%Paul J. Atzberger Wins NSF Faculty Early Career Development Award (NSF CAREER)+'

%lfloat text-align=left margin-top=5px margin-right=5px margin-bottom=10px margin-left=5px width=100px% Attach:atzbergerPhoto_board.jpg

Professor Paul J. Atzberger awarded NSF CAREER Award "Emergent Biological Mechanics of Cellular Microstructures." His proposed research aims to develop new methods combining approaches from stochastic analysis, statistical mechanics, and scientific computing to study fundamental problems related to the mechanics of biological materials. This $435K, five year grant "recognizes and supports the early career development activities of those faculty members who are most likely to become the academic leaders of the 21st century.” Significantly, this proposal will be funded by three NSF agencies: Mathematical Biology, Applied Mathematics, and the Office of Cyberinfrastructure.

\\

\\

More information about Professor Atzberger's research be found on his [[http://www.math.ucsb.edu/~atzberg/index.html | website]]. \\

\\

\\

----

'+%color555555%Carlos Garcia-Cervera Wins NSF Faculty Early Career Development Award (NSF CAREER)+'

%lfloat text-align=left margin-top=5px margin-right=5px margin-bottom=10px margin-left=5px width=100px% Attach:carlosSmiles.jpg

Professor Carlos Garcia-Cervera receives the prestigious NSF Career Award for his proposal "Multilevel Physics in the Study of Solids: Modeling, Analysis and Simulations".

The Faculty Early Career Development (CAREER) Program offers the NSF’s most prestigious awards in support of early career development activities of those teacher-scholars who are most likely to become the academic leaders of the 21st century.

The awards are for a minimum of $400,000 and support his research for five years providing funding

for postdoctoral researchers and graduate students. The proposed research program has the potential

to impact fundamental computational approaches used in studying solid materials. This is the first

NSF CAREER award given to a faculty member of the department of mathematics.\\

[[http://www.ia.ucsb.edu/93106/2007/November19/math.html | Full Article]]

\\

\\

More information about Professor Garcia-Cervera's research be found on his [[http://www.math.ucsb.edu/~cgarcia/index.html | website]]. \\

\\

\\

----

'+%color555555%Math Circle Started at UCSB+'

%lfloat text-align=left margin-top=5px margin-right=5px margin-bottom=10px margin-left=5px width=100px% Attach:mathCircleLogo.gif

A Math Circle has been started at UCSB for outreach to the local community. The Math Circle engages in mathematics pre-college

students from local high schools. The UCSB Math Circle offers a forum for the discussion of mathematical topics, mathematics education,

and careers involving mathematics. From the Applied Mathematics Group, [[http://www.math.ucsb.edu/~mbueno/index.html | Maribel Bueno Cachadina]] is playing a leading role in organizing the UCSB Math Circle. For more information see the Math Circle Website:\\

[[http://www.math.ucsb.edu/~mbueno/mathcircle/index.html | UCSB Math Circle Website]].\\

\\

----

[[#ResearchHighlights]]

!!Research Highlights

----

'+Fluid-Structure Interactions : Immersed Boundary Methods and Boundary Integral Methods+'

The mechanics of many physical systems depends importantly on the interaction of flexible elastic

structures with a fluid flow. Examples of macroscopic systems include the pumping of the heart in which blood flow interacts with valves, lift general in insect flight, and wave propagation in the cochlea of the inner ear. Examples of microscopic systems include the rheology of complex fluids and soft-matter which depends importantly on microstructures (such as colloids, lipids, polymers, vesicles) which interact with shear and extensional fluid flows serving through small-scale deformations to elastically store or dissipate energy. These microscopic processes often result macroscopically in material properties exhibiting interesting counter-intuitive phenomena and features hard to predict a priori. Immersed Boundary Methods (IBM) and Boundary Integral Methods (BIM) are numerical approaches for studying the mechanics of elastic structures which interact with a fluid.

%width=300px% Attach:SIB_Schematic.png

In the IBM formalism the hydrodynamic interactions of the composite system are handled by an approximate treatment of the fluid-structure stresses in which a Lagrangian representation of the immersed structures is coupled to an Eulerian representation of the fluid. In the BIM formalism the hydrodynamic equations are reduced to a description on the surface of an immersed structure usually taking the form of integral equations (possibly non-linear). The fluid-structure interaction problem and these underlying formulations present many interesting mathematical problems both for analysis and numerics.

Faculty members working in this area include:

* [[http://www.math.ucsb.edu/~atzberg/index.html | Dr. Atzberger]] : Prof. Atzberger has done work on utilizing immersed boundary methods to study properties of soft condensed matter. To account consistently for microstructure mechanics, hydrodynamic coupling, and thermal fluctuations he has extended the IBM formalism to incorporate stochastic driving fields consistent with statistical mechanics. The resulting stochastic partial differential equations (SPDEs) present many interesting challenges both for analysis and the development of numerical methods. A paper on the methodology can be found here : [[http://www.math.ucsb.edu/~atzberg/publications/preprintStochIB.pdf | A Stochastic Immersed Boundary Method for Fluid-Structure Dynamics at Microscopic Length Scales]]. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method and applications can be found here [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | [Video of IMA Talk]]].

* [[http://www.math.ucsb.edu/~hdc | Dr. Ceniceros]] : Prof. Ceniceros in joint work with UCSB grad student Jordan Fisher and [[http://www.ime.usp.br/~roma/index-1.html |Prof. Alexandre Roma]] (USP) has recently designed efficient implicit methods for the IBM formalisms significantly advancing the time-scales accessible in simulations of systems with stiff elastic structures. A soon to appear manuscript of the work can be found most likely here: [[http://www.math.ucsb.edu/~hdc/public/IBM_Implicit.pdf | Efficient solutions to robust, semi-implicit discretizations of the Immersed Boundary Method]].

----

'+Local and Global Wellposedness of Nonlinear Evolutionary Equations +'

Provide conditions on initial data which ensure the existence, uniqueness, and continuous dependence of solutions to the initial value problem for nonlinear

evolutionary partial differential equations.

Determine whether solutions exist globally in time or develop singularities in finite time. Explore the regularity and asymptotic behavior of solutions.

Applications to nonlinear dispersive equations, hydro- and elasto-dynamics.

Faculty members working in this area include:

* Dr. Sideris : [[http://www.math.ucsb.edu/~sideris/index.html | Research Website]].

* Dr. Ponce : [[http://www.math.ucsb.edu/~ponce/index.html | Research Website]].

----

!!Research Gallery \\

%width=200px% [[http://www.math.ucsb.edu/~atzberg/pmwiki_intranet/index.php?n=AtzbergerHomePage.HomePage?setskin=atzbergerHomepage1#ResearchSummaries | Attach:montage_sib.png]] %width=100px% [[http://www.math.ucsb.edu/~cgarcia/index.html | Attach:carlosImage.png]] %width=100px% [[http://www.math.ucsb.edu/~hdc/index.html | Attach:fingers.jpg]] %width=100px% [[http://www.math.ucsb.edu/~hdc/index.html | Attach:strings.jpg]] %width=125px% [[http://www.math.ucsb.edu/~atzberg/pmwiki_intranet/index.php?n=AtzbergerHomePage.HomePage?setskin=atzbergerHomepage1#ResearchSummaries | Attach:montage_osmosis.png]] %width=100px% [[http://www.math.ucsb.edu/~hdc/index.html | Attach:rolls.jpg]] %width=100px% [[http://www.math.ucsb.edu/~atzberg/pmwiki_intranet/index.php?n=AtzbergerHomePage.HomePage?setskin=atzbergerHomepage1#ResearchSummaries | Attach:atzbergerImage.png]] %width=200px% [[http://www.math.ucsb.edu/~atzberg/pmwiki_intranet/index.php?n=AtzbergerHomePage.HomePage?setskin=atzbergerHomepage1#ResearchSummaries | Attach:montage_molBio.png]]

----

Changed lines 22-112 from:

upcoming seminar talks, and highlights from recent research.

----

!!News

----

'+%color555555%Paul J. Atzberger Wins NSF Faculty Early Career Development Award (NSF CAREER)+'

%lfloat text-align=left margin-top=5px margin-right=5px margin-bottom=10px margin-left=5px width=100px% Attach:atzbergerPhoto_board.jpg

Professor Paul J. Atzberger awarded NSF CAREER Award "Emergent Biological Mechanics of Cellular Microstructures." His proposed research aims to develop new methods combining approaches from stochastic analysis, statistical mechanics, and scientific computing to study fundamental problems related to the mechanics of biological materials. This $435K, five year grant "recognizes and supports the early career development activities of those faculty members who are most likely to become the academic leaders of the 21st century.” Significantly, this proposal will be funded by three NSF agencies: Mathematical Biology, Applied Mathematics, and the Office of Cyberinfrastructure.

\\

\\

More information about Professor Atzberger's research be found on his [[http://www.math.ucsb.edu/~atzberg/index.html | website]]. \\

\\

\\

----

'+%color555555%Carlos Garcia-Cervera Wins NSF Faculty Early Career Development Award (NSF CAREER)+'

%lfloat text-align=left margin-top=5px margin-right=5px margin-bottom=10px margin-left=5px width=100px% Attach:carlosSmiles.jpg

Professor Carlos Garcia-Cervera receives the prestigious NSF Career Award for his proposal "Multilevel Physics in the Study of Solids: Modeling, Analysis and Simulations".

The Faculty Early Career Development (CAREER) Program offers the NSF’s most prestigious awards in support of early career development activities of those teacher-scholars who are most likely to become the academic leaders of the 21st century.

The awards are for a minimum of $400,000 and support his research for five years providing funding

for postdoctoral researchers and graduate students. The proposed research program has the potential

to impact fundamental computational approaches used in studying solid materials. This is the first

NSF CAREER award given to a faculty member of the department of mathematics.\\

[[http://www.ia.ucsb.edu/93106/2007/November19/math.html | Full Article]]

\\

\\

More information about Professor Garcia-Cervera's research be found on his [[http://www.math.ucsb.edu/~cgarcia/index.html | website]]. \\

\\

\\

----

'+%color555555%Math Circle Started at UCSB+'

%lfloat text-align=left margin-top=5px margin-right=5px margin-bottom=10px margin-left=5px width=100px% Attach:mathCircleLogo.gif

A Math Circle has been started at UCSB for outreach to the local community. The Math Circle engages in mathematics pre-college

students from local high schools. The UCSB Math Circle offers a forum for the discussion of mathematical topics, mathematics education,

and careers involving mathematics. From the Applied Mathematics Group, [[http://www.math.ucsb.edu/~mbueno/index.html | Maribel Bueno Cachadina]] is playing a leading role in organizing the UCSB Math Circle. For more information see the Math Circle Website:\\

[[http://www.math.ucsb.edu/~mbueno/mathcircle/index.html | UCSB Math Circle Website]].\\

\\

----

[[#ResearchHighlights]]

!!Research Highlights

----

'+Fluid-Structure Interactions : Immersed Boundary Methods and Boundary Integral Methods+'

The mechanics of many physical systems depends importantly on the interaction of flexible elastic

structures with a fluid flow. Examples of macroscopic systems include the pumping of the heart in which blood flow interacts with valves, lift general in insect flight, and wave propagation in the cochlea of the inner ear. Examples of microscopic systems include the rheology of complex fluids and soft-matter which depends importantly on microstructures (such as colloids, lipids, polymers, vesicles) which interact with shear and extensional fluid flows serving through small-scale deformations to elastically store or dissipate energy. These microscopic processes often result macroscopically in material properties exhibiting interesting counter-intuitive phenomena and features hard to predict a priori. Immersed Boundary Methods (IBM) and Boundary Integral Methods (BIM) are numerical approaches for studying the mechanics of elastic structures which interact with a fluid.

%width=300px% Attach:SIB_Schematic.png

In the IBM formalism the hydrodynamic interactions of the composite system are handled by an approximate treatment of the fluid-structure stresses in which a Lagrangian representation of the immersed structures is coupled to an Eulerian representation of the fluid. In the BIM formalism the hydrodynamic equations are reduced to a description on the surface of an immersed structure usually taking the form of integral equations (possibly non-linear). The fluid-structure interaction problem and these underlying formulations present many interesting mathematical problems both for analysis and numerics.

Faculty members working in this area include:

* [[http://www.math.ucsb.edu/~atzberg/index.html | Dr. Atzberger]] : Prof. Atzberger has done work on utilizing immersed boundary methods to study properties of soft condensed matter. To account consistently for microstructure mechanics, hydrodynamic coupling, and thermal fluctuations he has extended the IBM formalism to incorporate stochastic driving fields consistent with statistical mechanics. The resulting stochastic partial differential equations (SPDEs) present many interesting challenges both for analysis and the development of numerical methods. A paper on the methodology can be found here : [[http://dx.doi.org/10.1016/j.jcp.2006.11.015 | A Stochastic Immersed Boundary Method for Fluid-Structure Dynamics at Microscopic Length Scales]] and [[http://dx.doi.org/10.1016/j.jcp.2010.12.028 | Stochastic Eulerian-Langrain Methods for Fluid-Structure Interactions subject to Thermal Fluctuations.]].

* [[http://www.math.ucsb.edu/~hdc | Dr. Ceniceros]] : Prof. Ceniceros in joint work with UCSB grad student Jordan Fisher and [[http://www.ime.usp.br/~roma/index-1.html |Prof. Alexandre Roma]] (USP) has recently designed efficient implicit methods for the IBM formalisms significantly advancing the time-scales accessible in simulations of systems with stiff elastic structures. A soon to appear manuscript of the work can be found most likely here: [[http://www.math.ucsb.edu/~hdc/public/IBM_Implicit.pdf | Efficient solutions to robust, semi-implicit discretizations of the Immersed Boundary Method]].

----

'+Local and Global Wellposedness of Nonlinear Evolutionary Equations +'

Provide conditions on initial data which ensure the existence, uniqueness, and continuous dependence of solutions to the initial value problem for nonlinear

evolutionary partial differential equations.

Determine whether solutions exist globally in time or develop singularities in finite time. Explore the regularity and asymptotic behavior of solutions.

Applications to nonlinear dispersive equations, hydro- and elasto-dynamics.

Faculty members working in this area include:

* Dr. Sideris : [[http://www.math.ucsb.edu/~sideris/index.html | Research Website]].

* Dr. Ponce : [[http://www.math.ucsb.edu/~ponce/index.html | Research Website]].

----

!!Research Gallery \\

%width=200px% [[http://www.math.ucsb.edu/~atzberg/pmwiki_intranet/index.php?n=AtzbergerHomePage.HomePage?setskin=atzbergerHomepage1#ResearchSummaries | Attach:montage_sib.png]] %width=100px% [[http://www.math.ucsb.edu/~cgarcia/index.html | Attach:carlosImage.png]] %width=100px% [[http://www.math.ucsb.edu/~hdc/index.html | Attach:fingers.jpg]] %width=100px% [[http://www.math.ucsb.edu/~hdc/index.html | Attach:strings.jpg]] %width=125px% [[http://www.math.ucsb.edu/~atzberg/pmwiki_intranet/index.php?n=AtzbergerHomePage.HomePage?setskin=atzbergerHomepage1#ResearchSummaries | Attach:montage_osmosis.png]] %width=100px% [[http://www.math.ucsb.edu/~hdc/index.html | Attach:rolls.jpg]] %width=100px% [[http://www.math.ucsb.edu/~atzberg/pmwiki_intranet/index.php?n=AtzbergerHomePage.HomePage?setskin=atzbergerHomepage1#ResearchSummaries | Attach:atzbergerImage.png]] %width=200px% [[http://www.math.ucsb.edu/~atzberg/pmwiki_intranet/index.php?n=AtzbergerHomePage.HomePage?setskin=atzbergerHomepage1#ResearchSummaries | Attach:montage_molBio.png]]

----

to:

!! Affiliated Faculty Include:

!! Applied Mathematics and PDE Seminar

For more information, please see the above faculty webpages.

!! Applied Mathematics and PDE Seminar

For more information, please see the above faculty webpages.

Changed line 89 from:

* [[http://www.math.ucsb.edu/~atzberg/index.html | Dr. Atzberger]] : Prof. Atzberger has done work on utilizing immersed boundary methods to study properties of soft condensed matter. To account consistently for microstructure mechanics, hydrodynamic coupling, and thermal fluctuations he has extended the IBM formalism to incorporate stochastic driving fields consistent with statistical mechanics. The resulting stochastic partial differential equations (SPDEs) present many interesting challenges both for analysis and the development of numerical methods. A paper on the methodology can be found here : [[http://~~www~~.~~math~~.~~ucsb.edu~~/~~~atzberg~~/~~publications/preprintStochIB~~.~~pdf~~ | A Stochastic Immersed Boundary Method for Fluid-Structure Dynamics at Microscopic Length Scales]]~~. A recent talk given by Dr~~.~~ Atzberger on the~~ Stochastic ~~Immersed Boundary Method and applications can be found here [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | [Video of IMA Talk]]].~~

to:

* [[http://www.math.ucsb.edu/~atzberg/index.html | Dr. Atzberger]] : Prof. Atzberger has done work on utilizing immersed boundary methods to study properties of soft condensed matter. To account consistently for microstructure mechanics, hydrodynamic coupling, and thermal fluctuations he has extended the IBM formalism to incorporate stochastic driving fields consistent with statistical mechanics. The resulting stochastic partial differential equations (SPDEs) present many interesting challenges both for analysis and the development of numerical methods. A paper on the methodology can be found here : [[http://dx.doi.org/10.1016/j.jcp.2006.11.015 | A Stochastic Immersed Boundary Method for Fluid-Structure Dynamics at Microscopic Length Scales]] and [[http://dx.doi.org/10.1016/j.jcp.2010.12.028 | Stochastic Eulerian-Langrain Methods for Fluid-Structure Interactions subject to Thermal Fluctuations.]].

Changed line 33 from:

%lfloat text-align=left margin-top=5px margin-right=5px margin-bottom=10px margin-left=5px width=100px% Attach:atzbergerPhoto.jpg

to:

%lfloat text-align=left margin-top=5px margin-right=5px margin-bottom=10px margin-left=5px width=100px% Attach:atzbergerPhoto_board.jpg

Deleted lines 24-33:

'+%color555555%Kozato Postdoctoral Fellowship in Quantitative Biology+'

%lfloat text-align=left margin-top=5px margin-right=5px margin-bottom=10px margin-left=5px width=100px% Attach:UCSB_seal1.jpg

The University of California, Santa Barbara invites applications for the Kozato Postdoctoral Fellowship in Quantitative Biology. The fellowship will support research at the interface of the biological sciences with mathematics, computation, physics, or engineering. The postdoctoral appointment will be within the Department of Mathematics starting in September 2011, and is renewable for up to three years. UCSB offers a strong interdisciplinary environment for research with many opportunities for close interaction with both theoreticians and experimentalists on campus.

For more information see: [[http://www.math.ucsb.edu/~atzberg/KozatoFellowship/ | Kozato Fellowship in Quantitative Biology]].\\

\\

Changed line 27 from:

'+%color555555%Kozato ~~Graduate~~ Fellowship in Quantitative Biology+'

to:

'+%color555555%Kozato Postdoctoral Fellowship in Quantitative Biology+'

Changed lines 33-35 from:

For more information~~: ~~

\\

[[http://www.math.ucsb.edu/~atzberg/KozatoFellowship/ | Kozato Fellowship in Quantitative Biology]]\\

\\

[[http

to:

For more information see: [[http://www.math.ucsb.edu/~atzberg/KozatoFellowship/ | Kozato Fellowship in Quantitative Biology]].\\

Changed lines 31-33 from:

The ~~Kozato Fellowship in Quantitative Biology will offer competitive multi-year support comparable to the NSF Graduate Fellowship~~. The ~~position is to begin in~~ the ~~Fall~~ of ~~2011. The fellowship will support a student who has an interest in working on an interdisciplinary thesis project investigating a biological system using a combination of mathematical analysis and computational methods~~. ~~It is envisioned the supported graduate student would have a primary adviser in mathematics, but would also interact closely with theoreticians and experimental biologists on campus at UCSB. The fellowship is funded by a generous donation from Hiro Kozato, a distinguished alumnus of the Department of Mathematics.~~

For those students interested in mathematics and biology, please see the following page for more information:

For those students interested in mathematics and biology, please see the following page for

to:

The University of California, Santa Barbara invites applications for the Kozato Postdoctoral Fellowship in Quantitative Biology. The fellowship will support research at the interface of the biological sciences with mathematics, computation, physics, or engineering. The postdoctoral appointment will be within the Department of Mathematics starting in September 2011, and is renewable for up to three years. UCSB offers a strong interdisciplinary environment for research with many opportunities for close interaction with both theoreticians and experimentalists on campus.

For more information:

For more information:

Added lines 26-38:

'+%color555555%Kozato Graduate Fellowship in Quantitative Biology+'

%lfloat text-align=left margin-top=5px margin-right=5px margin-bottom=10px margin-left=5px width=100px% Attach:UCSB_seal1.jpg

The Kozato Fellowship in Quantitative Biology will offer competitive multi-year support comparable to the NSF Graduate Fellowship. The position is to begin in the Fall of 2011. The fellowship will support a student who has an interest in working on an interdisciplinary thesis project investigating a biological system using a combination of mathematical analysis and computational methods. It is envisioned the supported graduate student would have a primary adviser in mathematics, but would also interact closely with theoreticians and experimental biologists on campus at UCSB. The fellowship is funded by a generous donation from Hiro Kozato, a distinguished alumnus of the Department of Mathematics.

For those students interested in mathematics and biology, please see the following page for more information:

\\

[[http://www.math.ucsb.edu/~atzberg/KozatoFellowship/ | Kozato Fellowship in Quantitative Biology]]\\

\\

----

Deleted lines 73-84:

'+%color555555%Kozato Graduate Fellowship in Quantitative Biology+'

%lfloat text-align=left margin-top=5px margin-right=5px margin-bottom=10px margin-left=5px width=100px% Attach:UCSB_seal1.jpg

The Kozato Fellowship in Quantitative Biology will offer competitive multi-year support comparable to the NSF Graduate Fellowship. The position is to begin in the Fall of 2011. The fellowship will support a student who has an interest in working on an interdisciplinary thesis project investigating a biological system using a combination of mathematical analysis and computational methods. It is envisioned the supported graduate student would have a primary adviser in mathematics, but would also interact closely with theoreticians and experimental biologists on campus at UCSB. The fellowship is funded by a generous donation from Hiro Kozato, a distinguished alumnus of the Department of Mathematics.

For those students interested in mathematics and biology, please see the following page for more information:

\\

[[http://www.math.ucsb.edu/~atzberg/Kozato Fellowship/ | Kozato Fellowship in Quantitative Biology]]\\

\\

Deleted line 39:

Changed lines 41-48 from:

%lfloat text-align=left margin-top=5px margin-right=5px margin-bottom=10px margin

The Kozato Fellowship in Quantitative Biology will offer competitive multi-year support comparable to the NSF Graduate Fellowship. The position is to begin in the Fall of 2011

For those students interested in mathematics and biology, please see the following page for more information:

to:

'+%color555555%Carlos Garcia-Cervera Wins NSF Faculty Early Career Development Award (NSF CAREER)+'

%lfloat text-align=left margin-top=5px margin-right=5px margin-bottom=10px margin-left=5px width=100px% Attach:carlosSmiles.jpg

Professor Carlos Garcia-Cervera receives the prestigious NSF Career Award for his proposal "Multilevel Physics in the Study of Solids: Modeling, Analysis and Simulations".

The Faculty Early Career Development (CAREER) Program offers the NSF’s most prestigious awards in support of early career development activities of those teacher-scholars who are most likely to become the academic leaders of the 21st century.

The awards are for a minimum of $400,000 and support his research for five years providing funding

for postdoctoral researchers and graduate students. The proposed research program has the potential

to impact fundamental computational approaches used in studying solid materials. This is the first

NSF CAREER award given to a faculty member of the department of mathematics.\\

[[http://www.ia.ucsb.edu/93106/2007/November19/math.html | Full Article]]

%lfloat text-align=left margin-top=5px margin-right=5px margin-bottom=10px margin-left=5px width=100px% Attach:carlosSmiles.jpg

Professor Carlos Garcia-Cervera receives the prestigious NSF Career Award for his proposal "Multilevel Physics in the Study of Solids: Modeling, Analysis and Simulations".

The Faculty Early Career Development (CAREER) Program offers the NSF’s most prestigious awards in support of early career development activities of those teacher-scholars who are most likely to become the academic leaders of the 21st century.

The awards are for a minimum of $400,000 and support his research for five years providing funding

for postdoctoral researchers and graduate students. The proposed research program has the potential

to impact fundamental computational approaches used in studying solid materials. This is the first

NSF CAREER award given to a faculty member of the department of mathematics.\\

[[http://www.ia.ucsb.edu/93106/2007/November19/math.html | Full Article]]

Deleted line 52:

Changed lines 54-58 from:

to:

More information about Professor Garcia-Cervera's research be found on his [[http://www.math.ucsb.edu/~cgarcia/index.html | website]]. \\

\\

\\

\\

\\

Added lines 61-73:

'+%color555555%Kozato Graduate Fellowship in Quantitative Biology+'

%lfloat text-align=left margin-top=5px margin-right=5px margin-bottom=10px margin-left=5px width=100px% Attach:UCSB_seal1.jpg

The Kozato Fellowship in Quantitative Biology will offer competitive multi-year support comparable to the NSF Graduate Fellowship. The position is to begin in the Fall of 2011. The fellowship will support a student who has an interest in working on an interdisciplinary thesis project investigating a biological system using a combination of mathematical analysis and computational methods. It is envisioned the supported graduate student would have a primary adviser in mathematics, but would also interact closely with theoreticians and experimental biologists on campus at UCSB. The fellowship is funded by a generous donation from Hiro Kozato, a distinguished alumnus of the Department of Mathematics.

For those students interested in mathematics and biology, please see the following page for more information:

\\

[[http://www.math.ucsb.edu/~atzberg/Kozato Fellowship/ | Kozato Fellowship in Quantitative Biology]]\\

\\

----

%lfloat text-align=left margin-top=5px margin-right=5px margin-bottom=10px margin-left=5px width=100px% Attach:UCSB_seal1.jpg

The Kozato Fellowship in Quantitative Biology will offer competitive multi-year support comparable to the NSF Graduate Fellowship. The position is to begin in the Fall of 2011. The fellowship will support a student who has an interest in working on an interdisciplinary thesis project investigating a biological system using a combination of mathematical analysis and computational methods. It is envisioned the supported graduate student would have a primary adviser in mathematics, but would also interact closely with theoreticians and experimental biologists on campus at UCSB. The fellowship is funded by a generous donation from Hiro Kozato, a distinguished alumnus of the Department of Mathematics.

For those students interested in mathematics and biology, please see the following page for more information:

\\

[[http://www.math.ucsb.edu/~atzberg/Kozato Fellowship/ | Kozato Fellowship in Quantitative Biology]]\\

\\

----

Deleted lines 81-102:

----

'+%color555555%Carlos Garcia-Cervera Wins NSF Faculty Early Career Development Award (NSF CAREER)+'

%lfloat text-align=left margin-top=5px margin-right=5px margin-bottom=10px margin-left=5px width=100px% Attach:carlosSmiles.jpg

Professor Carlos Garcia-Cervera receives the prestigious NSF Career Award for his proposal "Multilevel Physics in the Study of Solids: Modeling, Analysis and Simulations".

The Faculty Early Career Development (CAREER) Program offers the NSF’s most prestigious awards in support of early career development activities of those teacher-scholars who are most likely to become the academic leaders of the 21st century.

The awards are for a minimum of $400,000 and support his research for five years providing funding

for postdoctoral researchers and graduate students. The proposed research program has the potential

to impact fundamental computational approaches used in studying solid materials. This is the first

NSF CAREER award given to a faculty member of the department of mathematics.\\

[[http://www.ia.ucsb.edu/93106/2007/November19/math.html | Full Article]]

\\

\\

More information about Professor Garcia-Cervera's research be found on his [[http://www.math.ucsb.edu/~cgarcia/index.html | website]]. \\

\\

\\

Changed line 49 from:

For those students interested in mathematics and biology ~~and this fellowship, please see the following webpage~~ for more information:

to:

For those students interested in mathematics and biology, please see the following page for more information:

Deleted lines 52-64:

\\

Advisory Panel:\\

\\

Paul Atzberger, Department of Mathematics.\\

Frank Brown, Department of Chemistry and Biochemistry.\\

Hector Ceniceros, Department of Mathematics.\\

Mustafa Kummash, Department of Mechanical Engineering.\\

Everett Lipman, Department of Physics.\\

Omar Saleh, Department of Materials.\\

Megan Valentine, Department of Mechanical Engineering.\\

Added lines 43-46:

'+%color555555%Kozato Graduate Fellowship in Quantitative Biology+'

%lfloat text-align=left margin-top=5px margin-right=5px margin-bottom=10px margin-left=5px width=100px% Attach:UCSB_seal1.jpg

%lfloat text-align=left margin-top=5px margin-right=5px margin-bottom=10px margin-left=5px width=100px% Attach:UCSB_seal1.jpg

Changed lines 54-64 from:

Advisory Panel:

Paul Atzberger, Department of Mathematics.

Frank Brown, Department of Chemistry and Biochemistry.

Hector Ceniceros, Department of Mathematics.

Mustafa Kummash, Department of Mechanical Engineering.

Everett Lipman, Department of Physics.

Omar Saleh, Department of Materials.

Megan Valentine, Department of Mechanical Engineering.

to:

\\

Advisory Panel:\\

\\

Paul Atzberger, Department of Mathematics.\\

Frank Brown, Department of Chemistry and Biochemistry.\\

Hector Ceniceros, Department of Mathematics.\\

Mustafa Kummash, Department of Mechanical Engineering.\\

Everett Lipman, Department of Physics.\\

Omar Saleh, Department of Materials.\\

Megan Valentine, Department of Mechanical Engineering.\\

Advisory Panel:\\

\\

Paul Atzberger, Department of Mathematics.\\

Frank Brown, Department of Chemistry and Biochemistry.\\

Hector Ceniceros, Department of Mathematics.\\

Mustafa Kummash, Department of Mechanical Engineering.\\

Everett Lipman, Department of Physics.\\

Omar Saleh, Department of Materials.\\

Megan Valentine, Department of Mechanical Engineering.\\

Added lines 40-61:

----

The Kozato Fellowship in Quantitative Biology will offer competitive multi-year support comparable to the NSF Graduate Fellowship. The position is to begin in the Fall of 2011. The fellowship will support a student who has an interest in working on an interdisciplinary thesis project investigating a biological system using a combination of mathematical analysis and computational methods. It is envisioned the supported graduate student would have a primary adviser in mathematics, but would also interact closely with theoreticians and experimental biologists on campus at UCSB. The fellowship is funded by a generous donation from Hiro Kozato, a distinguished alumnus of the Department of Mathematics.

For those students interested in mathematics and biology and this fellowship, please see the following webpage for more information:

\\

[[http://www.math.ucsb.edu/~atzberg/Kozato Fellowship/ | Kozato Fellowship in Quantitative Biology]]\\

\\

\\

Advisory Panel:

Paul Atzberger, Department of Mathematics.

Frank Brown, Department of Chemistry and Biochemistry.

Hector Ceniceros, Department of Mathematics.

Mustafa Kummash, Department of Mechanical Engineering.

Everett Lipman, Department of Physics.

Omar Saleh, Department of Materials.

Megan Valentine, Department of Mechanical Engineering.

Changed line 4 from:

!! Apply for Graduate Studies in Applied Mathematics [[http://www.math.ucsb.edu/~applmath/pmwiki/pmwiki.php?n=Main.prospectiveGraduateStudents | [more information here] ]] \\

to:

!! Apply for Graduate Studies in Applied Mathematics : [[http://www.math.ucsb.edu/~applmath/pmwiki/pmwiki.php?n=Main.prospectiveGraduateStudents | [more information here] ]] \\

Changed line 4 from:

!! Apply for Graduate Studies in Applied Mathematics [[http://www.math.ucsb.edu/~applmath/pmwiki/pmwiki.php?n=Main.prospectiveGraduateStudents | [more ~~info.~~ here] ]] \\

to:

!! Apply for Graduate Studies in Applied Mathematics [[http://www.math.ucsb.edu/~applmath/pmwiki/pmwiki.php?n=Main.prospectiveGraduateStudents | [more information here] ]] \\

Changed lines 34-35 from:

Professor Paul J. Atzberger awarded NSF CAREER Award "Emergent Biological Mechanics of Cellular Microstructures." His proposed research aims to develop new methods combining approaches from stochastic analysis, statistical mechanics, and scientific computing to study fundamental problems related to the mechanics of biological materials. This $435K, five year grant "recognizes and supports the early career development activities of those faculty members who are most likely to become the academic leaders of the 21st century.” Significantly, this proposal will be funded by three NSF agencies: Mathematical Biology, Applied Mathematics, and the Office of Cyberinfrastructure.\\

to:

Professor Paul J. Atzberger awarded NSF CAREER Award "Emergent Biological Mechanics of Cellular Microstructures." His proposed research aims to develop new methods combining approaches from stochastic analysis, statistical mechanics, and scientific computing to study fundamental problems related to the mechanics of biological materials. This $435K, five year grant "recognizes and supports the early career development activities of those faculty members who are most likely to become the academic leaders of the 21st century.” Significantly, this proposal will be funded by three NSF agencies: Mathematical Biology, Applied Mathematics, and the Office of Cyberinfrastructure.

\\

\\

Changed line 36 from:

More information about Professor Atzberger's research be found on his [[http://www.math.ucsb.edu/~atzberg/index.html | ~~homepage~~]]. \\

to:

More information about Professor Atzberger's research be found on his [[http://www.math.ucsb.edu/~atzberg/index.html | website]]. \\

Changed line 65 from:

More information about Professor Garcia-Cervera's research be found on his [[http://www.math.ucsb.edu/~cgarcia/index.html | ~~homepage~~]]. \\

to:

More information about Professor Garcia-Cervera's research be found on his [[http://www.math.ucsb.edu/~cgarcia/index.html | website]]. \\

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More information about Professor Atzberger's research be found ~~at ~~[[http://www.math.ucsb.edu/~atzberg/index.html | ~~http://www.math.ucsb.edu/~atzberg/index.html~~]]. \\

to:

More information about Professor Atzberger's research be found on his [[http://www.math.ucsb.edu/~atzberg/index.html | homepage]]. \\

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More information about Professor Garcia-Cervera's research be found ~~at ~~[[http://www.math.ucsb.edu/~cgarcia/index.html | ~~http://www.math.ucsb.edu/~cgarcia/index.html~~]]. \\

to:

More information about Professor Garcia-Cervera's research be found on his [[http://www.math.ucsb.edu/~cgarcia/index.html | homepage]]. \\

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More information about Professor Atzberger's research be found at [[http://www.math.ucsb.edu/~atzberg/index.html | http://www.math.ucsb.edu/~atzberg/index.html]]. \\

\\

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\\

More information about Professor Garcia-Cervera's research be found at [[http://www.math.ucsb.edu/~cgarcia/index.html | http://www.math.ucsb.edu/~cgarcia/index.html]]. \\

\\

More information about Professor Garcia-Cervera's research be found at [[http://www.math.ucsb.edu/~cgarcia/index.html | http://www.math.ucsb.edu/~cgarcia/index.html]]. \\

\\

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'+%color555555%Paul J. Atzberger Wins NSF Faculty Early Career Development Award (NSF CAREER)+'

%lfloat text-align=left margin-top=5px margin-right=5px margin-bottom=10px margin-left=5px width=100px% Attach:atzbergerPhoto.jpg

Professor Paul J. Atzberger awarded NSF CAREER Award "Emergent Biological Mechanics of Cellular Microstructures." His proposed research aims to develop new methods combining approaches from stochastic analysis, statistical mechanics, and scientific computing to study fundamental problems related to the mechanics of biological materials. This $435K, five year grant "recognizes and supports the early career development activities of those faculty members who are most likely to become the academic leaders of the 21st century.” Significantly, this proposal will be funded by three NSF agencies: Mathematical Biology, Applied Mathematics, and the Office of Cyberinfrastructure.\\

\\

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Professor Paul J. Atzberger awarded NSF CAREER Award "Emergent Biological Mechanics of Cellular Microstructures." His proposed research aims to develop new methods combining approaches from stochastic analysis, statistical mechanics, and scientific computing to study fundamental problems related to the mechanics of biological materials. This $435K, five year grant "recognizes and supports the early career development activities of those faculty members who are most likely to become the academic leaders of the 21st century.” Significantly, this proposal will be funded by three NSF agencies: Mathematical Biology, Applied Mathematics, and the Office of Cyberinfrastructure.\\

\\

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Carlos Garcia-Cervera receives the prestigious NSF Career Award for his proposal "Multilevel Physics in the Study of Solids: Modeling, Analysis and Simulations".

to:

Professor Carlos Garcia-Cervera receives the prestigious NSF Career Award for his proposal "Multilevel Physics in the Study of Solids: Modeling, Analysis and Simulations".

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!! Apply for Graduate Studies in Applied Mathematics~~ at UCSB~~ [[http://www.math.ucsb.edu/~applmath/pmwiki/pmwiki.php?n=Main.prospectiveGraduateStudents | [more info. here] ]] \\

to:

!! Apply for Graduate Studies in Applied Mathematics [[http://www.math.ucsb.edu/~applmath/pmwiki/pmwiki.php?n=Main.prospectiveGraduateStudents | [more info. here] ]] \\

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!! Apply ~~to the UCSB~~ Applied Mathematics ~~Program~~ [[http://www.math.ucsb.edu/~applmath/pmwiki/pmwiki.php?n=Main.prospectiveGraduateStudents | [more info. here] ]] \\

to:

!! Apply for Graduate Studies in Applied Mathematics at UCSB [[http://www.math.ucsb.edu/~applmath/pmwiki/pmwiki.php?n=Main.prospectiveGraduateStudents | [more info. here] ]] \\

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!! Apply to the UCSB Applied Mathematics Program [[http://www.math.ucsb.edu/~applmath/pmwiki/pmwiki.php?n=Main.prospectiveGraduateStudents | [more info. here] ]] \\

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and careers involving mathematics. From the Applied ~~Math~~ Group, [[http://www.math.ucsb.edu/~mbueno/index.html | Maribel Bueno Cachadina]] is playing a leading role in organizing the UCSB Math Circle. For more information see the Math Circle Website:\\

to:

and careers involving mathematics. From the Applied Mathematics Group, [[http://www.math.ucsb.edu/~mbueno/index.html | Maribel Bueno Cachadina]] is playing a leading role in organizing the UCSB Math Circle. For more information see the Math Circle Website:\\

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* ~~complex fluids~~ and ~~soft~~-~~condensed matter~~

* crystalline solids and ~~liquid crystals~~

* ~~density functional theory ~~

* analysisof ~~non~~-linear ~~evolutionary~~ PDE's (existence results / finite time singularities)

* ~~applied harmonic analysis~~

* ~~stochastic analysis~~.

* crystalline solids

* analysis

to:

* Complex Fluids and Soft-Condensed Matter Physics.

* Crystalline Solids and Liquid Crystals.

* Density Functional Theory.

* Analysis of Non-linear Evolutionary PDE's (existence results / finite time singularities).

* Applied Harmonic Analysis.

* Stochastic Analysis.

* Crystalline Solids and Liquid Crystals.

* Density Functional Theory.

* Analysis of Non-linear Evolutionary PDE's (existence results / finite time singularities).

* Applied Harmonic Analysis.

* Stochastic Analysis.

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and participate in collaborations with ~~a diverse collection of faculty on campus.~~

Researchareas include: complex fluids~~,~~ soft-condensed matter~~,~~ crystalline solids and

liquid crystals~~,~~ density functional theory~~,~~ analysis of non-linear

evolutionary PDE's (existence results / finite time singularities)~~, ~~

applied harmonic analysis~~, and~~ stochastic analysis.

Research

liquid crystals

evolutionary PDE's (existence results / finite time singularities)

applied harmonic analysis

to:

and participate in collaborations with many faculty on campus. Research areas include:

* complex fluids and soft-condensed matter

* crystalline solids and liquid crystals

* density functional theory

* analysis of non-linear evolutionary PDE's (existence results / finite time singularities)

* applied harmonic analysis

* stochastic analysis.

* complex fluids and soft-condensed matter

* crystalline solids and liquid crystals

* density functional theory

* analysis of non-linear evolutionary PDE's (existence results / finite time singularities)

* applied harmonic analysis

* stochastic analysis.

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and careers involving mathematics. From the Applied Math Group, [[http://www.math.ucsb.edu/~mbueno/index.html | Maribel Bueno Cachadina]] is playing a leading role in organizing the UCSB Math Circle. For more information see the Math Circle ~~website~~:\\

to:

and careers involving mathematics. From the Applied Math Group, [[http://www.math.ucsb.edu/~mbueno/index.html | Maribel Bueno Cachadina]] is playing a leading role in organizing the UCSB Math Circle. For more information see the Math Circle Website:\\

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[[http

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students from local high schools. The Math Circle offers a forum ~~in which ~~the ~~discuss~~ mathematical topics, mathematics education,

to:

students from local high schools. The UCSB Math Circle offers a forum for the discussion of mathematical topics, mathematics education,

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[[http://www.math.ucsb.edu/~mbueno/mathcircle/index.html | UCSB Math Circle Website]].

to:

[[http://www.math.ucsb.edu/~mbueno/mathcircle/index.html | UCSB Math Circle Website]].\\

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'+%color555555%Math Circle Started at UCSB+'

%lfloat text-align=left margin-top=5px margin-right=5px margin-bottom=10px margin-left=5px width=100px% Attach:mathCircleLogo.gif

A Math Circle has been started at UCSB for outreach to the local community. The Math Circle engages in mathematics pre-college

students from local high schools. The Math Circle offers a forum in which the discuss mathematical topics, mathematics education,

and careers involving mathematics. From the Applied Math Group, [[http://www.math.ucsb.edu/~mbueno/index.html | Maribel Bueno Cachadina]] is playing a leading role in organizing the UCSB Math Circle. For more information see the Math Circle website:\\

[[http://www.math.ucsb.edu/~mbueno/mathcircle/index.html | UCSB Math Circle Website]].

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Deleted lines 46-52:

%lfloat text-align=left margin-top=5px margin-right=5px margin-bottom=10px margin-left=5px width=100px% Attach:mathCircleLogo.gif

A Math Circle has been started at UCSB as outreach to the local community. The Math Circle engages in mathematics pre-college

students from local high schools. The Math Circle offers a forum in which the discuss mathematical topics, mathematics education,

and careers involving mathematics. From the Applied Math Group, [[http://www.math.ucsb.edu/~mbueno/index.html | Maribel Bueno Cachadina]] is playing a leading role in organizing the UCSB Math Circle. For more information see the Math Circle website:\\

[[http://www.math.ucsb.edu/~mbueno/mathcircle/index.html | UCSB Math Circle Website]].

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to:

\\

\\

\\

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%lfloat text-align=left margin-top=5px margin-right=5px margin-bottom=10px margin-left=5px width=100px% Attach:mathCircleLogo.~~jpg~~

to:

%lfloat text-align=left margin-top=5px margin-right=5px margin-bottom=10px margin-left=5px width=100px% Attach:mathCircleLogo.gif

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and careers involving mathematics. From the Applied Math Group, ~~Maribel Bueno Cachadina is playing a leading role in ~~

organizing the UCSB Math Circle. For more information see the Math Circle website:\\

[[ | UCSB Math Circle Website]].

organizing the UCSB Math

[[

to:

and careers involving mathematics. From the Applied Math Group, [[http://www.math.ucsb.edu/~mbueno/index.html | Maribel Bueno Cachadina]] is playing a leading role in organizing the UCSB Math Circle. For more information see the Math Circle website:\\

[[http://www.math.ucsb.edu/~mbueno/mathcircle/index.html | UCSB Math Circle Website]].

[[http://www.math.ucsb.edu/~mbueno/mathcircle/index.html | UCSB Math Circle Website]].

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to:

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and careers involving mathematics. ~~Maribel ... from the Applied Mathematics ~~Group ~~is play a leading role in organizing the UCSB Math Circle. ~~

For more information see the Math Circle website:\\

[[ | UCSB Math Circle Website]]

For more information see the Math Circle

[[ | UCSB Math Circle Website]]

to:

and careers involving mathematics. From the Applied Math Group, Maribel Bueno Cachadina is playing a leading role in

organizing the UCSB Math Circle. For more information see the Math Circle website:\\

[[ | UCSB Math Circle Website]].

organizing the UCSB Math Circle. For more information see the Math Circle website:\\

[[ | UCSB Math Circle Website]].

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'+%color555555%UCSB Math Circle+'

%lfloat text-align=left margin-top=5px margin-right=5px margin-bottom=10px margin-left=5px width=100px% Attach:carlosSmiles.jpg

A Math Circle has been started at UCSB as outreach to the local community. The Math Circle engages in mathematics pre-college

students from local high schools. The Math Circle offers a forum in which the discuss mathematical topics, mathematics education,

and careers involving mathematics. Maribel ... from the Applied Mathematics Group is play a leading role in organizing the UCSB Math Circle.

For more information see the Math Circle website:\\

[[ | UCSB Math Circle Website]]

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and participate in collaborations with ~~many departments~~ on campus.

to:

and participate in collaborations with a diverse collection of faculty on campus.

September 07, 2009, at 03:47 PM
by - minor change

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Applied mathematics ~~strives to integrate~~ the development of core areas of mathematics with

to:

Applied mathematics integrates the development of core areas of mathematics with

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Applied mathematics ~~refers to the branch of mathematics which strives ~~

to integrate the development of core areas of mathematics with

to integrate the development of core areas of mathematics with

to:

Applied mathematics strives to integrate the development of core areas of mathematics with

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and participate in ~~many ~~collaborations with ~~other~~ departments on campus.

to:

and participate in collaborations with many departments on campus.

August 27, 2009, at 09:41 PM
by - restored the page...test....

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Another basic test of notifications....

August 27, 2009, at 09:41 PM
by - Please help review any suspicious changes by looking at author and clicking on links below....

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----

to:

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Another basic test of notifications....

Another basic test of notifications....

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Test of the notification system to make sure it works. Will send e-mail summarizing changes made for the day, if any.

Test of the notification system to make sure it works. Will send e-mail summarizing changes made for the day, if any.

to:

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August 26, 2009, at 08:58 PM
by - Here is a summary of the changes made. This will send e-mail summarizing changes made for the day...

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Test of the notification system to make sure it works. Will send e-mail summarizing changes made for the day, if any.

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and participate in many collaborations with~~ faculty from~~ other departments on campus.

to:

and participate in many collaborations with other departments on campus.

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or engineering. Faculty of the Applied Mathematics Group are active in ~~many~~ areas

including: complex fluids, soft-condensed matter, crystalline solids and

including:

to:

or engineering. Faculty of the Applied Mathematics Group are active in diverse areas

and participate in many collaborations with faculty from other departments on campus.

Research areas include: complex fluids, soft-condensed matter, crystalline solids and

and participate in many collaborations with faculty from other departments on campus.

Research areas include: complex fluids, soft-condensed matter, crystalline solids and

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applied harmonic analysis, and stochastic analysis. Here you will find

information about our program in Applied Mathematics, current activities,

information about our program in Applied Mathematics, current activities,

to:

applied harmonic analysis, and stochastic analysis.

Here you will find information about our program in Applied Mathematics, current activities,

Here you will find information about our program in Applied Mathematics, current activities,

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%width=200px% [[http://www.math.ucsb.edu/~atzberg/pmwiki_intranet/index.php?n=AtzbergerHomePage.HomePage?setskin=atzbergerHomepage1#ResearchSummaries | Attach:montage_sib.png]] %width=100px% [[http://www.math.ucsb.edu/ | Attach:carlosImage.png]] %width=125px% [[http://www.math.ucsb.edu/~atzberg/pmwiki_intranet/index.php?n=AtzbergerHomePage.HomePage?setskin=atzbergerHomepage1#ResearchSummaries | Attach:montage_osmosis.png]] %width=100px% [[http://www.math.ucsb.edu/~atzberg/pmwiki_intranet/index.php?n=AtzbergerHomePage.HomePage?setskin=atzbergerHomepage1#ResearchSummaries | Attach:atzbergerImage.png]] %width=200px% [[http://www.math.ucsb.edu/~atzberg/pmwiki_intranet/index.php?n=AtzbergerHomePage.HomePage?setskin=atzbergerHomepage1#ResearchSummaries | Attach:montage_molBio.png]]

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%width=200px% [[http://www.math.ucsb.edu/~atzberg/pmwiki_intranet/index.php?n=AtzbergerHomePage.HomePage?setskin=atzbergerHomepage1#ResearchSummaries | Attach:montage_sib.png]] %width=100px% [[http://www.math.ucsb.edu/~cgarcia/index.html | Attach:carlosImage.png]] %width=125px% [[http://www.math.ucsb.edu/~atzberg/pmwiki_intranet/index.php?n=AtzbergerHomePage.HomePage?setskin=atzbergerHomepage1#ResearchSummaries | Attach:montage_osmosis.png]] %width=100px% [[http://www.math.ucsb.edu/~atzberg/pmwiki_intranet/index.php?n=AtzbergerHomePage.HomePage?setskin=atzbergerHomepage1#ResearchSummaries | Attach:atzbergerImage.png]] %width=200px% [[http://www.math.ucsb.edu/~atzberg/pmwiki_intranet/index.php?n=AtzbergerHomePage.HomePage?setskin=atzbergerHomepage1#ResearchSummaries | Attach:montage_molBio.png]]

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to:

%width=200px% [[http://www.math.ucsb.edu/~atzberg/pmwiki_intranet/index.php?n=AtzbergerHomePage.HomePage?setskin=atzbergerHomepage1#ResearchSummaries | Attach:montage_sib.png]] %width=100px% [[http://www.math.ucsb.edu/ | Attach:carlosImage.png]] %width=125px% [[http://www.math.ucsb.edu/~atzberg/pmwiki_intranet/index.php?n=AtzbergerHomePage.HomePage?setskin=atzbergerHomepage1#ResearchSummaries | Attach:montage_osmosis.png]] %width=100px% [[http://www.math.ucsb.edu/~atzberg/pmwiki_intranet/index.php?n=AtzbergerHomePage.HomePage?setskin=atzbergerHomepage1#ResearchSummaries | Attach:atzbergerImage.png]] %width=200px% [[http://www.math.ucsb.edu/~atzberg/pmwiki_intranet/index.php?n=AtzbergerHomePage.HomePage?setskin=atzbergerHomepage1#ResearchSummaries | Attach:montage_molBio.png]]

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to:

%width=200px% [[http://www.math.ucsb.edu/~atzberg/pmwiki_intranet/index.php?n=AtzbergerHomePage.HomePage#ResearchSummaries?setskin=atzbergerHomepage1 | Attach:montage_sib.png]] %width=100px% [[http://www.math.ucsb.edu/ | Attach:carlosImage.png]] %width=125px% [[http://www.math.ucsb.edu/~atzberg/pmwiki_intranet/index.php?n=AtzbergerHomePage.HomePage#ResearchSummaries | Attach:montage_osmosis.png]] %width=100px% [[http://www.math.ucsb.edu/~atzberg/pmwiki_intranet/index.php?n=AtzbergerHomePage.HomePage#ResearchSummaries | Attach:atzbergerImage.png]] %width=200px% [[http://www.math.ucsb.edu/~atzberg/index.html#researchSummaries | Attach:montage_molBio.png]]

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%width=200px% [[http://www.math.ucsb.edu/~atzberg/index.~~html~~#~~researchSummaries~~ | Attach:montage_sib.png]] %width=100px% [[http://www.math.ucsb.edu/ | Attach:carlosImage.png]] %width=125px% [[http://www.math.ucsb.edu/~atzberg/index.~~html~~#~~researchSummaries~~ | Attach:montage_osmosis.png]] %width=100px% [[http://www.math.ucsb.edu/~atzberg/index.~~html~~#~~researchSummaries~~ | Attach:atzbergerImage.png]] %width=200px% [[http://www.math.ucsb.edu/~atzberg/index.html#researchSummaries | Attach:montage_molBio.png]]

to:

%width=200px% [[http://www.math.ucsb.edu/~atzberg/pmwiki_intranet/index.php?n=AtzbergerHomePage.HomePage#ResearchSummaries | Attach:montage_sib.png]] %width=100px% [[http://www.math.ucsb.edu/ | Attach:carlosImage.png]] %width=125px% [[http://www.math.ucsb.edu/~atzberg/pmwiki_intranet/index.php?n=AtzbergerHomePage.HomePage#ResearchSummaries | Attach:montage_osmosis.png]] %width=100px% [[http://www.math.ucsb.edu/~atzberg/pmwiki_intranet/index.php?n=AtzbergerHomePage.HomePage#ResearchSummaries | Attach:atzbergerImage.png]] %width=200px% [[http://www.math.ucsb.edu/~atzberg/index.html#researchSummaries | Attach:montage_molBio.png]]

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%width=~~400px~~% [[http://www.math.ucsb.edu/~atzberg/index.html#researchSummaries | Attach:montage_sib.png]] %width=~~200px~~% [[http://www.math.ucsb.edu/ | Attach:carlosImage.png]] %width=~~250px~~% [[http://www.math.ucsb.edu/~atzberg/index.html#researchSummaries | Attach:montage_osmosis.png]] %width=~~200px~~% [[http://www.math.ucsb.edu/~atzberg/index.html#researchSummaries | Attach:atzbergerImage.png]] %width=~~400px~~% [[http://www.math.ucsb.edu/~atzberg/index.html#researchSummaries | Attach:montage_molBio.png]]

to:

%width=200px% [[http://www.math.ucsb.edu/~atzberg/index.html#researchSummaries | Attach:montage_sib.png]] %width=100px% [[http://www.math.ucsb.edu/ | Attach:carlosImage.png]] %width=125px% [[http://www.math.ucsb.edu/~atzberg/index.html#researchSummaries | Attach:montage_osmosis.png]] %width=100px% [[http://www.math.ucsb.edu/~atzberg/index.html#researchSummaries | Attach:atzbergerImage.png]] %width=200px% [[http://www.math.ucsb.edu/~atzberg/index.html#researchSummaries | Attach:montage_molBio.png]]

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!!Research Highlights ~~(select subset of recent activities)~~

to:

!!Research Highlights

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or engineering. ~~Faculyt~~ of the Applied Mathematics Group are active in many areas

to:

or engineering. Faculty of the Applied Mathematics Group are active in many areas

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to:

Applied mathematics refers to the branch of mathematics which strives

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or engineering. ~~Specific areas in which faculty~~ are ~~involved include~~

the study of complex fluids ~~/ ~~soft-condensed matter, ~~computational fluid ~~

dynamics, boundary integral methods, ~~immersed boundary methods~~,

crystalline solids and liquid crystals, density functional theory,

analysis of non-linear evolutionary PDE's, study of existence or

~~development of singularities in finite time, applied harmonic ~~

analysis, and stochastic differential equations. Here you will

find researchhighlights~~, upcoming seminar talks, and information ~~

concerning recent news or current activities of the applied mathematics group.

the study of

dynamics, boundary integral methods

crystalline solids and liquid crystals, density functional theory,

analysis of non-linear evolutionary PDE's, study of existence or

analysis, and stochastic differential equations. Here you will

find research

concerning recent news or current activities of the applied mathematics group

to:

or engineering. Faculyt of the Applied Mathematics Group are active in many areas

including: complex fluids, soft-condensed matter, crystalline solids and

liquid crystals, density functional theory, analysis of non-linear

evolutionary PDE's (existence results / finite time singularities),

applied harmonic analysis, and stochastic analysis. Here you will find

information about our program in Applied Mathematics, current activities,

upcoming seminar talks, and highlights from recent research.

including: complex fluids, soft-condensed matter, crystalline solids and

liquid crystals, density functional theory, analysis of non-linear

evolutionary PDE's (existence results / finite time singularities),

applied harmonic analysis, and stochastic analysis. Here you will find

information about our program in Applied Mathematics, current activities,

upcoming seminar talks, and highlights from recent research.

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Provide conditions on initial data which ensure the existence, uniqueness, and continuous dependence of solutions to the initial value problem for nonlinear

evolutionary partial differential equations.

Determine whether solutions exist globally in time or develop singularities in finite time. Explore the regularity and asymptotic behavior of solutions.

Applications to nonlinear dispersive equations, hydro- and elasto-dynamics.

Faculty members working in this area include:

* Dr. Sideris : [[http://www.math.ucsb.edu/~sideris/index.html | Research Website]].

* Dr. Ponce : [[http://www.math.ucsb.edu/~ponce/index.html | Research Website]].

----

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'+Local and Global Wellposedness of Nonlinear Evolutionary Equations +'

Provide conditions on initial data which ensure the existence, uniqueness, and continuous dependence of solutions to the initial value problem for nonlinear

evolutionary partial differential equations.

Determine whether solutions exist globally in time or develop singularities in finite time. Explore the regularity and asymptotic behavior of solutions.

Applications to nonlinear dispersive equations, hydro- and elasto-dynamics.

Faculty members working in this area include:

* Dr. Sideris : [[http://www.math.ucsb.edu/~sideris/index.html | Research Website]].

* Dr. Ponce : [[http://www.math.ucsb.edu/~ponce/index.html | Research Website]].

----

!!Research Gallery \\

%width=400px% [[http://www.math.ucsb.edu/~atzberg/index.html#researchSummaries | Attach:montage_sib.png]] %width=200px% [[http://www.math.ucsb.edu/ | Attach:carlosImage.png]] %width=250px% [[http://www.math.ucsb.edu/~atzberg/index.html#researchSummaries | Attach:montage_osmosis.png]] %width=200px% [[http://www.math.ucsb.edu/~atzberg/index.html#researchSummaries | Attach:atzbergerImage.png]] %width=400px% [[http://www.math.ucsb.edu/~atzberg/index.html#researchSummaries | Attach:montage_molBio.png]]

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to:

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* [[http://www.math.ucsb.edu/~atzberg/index.html | Dr. Atzberger]] : Prof. Atzberger has done work on utilizing immersed boundary methods to study properties of soft condensed matter. To account consistently for microstructure mechanics, hydrodynamic coupling, and thermal fluctuations he has extended the IBM formalism to incorporate stochastic driving fields consistent with statistical mechanics. The resulting stochastic partial differential equations (SPDEs) present many interesting challenges both for analysis and the development of numerical methods. A paper on the methodology can be found here : [[http://www.math.ucsb.edu/~atzberg/publications/preprintStochIB.pdf | A Stochastic Immersed Boundary Method for Fluid-Structure Dynamics at Microscopic Length Scales]]. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | [Video of IMA Talk]]].

to:

* [[http://www.math.ucsb.edu/~atzberg/index.html | Dr. Atzberger]] : Prof. Atzberger has done work on utilizing immersed boundary methods to study properties of soft condensed matter. To account consistently for microstructure mechanics, hydrodynamic coupling, and thermal fluctuations he has extended the IBM formalism to incorporate stochastic driving fields consistent with statistical mechanics. The resulting stochastic partial differential equations (SPDEs) present many interesting challenges both for analysis and the development of numerical methods. A paper on the methodology can be found here : [[http://www.math.ucsb.edu/~atzberg/publications/preprintStochIB.pdf | A Stochastic Immersed Boundary Method for Fluid-Structure Dynamics at Microscopic Length Scales]]. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method and applications can be found here [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | [Video of IMA Talk]]].

Changed line 75 from:

* [[http://www.math.ucsb.edu/~hdc | Dr. Ceniceros]] : Prof. Ceniceros in joint work with UCSB grad student Jordan Fisher and [[http://www.ime.usp.br/~roma/index-1.html |Prof. Alexandre Roma]] (USP) has recently designed efficient implicit methods for the IBM formalisms significantly advancing the time-scales accessible in simulations of systems with stiff elastic structures. A soon to appear manuscript of the work can be found here: [[http://www.math.ucsb.edu/~hdc/public/IBM_Implicit.pdf | Efficient solutions to robust, semi-implicit discretizations of the Immersed Boundary Method]].

to:

* [[http://www.math.ucsb.edu/~hdc | Dr. Ceniceros]] : Prof. Ceniceros in joint work with UCSB grad student Jordan Fisher and [[http://www.ime.usp.br/~roma/index-1.html |Prof. Alexandre Roma]] (USP) has recently designed efficient implicit methods for the IBM formalisms significantly advancing the time-scales accessible in simulations of systems with stiff elastic structures. A soon to appear manuscript of the work can be found most likely here: [[http://www.math.ucsb.edu/~hdc/public/IBM_Implicit.pdf | Efficient solutions to robust, semi-implicit discretizations of the Immersed Boundary Method]].

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to:

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* [[http://www.math.ucsb.edu/~atzberg/index.html | Dr. Atzberger]] : Prof. Atzberger has ~~been working~~ on utilizing immersed boundary methods to study properties of soft condensed matter. To account consistently for microstructure mechanics, hydrodynamic coupling, and thermal fluctuations he has extended the IBM formalism to incorporate stochastic driving fields consistent with statistical mechanics. The resulting stochastic partial differential equations (SPDEs) present many interesting challenges both for analysis and the development of numerical methods. A paper on the methodology can be found here : [[http://www.math.ucsb.edu/~atzberg/publications/preprintStochIB.pdf | A Stochastic Immersed Boundary Method for Fluid-Structure Dynamics at Microscopic Length Scales]]. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | [Video of IMA Talk]]].

to:

* [[http://www.math.ucsb.edu/~atzberg/index.html | Dr. Atzberger]] : Prof. Atzberger has done work on utilizing immersed boundary methods to study properties of soft condensed matter. To account consistently for microstructure mechanics, hydrodynamic coupling, and thermal fluctuations he has extended the IBM formalism to incorporate stochastic driving fields consistent with statistical mechanics. The resulting stochastic partial differential equations (SPDEs) present many interesting challenges both for analysis and the development of numerical methods. A paper on the methodology can be found here : [[http://www.math.ucsb.edu/~atzberg/publications/preprintStochIB.pdf | A Stochastic Immersed Boundary Method for Fluid-Structure Dynamics at Microscopic Length Scales]]. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | [Video of IMA Talk]]].

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* [[http://www.math.ucsb.edu/~atzberg/index.html | Dr. Atzberger]] : Prof. Atzberger has been working on utilizing immersed boundary methods to study properties of soft condensed matter. To account consistently for microstructure mechanics, hydrodynamic coupling, and thermal fluctuations he has extended the IBM formalism to incorporate stochastic driving fields consistent with statistical mechanics. The resulting stochastic partial differential equations (SPDEs) present many interesting challenges both for analysis and the development of numerical methods. A paper on the methodology can be found here : [[http://www.math.ucsb.edu/~atzberg/publications/preprintStochIB.pdf | A Stochastic Immersed Boundary Method for Fluid-Structure Dynamics at Microscopic Length Scales]]. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | [Video of IMA Talk]]]. ~~Additional papers can be found on his [[http://www.math.ucsb.edu/~atzberg/index.html | research website]].~~

to:

* [[http://www.math.ucsb.edu/~atzberg/index.html | Dr. Atzberger]] : Prof. Atzberger has been working on utilizing immersed boundary methods to study properties of soft condensed matter. To account consistently for microstructure mechanics, hydrodynamic coupling, and thermal fluctuations he has extended the IBM formalism to incorporate stochastic driving fields consistent with statistical mechanics. The resulting stochastic partial differential equations (SPDEs) present many interesting challenges both for analysis and the development of numerical methods. A paper on the methodology can be found here : [[http://www.math.ucsb.edu/~atzberg/publications/preprintStochIB.pdf | A Stochastic Immersed Boundary Method for Fluid-Structure Dynamics at Microscopic Length Scales]]. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | [Video of IMA Talk]]].

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* [[http://www.math.ucsb.edu/~atzberg/index.html | Dr. Atzberger]] : Prof. Atzberger has been working on utilizing immersed boundary methods to study properties of soft condensed matter. To account consistently for microstructure mechanics, hydrodynamic coupling, and thermal fluctuations he has extended the IBM formalism to incorporate stochastic driving fields consistent with statistical mechanics. ~~Application areas include polymeric fluids, gels, and lipid bilayer membranes. The resulting stochastic partial differential equations (SPDEs) present many interesting challenges both for analysis and the development of numerical methods. A paper on the methodology can be found here :~~

[[http://www.math.ucsb.edu/~atzberg/publications/preprintStochIB.pdf | A Stochastic Immersed Boundary Method for Fluid-Structure Dynamics at Microscopic Length Scales]]. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | [Video of IMA Talk]]]. Additional papers can be found on his [[http://www.math.ucsb.edu/~atzberg/index.html | research website]].

[[http://www.math.ucsb.edu/~atzberg/publications/preprintStochIB.pdf | A Stochastic Immersed Boundary Method for Fluid-Structure Dynamics at Microscopic Length Scales]]. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | [Video of IMA Talk]]]. Additional papers can be found on his [[http://www.math.ucsb.edu/~atzberg/index.html | research website]].

to:

* [[http://www.math.ucsb.edu/~atzberg/index.html | Dr. Atzberger]] : Prof. Atzberger has been working on utilizing immersed boundary methods to study properties of soft condensed matter. To account consistently for microstructure mechanics, hydrodynamic coupling, and thermal fluctuations he has extended the IBM formalism to incorporate stochastic driving fields consistent with statistical mechanics. The resulting stochastic partial differential equations (SPDEs) present many interesting challenges both for analysis and the development of numerical methods. A paper on the methodology can be found here : [[http://www.math.ucsb.edu/~atzberg/publications/preprintStochIB.pdf | A Stochastic Immersed Boundary Method for Fluid-Structure Dynamics at Microscopic Length Scales]]. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | [Video of IMA Talk]]]. Additional papers can be found on his [[http://www.math.ucsb.edu/~atzberg/index.html | research website]].

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* [[http://www.math.ucsb.edu/~atzberg/index.html | Dr. Atzberger]] : Prof. Atzberger has been working on utilizing immersed boundary methods to study properties of soft condensed matter. To account consistently for microstructure mechanics, hydrodynamic coupling, and thermal fluctuations he has extended the IBM formalism to incorporate stochastic driving fields consistent with statistical mechanics. Application areas include polymeric fluids, gels, and lipid bilayer membranes. The resulting stochastic partial differential equations (SPDEs) present many interesting challenges both for analysis and the development of numerical methods. A ~~recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here ~~[[http://www.~~ima~~.~~umn~~.edu/~~2008-2009~~/~~W11~~.~~3-7.08/abstracts.html#Atzberger-Paul | [Video of IMA Talk]]]. Related papers can be found on his [[http://www~~.~~math.ucsb.edu/~atzberg/index.html | Research Website]]~~.

to:

* [[http://www.math.ucsb.edu/~atzberg/index.html | Dr. Atzberger]] : Prof. Atzberger has been working on utilizing immersed boundary methods to study properties of soft condensed matter. To account consistently for microstructure mechanics, hydrodynamic coupling, and thermal fluctuations he has extended the IBM formalism to incorporate stochastic driving fields consistent with statistical mechanics. Application areas include polymeric fluids, gels, and lipid bilayer membranes. The resulting stochastic partial differential equations (SPDEs) present many interesting challenges both for analysis and the development of numerical methods. A paper on the methodology can be found here :

[[http://www.math.ucsb.edu/~atzberg/publications/preprintStochIB.pdf | A Stochastic Immersed Boundary Method for Fluid-Structure Dynamics at Microscopic Length Scales]]. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | [Video of IMA Talk]]]. Additional papers can be found on his [[http://www.math.ucsb.edu/~atzberg/index.html | research website]].

[[http://www.math.ucsb.edu/~atzberg/publications/preprintStochIB.pdf | A Stochastic Immersed Boundary Method for Fluid-Structure Dynamics at Microscopic Length Scales]]. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | [Video of IMA Talk]]]. Additional papers can be found on his [[http://www.math.ucsb.edu/~atzberg/index.html | research website]].

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* [[http://www.math.ucsb.edu/~atzberg/index.html | Dr. Atzberger]] : Prof. Atzberger has been working on utilizing immersed boundary methods to study properties of soft condensed matter. To account consistently for microstructure mechanics, hydrodynamic coupling, and thermal fluctuations he has extended the IBM formalism to incorporate stochastic driving fields consistent with statistical mechanics. ~~Applications of the new methodology include the study of~~ polymeric fluids, gels, and lipid bilayer membranes. The resulting stochastic partial differential equations (SPDEs) present many interesting challenges both for analysis and the development of numerical methods. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | [Video of IMA Talk]]]. Related papers can be found on his [[http://www.math.ucsb.edu/~atzberg/index.html | Research Website]].

to:

* [[http://www.math.ucsb.edu/~atzberg/index.html | Dr. Atzberger]] : Prof. Atzberger has been working on utilizing immersed boundary methods to study properties of soft condensed matter. To account consistently for microstructure mechanics, hydrodynamic coupling, and thermal fluctuations he has extended the IBM formalism to incorporate stochastic driving fields consistent with statistical mechanics. Application areas include polymeric fluids, gels, and lipid bilayer membranes. The resulting stochastic partial differential equations (SPDEs) present many interesting challenges both for analysis and the development of numerical methods. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | [Video of IMA Talk]]]. Related papers can be found on his [[http://www.math.ucsb.edu/~atzberg/index.html | Research Website]].

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* [[http://www.math.ucsb.edu/~atzberg/index.html | Dr. Atzberger]] : Prof. Atzberger ~~uses immersed boundary methods to study properties of soft condensed matter. To account consistently for microstructure mechanics, hydrodynamic coupling, and thermal fluctuations he has extended the immersed boundary method to incorporate stochastic driving fields consistent with statistical mechanics. The resulting stochastic partial differential equations (SPDEs) present many interesting challenges both for analysis~~ and ~~the development of numerical methods. His work is also concerned with applications of the methodology, in particular, to~~ the ~~study~~ of ~~polymeric fluids, gels, and lipid bilayer membranes~~. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | [Video of IMA Talk]]]. Related papers can be found on his [[http://www.math.ucsb.edu/~atzberg/index.html | Research Website]].

to:

* [[http://www.math.ucsb.edu/~atzberg/index.html | Dr. Atzberger]] : Prof. Atzberger has been working on utilizing immersed boundary methods to study properties of soft condensed matter. To account consistently for microstructure mechanics, hydrodynamic coupling, and thermal fluctuations he has extended the IBM formalism to incorporate stochastic driving fields consistent with statistical mechanics. Applications of the new methodology include the study of polymeric fluids, gels, and lipid bilayer membranes. The resulting stochastic partial differential equations (SPDEs) present many interesting challenges both for analysis and the development of numerical methods. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | [Video of IMA Talk]]]. Related papers can be found on his [[http://www.math.ucsb.edu/~atzberg/index.html | Research Website]].

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* [[http://www.math.ucsb.edu/~atzberg/index.html | Dr. Atzberger]] : Prof. Atzberger ~~is working on utilizing~~ immersed boundary methods to study properties of soft condensed matter. To account consistently for microstructure mechanics, hydrodynamic coupling, and thermal fluctuations he has extended the immersed boundary method to incorporate stochastic driving fields consistent with statistical mechanics. The resulting stochastic partial differential equations (SPDEs) present many interesting challenges both for analysis and the development of numerical methods. His work is also concerned with applications of the methodology, in particular, to the study of polymeric fluids, gels, and lipid bilayer membranes. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | [Video of IMA Talk]]]. Related papers can be found on his [[http://www.math.ucsb.edu/~atzberg/index.html | Research Website]].

to:

* [[http://www.math.ucsb.edu/~atzberg/index.html | Dr. Atzberger]] : Prof. Atzberger uses immersed boundary methods to study properties of soft condensed matter. To account consistently for microstructure mechanics, hydrodynamic coupling, and thermal fluctuations he has extended the immersed boundary method to incorporate stochastic driving fields consistent with statistical mechanics. The resulting stochastic partial differential equations (SPDEs) present many interesting challenges both for analysis and the development of numerical methods. His work is also concerned with applications of the methodology, in particular, to the study of polymeric fluids, gels, and lipid bilayer membranes. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | [Video of IMA Talk]]]. Related papers can be found on his [[http://www.math.ucsb.edu/~atzberg/index.html | Research Website]].

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* [[http://www.math.ucsb.edu/~atzberg/index.html | Dr. Atzberger]] : Prof. Atzberger is working on utilizing immersed boundary methods to study properties of soft condensed matter. To account consistently for microstructure mechanics, hydrodynamic coupling, and

thermal fluctuations he has extended the immersed boundary method to incorporate stochastic driving fields consistent with statistical mechanics. The resulting stochastic partial differential equations (SPDEs) present many interesting challenges both for analysis and the development of numerical methods. His work is also concerned with applications of the methodology, in particular, to the study of polymeric fluids, gels, and lipid bilayer membranes. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | [Video of IMA Talk]]]. Related papers can be found on his [[http://www.math.ucsb.edu/~atzberg/index.html | Research Website]].

thermal fluctuations he has extended the immersed boundary method to incorporate stochastic driving fields consistent with statistical mechanics. The resulting stochastic partial differential equations (SPDEs) present many interesting challenges both for analysis and the development of numerical methods. His work is also concerned with applications of the methodology, in particular, to the study of polymeric fluids, gels, and lipid bilayer membranes. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | [Video of IMA Talk]]]. Related papers can be found on his [[http://www.math.ucsb.edu/~atzberg/index.html | Research Website]].

to:

* [[http://www.math.ucsb.edu/~atzberg/index.html | Dr. Atzberger]] : Prof. Atzberger is working on utilizing immersed boundary methods to study properties of soft condensed matter. To account consistently for microstructure mechanics, hydrodynamic coupling, and thermal fluctuations he has extended the immersed boundary method to incorporate stochastic driving fields consistent with statistical mechanics. The resulting stochastic partial differential equations (SPDEs) present many interesting challenges both for analysis and the development of numerical methods. His work is also concerned with applications of the methodology, in particular, to the study of polymeric fluids, gels, and lipid bilayer membranes. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | [Video of IMA Talk]]]. Related papers can be found on his [[http://www.math.ucsb.edu/~atzberg/index.html | Research Website]].

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* [[http://www.math.ucsb.edu/~atzberg/index.html | Dr. Atzberger]] : Prof. Atzberger is working on utilizing immersed boundary methods to study properties of soft matter ~~materials, which contain hydrodynamically coupled microstructures subject to thermal fluctuations.~~ ~~To account for thermal fluctuations he has extended the immersed boundary method to incorporate stochastic driving fields which are consistent with statistical mechanics. The resulting formalism is cast in terms of a system~~ of ~~stochastic partial differential equations (SPDEs) which present interesting challenges both for analysis and the development of numerical methods.~~ A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | [Video of IMA Talk]]]. Related papers can be found on his [[http://www.math.ucsb.edu/~atzberg/index.html | Research Website]].

to:

thermal fluctuations he has extended the immersed boundary method to incorporate stochastic driving fields consistent with statistical mechanics. The resulting stochastic partial differential equations (SPDEs) present many interesting challenges both for analysis and the development of numerical methods. His work is also concerned with applications of the methodology, in particular, to the study of polymeric fluids, gels, and lipid bilayer membranes. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | [Video of IMA Talk]]]. Related papers can be found on his [[http://www.math.ucsb.edu/~atzberg/index.html | Research Website]].

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the solution of

specific problems arising in applications often in the basic sciences

specific problems arising in applications often in the basic sciences

to:

the solution of specific problems arising in applications, often in the basic sciences

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to:

concerning recent news or current activities of the applied mathematics group.

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* [[http://www.math.ucsb.edu/~atzberg/index.html | Dr. Atzberger]] : Prof. Atzberger is working on utilizing immersed boundary

methods to study properties of soft matter materials, which contain hydrodynamically coupled microstructures subject to thermal fluctuations. To account for thermal fluctuations he has extended the immersed boundary method to incorporate stochastic driving fields which are consistent with statistical mechanics. The resulting formalism is cast in terms of a system of stochastic partial differential equations (SPDEs) which present interesting challenges both for analysis and the development of numerical methods. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | [Video of IMA Talk]]]. Related papers can be found on his [[http://www.math.ucsb.edu/~atzberg/index.html | Research Website]].

methods to study properties of soft matter materials, which contain hydrodynamically coupled microstructures subject to thermal fluctuations. To account for thermal fluctuations he has extended the immersed boundary method to incorporate stochastic driving fields which are consistent with statistical mechanics. The resulting formalism is cast in terms of a system of stochastic partial differential equations (SPDEs) which present interesting challenges both for analysis and the development of numerical methods. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | [Video of IMA Talk]]]. Related papers can be found on his [[http://www.math.ucsb.edu/~atzberg/index.html | Research Website]].

to:

* [[http://www.math.ucsb.edu/~atzberg/index.html | Dr. Atzberger]] : Prof. Atzberger is working on utilizing immersed boundary methods to study properties of soft matter materials, which contain hydrodynamically coupled microstructures subject to thermal fluctuations. To account for thermal fluctuations he has extended the immersed boundary method to incorporate stochastic driving fields which are consistent with statistical mechanics. The resulting formalism is cast in terms of a system of stochastic partial differential equations (SPDEs) which present interesting challenges both for analysis and the development of numerical methods. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | [Video of IMA Talk]]]. Related papers can be found on his [[http://www.math.ucsb.edu/~atzberg/index.html | Research Website]].

Changed lines 73-74 from:

methods to study properties of soft matter materials, which contain hydrodynamically coupled microstructures subject to thermal fluctuations. To account for thermal fluctuations he has extended the immersed boundary method to incorporate

stochastic driving fields which are consistent with statistical mechanics. The resulting formalism is cast in terms of a system of stochastic partial differential equations (SPDEs) which present interesting challenges both for analysis and the development of numerical methods. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | [Video of IMA Talk]]]. Related papers can be found on his [[http://www.math.ucsb.edu/~atzberg/index.html | Research Website]].

stochastic driving fields which are consistent with statistical mechanics. The resulting formalism is cast in terms of a system of stochastic partial differential equations (SPDEs) which present interesting challenges both for analysis and the development of numerical methods. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | [Video of IMA Talk]]]. Related papers can be found on his [[http://www.math.ucsb.edu/~atzberg/index.html | Research Website]].

to:

methods to study properties of soft matter materials, which contain hydrodynamically coupled microstructures subject to thermal fluctuations. To account for thermal fluctuations he has extended the immersed boundary method to incorporate stochastic driving fields which are consistent with statistical mechanics. The resulting formalism is cast in terms of a system of stochastic partial differential equations (SPDEs) which present interesting challenges both for analysis and the development of numerical methods. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | [Video of IMA Talk]]]. Related papers can be found on his [[http://www.math.ucsb.edu/~atzberg/index.html | Research Website]].

Changed lines 72-74 from:

* [[http://www.math.ucsb.edu/~atzberg/index.html | Dr. Atzberger]] : Prof. Atzberger ~~has extended the~~ immersed boundary ~~method ~~to ~~incorporate thermal fluctuations consistent with statistical mechanics for applications involving microscopic mechanical systems~~. The resulting formalism is cast in terms of a system of stochastic partial differential equations (SPDEs) which present interesting challenges both for analysis and the development of numerical methods. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | [Video of IMA Talk]]]. Related papers can be found on his [[http://www.math.ucsb.edu/~atzberg/index.html | Research Website]].

to:

methods to study properties of soft matter materials, which contain hydrodynamically coupled microstructures subject to thermal fluctuations. To account for thermal fluctuations he has extended the immersed boundary method to incorporate

stochastic driving fields which are consistent with statistical mechanics. The resulting formalism is cast in terms of a system of stochastic partial differential equations (SPDEs) which present interesting challenges both for analysis and the development of numerical methods. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | [Video of IMA Talk]]]. Related papers can be found on his [[http://www.math.ucsb.edu/~atzberg/index.html | Research Website]].

Changed line 72 from:

* [[http://www.math.ucsb.edu/~atzberg/index.html | Dr. Atzberger]] : Prof. Atzberger has extended the immersed boundary method to incorporate thermal fluctuations consistent with statistical mechanics for applications involving microscopic mechanical systems. The resulting formalism is cast in terms of a system of stochastic partial differential equations (SPDEs) which present interesting challenges both for analysis and the development of numerical methods. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | [Video of IMA Talk]]]. Related papers can be found on his ~~website ~~[[http://www.math.ucsb.edu/~atzberg/index.html | ~~publications~~]].

to:

* [[http://www.math.ucsb.edu/~atzberg/index.html | Dr. Atzberger]] : Prof. Atzberger has extended the immersed boundary method to incorporate thermal fluctuations consistent with statistical mechanics for applications involving microscopic mechanical systems. The resulting formalism is cast in terms of a system of stochastic partial differential equations (SPDEs) which present interesting challenges both for analysis and the development of numerical methods. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | [Video of IMA Talk]]]. Related papers can be found on his [[http://www.math.ucsb.edu/~atzberg/index.html | Research Website]].

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* [[http://www.math.ucsb.edu/~hdc | Dr. Ceniceros]]~~)~~ : Prof. Ceniceros in joint work with UCSB grad student Jordan Fisher and [[http://www.ime.usp.br/~roma/index-1.html |Prof. Alexandre Roma]] (USP) has recently designed efficient implicit methods for the IBM formalisms significantly advancing the time-scales accessible in simulations of systems with stiff elastic structures. A soon to appear manuscript of the work can be found here: [[http://www.math.ucsb.edu/~hdc/public/IBM_Implicit.pdf | Efficient solutions to robust, semi-implicit discretizations of the Immersed Boundary Method]].

to:

* [[http://www.math.ucsb.edu/~hdc | Dr. Ceniceros]] : Prof. Ceniceros in joint work with UCSB grad student Jordan Fisher and [[http://www.ime.usp.br/~roma/index-1.html |Prof. Alexandre Roma]] (USP) has recently designed efficient implicit methods for the IBM formalisms significantly advancing the time-scales accessible in simulations of systems with stiff elastic structures. A soon to appear manuscript of the work can be found here: [[http://www.math.ucsb.edu/~hdc/public/IBM_Implicit.pdf | Efficient solutions to robust, semi-implicit discretizations of the Immersed Boundary Method]].

Changed lines 72-74 from:

* ~~Dr. Atzberger (~~[[http://www.math.ucsb.edu/~atzberg/index.html | ~~Research Website~~]]~~)~~ Prof. Atzberger has extended the immersed boundary method to incorporate thermal fluctuations consistent with statistical mechanics for applications involving microscopic mechanical systems. The resulting formalism is cast in terms of a system of stochastic partial differential equations (SPDEs) which present interesting challenges both for analysis and the development of numerical methods. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | [Video of IMA Talk]]]. Related papers can be found on his website [[http://www.math.ucsb.edu/~atzberg/index.html | publications]].

*~~Dr. Ceniceros (~~[[http://www.math.ucsb.edu/~hdc | ~~Research Website~~]]) Prof. Ceniceros in joint work with UCSB grad student Jordan Fisher and [[http://www.ime.usp.br/~roma/index-1.html |Prof. Alexandre Roma]] (USP) has recently designed efficient implicit methods for the IBM formalisms significantly advancing the time-scales accessible in simulations of systems with stiff elastic structures. A soon to appear manuscript of the work can be found here: [[http://www.math.ucsb.edu/~hdc/public/IBM_Implicit.pdf | Efficient solutions to robust, semi-implicit discretizations of the Immersed Boundary Method]].

*

to:

* [[http://www.math.ucsb.edu/~atzberg/index.html | Dr. Atzberger]] : Prof. Atzberger has extended the immersed boundary method to incorporate thermal fluctuations consistent with statistical mechanics for applications involving microscopic mechanical systems. The resulting formalism is cast in terms of a system of stochastic partial differential equations (SPDEs) which present interesting challenges both for analysis and the development of numerical methods. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | [Video of IMA Talk]]]. Related papers can be found on his website [[http://www.math.ucsb.edu/~atzberg/index.html | publications]].

* [[http://www.math.ucsb.edu/~hdc | Dr. Ceniceros]]) : Prof. Ceniceros in joint work with UCSB grad student Jordan Fisher and [[http://www.ime.usp.br/~roma/index-1.html |Prof. Alexandre Roma]] (USP) has recently designed efficient implicit methods for the IBM formalisms significantly advancing the time-scales accessible in simulations of systems with stiff elastic structures. A soon to appear manuscript of the work can be found here: [[http://www.math.ucsb.edu/~hdc/public/IBM_Implicit.pdf | Efficient solutions to robust, semi-implicit discretizations of the Immersed Boundary Method]].

* [[http://www.math.ucsb.edu/~hdc | Dr. Ceniceros]]) : Prof. Ceniceros in joint work with UCSB grad student Jordan Fisher and [[http://www.ime.usp.br/~roma/index-1.html |Prof. Alexandre Roma]] (USP) has recently designed efficient implicit methods for the IBM formalisms significantly advancing the time-scales accessible in simulations of systems with stiff elastic structures. A soon to appear manuscript of the work can be found here: [[http://www.math.ucsb.edu/~hdc/public/IBM_Implicit.pdf | Efficient solutions to robust, semi-implicit discretizations of the Immersed Boundary Method]].

Changed lines 72-74 from:

* Dr. Atzberger :~~ [[http:~~//www.math.ucsb.edu/~atzberg/index.html | Research Website]]~~.~~ Prof. Atzberger has extended the immersed boundary method to incorporate thermal fluctuations consistent with statistical mechanics for applications involving microscopic mechanical systems. The resulting formalism is cast in terms of a system of stochastic partial differential equations (SPDEs) which present interesting challenges both for analysis and the development of numerical methods. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | [Video of IMA Talk]]]. Related papers can be found on his website [[http://www.math.ucsb.edu/~atzberg/index.html | publications]].

* Dr. Ceniceros :~~ [[http:~~//www.math.ucsb.edu/~hdc | Research Website]]~~.~~ Prof. Ceniceros in joint work with UCSB grad student Jordan Fisher and [[http://www.ime.usp.br/~roma/index-1.html |Prof. Alexandre Roma]] (USP) has recently designed efficient implicit methods for the IBM formalisms significantly advancing the time-scales accessible in simulations of systems with stiff elastic structures. A soon to appear manuscript of the work can be found here: [[http://www.math.ucsb.edu/~hdc/public/IBM_Implicit.pdf | Efficient solutions to robust, semi-implicit discretizations of the Immersed Boundary Method]].

* Dr. Ceniceros :

to:

* Dr. Atzberger ([[http://www.math.ucsb.edu/~atzberg/index.html | Research Website]]) Prof. Atzberger has extended the immersed boundary method to incorporate thermal fluctuations consistent with statistical mechanics for applications involving microscopic mechanical systems. The resulting formalism is cast in terms of a system of stochastic partial differential equations (SPDEs) which present interesting challenges both for analysis and the development of numerical methods. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | [Video of IMA Talk]]]. Related papers can be found on his website [[http://www.math.ucsb.edu/~atzberg/index.html | publications]].

* Dr. Ceniceros ([[http://www.math.ucsb.edu/~hdc | Research Website]]) Prof. Ceniceros in joint work with UCSB grad student Jordan Fisher and [[http://www.ime.usp.br/~roma/index-1.html |Prof. Alexandre Roma]] (USP) has recently designed efficient implicit methods for the IBM formalisms significantly advancing the time-scales accessible in simulations of systems with stiff elastic structures. A soon to appear manuscript of the work can be found here: [[http://www.math.ucsb.edu/~hdc/public/IBM_Implicit.pdf | Efficient solutions to robust, semi-implicit discretizations of the Immersed Boundary Method]].

* Dr. Ceniceros ([[http://www.math.ucsb.edu/~hdc | Research Website]]) Prof. Ceniceros in joint work with UCSB grad student Jordan Fisher and [[http://www.ime.usp.br/~roma/index-1.html |Prof. Alexandre Roma]] (USP) has recently designed efficient implicit methods for the IBM formalisms significantly advancing the time-scales accessible in simulations of systems with stiff elastic structures. A soon to appear manuscript of the work can be found here: [[http://www.math.ucsb.edu/~hdc/public/IBM_Implicit.pdf | Efficient solutions to robust, semi-implicit discretizations of the Immersed Boundary Method]].

Changed line 72 from:

* Dr. Atzberger : [[http://www.math.ucsb.edu/~atzberg/index.html | Research Website]]. Prof. Atzberger has extended the immersed boundary method to incorporate thermal fluctuations consistent with statistical mechanics for applications involving microscopic mechanical systems. The resulting formalism is cast in terms of a system of stochastic partial differential equations (SPDEs) which present interesting challenges both for analysis and the development of numerical methods. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here ~~: ~~[[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | ~~IMA Workshop on Multiscale Methods.~~]] Related papers can be found [[http://www.math.ucsb.edu/~atzberg/index.html | ~~here~~]].

to:

* Dr. Atzberger : [[http://www.math.ucsb.edu/~atzberg/index.html | Research Website]]. Prof. Atzberger has extended the immersed boundary method to incorporate thermal fluctuations consistent with statistical mechanics for applications involving microscopic mechanical systems. The resulting formalism is cast in terms of a system of stochastic partial differential equations (SPDEs) which present interesting challenges both for analysis and the development of numerical methods. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | [Video of IMA Talk]]]. Related papers can be found on his website [[http://www.math.ucsb.edu/~atzberg/index.html | publications]].

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%width=300px% Attach:~~southHallView1~~.jpg

to:

%width=300px% Attach:UCSBLagoon.jpg

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!!Research Highlights (select subset of activities)

to:

!!Research Highlights (select subset of recent activities)

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!!Research Highlights (select subset of activities)

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----

!! Local and Global Wellposedness of Nonlinear Evolutionary Equations

to:

'+Local and Global Wellposedness of Nonlinear Evolutionary Equations +'

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to:

'+Fluid-Structure Interactions : Immersed Boundary Methods and Boundary Integral Methods+'

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'+%color555555%Carlos Garcia-Cervera Wins NSF Faculty Early Career Development Award (NSF CAREER)+'

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to:

!%color555555%Carlos Garcia-Cervera Wins NSF Faculty Early Career Development Award (NSF CAREER)

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!!~~%blue%~~Research Gallery \\

to:

!!Research Gallery \\

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!!~~%blue%~~Research Highlights (select subset of activities)

to:

!!Research Highlights (select subset of activities)

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!!%~~color$555555~~%Carlos Garcia-Cervera Wins NSF Faculty Early Career Development Award (NSF CAREER)

to:

!!%color555555%Carlos Garcia-Cervera Wins NSF Faculty Early Career Development Award (NSF CAREER)

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!!%~~red~~%Carlos Garcia-Cervera Wins NSF Faculty Early Career Development Award (NSF CAREER)

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!!%color$555555%Carlos Garcia-Cervera Wins NSF Faculty Early Career Development Award (NSF CAREER)

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!!News

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!!Carlos Garcia-Cervera Wins NSF Faculty Early Career Development Award (NSF CAREER)

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!!%red%Carlos Garcia-Cervera Wins NSF Faculty Early Career Development Award (NSF CAREER)

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News

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!!%blue%Research ~~Areas~~ (select subset of activities)

to:

[[#ResearchHighlights]]

----

!!%blue%Research Highlights (select subset of activities)

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!!%blue%Research Areas (select subset of~~ recent~~ activities)

to:

!!%blue%Research Areas (select subset of activities)

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!!%blue%Research Areas (~~selected~~ subset of activities)

to:

!!%blue%Research Areas (select subset of recent activities)

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%width=~~400px~~% Attach:SIB_Schematic.png

to:

%width=300px% Attach:SIB_Schematic.png

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!!Fluid-Structure ~~Dynamics~~ : Immersed Boundary Methods and Boundary Integral Methods

to:

!!Fluid-Structure Interactions : Immersed Boundary Methods and Boundary Integral Methods

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* Dr. Ceniceros : [[http://www.math.ucsb.edu/~hdc | Research Website]]. Prof. Ceniceros in joint work with UCSB grad student Jordan Fisher and [[http://www.ime.usp.br/~roma/index-1.html |Prof. Alexandre Roma]] (USP) has recently designed efficient implicit methods for the IBM formalisms significantly advancing the time-scales accessible in simulations of systems with stiff elastic structures. A soon to appear manuscript of the work can be found here: [[http://www.math.ucsb.edu/~hdc/public/IBM_Implicit.pdf | Efficient solutions to robust, semi-implicit discretizations of the Immersed Boundary Method~~]]~~

----

!! Liquid Crystals / Lipid Bilayer Membranes / Complex Polymeric Fluids

Brief article outlining basic area of research, interesting math. issues...

Faculty members working in this area include:

* Dr. Garcia-Cervera : [[http://www.math.ucsb.edu/~atzberg/index.html | Research Website]].

* Dr. Ceniceros : [[http://www.math.ucsb.edu/~hdc | Research Website]].

* Dr. Atzbeger : [[http://www.math.ucsb.edu/~atzberg/index.html | Research Website]].

----

!! Liquid Crystals / Lipid Bilayer Membranes / Complex Polymeric Fluids

Brief article outlining basic area of research, interesting math. issues...

Faculty members working in this area include:

* Dr. Garcia-Cervera : [[http://www.math.ucsb.edu/~atzberg/index.html | Research Website]].

* Dr. Ceniceros : [[http://www.math.ucsb.edu/~hdc | Research Website]].

* Dr. Atzbeger : [[http://www.math.ucsb.edu/~atzberg/index.html | Research Website

to:

* Dr. Ceniceros : [[http://www.math.ucsb.edu/~hdc | Research Website]]. Prof. Ceniceros in joint work with UCSB grad student Jordan Fisher and [[http://www.ime.usp.br/~roma/index-1.html |Prof. Alexandre Roma]] (USP) has recently designed efficient implicit methods for the IBM formalisms significantly advancing the time-scales accessible in simulations of systems with stiff elastic structures. A soon to appear manuscript of the work can be found here: [[http://www.math.ucsb.edu/~hdc/public/IBM_Implicit.pdf | Efficient solutions to robust, semi-implicit discretizations of the Immersed Boundary Method]].

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!!%blue%Research Areas (~~Selected~~ subset of activities)

to:

!!%blue%Research Areas (selected subset of activities)

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!!%blue%Research Areas (Selected ~~Subset~~ of ~~Activities~~)

to:

!!%blue%Research Areas (Selected subset of activities)

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%width=~~200px~~% Attach:carlosImage.png %width=~~200px~~% Attach:atzbergerImage.png

to:

%width=100px% Attach:carlosImage.png %width=100px% Attach:atzbergerImage.png

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%width=200px% Attach:carlosImage.png %width=200px% Attach:atzbergerImage.png

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%width=200px% Attach:carlosImage.png %width=200px% Attach:atzbergerImage.png ~~%width=200px% Attach:carlosImage.png ~~

(images / movies, here, etc...)

(images / movies, here, etc...)

to:

%width=200px% Attach:carlosImage.png

%width=200px% Attach:atzbergerImage.png

%width=200px% Attach:atzbergerImage.png

Deleted lines 89-111:

----

!!%blue%Discussion of Above Items

Above is an experiment and rough draft / brainstorm. Idea is to give undergraduate / graduate students and general public and scientific audience sense of what types of work our group does. Above is meant to give an example of some themes and what we might post to highlight our specific research programs and on-going work both at the level of light-reading and in more detail. I wrote mostly about my own work, since I know the most about this activity presumably. :) I propose up-top we have short gallery style presentation of results for the light-of-heart. We then write in more detail a few of these short articles which discuss general thematic areas of research of the group (which of course can be modified over time to freshen things up and as our collective interests develop). This means people encounter what's new and light first, and then depending on their level of interest can scroll down for a more detailed desciption of the group.

Another model is not to have thematic articles, but to only have a few images up-top with a short caption and links to researchers webpages with more detailed info... [see UNC site which is quite nicely done

http://amath.unc.edu/]. In my opinion our group runs the risk of not presenting a well-defined core and anchored research program communicated to people when they visit if we only include a collection of images with captions. Maybe there is some happy medium, please write-up some example or express your ideas.

Please take a shot at posting/editing the welcome message and some materials for discussion.

test

[All pages are under-construction]

Please feel free to edit and taking a shot at writing these materials.

We can collectively edit over time until we get something we are

all happy with.

(will work on embedding some floating boxes on the right

to list in an accessible format "news items and current events",

see http://www.me.ucsb.edu/ for stylistic sense of what I

have in mind)

Changed lines 7-9 from:

Welcome to the applied mathematics group's homepage. Applied mathematics

refers to the branch of mathematics which strives to integrate the

development of core areas of mathematics with the solution of

refers to the branch of mathematics which strives to integrate the

development of core areas of mathematics with the solution of

to:

Welcome to the applied mathematics group's homepage. Applied mathematics refers to the branch of mathematics which strives

to integrate the development of core areas of mathematics with

the solution of

to integrate the development of core areas of mathematics with

the solution of

Changed lines 29-30 from:

!!~~%grey%~~Carlos Garcia-Cervera Wins NSF Faculty Early Career Development Award (NSF CAREER)

to:

!!Carlos Garcia-Cervera Wins NSF Faculty Early Career Development Award (NSF CAREER)

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!!Research Gallery \\

to:

!!%blue%Research Gallery \\

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!!Research Areas (Selected Subset of Activities)

to:

!!%blue%Research Areas (Selected Subset of Activities)

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!!Discussion of Above Items

to:

!!%blue%Discussion of Above Items

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!!Research Highlights \\

to:

!!%blue%Research Highlights \\

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!!%~~blue~~%Carlos Garcia-Cervera Wins NSF Faculty Early Career Development Award (NSF CAREER)

to:

!!%grey%Carlos Garcia-Cervera Wins NSF Faculty Early Career Development Award (NSF CAREER)

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%blue%

!!Carlos Garcia-Cervera Wins NSF Faculty Early Career Development Award (NSF CAREER)

%black%

!!

%black%

to:

!!%blue%Carlos Garcia-Cervera Wins NSF Faculty Early Career Development Award (NSF CAREER)

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dynamics, boundary integral methods, immersed boundary methods~~)~~,

to:

dynamics, boundary integral methods, immersed boundary methods,

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%width=300px% Attach:southHallView1.jpg

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%width=200px% Attach:southHallView1.jpg

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%width=200px% Attach:~~southHallView1~~.~~jpg~~

South Hall

South Hall

to:

%width=200px% Attach:southHallView2.jpg

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to:

South Hall

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Department of Mathematics : South Hall [Image Credit:Statistics Homepage]

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\\

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(Image from UCSB Statistics Homepage)

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[[#ResearchHighlights]]

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\\

(Carlos: Please finish writing this synposis.)

\\

\\

\\

\\

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dynamics ~~for systems with moving boundaries (boundary integral ~~methods

~~/ immersed boundary methods), crystalline solids and liquid crystals~~,

~~density functional theory, analysis of non-linear evolutionary PDE's, ~~

study of ~~existence or development of singularities in finite time,~~

applied harmonic analysis, and stochastic differential equations. Here

you willfind research highlights, upcoming seminar talks, and information

study

applied harmonic analysis, and stochastic differential equations. Here

you will

to:

dynamics, boundary integral methods, immersed boundary methods),

crystalline solids and liquid crystals, density functional theory,

analysis of non-linear evolutionary PDE's, study of existence or

development of singularities in finite time, applied harmonic

analysis, and stochastic differential equations. Here you will

find research highlights, upcoming seminar talks, and information

crystalline solids and liquid crystals, density functional theory,

analysis of non-linear evolutionary PDE's, study of existence or

development of singularities in finite time, applied harmonic

analysis, and stochastic differential equations. Here you will

find research highlights, upcoming seminar talks, and information

Changed lines 9-25 from:

dynamics ~~(boundary integral methods / immersed~~ boundary methods~~),~~

~~crystalline solids and liquid crystals, density functional theory, ~~

analysis of non-linear hyperbolic PDE's (?), applied harmonic analysis,

~~stochastic differential equations. Here you will find research highlights, ~~

upcoming seminar talks, and ~~information about news and current activities ~~

of the applied mathematics group.

test

[All pages are under-construction]

Please feel free to editand ~~taking a shot at writing these materials~~.~~ ~~

We can collectively edit over time until we get something we are

all happy with.

(will work on embedding some floating boxes on the right

to list in an accessible format "news items and current events",

see http://www.me.ucsb.edu/ for stylistic sense of what I

have in mind)

analysis of non-linear hyperbolic PDE's (?), applied harmonic analysis

upcoming seminar talks

of the applied mathematics group.

test

[All pages are under-construction]

Please feel free to edit

We can collectively edit over time until we get something we are

all happy with.

(will work on embedding some floating boxes on the right

to list in an accessible format "news items and current events",

see http://www.me.ucsb.edu/ for stylistic sense of what I

have in mind)

to:

dynamics for systems with moving boundaries (boundary integral methods

/ immersed boundary methods), crystalline solids and liquid crystals,

density functional theory, analysis of non-linear evolutionary PDE's,

study of existence or development of singularities in finite time,

applied harmonic analysis, and stochastic differential equations. Here

you will find research highlights, upcoming seminar talks, and information

about news and current activities of the applied mathematics group.

/ immersed boundary methods), crystalline solids and liquid crystals,

density functional theory, analysis of non-linear evolutionary PDE's,

study of existence or development of singularities in finite time,

applied harmonic analysis, and stochastic differential equations. Here

you will find research highlights, upcoming seminar talks, and information

about news and current activities of the applied mathematics group.

Added lines 105-116:

test

[All pages are under-construction]

Please feel free to edit and taking a shot at writing these materials.

We can collectively edit over time until we get something we are

all happy with.

(will work on embedding some floating boxes on the right

to list in an accessible format "news items and current events",

see http://www.me.ucsb.edu/ for stylistic sense of what I

have in mind)

Changed lines 42-46 from:

The ~~award will support his research for five years providing funding~~ for ~~postdoctoral researchers~~

and graduate students. ~~The proposed research program has the potential to impact fundamental~~

computational approaches used in studying solid materials taking into account important

quantum effects. This is the first NSF CAREER award given to a faculty

member of the department of mathematics.\\

and graduate students.

computational approaches used in studying solid materials taking into account important

quantum effects.

member of the department of mathematics.\\

to:

The awards are for a minimum of $400,000 and support his research for five years providing funding

for postdoctoral researchers and graduate students. The proposed research program has the potential

to impact fundamental computational approaches used in studying solid materials. This is the first

NSF CAREER award given to a faculty member of the department of mathematics.\\

for postdoctoral researchers and graduate students. The proposed research program has the potential

to impact fundamental computational approaches used in studying solid materials. This is the first

NSF CAREER award given to a faculty member of the department of mathematics.\\

Added line 41:

The Faculty Early Career Development (CAREER) Program offers the NSF’s most prestigious awards in support of early career development activities of those teacher-scholars who are most likely to become the academic leaders of the 21st century.

Changed lines 43-44 from:

computational approaches used in studying ~~quantum effects in a wide range of systems from ~~

semiconductors to biological molecules. This is the first NSF CAREER award given to a faculty

semiconductors to biological molecules

to:

computational approaches used in studying solid materials taking into account important

quantum effects. This is the first NSF CAREER award given to a faculty

quantum effects. This is the first NSF CAREER award given to a faculty

Changed lines 41-43 from:

The award will ~~.... and ... The proposed research program has the potential to ~~

impact.~~..~~ ~~This is the first NSF CAREER award given ~~to ~~a faculty member of the ~~

department of mathematics.\\

impact

department

to:

The award will support his research for five years providing funding for postdoctoral researchers

and graduate students. The proposed research program has the potential to impact fundamental

computational approaches used in studying quantum effects in a wide range of systems from

semiconductors to biological molecules. This is the first NSF CAREER award given to a faculty

member of the department of mathematics.\\

and graduate students. The proposed research program has the potential to impact fundamental

computational approaches used in studying quantum effects in a wide range of systems from

semiconductors to biological molecules. This is the first NSF CAREER award given to a faculty

member of the department of mathematics.\\

Deleted lines 111-134:

Not sure if this is necessary (formal rules for editing the Wiki website):\\

\\

'''Applied math. group wiki by-laws:'''\\

\\

To handle the issue of any members putting inappropriate things on

the public part of the website all content editing will be password protected (admin or

core members). To avoid abuse by any one group member.

I propose we shall have the official convention that all core members "vote"

on the "hidden" page draft content before anything is put on the

homepage (password protected by admin). This way if requested we can allow

in fairness anyone in the group to post material, but everything on-line

reflects the group consensus. Anything failing the vote and revisions process

will not be copied to the homepage [kind of like a journal peer-review process].

Basically, we will post on the hidden page content "approved PJA", "revise xyz PJA",

"do-not-approve PJA", after all members post the admin will copy... We could

also agree to authorize certain individuals (by majority vote) to have the

right to post content on-line without prior approval with provision they

remove anything to which someone objects and the majority does not support.

I am not sure this is necessary, but

these paragraphs could be copied to a formal manual on by-laws for the pages

if this is required by university to avoid any formal objections being made

to how the pages are collectively managed.

Changed line 56 from:

%width=200px% Attach:carlosImage.png %width=200px% Attach:atzbergerImage.png %width=200px% Attach:carlosImage.png ~~%width=200px% Attach:atzbergerImage.png %width=200px% Attach:carlosImage.png %width=200px% Attach:atzbergerImage.png %width=200px% Attach:carlosImage.png~~

to:

%width=200px% Attach:carlosImage.png %width=200px% Attach:atzbergerImage.png %width=200px% Attach:carlosImage.png

Changed lines 1-2 from:

!! Welcome

to:

!! Welcome

Added line 16:

[All pages are under-construction]

Changed line 86 from:

* Dr. Atzberger : [[http://www.math.ucsb.edu/~atzberg/index.html | Research Website]]. Prof. Atzberger has extended the immersed boundary method to incorporate thermal fluctuations consistent with statistical mechanics for applications involving microscopic mechanical systems. The resulting formalism is cast in terms of a system of stochastic partial differential equations (SPDEs) which present interesting challenges both for analysis and the development of numerical methods. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here : [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | IMA Workshop on Multiscale Methods.]]

to:

* Dr. Atzberger : [[http://www.math.ucsb.edu/~atzberg/index.html | Research Website]]. Prof. Atzberger has extended the immersed boundary method to incorporate thermal fluctuations consistent with statistical mechanics for applications involving microscopic mechanical systems. The resulting formalism is cast in terms of a system of stochastic partial differential equations (SPDEs) which present interesting challenges both for analysis and the development of numerical methods. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here : [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | IMA Workshop on Multiscale Methods.]] Related papers can be found [[http://www.math.ucsb.edu/~atzberg/index.html | here]].

Changed line 86 from:

* Dr. Atzberger : [[http://www.math.ucsb.edu/~atzberg/index.html | Research Website]]. Prof. Atzberger has extended the immersed boundary method to incorporate thermal fluctuations ~~for applications involving microscopic mechanical systems. The formalism is cast in terms of a system of stochastic partial differential equations (SPDEs) obtained by introducing an appropriate stochastic driving field in the fluid equations.~~ A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here : [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | IMA Workshop on Multiscale Methods.]]

to:

* Dr. Atzberger : [[http://www.math.ucsb.edu/~atzberg/index.html | Research Website]]. Prof. Atzberger has extended the immersed boundary method to incorporate thermal fluctuations consistent with statistical mechanics for applications involving microscopic mechanical systems. The resulting formalism is cast in terms of a system of stochastic partial differential equations (SPDEs) which present interesting challenges both for analysis and the development of numerical methods. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here : [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | IMA Workshop on Multiscale Methods.]]

Changed lines 86-87 from:

* Dr. Atzberger : [[http://www.math.ucsb.edu/~atzberg/index.html | Research Website]]. Prof. Atzberger has extended the immersed boundary method to incorporate thermal fluctuations for applications involving microscopic

mechanical systems. The formalism is cast in terms of a system of stochastic partial differential equations (SPDEs) obtained by introducing an appropriate stochastic driving field in the fluid equations. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here : [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | IMA Workshop on Multiscale Methods.]]

mechanical systems. The formalism is cast in terms of a system of stochastic partial differential equations (SPDEs) obtained by introducing an appropriate stochastic driving field in the fluid equations. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here : [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | IMA Workshop on Multiscale Methods.]]

to:

* Dr. Atzberger : [[http://www.math.ucsb.edu/~atzberg/index.html | Research Website]]. Prof. Atzberger has extended the immersed boundary method to incorporate thermal fluctuations for applications involving microscopic mechanical systems. The formalism is cast in terms of a system of stochastic partial differential equations (SPDEs) obtained by introducing an appropriate stochastic driving field in the fluid equations. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here : [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | IMA Workshop on Multiscale Methods.]]

Changed lines 87-88 from:

mechanical systems. The formalism is cast in terms of a system of stochastic partial differential equations (SPDEs)

obtained by introducing an appropriate stochastic driving field in the fluid equations. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here : [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | IMA Workshop on Multiscale Methods.]]

obtained by introducing an appropriate stochastic driving field in the fluid equations. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here : [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | IMA Workshop on Multiscale Methods.]]

to:

mechanical systems. The formalism is cast in terms of a system of stochastic partial differential equations (SPDEs) obtained by introducing an appropriate stochastic driving field in the fluid equations. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here : [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | IMA Workshop on Multiscale Methods.]]

Changed lines 86-87 from:

* Dr. Atzberger : [[http://www.math.ucsb.edu/~atzberg/index.html | Research Website]]. Prof. Atzberger has ~~worked on extending the immersed boundary method to incorporate thermal fluctuations for applications involving microscopic~~

~~mechanical systems.~~ A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here : [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | IMA Workshop on Multiscale Methods.]]

to:

mechanical systems. The formalism is cast in terms of a system of stochastic partial differential equations (SPDEs)

obtained by introducing an appropriate stochastic driving field in the fluid equations. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here : [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | IMA Workshop on Multiscale Methods.]]

Changed lines 86-88 from:

* Dr. Atzberger : [[http://www.math.ucsb.edu/~atzberg/index.html | Research Website]]. ~~A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here : [[http://www~~.~~ima~~.~~umn.edu/2008-2009/W11.3-7.08/abstracts.html#~~Atzberger~~-Paul | IMA Workshop on Multiscale Methods.]]~~

* Dr. Ceniceros :[[http://www.~~math~~.~~ucsb~~.edu/~~~hdc | Research Website]]~~.~~ Prof~~.~~ Ceniceros in joint work with UCSB grad student Jordan Fisher and ~~[[http://www.~~ime~~.~~usp~~.~~br~~/~~~roma/index-1.html~~ |~~Prof. Alexandre Roma~~]](USP) has recently designed efficient implicit methods for the IBM formalisms significantly advancing the time-scales accessible in simulations of systems with stiff elastic structures. A soon to appear manuscript of the work can be found here: [[http://www.math.ucsb.edu/~hdc/public/IBM_Implicit.pdf | Efficient solutions to robust, semi-implicit discretizations of the Immersed Boundary Method]]

* Dr. Ceniceros :

to:

* Dr. Atzberger : [[http://www.math.ucsb.edu/~atzberg/index.html | Research Website]]. Prof. Atzberger has worked on extending the immersed boundary method to incorporate thermal fluctuations for applications involving microscopic

mechanical systems. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here : [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | IMA Workshop on Multiscale Methods.]]

* Dr. Ceniceros : [[http://www.math.ucsb.edu/~hdc | Research Website]]. Prof. Ceniceros in joint work with UCSB grad student Jordan Fisher and [[http://www.ime.usp.br/~roma/index-1.html |Prof. Alexandre Roma]] (USP) has recently designed efficient implicit methods for the IBM formalisms significantly advancing the time-scales accessible in simulations of systems with stiff elastic structures. A soon to appear manuscript of the work can be found here: [[http://www.math.ucsb.edu/~hdc/public/IBM_Implicit.pdf | Efficient solutions to robust, semi-implicit discretizations of the Immersed Boundary Method]]

mechanical systems. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here : [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | IMA Workshop on Multiscale Methods.]]

* Dr. Ceniceros : [[http://www.math.ucsb.edu/~hdc | Research Website]]. Prof. Ceniceros in joint work with UCSB grad student Jordan Fisher and [[http://www.ime.usp.br/~roma/index-1.html |Prof. Alexandre Roma]] (USP) has recently designed efficient implicit methods for the IBM formalisms significantly advancing the time-scales accessible in simulations of systems with stiff elastic structures. A soon to appear manuscript of the work can be found here: [[http://www.math.ucsb.edu/~hdc/public/IBM_Implicit.pdf | Efficient solutions to robust, semi-implicit discretizations of the Immersed Boundary Method]]

Changed line 55 from:

!!Research Areas (Selected Subset ~~for Highlights~~)

to:

!!Research Areas (Selected Subset of Activities)

Added lines 57-71:

!! Local and Global Wellposedness of Nonlinear Evolutionary Equations

Provide conditions on initial data which ensure the existence, uniqueness, and continuous dependence of solutions to the initial value problem for nonlinear

evolutionary partial differential equations.

Determine whether solutions exist globally in time or develop singularities in finite time. Explore the regularity and asymptotic behavior of solutions.

Applications to nonlinear dispersive equations, hydro- and elasto-dynamics.

Faculty members working in this area include:

* Dr. Sideris : [[http://www.math.ucsb.edu/~sideris/index.html | Research Website]].

* Dr. Ponce : [[http://www.math.ucsb.edu/~ponce/index.html | Research Website]].

----

Deleted lines 85-97:

----

!! Local and Global Wellposedness of Nonlinear Evolutionary Equations

Provide conditions on initial data which ensure the existence, uniqueness, and continuous dependence of solutions to the initial value problem for nonlinear

evolutionary partial differential equations.

Determine whether solutions exist globally in time or develop singularities in finite time. Explore the regularity and asymptotic behavior of solutions.

Applications to nonlinear dispersive equations, hydro- and elasto-dynamics.

Faculty members working in this area include:

* Dr. Sideris : [[http://www.math.ucsb.edu/~sideris/index.html | Research Website]].

* Dr. Ponce : [[http://www.math.ucsb.edu/~ponce/index.html | Research Website]].

Changed line 36 from:

%lfloat text-align=left margin-top=5px margin-right=5px margin-bottom=10px margin-left=5px width=100px% Attach:carlosSmiles.jpg ~~Attach:boris.jpg~~

to:

%lfloat text-align=left margin-top=5px margin-right=5px margin-bottom=10px margin-left=5px width=100px% Attach:carlosSmiles.jpg

Changed line 36 from:

%lfloat text-align=left margin-top=5px margin-right=5px margin-bottom=10px margin-left=5px width=100px% Attach:carlosSmiles.jpg

to:

%lfloat text-align=left margin-top=5px margin-right=5px margin-bottom=10px margin-left=5px width=100px% Attach:carlosSmiles.jpg Attach:boris.jpg

Changed lines 73-78 from:

!! Local and Global ~~Well-posedness~~ of Nonlinear Evolutionary Equations

~~(Tom and Gustavo, please write brief outline of research areas~~ and ~~edit URLs below)~~

Brief article outlining basic area of research, interesting math. issues.

~~Dr. Sideris's work and Dr. Ponce's work highlighted here~~...

Brief article outlining basic area of research, interesting math. issues

to:

!! Local and Global Wellposedness of Nonlinear Evolutionary Equations

Provide conditions on initial data which ensure the existence, uniqueness, and continuous dependence of solutions to the initial value problem for nonlinear

evolutionary partial differential equations.

Determine whether solutions exist globally in time or develop singularities in finite time. Explore the regularity and asymptotic behavior of solutions.

Applications to nonlinear dispersive equations, hydro- and elasto-dynamics.

Provide conditions on initial data which ensure the existence, uniqueness, and continuous dependence of solutions to the initial value problem for nonlinear

evolutionary partial differential equations.

Determine whether solutions exist globally in time or develop singularities in finite time. Explore the regularity and asymptotic behavior of solutions.

Applications to nonlinear dispersive equations, hydro- and elasto-dynamics.

Changed line 51 from:

%width=200px% Attach:carlosImage.png %width=200px% Attach:atzbergerImage.png %width=200px% Attach:carlosImage.png %width=200px% Attach:atzbergerImage.png %width=200px% Attach:carlosImage.png %width=200px% Attach:atzbergerImage.png %width=200px% Attach:carlosImage.~~png %width=200px% Attach:/Users/sideris/Desktop/boris.jpg~~

to:

%width=200px% Attach:carlosImage.png %width=200px% Attach:atzbergerImage.png %width=200px% Attach:carlosImage.png %width=200px% Attach:atzbergerImage.png %width=200px% Attach:carlosImage.png %width=200px% Attach:atzbergerImage.png %width=200px% Attach:carlosImage.png

Changed lines 73-74 from:

!! ~~Analysis of XYZ... Non~~-~~linear Elasticity.... Schrodinger Equ... (please edit)~~

to:

!! Local and Global Well-posedness of Nonlinear Evolutionary Equations

Changed lines 81-84 from:

* Dr. Sideris : [[http://www.math.ucsb.edu/~~~atzberg~~/index.html | Research Website]].

* Dr. Ponce : [[http://www.math.ucsb.edu/~~~atzberg~~/index.html | Research Website]].

* Dr. Ponce : [[http://www.math.ucsb.edu/~

to:

* Dr. Sideris : [[http://www.math.ucsb.edu/~sideris/index.html | Research Website]].

* Dr. Ponce : [[http://www.math.ucsb.edu/~ponce/index.html | Research Website]].

* Dr. Ponce : [[http://www.math.ucsb.edu/~ponce/index.html | Research Website]].

Changed line 130 from:

----

to:

----

Changed line 51 from:

%width=200px% Attach:carlosImage.png %width=200px% Attach:atzbergerImage.png %width=200px% Attach:carlosImage.png %width=200px% Attach:atzbergerImage.png %width=200px% Attach:carlosImage.png %width=200px% Attach:atzbergerImage.png %width=200px% Attach:carlosImage.~~png~~

to:

%width=200px% Attach:carlosImage.png %width=200px% Attach:atzbergerImage.png %width=200px% Attach:carlosImage.png %width=200px% Attach:atzbergerImage.png %width=200px% Attach:carlosImage.png %width=200px% Attach:atzbergerImage.png %width=200px% Attach:carlosImage.png %width=200px% Attach:/Users/sideris/Desktop/boris.jpg

Changed lines 69-70 from:

* Dr. Ceniceros : [[http://www.math.ucsb.edu/~hdc | Research Website]]. Prof. Ceniceros in joint work with UCSB grad student Jordan Fisher and ~~Prof~~. Alexandre Roma~~ ~~(USP) has recently designed efficient implicit methods for the IBM formalisms significantly advancing the time-scales accessible in simulations of systems with stiff elastic structures. A soon to appear manuscript of the work can be found here: ~~ ~~

[[http://www.math.ucsb.edu/~hdc/public/IBM_Implicit.pdf | Efficient solutions to robust, semi-implicit discretizations of the Immersed Boundary Method]]

[[http://www.math.ucsb.edu/~hdc/public/IBM_Implicit.pdf | Efficient solutions to robust, semi-implicit discretizations of the Immersed Boundary Method]]

to:

* Dr. Ceniceros : [[http://www.math.ucsb.edu/~hdc | Research Website]]. Prof. Ceniceros in joint work with UCSB grad student Jordan Fisher and [[http://www.ime.usp.br/~roma/index-1.html |Prof. Alexandre Roma]](USP) has recently designed efficient implicit methods for the IBM formalisms significantly advancing the time-scales accessible in simulations of systems with stiff elastic structures. A soon to appear manuscript of the work can be found here: [[http://www.math.ucsb.edu/~hdc/public/IBM_Implicit.pdf | Efficient solutions to robust, semi-implicit discretizations of the Immersed Boundary Method]]

Changed lines 69-70 from:

* Dr. ~~Cinceros~~ : [[http://www.math.ucsb.edu/~~~cinceros/index.html~~ | Research Website]]. ~~Dr~~. ~~Cinceros has recently formulated efficient implicit methods for the IBM formalisms significantly advancing the time-scales accessible in simulations of systems with stiff elastic structures, papers can be found here [link]... (Hector please edit profile and above description as you see fit~~...~~)~~

to:

* Dr. Ceniceros : [[http://www.math.ucsb.edu/~hdc | Research Website]]. Prof. Ceniceros in joint work with UCSB grad student Jordan Fisher and Prof. Alexandre Roma (USP) has recently designed efficient implicit methods for the IBM formalisms significantly advancing the time-scales accessible in simulations of systems with stiff elastic structures. A soon to appear manuscript of the work can be found here:

[[http://www.math.ucsb.edu/~hdc/public/IBM_Implicit.pdf | Efficient solutions to robust, semi-implicit discretizations of the Immersed Boundary Method]]

[[http://www.math.ucsb.edu/~hdc/public/IBM_Implicit.pdf | Efficient solutions to robust, semi-implicit discretizations of the Immersed Boundary Method]]

Changed line 93 from:

* Dr. ~~Cinceros~~ : [[http://www.math.ucsb.edu/~~~atzberg/index.html~~ | Research Website]].

to:

* Dr. Ceniceros : [[http://www.math.ucsb.edu/~hdc | Research Website]].

Changed line 59 from:

The mechanics of many physical systems depends ~~crucially~~ on the interaction of flexible elastic

to:

The mechanics of many physical systems depends importantly on the interaction of flexible elastic

Changed lines 59-60 from:

to:

The mechanics of many physical systems depends crucially on the interaction of flexible elastic

structures with a fluid flow. Examples of macroscopic systems include the pumping of the heart in which blood flow interacts with valves, lift general in insect flight, and wave propagation in the cochlea of the inner ear. Examples of microscopic systems include the rheology of complex fluids and soft-matter which depends importantly on microstructures (such as colloids, lipids, polymers, vesicles) which interact with shear and extensional fluid flows serving through small-scale deformations to elastically store or dissipate energy. These microscopic processes often result macroscopically in material properties exhibiting interesting counter-intuitive phenomena and features hard to predict a priori. Immersed Boundary Methods (IBM) and Boundary Integral Methods (BIM) are numerical approaches for studying the mechanics of elastic structures which interact with a fluid.

structures with a fluid flow. Examples of macroscopic systems include the pumping of the heart in which blood flow interacts with valves, lift general in insect flight, and wave propagation in the cochlea of the inner ear. Examples of microscopic systems include the rheology of complex fluids and soft-matter which depends importantly on microstructures (such as colloids, lipids, polymers, vesicles) which interact with shear and extensional fluid flows serving through small-scale deformations to elastically store or dissipate energy. These microscopic processes often result macroscopically in material properties exhibiting interesting counter-intuitive phenomena and features hard to predict a priori. Immersed Boundary Methods (IBM) and Boundary Integral Methods (BIM) are numerical approaches for studying the mechanics of elastic structures which interact with a fluid.

Changed lines 124-125 from:

if this is required by university to avoid any ~~issues of "free speech" and ~~

to guard against any formal objections being made to fairness.

to guard against any formal objections being made to fairness

to:

if this is required by university to avoid any formal objections being made

to how the pages are collectively managed.

to how the pages are collectively managed.

Changed line 106 from:

'''Applied math. wiki~~-edit~~ by-laws:'''\\

to:

'''Applied math. group wiki by-laws:'''\\

Changed line 106 from:

'''~~Wiki-edit By~~-~~Laws~~'''\\

to:

'''Applied math. wiki-edit by-laws:'''\\

Changed lines 68-69 from:

* Dr. Cinceros : [[http://www.math.ucsb.edu/~cinceros/index.html | Research Website]]. Dr. Cinceros has recently formulated efficient implicit methods for the IBM formalisms significantly advancing the time-scales accessible in simulations of systems with stiff elastic structures, papers can be

found here [link]... (Hector please edit profile and above description as you see fit...)

found here [link]... (Hector please edit profile and above description as you see fit...)

to:

* Dr. Cinceros : [[http://www.math.ucsb.edu/~cinceros/index.html | Research Website]]. Dr. Cinceros has recently formulated efficient implicit methods for the IBM formalisms significantly advancing the time-scales accessible in simulations of systems with stiff elastic structures, papers can be found here [link]... (Hector please edit profile and above description as you see fit...)

Changed lines 68-69 from:

* Dr. Cinceros~~'s~~ : [[http://www.math.ucsb.edu/~cinceros/index.html | Research Website]]. Dr. Cinceros has recently formulated efficient implicit methods for the IBM formalisms significantly advancing the time-scales accessible in simulations of systems with stiff elastic structures... (Hector please edit profile and above description as you see fit...)

to:

* Dr. Cinceros : [[http://www.math.ucsb.edu/~cinceros/index.html | Research Website]]. Dr. Cinceros has recently formulated efficient implicit methods for the IBM formalisms significantly advancing the time-scales accessible in simulations of systems with stiff elastic structures, papers can be

found here [link]... (Hector please edit profile and above description as you see fit...)

found here [link]... (Hector please edit profile and above description as you see fit...)

Changed line 57 from:

!!Fluid-Structure Dynamics: Immersed Boundary Methods and Boundary Integral Methods

to:

!!Fluid-Structure Dynamics : Immersed Boundary Methods and Boundary Integral Methods

Changed line 59 from:

Immersed Boundary Methods (IBM) and Boundary Integral Methods (BIM) are numerical approaches for studying the mechanics of elastic structures which interact with a fluid. Examples macroscopic systems include the pumping of the heart in which blood flow interacts with valves, lift general in insect flight, and wave propagation in the cochlea of the inner ear. In microscopic systems examples include the rheology of complex fluids and soft-matter which depends importantly on microstructures (such as colloids, lipids, polymers, vesicles) which interact with shear and extensional fluid flows serving through small-scale deformations to elastically store or dissipate energy. These microscopic processes often result macroscopically in material properties exhibiting interesting counter-intuitive phenomena and ~~a priori ~~hard to predict ~~features. ~~

to:

Immersed Boundary Methods (IBM) and Boundary Integral Methods (BIM) are numerical approaches for studying the mechanics of elastic structures which interact with a fluid. Examples macroscopic systems include the pumping of the heart in which blood flow interacts with valves, lift general in insect flight, and wave propagation in the cochlea of the inner ear. In microscopic systems examples include the rheology of complex fluids and soft-matter which depends importantly on microstructures (such as colloids, lipids, polymers, vesicles) which interact with shear and extensional fluid flows serving through small-scale deformations to elastically store or dissipate energy. These microscopic processes often result macroscopically in material properties exhibiting interesting counter-intuitive phenomena and features hard to predict a priori.

Changed line 59 from:

Immersed Boundary Methods (IBM) and Boundary Integral Methods (BIM) are numerical approaches for studying the mechanics of elastic structures which interact with a fluid. Examples macroscopic systems include the pumping of the heart in which blood flow interacts with valves, lift general in insect flight, and wave propagation in the cochlea. In microscopic systems examples include the rheology of complex fluids and soft-matter which depends importantly on microstructures (such as colloids, lipids, polymers, vesicles) which interact with shear and extensional fluid flows serving through small-scale deformations to elastically store or dissipate energy. These microscopic processes often result macroscopically in material properties exhibiting interesting counter-intuitive phenomena and a priori hard to predict features.

to:

Immersed Boundary Methods (IBM) and Boundary Integral Methods (BIM) are numerical approaches for studying the mechanics of elastic structures which interact with a fluid. Examples macroscopic systems include the pumping of the heart in which blood flow interacts with valves, lift general in insect flight, and wave propagation in the cochlea of the inner ear. In microscopic systems examples include the rheology of complex fluids and soft-matter which depends importantly on microstructures (such as colloids, lipids, polymers, vesicles) which interact with shear and extensional fluid flows serving through small-scale deformations to elastically store or dissipate energy. These microscopic processes often result macroscopically in material properties exhibiting interesting counter-intuitive phenomena and a priori hard to predict features.

Changed lines 66-70 from:

* Dr. Atzberger : [[http://www.math.ucsb.edu/~atzberg/index.html | Research Website]].

A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found[[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | ~~here~~.]]

* Dr. Cinceros's : [[http://www.math.ucsb.edu/~cinceros/index.html | Research Website]].

Dr. Cinceros has recently formulated efficient implicit methods for the IBM formalisms significantly advancing the time-scales accessible in simulations of systems with stiff elastic structures... (Hector please edit profile and above description as you see fit...)

A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found

* Dr. Cinceros's : [[http://www.math.ucsb.edu/~cinceros/index.html | Research Website]].

Dr. Cinceros has recently formulated efficient implicit methods for the IBM formalisms significantly advancing the time-scales accessible in simulations of systems with stiff elastic structures... (Hector please edit profile and above description as you see fit...)

to:

* Dr. Atzberger : [[http://www.math.ucsb.edu/~atzberg/index.html | Research Website]]. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here : [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | IMA Workshop on Multiscale Methods.]]

* Dr. Cinceros's : [[http://www.math.ucsb.edu/~cinceros/index.html | Research Website]]. Dr. Cinceros has recently formulated efficient implicit methods for the IBM formalisms significantly advancing the time-scales accessible in simulations of systems with stiff elastic structures... (Hector please edit profile and above description as you see fit...)

* Dr. Cinceros's : [[http://www.math.ucsb.edu/~cinceros/index.html | Research Website]]. Dr. Cinceros has recently formulated efficient implicit methods for the IBM formalisms significantly advancing the time-scales accessible in simulations of systems with stiff elastic structures... (Hector please edit profile and above description as you see fit...)

Changed lines 66-68 from:

* Dr. Atzberger : [[http://www.math.ucsb.edu/~atzberg/index.html | Research Website]]. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | here.]]

* Dr. Cinceros's : [[http://www.math.ucsb.edu/~cinceros/index.html | Research Website]]. Dr. Cinceros has recently formulated efficient implicit methods for the IBM formalisms significantly advancing the time-scales accessible in simulations of systems with stiff elastic structures... (Hector please edit profile and above description as you see fit...)

* Dr. Cinceros's : [[http://www.math.ucsb.edu/~cinceros/index.html | Research Website]]. Dr. Cinceros has recently formulated efficient implicit methods for the IBM formalisms significantly advancing the time-scales accessible in simulations of systems with stiff elastic structures... (Hector please edit profile and above description as you see fit...)

to:

* Dr. Atzberger : [[http://www.math.ucsb.edu/~atzberg/index.html | Research Website]].

A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | here.]]

* Dr. Cinceros's : [[http://www.math.ucsb.edu/~cinceros/index.html | Research Website]].

Dr. Cinceros has recently formulated efficient implicit methods for the IBM formalisms significantly advancing the time-scales accessible in simulations of systems with stiff elastic structures... (Hector please edit profile and above description as you see fit...)

A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | here.]]

* Dr. Cinceros's : [[http://www.math.ucsb.edu/~cinceros/index.html | Research Website]].

Dr. Cinceros has recently formulated efficient implicit methods for the IBM formalisms significantly advancing the time-scales accessible in simulations of systems with stiff elastic structures... (Hector please edit profile and above description as you see fit...)

Changed line 55 from:

!!Research Areas (Selected)

to:

!!Research Areas (Selected Subset for Highlights)

Changed lines 63-68 from:

In the IBM formalism the hydrodynamic interactions of the composite system are handled by an approximate treatment of the fluid-structure stresses in which a Lagrangian representation of the immersed structures is coupled to an Eulerian representation of the fluid. In the BIM formalism the hydrodynamic equations are reduced to a description on the surface of an immersed structure usually taking the form of integral equations (possibly non-linear). The fluid-structure interaction problem and these underlying formulations present many interesting mathematical problems both for analysis and numerics. ~~Several faculty ~~members ~~of the applied group work in this area both on analysis of fluid-structure systems and the development of efficient numerical methods. These include:~~

* Dr. Atzberger who has extended the IB methodology to include thermal fluctuations.~~ For a more in~~-~~depth discussion see Dr~~.~~ ~~Atzberger~~'s [[http://www~~.~~math~~.~~ucsb.edu/~atzberg/index.html | research website]]~~. ~~A recent talk given by ~~Dr. ~~Atzberger on the Stochastic Immersed Boundary Method can be found [[http://www.ima.umn.edu/2008~~-~~2009/W11.3-7.08/abstracts.html#Atzberger-Paul | here.]]~~

* Dr. Cinceros's who has recently formulated efficient implicit methods for the IBM formalisms significantly advancing the time-scales accessible in simulations of systems with stiff elastic structures...

* Dr. Atzberger who has extended the IB methodology to include thermal fluctuations

* Dr. Cinceros's who has recently formulated efficient implicit methods for the IBM formalisms significantly advancing the time-scales accessible in simulations of systems with stiff elastic structures

to:

In the IBM formalism the hydrodynamic interactions of the composite system are handled by an approximate treatment of the fluid-structure stresses in which a Lagrangian representation of the immersed structures is coupled to an Eulerian representation of the fluid. In the BIM formalism the hydrodynamic equations are reduced to a description on the surface of an immersed structure usually taking the form of integral equations (possibly non-linear). The fluid-structure interaction problem and these underlying formulations present many interesting mathematical problems both for analysis and numerics.

Faculty members working in this area include:

* Dr. Atzberger : [[http://www.math.ucsb.edu/~atzberg/index.html | Research Website]]. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | here.]]

* Dr. Cinceros's : [[http://www.math.ucsb.edu/~cinceros/index.html | Research Website]]. Dr. Cinceros has recently formulated efficient implicit methods for the IBM formalisms significantly advancing the time-scales accessible in simulations of systems with stiff elastic structures... (Hector please edit profile and above description as you see fit...)

Faculty members working in this area include:

* Dr. Atzberger : [[http://www.math.ucsb.edu/~atzberg/index.html | Research Website]]. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | here.]]

* Dr. Cinceros's : [[http://www.math.ucsb.edu/~cinceros/index.html | Research Website]]. Dr. Cinceros has recently formulated efficient implicit methods for the IBM formalisms significantly advancing the time-scales accessible in simulations of systems with stiff elastic structures... (Hector please edit profile and above description as you see fit...)

Added lines 73-74:

(Tom and Gustavo, please write brief outline of research areas and edit URLs below)

Changed lines 77-78 from:

to:

Faculty members working in this area include:

* Dr. Sideris : [[http://www.math.ucsb.edu/~atzberg/index.html | Research Website]].

* Dr. Ponce : [[http://www.math.ucsb.edu/~atzberg/index.html | Research Website]].

Changed lines 86-88 from:

Brief article outlining basic area of research, interesting math. issues.

~~Mention Dr~~. ~~Garcia-Cervera's, Dr. Cinceros's, and ~~

Dr. Atzbeger's specific work in this area...

Dr. Atzbeger's specific work in this area

to:

Brief article outlining basic area of research, interesting math. issues...

Faculty members working in this area include:

* Dr. Garcia-Cervera : [[http://www.math.ucsb.edu/~atzberg/index.html | Research Website]].

* Dr. Cinceros : [[http://www.math.ucsb.edu/~atzberg/index.html | Research Website]].

* Dr. Atzbeger : [[http://www.math.ucsb.edu/~atzberg/index.html | Research Website]].

Faculty members working in this area include:

* Dr. Garcia-Cervera : [[http://www.math.ucsb.edu/~atzberg/index.html | Research Website]].

* Dr. Cinceros : [[http://www.math.ucsb.edu/~atzberg/index.html | Research Website]].

* Dr. Atzbeger : [[http://www.math.ucsb.edu/~atzberg/index.html | Research Website]].

Changed lines 63-67 from:

In the IBM formalism the hydrodynamic interactions of the composite system are handled by an approximate treatment of the fluid-structure stresses in which a Lagrangian representation of the immersed structures is coupled to an Eulerian representation of the fluid. In the BIM formalism the hydrodynamic equations are reduced to a description on the surface of an immersed structure usually taking the form of integral equations (possibly non-linear). The fluid-structure interaction problem and these underlying formulations present many interesting mathematical problems both for analysis and numerics. ~~A common theme often arising in practice is that the resulting system of equations stiff~~

as a consequence of fast time-scales introduced into the fluid-structure dynamics either by the elastic structures or in microscopic systems by thermal fluctuations. Several faculty members of the applied group work in this area both on analysis of fluid-structure systems and the development of efficient numerical methods.

Faculty members working on fluid-structure problems include:

* Dr. Atzberger who has extended the IB methodology to include thermal fluctuations, by an appropriate stochastic forcing of the fluid-structure equations in accordance with the principles of statistical mechanics. Mathematically, the formalism is cast in terms of a system of Stochastic Partial Differential Equations (SPDE's). Uses results from stochastic calculus he has developed efficient stochastic numerical methods for the formalism. In collaboration with the Brown Group, Department of Chemistry, Dr. Atzberger's group is developing dynamic coarse-grained models of lipid bilayer membranes using the SIB formalism to account for molecular level interactions (lipid-lipid and lipid-solvent) along with hydrodynamic coupling and thermal fluctuations. For a more in-depth discussion see Dr. Atzberger's [[http://www.math.ucsb.edu/~atzberg/index.html | research website]]. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | here.]]

as a consequence of fast time-scales introduced into the fluid-structure dynamics either by the elastic structures or in microscopic systems by thermal fluctuations. Several faculty members of the applied group work in this area both on analysis of fluid-structure systems and the development of efficient numerical methods.

Faculty members working on fluid-structure problems include:

* Dr. Atzberger who has extended the IB methodology to include thermal fluctuations, by an appropriate stochastic forcing of the fluid-structure equations in accordance with the principles of statistical mechanics. Mathematically, the formalism is cast in terms of a system of Stochastic Partial Differential Equations (SPDE's). Uses results from stochastic calculus he has developed efficient stochastic numerical methods for the formalism. In collaboration with the Brown Group, Department of Chemistry, Dr. Atzberger's group is developing dynamic coarse-grained models of lipid bilayer membranes using the SIB formalism to account for molecular level interactions (lipid-lipid and lipid-solvent) along with hydrodynamic coupling and

to:

In the IBM formalism the hydrodynamic interactions of the composite system are handled by an approximate treatment of the fluid-structure stresses in which a Lagrangian representation of the immersed structures is coupled to an Eulerian representation of the fluid. In the BIM formalism the hydrodynamic equations are reduced to a description on the surface of an immersed structure usually taking the form of integral equations (possibly non-linear). The fluid-structure interaction problem and these underlying formulations present many interesting mathematical problems both for analysis and numerics. Several faculty members of the applied group work in this area both on analysis of fluid-structure systems and the development of efficient numerical methods. These include:

* Dr. Atzberger who has extended the IB methodology to include thermal fluctuations. For a more in-depth discussion see Dr. Atzberger's [[http://www.math.ucsb.edu/~atzberg/index.html | research website]]. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | here.]]

* Dr. Atzberger who has extended the IB methodology to include thermal fluctuations. For a more in-depth discussion see Dr. Atzberger's [[http://www.math.ucsb.edu/~atzberg/index.html | research website]]. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | here.]]

Changed line 55 from:

!!Research Areas (~~Select Subset~~)

to:

!!Research Areas (Selected)

Changed line 55 from:

!!~~Select ~~Research ~~Activities~~

to:

!!Research Areas (Select Subset)

Changed line 55 from:

!!Research Activities ~~(Subset)~~

to:

!!Select Research Activities

Changed line 55 from:

!!Research ~~Activities~~

to:

!!Research Activities (Subset)

Changed line 55 from:

!!~~Highlighted ~~Research ~~Areas~~

to:

!!Research Activities

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!!Research Gallery~~ (images / movies, here, etc...)~~ \\

to:

!!Research Gallery \\

Added line 53:

(images / movies, here, etc...)

Changed lines 20-21 from:

(will work on embedding some floating boxes ~~that list news items and current events,~~

see http://www.me.ucsb.edu/ for some stylistic ideas)

see http://www.me.ucsb.edu/ for some stylistic ideas

to:

(will work on embedding some floating boxes on the right

to list in an accessible format "news items and current events",

see http://www.me.ucsb.edu/ for stylistic sense of what I

have in mind)

to list in an accessible format "news items and current events",

see http://www.me.ucsb.edu/ for stylistic sense of what I

have in mind)

Added lines 19-21:

(will work on embedding some floating boxes that list news items and current events,

see http://www.me.ucsb.edu/ for some stylistic ideas)

Changed lines 82-83 from:

Another model is not to have thematic articles, but to only have a few images up-top with a short caption and links to researchers webpages with more detailed info... [see UNC site which is quite nicely done]. In my opinion our group runs the risk of not presenting a well-defined core and anchored research program communicated to people when they visit if we only include a collection of images with captions. Maybe there is some happy medium, please write-up some example or express your ideas.

to:

Another model is not to have thematic articles, but to only have a few images up-top with a short caption and links to researchers webpages with more detailed info... [see UNC site which is quite nicely done

http://amath.unc.edu/]. In my opinion our group runs the risk of not presenting a well-defined core and anchored research program communicated to people when they visit if we only include a collection of images with captions. Maybe there is some happy medium, please write-up some example or express your ideas.

http://amath.unc.edu/]. In my opinion our group runs the risk of not presenting a well-defined core and anchored research program communicated to people when they visit if we only include a collection of images with captions. Maybe there is some happy medium, please write-up some example or express your ideas.

Changed line 82 from:

Another model is not to have thematic articles, but to only have a few images up-top with a short caption and links to researchers webpages with more detailed info... [see UNC site which is quite nicely done]. In my opinion our group runs the risk of not presenting a well-defined core and anchored research program communicated ~~on the site to people when they visit if we only include a collection of images with captions~~.

to:

Another model is not to have thematic articles, but to only have a few images up-top with a short caption and links to researchers webpages with more detailed info... [see UNC site which is quite nicely done]. In my opinion our group runs the risk of not presenting a well-defined core and anchored research program communicated to people when they visit if we only include a collection of images with captions. Maybe there is some happy medium, please write-up some example or express your ideas.

Changed line 82 from:

Another model is not to have thematic articles, but to only have a few images up-top with a short caption and links to researchers webpages with more detailed info... [see UNC site].

to:

Another model is not to have thematic articles, but to only have a few images up-top with a short caption and links to researchers webpages with more detailed info... [see UNC site which is quite nicely done]. In my opinion our group runs the risk of not presenting a well-defined core and anchored research program communicated on the site to people when they visit if we only include a collection of images with captions.

Changed line 31 from:

%lfloat text-align=left margin-top=5px margin-right=5px margin-bottom=10px margin-left=5px width=100px% Attach:~~hectorImage~~.~~png~~

to:

%lfloat text-align=left margin-top=5px margin-right=5px margin-bottom=10px margin-left=5px width=100px% Attach:carlosSmiles.jpg

Changed lines 68-69 from:

to:

Changed lines 74-75 from:

Mention Dr. Garcia-Cervera's ~~group and ~~Dr. Cinceros's ~~group~~...

to:

Mention Dr. Garcia-Cervera's, Dr. Cinceros's, and

Dr. Atzbeger's specific work in this area...

Dr. Atzbeger's specific work in this area...

Changed line 43 from:

!!Gallery ~~of Recent Results~~ (images / movies, here, etc...) \\

to:

!!Research Gallery (images / movies, here, etc...) \\

Changed lines 64-65 from:

!! ~~Liquid Crystals / Lipid Bilayer Membranes / Complex Polymer Fluids~~

to:

!! Analysis of XYZ... Non-linear Elasticity.... Schrodinger Equ... (please edit)

Changed lines 67-68 from:

to:

Dr. Sideris's work and Dr. Ponce's work highlighted here...

Changed lines 70-71 from:

!! ~~Analysis of XYZ... Non-linear Elasticity.... Schrodinger Equ... (please edit)~~

to:

!! Liquid Crystals / Lipid Bilayer Membranes / Complex Polymeric Fluids

Changed lines 73-75 from:

Dr. ~~Sideris~~'s ~~work~~ and Dr. ~~Ponce~~'s ~~work highlighted here~~...

to:

Mention Dr. Garcia-Cervera's group and Dr. Cinceros's group...

Added lines 76-77:

!!Discussion of Above Items

Changed lines 77-79 from:

Above is an experiment and rough draft / brainstorm. Idea is to give ~~newbie~~ graduate students and general ~~audience sense of what our group does. Above is meant to give an example of some themes and what we might post to highlight our specific research programs and on-going work. I wrote perhaps a little too much about myself, but this is since I know the most about this activity presumably. :) ~~ I ~~propose we write several of these short articles which will be persistent for themes of the group (and modify over time as things develop). Up-top we then include some short descriptions~~ of ~~"fresh work"~~

before these thematic short-articles. This means people encounter what's new first, but can scroll down for a more detailed view of our group.

before these thematic short-articles. This means people encounter what's new first, but can scroll down for a more detailed view of our

to:

Above is an experiment and rough draft / brainstorm. Idea is to give undergraduate / graduate students and general public and scientific audience sense of what types of work our group does. Above is meant to give an example of some themes and what we might post to highlight our specific research programs and on-going work both at the level of light-reading and in more detail. I wrote mostly about my own work, since I know the most about this activity presumably. :) I propose up-top we have short gallery style presentation of results for the light-of-heart. We then write in more detail a few of these short articles which discuss general thematic areas of research of the group (which of course can be modified over time to freshen things up and as our collective interests develop). This means people encounter what's new and light first, and then depending on their level of interest can scroll down for a more detailed desciption of the group.

Changed lines 81-84 from:

if you think

Not sure if this is necessary

to:

Please take a shot at posting/editing the welcome message and some materials for discussion.

Not sure if this is necessary (formal rules for editing the Wiki website):\\

Not sure if this is necessary (formal rules for editing the Wiki website):\\

Changed line 44 from:

%width=200px% Attach:carlosImage.png %width=200px% Attach:atzbergerImage.png %width=200px% Attach:carlosImage.png

to:

%width=200px% Attach:carlosImage.png %width=200px% Attach:atzbergerImage.png %width=200px% Attach:carlosImage.png %width=200px% Attach:atzbergerImage.png %width=200px% Attach:carlosImage.png %width=200px% Attach:atzbergerImage.png %width=200px% Attach:carlosImage.png

Changed lines 44-46 from:

%width=200px% Attach:carlosImage.png

%width=200px% Attach:atzbergerImage.png

%width=200px% Attach:carlosImage.png

%width=200px% Attach:carlosImage.png

to:

Changed lines 44-47 from:

%width=~~300px~~% Attach:carlosImage.png

%width=~~300px~~% Attach:atzbergerImage.png

%width=~~300px~~% Attach:carlosImage.png

%width=300px% Attach:atzbergerImage.png

%width=

%width=

%width=300px% Attach:atzbergerImage.png

to:

%width=200px% Attach:atzbergerImage.png

%width=200px% Attach:carlosImage.png

Added lines 41-49:

!!Gallery of Recent Results (images / movies, here, etc...) \\

\\

%width=300px% Attach:carlosImage.png

%width=300px% Attach:atzbergerImage.png

%width=300px% Attach:carlosImage.png

%width=300px% Attach:atzbergerImage.png

----

\\

%width=300px% Attach:carlosImage.png

%width=300px% Attach:atzbergerImage.png

%width=300px% Attach:carlosImage.png

%width=300px% Attach:atzbergerImage.png

----

Changed lines 71-72 from:

!! Analysis of XYZ...

to:

!! Analysis of XYZ... Non-linear Elasticity.... Schrodinger Equ... (please edit)

Changed lines 74-76 from:

to:

Dr. Sideris's work and Dr. Ponce's work highlighted here...

Changed lines 78-81 from:

Above is an experiment and rough draft / brainstorm. ~~Above~~ is ~~meant ~~to give ~~an example of what we might post to highlight~~ our ~~research programs and on-going work. I wrote about myself since I know the most about this activity presumably. :) We may have a few short articles and either leave in place for awhile or copy these to "hidden" pages and each month rotate through the content descriptions making modifications, new articles, and updates as research develops... ~~

Another model is to have simply an image with a short caption and links to researchers webpages with more detailed into... [see UNC site].

Another model is to have simply an image with a short caption and links to researchers webpages with more detailed into...

to:

Above is an experiment and rough draft / brainstorm. Idea is to give newbie graduate students and general audience sense of what our group does. Above is meant to give an example of some themes and what we might post to highlight our specific research programs and on-going work. I wrote perhaps a little too much about myself, but this is since I know the most about this activity presumably. :) I propose we write several of these short articles which will be persistent for themes of the group (and modify over time as things develop). Up-top we then include some short descriptions of "fresh work"

before these thematic short-articles. This means people encounter what's new first, but can scroll down for a more detailed view of our group.

Another model is not to have thematic articles, but to only have a few images up-top with a short caption and links to researchers webpages with more detailed info... [see UNC site].

before these thematic short-articles. This means people encounter what's new first, but can scroll down for a more detailed view of our group.

Another model is not to have thematic articles, but to only have a few images up-top with a short caption and links to researchers webpages with more detailed info... [see UNC site].

Changed lines 86-87 from:

to:

Not sure if this is necessary:\\

\\

\\

Deleted lines 106-111:

!!Other highlights here...(images / movies, etc...) \\

\\

%width=100px% Attach:carlosImage.png %width=100px% Attach:atzbergerImage.png

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!!~~Immersed Boundary Methods and ~~Boundary ~~Integral ~~Methods ~~for Fluid-Structure Dynamics:~~

to:

!!Fluid-Structure Dynamics: Immersed Boundary Methods and Boundary Integral Methods

Changed lines 47-48 from:

In the IBM formalism the hydrodynamic interactions of the composite system are handled by an approximate treatment of the fluid-structure stresses in which a Lagrangian representation of the immersed structures is coupled to an Eulerian representation of the fluid. In the BIM formalism the hydrodynamic equations are reduced to a description on the surface of an immersed structure usually taking the form of integral equations (possibly non-linear). The fluid-structure interaction problem and these underlying formulations present many interesting mathematical problems for analysis~~. A common theme often arising in practice os that fast time scales are introduced into the fluid-structure dynamics by the elastic structures or in microscopic system by thermal fluctuations making ~~the ~~resulting system of equations stiff. Several faculty members of the applied group work in this area. ~~

to:

In the IBM formalism the hydrodynamic interactions of the composite system are handled by an approximate treatment of the fluid-structure stresses in which a Lagrangian representation of the immersed structures is coupled to an Eulerian representation of the fluid. In the BIM formalism the hydrodynamic equations are reduced to a description on the surface of an immersed structure usually taking the form of integral equations (possibly non-linear). The fluid-structure interaction problem and these underlying formulations present many interesting mathematical problems both for analysis and numerics. A common theme often arising in practice is that the resulting system of equations stiff

as a consequence of fast time-scales introduced into the fluid-structure dynamics either by the elastic structures or in microscopic systems by thermal fluctuations. Several faculty members of the applied group work in this area both on analysis of fluid-structure systems and the development of efficient numerical methods.

as a consequence of fast time-scales introduced into the fluid-structure dynamics either by the elastic structures or in microscopic systems by thermal fluctuations. Several faculty members of the applied group work in this area both on analysis of fluid-structure systems and the development of efficient numerical methods.

Changed lines 43-44 from:

Immersed Boundary Methods (IBM) and Boundary Integral Methods (BIM) are numerical approaches for studying the mechanics of elastic structures which interact with a fluid. Examples macroscopic systems include the pumping of the heart in which blood flow interacts with valves, lift general in insect flight, and wave propagation in the cochlea. In microscopic systems examples include the rheology of complex fluids ~~/~~ soft-matter which depends importantly on microstructures (such as colloids, lipids, polymers, vesicles) interact with shear and extensional fluid flows serving through small-scale deformations to elastically store or dissipate energy.

to:

Immersed Boundary Methods (IBM) and Boundary Integral Methods (BIM) are numerical approaches for studying the mechanics of elastic structures which interact with a fluid. Examples macroscopic systems include the pumping of the heart in which blood flow interacts with valves, lift general in insect flight, and wave propagation in the cochlea. In microscopic systems examples include the rheology of complex fluids and soft-matter which depends importantly on microstructures (such as colloids, lipids, polymers, vesicles) which interact with shear and extensional fluid flows serving through small-scale deformations to elastically store or dissipate energy. These microscopic processes often result macroscopically in material properties exhibiting interesting counter-intuitive phenomena and a priori hard to predict features.

Changed line 47 from:

In the IBM formalism the hydrodynamic interactions of the composite system are handled by an approximate treatment of the fluid-structure stresses in which a Lagrangian representation of the immersed structures is coupled to an Eulerian representation of the fluid. In the BIM formalism the hydrodynamic equations are reduced to a description on the surface of an immersed structure usually taking the form of ~~possibly non-linear integral equations~~. The fluid-structure interaction problem and these underlying formulations present many interesting mathematical problems for analysis. A common theme often arising in practice os that fast time scales are introduced into the fluid-structure dynamics by the elastic structures or in microscopic system by thermal fluctuations making the resulting system of equations stiff. Several faculty members of the applied group work in this area.

to:

In the IBM formalism the hydrodynamic interactions of the composite system are handled by an approximate treatment of the fluid-structure stresses in which a Lagrangian representation of the immersed structures is coupled to an Eulerian representation of the fluid. In the BIM formalism the hydrodynamic equations are reduced to a description on the surface of an immersed structure usually taking the form of integral equations (possibly non-linear). The fluid-structure interaction problem and these underlying formulations present many interesting mathematical problems for analysis. A common theme often arising in practice os that fast time scales are introduced into the fluid-structure dynamics by the elastic structures or in microscopic system by thermal fluctuations making the resulting system of equations stiff. Several faculty members of the applied group work in this area.

Changed lines 41-44 from:

!!Immersed Boundary Methods ~~for Fluid-Structure Dynamics: ~~

Immersed Boundary Methods (IBM) are numerical approaches for studying the mechanics of elastic structures which interact with a fluid. Immersed structures ~~in IBM can be used to represent the mechanics of a variety~~ of ~~hydrodynamic systems from the macroscopic to microscopic. Examples include for macroscopic systems blood flow in the heart and interaction with valves, lift general in insect flight, and wave propagation in the cochlear. In microscopic systems examples include rheology of complex fluids / soft-matter as a results of microstructures interacting with fluid flows at ~~small-~~scales where immersed structures represent solute particles, polymers, or membrane structures.~~

Immersed Boundary Methods (IBM) are numerical approaches for studying the mechanics of elastic structures which interact with a fluid. Immersed

to:

!!Immersed Boundary Methods and Boundary Integral Methods for Fluid-Structure Dynamics:

Immersed Boundary Methods (IBM) and Boundary Integral Methods (BIM) are numerical approaches for studying the mechanics of elastic structures which interact with a fluid. Examples macroscopic systems include the pumping of the heart in which blood flow interacts with valves, lift general in insect flight, and wave propagation in the cochlea. In microscopic systems examples include the rheology of complex fluids / soft-matter which depends importantly on microstructures (such as colloids, lipids, polymers, vesicles) interact with shear and extensional fluid flows serving through small-scale deformations to elastically store or dissipate energy.

Immersed Boundary Methods (IBM) and Boundary Integral Methods (BIM) are numerical approaches for studying the mechanics of elastic structures which interact with a fluid. Examples macroscopic systems include the pumping of the heart in which blood flow interacts with valves, lift general in insect flight, and wave propagation in the cochlea. In microscopic systems examples include the rheology of complex fluids / soft-matter which depends importantly on microstructures (such as colloids, lipids, polymers, vesicles) interact with shear and extensional fluid flows serving through small-scale deformations to elastically store or dissipate energy.

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In the IBM formalism the hydrodynamic interactions of the composite system are handled by an approximate treatment of the fluid-structure stresses in which a Lagrangian representation of the immersed structures is coupled to an Eulerian representation of the fluid. ~~Many interesting mathematical challenges arise both in the study of specific fluid-structure systems and in obtaining in general efficient numerical methods. In practice, fast time scales are often introduced into the ~~fluid-structure ~~dynamics by the elastic structures or in microscopic system by thermal fluctuations making the resulting system of equations~~ stiff.

to:

In the IBM formalism the hydrodynamic interactions of the composite system are handled by an approximate treatment of the fluid-structure stresses in which a Lagrangian representation of the immersed structures is coupled to an Eulerian representation of the fluid. In the BIM formalism the hydrodynamic equations are reduced to a description on the surface of an immersed structure usually taking the form of possibly non-linear integral equations. The fluid-structure interaction problem and these underlying formulations present many interesting mathematical problems for analysis. A common theme often arising in practice os that fast time scales are introduced into the fluid-structure dynamics by the elastic structures or in microscopic system by thermal fluctuations making the resulting system of equations stiff. Several faculty members of the applied group work in this area.

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!!~~Stochastic ~~Immersed Boundary Methods for Fluid-Structure Dynamics:

~~[[http://www.math.ucsb.edu/~atzberg/index.html | '+Paul J. Atzberger+']]~~

Stochastic Immersed Boundary Methods (SIB) are numerical approaches for studying the mechanics of elastic structures which interact with a fluid in microscopic systems where thermal fluctuations play an important role. Immersed structures in SIB can be used to represent the mechanics of a variety of microscopic hydrodynamic systems, for example, in a complex fluid the structures could represent solute particles, polymers, or membrane structures.

Stochastic Immersed Boundary Methods (SIB) are numerical approaches for studying the mechanics of elastic structures which interact with a fluid in microscopic systems where thermal fluctuations play an important role. Immersed structures in SIB can be used to represent the mechanics of a variety of microscopic hydrodynamic systems, for example, in a complex fluid the structures could

to:

!!Immersed Boundary Methods for Fluid-Structure Dynamics:

Immersed Boundary Methods (IBM) are numerical approaches for studying the mechanics of elastic structures which interact with a fluid. Immersed structures in IBM can be used to represent the mechanics of a variety of hydrodynamic systems from the macroscopic to microscopic. Examples include for macroscopic systems blood flow in the heart and interaction with valves, lift general in insect flight, and wave propagation in the cochlear. In microscopic systems examples include rheology of complex fluids / soft-matter as a results of microstructures interacting with fluid flows at small-scales where immersed structures represent solute particles, polymers, or membrane structures.

Immersed Boundary Methods (IBM) are numerical approaches for studying the mechanics of elastic structures which interact with a fluid. Immersed structures in IBM can be used to represent the mechanics of a variety of hydrodynamic systems from the macroscopic to microscopic. Examples include for macroscopic systems blood flow in the heart and interaction with valves, lift general in insect flight, and wave propagation in the cochlear. In microscopic systems examples include rheology of complex fluids / soft-matter as a results of microstructures interacting with fluid flows at small-scales where immersed structures represent solute particles, polymers, or membrane structures.

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In the ~~SIB~~ formalism the hydrodynamic interactions of the composite system are handled by an approximate treatment of the fluid-structure stresses in which a Lagrangian representation of the immersed structures is coupled to an Eulerian representation of the fluid. ~~Thermal fluctuations are accounted for in the system by an appropriate stochastic forcing of the fluid-structure equations~~ in ~~accordance with the principles of statistical mechanics. Mathematically~~, ~~the formalism is cast in terms of a system of Stochastic Partial Differential Equations (SPDE's). ~~

Many interesting mathematical challenges arise in obtaining efficient numerical methods as a result of fast time scales introduced into the fluid dynamics by the ~~thermal fluctuations making the resulting system of equations stiff. ~~

Dr. Atzberger's group uses results from stochastic calculus to develop efficient stochastic numerical methods forthe formalism~~. In collaboration with the Brown Group, Department ~~of ~~Chemistry, Dr. Atzberger's group is developing dynamic coarse-grained models of lipid bilayer membranes using the SIB formalism to account ~~for ~~molecular level interactions (lipid-lipid and lipid-solvent) along with hydrodynamic coupling and thermal fluctuations~~. ~~For a more in-depth discussion see Dr. Atzberger's [[http://www.math.ucsb.edu/~atzberg/index.html | research website]].~~

A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found

[[http://www.~~ima.umn.edu/2008~~-~~2009/W11~~.~~3-7.08/abstracts.html#~~Atzberger~~-Paul | here~~.]]

Many interesting mathematical challenges arise in obtaining efficient numerical methods as a result of fast time scales introduced into the fluid dynamics by

Dr. Atzberger's group uses results from stochastic calculus to develop efficient stochastic numerical methods for

A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found

[[http://www

to:

In the IBM formalism the hydrodynamic interactions of the composite system are handled by an approximate treatment of the fluid-structure stresses in which a Lagrangian representation of the immersed structures is coupled to an Eulerian representation of the fluid. Many interesting mathematical challenges arise both in the study of specific fluid-structure systems and in obtaining in general efficient numerical methods. In practice, fast time scales are often introduced into the fluid-structure dynamics by the elastic structures or in microscopic system by thermal fluctuations making the resulting system of equations stiff.

Faculty members working on fluid-structure problems include:

* Dr. Atzberger who has extended the IB methodology to include thermal fluctuations, by an appropriate stochastic forcing of the fluid-structure equations in accordance with the principles of statistical mechanics. Mathematically, the formalism is cast in terms of a system of Stochastic Partial Differential Equations (SPDE's). Uses results from stochastic calculus he has developed efficient stochastic numerical methods for the formalism. In collaboration with the Brown Group, Department of Chemistry, Dr. Atzberger's group is developing dynamic coarse-grained models of lipid bilayer membranes using the SIB formalism to account for molecular level interactions (lipid-lipid and lipid-solvent) along with hydrodynamic coupling and thermal fluctuations. For a more in-depth discussion see Dr. Atzberger's [[http://www.math.ucsb.edu/~atzberg/index.html | research website]]. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | here.]]

* Dr. Cinceros's who has recently formulated efficient implicit methods for the IBM formalisms significantly advancing the time-scales accessible in simulations of systems with stiff elastic structures...

Faculty members working on fluid-structure problems include:

* Dr. Atzberger who has extended the IB methodology to include thermal fluctuations, by an appropriate stochastic forcing of the fluid-structure equations in accordance with the principles of statistical mechanics. Mathematically, the formalism is cast in terms of a system of Stochastic Partial Differential Equations (SPDE's). Uses results from stochastic calculus he has developed efficient stochastic numerical methods for the formalism. In collaboration with the Brown Group, Department of Chemistry, Dr. Atzberger's group is developing dynamic coarse-grained models of lipid bilayer membranes using the SIB formalism to account for molecular level interactions (lipid-lipid and lipid-solvent) along with hydrodynamic coupling and thermal fluctuations. For a more in-depth discussion see Dr. Atzberger's [[http://www.math.ucsb.edu/~atzberg/index.html | research website]]. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found [[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | here.]]

* Dr. Cinceros's who has recently formulated efficient implicit methods for the IBM formalisms significantly advancing the time-scales accessible in simulations of systems with stiff elastic structures...

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!! ~~Implicit Immersed Boundary Methods...~~

to:

!! Liquid Crystals / Lipid Bilayer Membranes / Complex Polymer Fluids

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Mention Dr. ~~Cinceros~~'s group.~~.. (maybe merge SIB and IIBM approaches into one article on IB methods and boundary integral methods and then reference ~~group~~ members~~.~~)~~

to:

Mention Dr. Garcia-Cervera's group and Dr. Cinceros's group...

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!! ~~Liquid Crystals and ~~XYZ

to:

!! Analysis of XYZ...

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Mention Dr. ~~Garcia-Cervera~~'s ~~group~~ and Dr. ~~Cinceros~~'s ~~group...~~

----

!! Analysis of XYZ...

Brief article outlining basic area of research, interesting math. issues.

Mention Dr. Garcia-Cervera's group and Dr. Cinceros's group...

----

!! Analysis of XYZ...

Brief article outlining basic area of research, interesting math. issues.

Mention Dr. Garcia-Cervera's group and Dr. Cinceros's group

to:

Mention Dr. Sideris's work and Dr. Ponce's work...

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are numerical approaches for studying the mechanics of elastic structures which interact with a fluid in systems at small length-scales where thermal fluctuations play an important role. The hydrodynamic interactions

to:

Stochastic Immersed Boundary Methods (SIB) are numerical approaches for studying the mechanics of elastic structures which interact with a fluid in microscopic systems where thermal fluctuations play an important role. Immersed structures in SIB can be used to represent the mechanics of a variety of microscopic hydrodynamic systems, for example, in a complex fluid the structures could represent solute particles, polymers, or membrane structures.

Changed lines 48-49 from:

to:

In the SIB formalism the hydrodynamic interactions of the composite system are handled by an approximate treatment of the fluid-structure stresses in which a Lagrangian representation of the immersed structures is coupled to an Eulerian representation of the fluid. Thermal fluctuations are accounted for in the system by an appropriate stochastic forcing of the fluid-structure equations in accordance with the principles of statistical mechanics. Mathematically, the formalism is cast in terms of a system of Stochastic Partial Differential Equations (SPDE's).

Many interesting mathematical challenges arise in obtaining efficient numerical methods as a result of fast time scales introduced into the fluid dynamics by the thermal fluctuations making the resulting system of equations stiff.

Dr. Atzberger's group uses results from stochastic calculus to develop efficient stochastic numerical methods for the formalism. In collaboration with the Brown Group, Department of Chemistry, Dr. Atzberger's group is developing dynamic coarse-grained models of lipid bilayer membranes using the SIB formalism to account for molecular level interactions (lipid-lipid and lipid-solvent) along with hydrodynamic coupling and thermal fluctuations. For a more in-depth discussion see Dr. Atzberger's [[http://www.math.ucsb.edu/~atzberg/index.html | research website]].

Many interesting mathematical challenges arise in obtaining efficient numerical methods as a result of fast time scales introduced into the fluid dynamics by the thermal fluctuations making the resulting system of equations stiff.

Dr. Atzberger's group uses results from stochastic calculus to develop efficient stochastic numerical methods for the formalism. In collaboration with the Brown Group, Department of Chemistry, Dr. Atzberger's group is developing dynamic coarse-grained models of lipid bilayer membranes using the SIB formalism to account for molecular level interactions (lipid-lipid and lipid-solvent) along with hydrodynamic coupling and thermal fluctuations. For a more in-depth discussion see Dr. Atzberger's [[http://www.math.ucsb.edu/~atzberg/index.html | research website]].

Added lines 56-75:

----

!! Implicit Immersed Boundary Methods...

Brief article outlining basic area of research, interesting math. issues.

Mention Dr. Cinceros's group... (maybe merge SIB and IIBM approaches into one article on IB methods and boundary integral methods and then reference group members.)

----

!! Liquid Crystals and XYZ

Brief article outlining basic area of research, interesting math. issues.

Mention Dr. Garcia-Cervera's group and Dr. Cinceros's group...

----

!! Analysis of XYZ...

Brief article outlining basic area of research, interesting math. issues.

Mention Dr. Garcia-Cervera's group and Dr. Cinceros's group...

!! Implicit Immersed Boundary Methods...

Brief article outlining basic area of research, interesting math. issues.

Mention Dr. Cinceros's group... (maybe merge SIB and IIBM approaches into one article on IB methods and boundary integral methods and then reference group members.)

----

!! Liquid Crystals and XYZ

Brief article outlining basic area of research, interesting math. issues.

Mention Dr. Garcia-Cervera's group and Dr. Cinceros's group...

----

!! Analysis of XYZ...

Brief article outlining basic area of research, interesting math. issues.

Mention Dr. Garcia-Cervera's group and Dr. Cinceros's group...

Changed lines 77-83 from:

Above is ~~(rough draft / brainstorm) Above is meant to give an example of what we might post about~~

our work. We can discuss style of the research highlights and how we present things

if you think this is too much.~~.. In any case, the idea is to post things here before ~~

we go public to discuss overall theme and criteria for content... Please also take

a shot at posting some materials for discussion [present in near-final form].

~~The working process will eventually be to have a "hidden" page we can all edit~~

where we write the materials and review before copying to the homepage.

our work. We can discuss style of the research highlights and how we present things

if you think this is too much

we go public to discuss overall theme and criteria for content... Please also take

a shot at posting some materials for discussion [present in near-final form].

where

to:

Above is an experiment and rough draft / brainstorm. Above is meant to give an example of what we might post to highlight our research programs and on-going work. I wrote about myself since I know the most about this activity presumably. :) We may have a few short articles and either leave in place for awhile or copy these to "hidden" pages and each month rotate through the content descriptions making modifications, new articles, and updates as research develops...

Another model is to have simply an image with a short caption and links to researchers webpages with more detailed into... [see UNC site].

We can discuss style of the research highlights and how we present things

if you think this is too much... In any case, the idea is to post things here before we go public to discuss overall theme and criteria for content... Please also take a shot at posting some materials for discussion [present in near-final form]. The working process will eventually be to have a "hidden" page we can all edit where we write the materials and review before copying to the homepage.

Another model is to have simply an image with a short caption and links to researchers webpages with more detailed into... [see UNC site].

We can discuss style of the research highlights and how we present things

if you think this is too much... In any case, the idea is to post things here before we go public to discuss overall theme and criteria for content... Please also take a shot at posting some materials for discussion [present in near-final form]. The working process will eventually be to have a "hidden" page we can all edit where we write the materials and review before copying to the homepage.

Changed lines 45-46 from:

are numerical approaches for studying the mechanics of elastic structures which interact with a fluid in systems at small length-scales where thermal fluctuations play an important role. The hydrodynamic interactions of the composite system are handled by an approximate treatment of the fluid-structure stresses in which a Lagrangian representation of the immersed structures is coupled to an Eulerian representation of the fluid. Thermal fluctuations are accounted for in the system by an appropriate stochastic forcing of the fluid-structure equations in accordance with the principles of statistical mechanics. The formalism is cast in terms of a system of Stochastic Partial Differential Equations (SPDE's). Fast time scales introduced into the fluid dynamics by the thermal fluctuations pose a challenge for conventional approaches to numerical approximation. Using results from stochastic calculus, ~~we are~~ developing efficient stochastic numerical methods for the formalism.

to:

are numerical approaches for studying the mechanics of elastic structures which interact with a fluid in systems at small length-scales where thermal fluctuations play an important role. The hydrodynamic interactions of the composite system are handled by an approximate treatment of the fluid-structure stresses in which a Lagrangian representation of the immersed structures is coupled to an Eulerian representation of the fluid. Thermal fluctuations are accounted for in the system by an appropriate stochastic forcing of the fluid-structure equations in accordance with the principles of statistical mechanics. The formalism is cast in terms of a system of Stochastic Partial Differential Equations (SPDE's). Fast time scales introduced into the fluid dynamics by the thermal fluctuations pose a challenge for conventional approaches to numerical approximation. Using results from stochastic calculus, he is developing efficient stochastic numerical methods for the formalism.

Changed line 49 from:

Immersed structures in SIB can be used to represent the mechanics of a variety of microscopic hydrodynamic systems, for example, in a complex fluid the structures could represent solute particles, polymers, or membrane structures. In collaboration with the Brown Group, Department of Chemistry, Dr. Atzberger's group is developing dynamic coarse-grained models of lipid bilayer membranes ~~are being developed using the SIB formalism to account for molecular level interactions, ~~lipid-~~lipid and lipid-solvent~~ hydrodynamic coupling~~,~~ and thermal fluctuations. For a more in-depth discussion see Dr. Atzberger's [[http://www.math.ucsb.edu/~atzberg/index.html | research website]].

to:

Immersed structures in SIB can be used to represent the mechanics of a variety of microscopic hydrodynamic systems, for example, in a complex fluid the structures could represent solute particles, polymers, or membrane structures. In collaboration with the Brown Group, Department of Chemistry, Dr. Atzberger's group is developing dynamic coarse-grained models of lipid bilayer membranes using the SIB formalism to account for molecular level interactions (lipid-lipid and lipid-solvent) along with hydrodynamic coupling and thermal fluctuations. For a more in-depth discussion see Dr. Atzberger's [[http://www.math.ucsb.edu/~atzberg/index.html | research website]].

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are numerical approaches for studying the mechanics of elastic structures which interact with a fluid ~~at small length scales in which~~ thermal fluctuations play an important role. The hydrodynamic interactions of the composite system are handled by an approximate treatment of the fluid-structure stresses in which a Lagrangian representation of the immersed structures is coupled to an Eulerian representation of the fluid. Thermal fluctuations are accounted for in the system by an appropriate stochastic forcing of the fluid-structure equations in accordance with the principles of statistical mechanics. The formalism is cast in terms of a system of Stochastic Partial Differential Equations (SPDE's). Fast time scales introduced into the fluid dynamics by the thermal fluctuations pose a challenge for conventional approaches to numerical approximation. Using results from stochastic calculus, we are developing efficient stochastic numerical methods for the formalism.

to:

are numerical approaches for studying the mechanics of elastic structures which interact with a fluid in systems at small length-scales where thermal fluctuations play an important role. The hydrodynamic interactions of the composite system are handled by an approximate treatment of the fluid-structure stresses in which a Lagrangian representation of the immersed structures is coupled to an Eulerian representation of the fluid. Thermal fluctuations are accounted for in the system by an appropriate stochastic forcing of the fluid-structure equations in accordance with the principles of statistical mechanics. The formalism is cast in terms of a system of Stochastic Partial Differential Equations (SPDE's). Fast time scales introduced into the fluid dynamics by the thermal fluctuations pose a challenge for conventional approaches to numerical approximation. Using results from stochastic calculus, we are developing efficient stochastic numerical methods for the formalism.

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are numerical approaches for studying the mechanics of elastic structures which interact with a fluid ~~in the presence of thermal~~ fluctuations. The hydrodynamic interactions of the composite system are handled by an approximate treatment of the fluid-structure stresses in which a Lagrangian representation of the immersed structures is coupled to an Eulerian representation of the fluid. Thermal fluctuations are accounted for in the system by an appropriate stochastic forcing of the fluid-structure equations in accordance with the principles of statistical mechanics. The formalism is cast in terms of a system of Stochastic Partial Differential Equations (SPDE's). Fast time scales introduced into the fluid dynamics by the thermal fluctuations pose a challenge for conventional approaches to numerical approximation. Using results from stochastic calculus, we are developing efficient stochastic numerical methods for the formalism.

to:

are numerical approaches for studying the mechanics of elastic structures which interact with a fluid at small length scales in which thermal fluctuations play an important role. The hydrodynamic interactions of the composite system are handled by an approximate treatment of the fluid-structure stresses in which a Lagrangian representation of the immersed structures is coupled to an Eulerian representation of the fluid. Thermal fluctuations are accounted for in the system by an appropriate stochastic forcing of the fluid-structure equations in accordance with the principles of statistical mechanics. The formalism is cast in terms of a system of Stochastic Partial Differential Equations (SPDE's). Fast time scales introduced into the fluid dynamics by the thermal fluctuations pose a challenge for conventional approaches to numerical approximation. Using results from stochastic calculus, we are developing efficient stochastic numerical methods for the formalism.

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!!Stochastic Immersed Boundary Methods for~~ Computational~~ Fluid-Structure Dynamics:

to:

!!Stochastic Immersed Boundary Methods for Fluid-Structure Dynamics:

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!!Stochastic Immersed Boundary Methods for Computational Fluid Dynamics:

to:

!!Stochastic Immersed Boundary Methods for Computational Fluid-Structure Dynamics:

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!!Stochastic Immersed Boundary Methods for Computational Fluid Dynamics: [[http://www.math.ucsb.edu/~atzberg/index.html | '+~~Dr. ~~Paul J. Atzberger+']]

to:

!!Stochastic Immersed Boundary Methods for Computational Fluid Dynamics:

[[http://www.math.ucsb.edu/~atzberg/index.html | '+Paul J. Atzberger+']]

[[http://www.math.ucsb.edu/~atzberg/index.html | '+Paul J. Atzberger+']]

Changed lines 45-46 from:

are numerical approaches for studying the mechanics of elastic structures which interact with a fluid in the presence of thermal fluctuations. The hydrodynamic interactions of the composite system are handled by an approximate treatment of the fluid-structure stresses in which a Lagrangian representation of the immersed structures is coupled to an Eulerian representation of the fluid. Thermal fluctuations are accounted for in the system by an appropriate stochastic forcing of the fluid-structure equations in accordance with the principles of statistical mechanics.

to:

are numerical approaches for studying the mechanics of elastic structures which interact with a fluid in the presence of thermal fluctuations. The hydrodynamic interactions of the composite system are handled by an approximate treatment of the fluid-structure stresses in which a Lagrangian representation of the immersed structures is coupled to an Eulerian representation of the fluid. Thermal fluctuations are accounted for in the system by an appropriate stochastic forcing of the fluid-structure equations in accordance with the principles of statistical mechanics. The formalism is cast in terms of a system of Stochastic Partial Differential Equations (SPDE's). Fast time scales introduced into the fluid dynamics by the thermal fluctuations pose a challenge for conventional approaches to numerical approximation. Using results from stochastic calculus, we are developing efficient stochastic numerical methods for the formalism.

Changed lines 49-51 from:

Immersed structures in SIB can be used to represent the mechanics of a variety of microscopic hydrodynamic systems, for example, in a complex fluid the structures could represent solute particles, polymers, or membrane structures

to:

Immersed structures in SIB can be used to represent the mechanics of a variety of microscopic hydrodynamic systems, for example, in a complex fluid the structures could represent solute particles, polymers, or membrane structures. In collaboration with the Brown Group, Department of Chemistry, Dr. Atzberger's group is developing dynamic coarse-grained models of lipid bilayer membranes are being developed using the SIB formalism to account for molecular level interactions, lipid-lipid and lipid-solvent hydrodynamic coupling, and thermal fluctuations. For a more in-depth discussion see Dr. Atzberger's [[http://www.math.ucsb.edu/~atzberg/index.html | research website]].

Changed lines 41-44 from:

!!Stochastic Immersed Boundary Methods for Computational Fluid Dynamics:

[[http://www.math.ucsb.edu/~atzberg/index.html | '+Dr. Paul J. Atzberger+']]

to:

!!Stochastic Immersed Boundary Methods for Computational Fluid Dynamics: [[http://www.math.ucsb.edu/~atzberg/index.html | '+Dr. Paul J. Atzberger+']]

Changed lines 42-45 from:

to:

[[http://www.math.ucsb.edu/~atzberg/index.html | '+Dr. Paul J. Atzberger+']]

Changed line 52 from:

The formalism is cast in terms of a system of Stochastic Partial Differential Equations (SPDE's). Fast time scales introduced into the fluid dynamics by the thermal fluctuations pose a challenge for conventional approaches to numerical approximation. Using results from stochastic calculus, we are developing efficient stochastic numerical methods for the formalism. Additional work includes development of stochastic numerical methods for non-periodic and adaptive multilevel meshes~~, see Dr~~.~~ Atzberger's [[http://www.math.ucsb.edu/~atzberg/index.html | papers.]]~~

to:

The formalism is cast in terms of a system of Stochastic Partial Differential Equations (SPDE's). Fast time scales introduced into the fluid dynamics by the thermal fluctuations pose a challenge for conventional approaches to numerical approximation. Using results from stochastic calculus, we are developing efficient stochastic numerical methods for the formalism. Additional work includes development of stochastic numerical methods for non-periodic and adaptive multilevel meshes.

Changed lines 44-45 from:

to:

Added lines 48-49:

%width=400px% Attach:SIB_Schematic.png

Added lines 44-45:

%width=400px% Attach:SIB_Schematic.png

Changed lines 47-51 from:

are numerical approaches for studying the mechanics of elastic structures which interact with a fluid in the presence of thermal fluctuations. The hydrodynamic interactions of the composite system are handled by an approximate treatment of the fluid-structure stresses in which a Lagrangian representation of the immersed structures is coupled to an Eulerian representation of the fluid. Thermal fluctuations are accounted for in the system by an appropriate stochastic forcing of the fluid-structure equations in accordance with the principles of statistical mechanics. The formalism is cast in terms of a system of Stochastic Partial Differential Equations (SPDE's). Fast time scales introduced into the fluid dynamics by the thermal fluctuations pose a challenge for conventional approaches to numerical approximation. Using results from stochastic calculus, we are developing efficient stochastic numerical methods for the formalism. Additional work includes development of stochastic numerical methods for non-periodic and adaptive multilevel meshes, see Dr. Atzberger's [[http://www.math.ucsb.edu/~atzberg/index.html | papers.]]

~~%width=400px% Attach:~~SIB~~_Schematic.png~~

Immersed structures in SIB can be used to represent the mechanics of ~~a variety of microscopic hydrodynamic systems~~, ~~for example, in a complex fluid the structures could represent solute ~~particles, polymers, or membrane structures. In ~~the figure some simulations demonstrating the methodology for a few basic physical systems are shown. Click on the images to play the associated movies. From top~~ to ~~bottom are: (i) polymer knot simulations showing SIB preservation of knot topology without the need for excluded volume interactions, (ii) simulations demonstrating a tethered membrane model using SIB for the hydrodynamic coupling, (iii) simulations showing how the methodology may be used to simulate more complex mechanical systems subject to thermal fluctuations, in this case a basic model from biology of a motor protein transporting a cargo vesicle under an imposed hydrodynamic load~~.~~ In collaboration with the Brown Group, Department of Chemistry, Dr. Atzberger's group is developing dynamic coarse-grained models of lipid bilayer membranes are being developed using the SIB formalism to account for molecular level interactions, lipid-lipid and lipid-solvent hydrodynamic coupling, and thermal fluctuations. For a more in-depth discussion see the publications section.~~

Immersed structures in SIB can be used to represent the mechanics

to:

are numerical approaches for studying the mechanics of elastic structures which interact with a fluid in the presence of thermal fluctuations. The hydrodynamic interactions of the composite system are handled by an approximate treatment of the fluid-structure stresses in which a Lagrangian representation of the immersed structures is coupled to an Eulerian representation of the fluid. Thermal fluctuations are accounted for in the system by an appropriate stochastic forcing of the fluid-structure equations in accordance with the principles of statistical mechanics.

The formalism is cast in terms of a system of Stochastic Partial Differential Equations (SPDE's). Fast time scales introduced into the fluid dynamics by the thermal fluctuations pose a challenge for conventional approaches to numerical approximation. Using results from stochastic calculus, we are developing efficient stochastic numerical methods for the formalism. Additional work includes development of stochastic numerical methods for non-periodic and adaptive multilevel meshes, see Dr. Atzberger's [[http://www.math.ucsb.edu/~atzberg/index.html | papers.]]

Immersed structures in SIB can be used to represent the mechanics of a variety of microscopic hydrodynamic systems, for example, in a complex fluid the structures could represent solute particles, polymers, or membrane structures. In collaboration with the Brown Group, Department of Chemistry, Dr. Atzberger's group is developing dynamic coarse-grained models of lipid bilayer membranes are being developed using the SIB formalism to account for molecular level interactions, lipid-lipid and lipid-solvent hydrodynamic coupling, and thermal fluctuations. For a more in-depth discussion see Dr. Atzberger's [[http://www.math.ucsb.edu/~atzberg/index.html | research website.]]

The formalism is cast in terms of a system of Stochastic Partial Differential Equations (SPDE's). Fast time scales introduced into the fluid dynamics by the thermal fluctuations pose a challenge for conventional approaches to numerical approximation. Using results from stochastic calculus, we are developing efficient stochastic numerical methods for the formalism. Additional work includes development of stochastic numerical methods for non-periodic and adaptive multilevel meshes, see Dr. Atzberger's [[http://www.math.ucsb.edu/~atzberg/index.html | papers.]]

Immersed structures in SIB can be used to represent the mechanics of a variety of microscopic hydrodynamic systems, for example, in a complex fluid the structures could represent solute particles, polymers, or membrane structures. In collaboration with the Brown Group, Department of Chemistry, Dr. Atzberger's group is developing dynamic coarse-grained models of lipid bilayer membranes are being developed using the SIB formalism to account for molecular level interactions, lipid-lipid and lipid-solvent hydrodynamic coupling, and thermal fluctuations. For a more in-depth discussion see Dr. Atzberger's [[http://www.math.ucsb.edu/~atzberg/index.html | research website.]]

Changed lines 54-55 from:

(rough draft / brainstorm) Above is meant to give an example of what we might post about

to:

----

Above is (rough draft / brainstorm) Above is meant to give an example of what we might post about

Above is (rough draft / brainstorm) Above is meant to give an example of what we might post about

Changed line 64 from:

the website all content editing will be password protected (admin or

to:

the public part of the website all content editing will be password protected (admin or

Changed lines 74-76 from:

also agree to authorize certain individuals ~~to post content with provision they~~

remove anything to ~~which a majority in the group objects.~~

These paragraphs could be copied to a formal manual on by-laws for the pages

remove anything

These

to:

also agree to authorize certain individuals (by majority vote) to have the

right to post content on-line without prior approval with provision they

remove anything to which someone objects and the majority does not support.

I am not sure this is necessary, but

these paragraphs could be copied to a formal manual on by-laws for the pages

right to post content on-line without prior approval with provision they

remove anything to which someone objects and the majority does not support.

I am not sure this is necessary, but

these paragraphs could be copied to a formal manual on by-laws for the pages

Changed line 63 from:

To handle the issue of any members putting ~~in appropriate~~ things on

to:

To handle the issue of any members putting inappropriate things on

Changed lines 65-66 from:

core members). To avoid abuse by any group ~~members, mainly the usual one,~~

we shall have the convention that all core members "vote"

we shall have the

to:

core members). To avoid abuse by any one group member.

I propose we shall have the official convention that all core members "vote"

I propose we shall have the official convention that all core members "vote"

Changed lines 73-79 from:

"do-not-approve PJA", after all members post the admin will copy...

~~[This paragraph will be copied~~ to ~~our manual of by-laws for the pages to ~~

avoid any university issues if anyone formally objects to not being able

to post anything they like...]. Another work around might be to start out

own "Center" or "Off-Center" around Applied and Computational Analysis

~~and make the pages based on that group to avoid having~~ to ~~deal with ~~

certain members. In any case, the group should brainstorm here.

avoid any university issues if anyone formally objects to not being able

to post anything they like...]. Another work around might be to start out

own "Center" or "Off-Center" around Applied and Computational Analysis

certain members. In any case, the group should brainstorm here

to:

"do-not-approve PJA", after all members post the admin will copy... We could

also agree to authorize certain individuals to post content with provision they

remove anything to which a majority in the group objects.

These paragraphs could be copied to a formal manual on by-laws for the pages

if this is required by university to avoid any issues of "free speech" and

to guard against any formal objections being made to fairness.

also agree to authorize certain individuals to post content with provision they

remove anything to which a majority in the group objects.

These paragraphs could be copied to a formal manual on by-laws for the pages

if this is required by university to avoid any issues of "free speech" and

to guard against any formal objections being made to fairness.

Changed lines 63-65 from:

To ~~avoid~~ the ~~all-too common wacky-ness from occuring by some appl. members,~~

to:

To handle the issue of any members putting in appropriate things on

the website all content editing will be password protected (admin or

core members). To avoid abuse by any group members, mainly the usual one,

the website all content editing will be password protected (admin or

core members). To avoid abuse by any group members, mainly the usual one,

Changed lines 69-72 from:

in fairness ~~his wacki-ness to post~~ material, but everything on-line reflects

the group consensus. Anything failing the vote and revisions process will not

be copied to the homepage [kind of like a journal peer-review process]. Basically,

we will post on the hidden page content "approved PJA", "revise xyz PJA",

the group consensus. Anything failing the vote and revisions process will not

be copied to the homepage [kind of like a journal peer-review process]. Basically,

we will post on the hidden page content "approved PJA", "revise xyz PJA",

to:

in fairness anyone in the group to post material, but everything on-line

reflects the group consensus. Anything failing the vote and revisions process

will not be copied to the homepage [kind of like a journal peer-review process].

Basically, we will post on the hidden page content "approved PJA", "revise xyz PJA",

reflects the group consensus. Anything failing the vote and revisions process

will not be copied to the homepage [kind of like a journal peer-review process].

Basically, we will post on the hidden page content "approved PJA", "revise xyz PJA",

Changed lines 76-79 from:

to post anything they like...].

to:

to post anything they like...]. Another work around might be to start out

own "Center" or "Off-Center" around Applied and Computational Analysis

and make the pages based on that group to avoid having to deal with

certain members. In any case, the group should brainstorm here.

own "Center" or "Off-Center" around Applied and Computational Analysis

and make the pages based on that group to avoid having to deal with

certain members. In any case, the group should brainstorm here.

Changed lines 72-73 from:

[This paragraph will be copied to our manual ~~on~~ by-laws for the pages to

avoid any university issues if~~any wacko's object~~...].

avoid any university issues if

to:

[This paragraph will be copied to our manual of by-laws for the pages to

avoid any university issues if anyone formally objects to not being able

to post anything they like...].

avoid any university issues if anyone formally objects to not being able

to post anything they like...].

Changed lines 60-73 from:

where we write the materials and review before copying to the homepage.

to:

where we write the materials and review before copying to the homepage.

To avoid the all-too common wacky-ness from occuring by some appl. members,

we shall have the convention that all core members "vote"

on the "hidden" page draft content before anything is put on the

homepage (password protected by admin). This way if requested we can allow

in fairness his wacki-ness to post material, but everything on-line reflects

the group consensus. Anything failing the vote and revisions process will not

be copied to the homepage [kind of like a journal peer-review process]. Basically,

we will post on the hidden page content "approved PJA", "revise xyz PJA",

"do-not-approve PJA", after all members post the admin will copy...

[This paragraph will be copied to our manual on by-laws for the pages to

avoid any university issues if any wacko's object...].

To avoid the all-too common wacky-ness from occuring by some appl. members,

we shall have the convention that all core members "vote"

on the "hidden" page draft content before anything is put on the

homepage (password protected by admin). This way if requested we can allow

in fairness his wacki-ness to post material, but everything on-line reflects

the group consensus. Anything failing the vote and revisions process will not

be copied to the homepage [kind of like a journal peer-review process]. Basically,

we will post on the hidden page content "approved PJA", "revise xyz PJA",

"do-not-approve PJA", after all members post the admin will copy...

[This paragraph will be copied to our manual on by-laws for the pages to

avoid any university issues if any wacko's object...].

Changed line 38 from:

to:

(Carlos: Please finish writing this synposis.)

Changed line 8 from:

the study of complex fluids / soft~~ condense~~ matter, computational fluid

to:

the study of complex fluids / soft-condensed matter, computational fluid

Changed lines 11-17 from:

analysis of non-linear hyperbolic PDE's (?), applied harmonic analysis~~.~~

Here you will find research highlights, upcoming seminar talks, and

~~information about news~~ and ~~current activities of the applied mathematics~~

group.

~~(~~Please ~~edit and take a shot at writing this materials. We can collectively edit~~

over time until we get something we ~~are all happy~~ with~~.)~~.

Here you will find research highlights, upcoming seminar talks, and

group.

over time until we get something

to:

analysis of non-linear hyperbolic PDE's (?), applied harmonic analysis,

stochastic differential equations. Here you will find research highlights,

upcoming seminar talks, and information about news and current activities

of the applied mathematics group.

Please feel free to edit and taking a shot at writing these materials.

We can collectively edit over time until we get something we are

all happy with.

stochastic differential equations. Here you will find research highlights,

upcoming seminar talks, and information about news and current activities

of the applied mathematics group.

Please feel free to edit and taking a shot at writing these materials.

We can collectively edit over time until we get something we are

all happy with.

Changed lines 54-60 from:

(~~We can discuss style of the research highlights and how we present things if you think this is too much~~.~~.. In any case, the idea is to post things here before~~ we ~~go public to discuss overall theme and criteria for content~~... ~~ Please also take a shot at posting some materials for discussion [present in near-final form]~~.~~)~~

to:

(rough draft / brainstorm) Above is meant to give an example of what we might post about

our work. We can discuss style of the research highlights and how we present things

if you think this is too much... In any case, the idea is to post things here before

we go public to discuss overall theme and criteria for content... Please also take

a shot at posting some materials for discussion [present in near-final form].

The working process will eventually be to have a "hidden" page we can all edit

where we write the materials and review before copying to the homepage.

our work. We can discuss style of the research highlights and how we present things

if you think this is too much... In any case, the idea is to post things here before

we go public to discuss overall theme and criteria for content... Please also take

a shot at posting some materials for discussion [present in near-final form].

The working process will eventually be to have a "hidden" page we can all edit

where we write the materials and review before copying to the homepage.

Changed lines 5-6 from:

development of core areas of mathematics ~~motivated by ~~the solution ~~to~~

specific problems arising in applications~~, such as arise~~ in the basic sciences

specific problems arising in applications

to:

development of core areas of mathematics with the solution of

specific problems arising in applications often in the basic sciences

specific problems arising in applications often in the basic sciences

Changed line 6 from:

problems arising in applications, such as arise in the basic sciences

to:

specific problems arising in applications, such as arise in the basic sciences

Changed lines 5-7 from:

development of core areas of mathematics ~~while ~~motivated by the solution to

problems arising in applications, such as arise in the sciences

~~and~~ engineering. Specific areas in which faculty are involved include

problems arising in applications, such as arise in the sciences

to:

development of core areas of mathematics motivated by the solution to

problems arising in applications, such as arise in the basic sciences

or engineering. Specific areas in which faculty are involved include

problems arising in applications, such as arise in the basic sciences

or engineering. Specific areas in which faculty are involved include

Changed lines 3-7 from:

Welcome to the applied mathematics group's homepage. ~~Here you will find~~

information about current research activities and events around campus

related to applied mathematics. Applied mathematics refers to the

branch of mathematics which strives to integrate the development of

core areas of mathematics while motivated by the solution to

information about current research activities and events around campus

related to applied mathematics. Applied mathematics refers to the

branch of mathematics which strives to integrate the development of

core areas of mathematics while motivated by the solution to

to:

Welcome to the applied mathematics group's homepage. Applied mathematics

refers to the branch of mathematics which strives to integrate the

development of core areas of mathematics while motivated by the solution to

refers to the branch of mathematics which strives to integrate the

development of core areas of mathematics while motivated by the solution to

Changed lines 7-11 from:

and engineering. ~~Here you will find research highlights, upcoming~~

seminar talks, and information about news and current activities of

the applied mathematics group.

(please take a shot at writing this and we can collectively edit).

seminar talks, and information about news and current activities of

the applied mathematics group.

(please take a shot at writing this and we can collectively edit

to:

and engineering. Specific areas in which faculty are involved include

the study of complex fluids / soft condense matter, computational fluid

dynamics (boundary integral methods / immersed boundary methods),

crystalline solids and liquid crystals, density functional theory,

analysis of non-linear hyperbolic PDE's (?), applied harmonic analysis.

Here you will find research highlights, upcoming seminar talks, and

information about news and current activities of the applied mathematics

group.

(Please edit and take a shot at writing this materials. We can collectively edit

over time until we get something we are all happy with.).

the study of complex fluids / soft condense matter, computational fluid

dynamics (boundary integral methods / immersed boundary methods),

crystalline solids and liquid crystals, density functional theory,

analysis of non-linear hyperbolic PDE's (?), applied harmonic analysis.

Here you will find research highlights, upcoming seminar talks, and

information about news and current activities of the applied mathematics

group.

(Please edit and take a shot at writing this materials. We can collectively edit

over time until we get something we are all happy with.).

Changed lines 3-4 from:

Welcome to the applied mathematics group's homepage.~~..~~

~~blurb about unifying themes and mission~~...

to:

Welcome to the applied mathematics group's homepage. Here you will find

information about current research activities and events around campus

related to applied mathematics. Applied mathematics refers to the

branch of mathematics which strives to integrate the development of

core areas of mathematics while motivated by the solution to

problems arising in applications, such as arise in the sciences

and engineering. Here you will find research highlights, upcoming

seminar talks, and information about news and current activities of

the applied mathematics group.

information about current research activities and events around campus

related to applied mathematics. Applied mathematics refers to the

branch of mathematics which strives to integrate the development of

core areas of mathematics while motivated by the solution to

problems arising in applications, such as arise in the sciences

and engineering. Here you will find research highlights, upcoming

seminar talks, and information about news and current activities of

the applied mathematics group.

Changed lines 27-35 from:

\\

%width=100px% Attach:carlosImage.png %width=100px% Attach:atzbergerImage.png

----

to:

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to:

!!Other highlights here...(images / movies, etc...) \\

\\

%width=100px% Attach:carlosImage.png %width=100px% Attach:atzbergerImage.png

----

\\

%width=100px% Attach:carlosImage.png %width=100px% Attach:atzbergerImage.png

----

Changed line 36 from:

!!Stochastic Immersed Boundary Methods ~~/~~ Computational Fluid Dynamics:

to:

!!Stochastic Immersed Boundary Methods for Computational Fluid Dynamics:

Changed line 40 from:

are~~ a~~ numerical approaches for studying the mechanics of elastic structures which interact with a fluid in the presence of thermal fluctuations. The hydrodynamic interactions of the composite system are handled by an approximate treatment of the fluid-structure stresses in which a Lagrangian representation of the immersed structures is coupled to an Eulerian representation of the fluid. Thermal fluctuations are accounted for in the system by an appropriate stochastic forcing of the fluid-structure equations in accordance with the principles of statistical mechanics. The formalism is cast in terms of a system of Stochastic Partial Differential Equations (SPDE's). Fast time scales introduced into the fluid dynamics by the thermal fluctuations pose a challenge for conventional approaches to numerical approximation. Using results from stochastic calculus, we are developing efficient stochastic numerical methods for the formalism. Additional work includes development of stochastic numerical methods for non-periodic and adaptive multilevel meshes, see Dr. Atzberger's [[http://www.math.ucsb.edu/~atzberg/index.html | papers.]]

to:

are numerical approaches for studying the mechanics of elastic structures which interact with a fluid in the presence of thermal fluctuations. The hydrodynamic interactions of the composite system are handled by an approximate treatment of the fluid-structure stresses in which a Lagrangian representation of the immersed structures is coupled to an Eulerian representation of the fluid. Thermal fluctuations are accounted for in the system by an appropriate stochastic forcing of the fluid-structure equations in accordance with the principles of statistical mechanics. The formalism is cast in terms of a system of Stochastic Partial Differential Equations (SPDE's). Fast time scales introduced into the fluid dynamics by the thermal fluctuations pose a challenge for conventional approaches to numerical approximation. Using results from stochastic calculus, we are developing efficient stochastic numerical methods for the formalism. Additional work includes development of stochastic numerical methods for non-periodic and adaptive multilevel meshes, see Dr. Atzberger's [[http://www.math.ucsb.edu/~atzberg/index.html | papers.]]

Changed lines 42-43 from:

%width=~~300px~~% Attach:SIB_Schematic.png

to:

%width=400px% Attach:SIB_Schematic.png

Added line 49:

(We can discuss style of the research highlights and how we present things if you think this is too much... In any case, the idea is to post things here before we go public to discuss overall theme and criteria for content... Please also take a shot at posting some materials for discussion [present in near-final form].)

Changed lines 39-40 from:

to:

Dr. Atzberger's group works on Stochastic Immersed Boundary Methods (SIB) which

are a numerical approaches for studying the mechanics of elastic structures which interact with a fluid in the presence of thermal fluctuations. The hydrodynamic interactions of the composite system are handled by an approximate treatment of the fluid-structure stresses in which a Lagrangian representation of the immersed structures is coupled to an Eulerian representation of the fluid. Thermal fluctuations are accounted for in the system by an appropriate stochastic forcing of the fluid-structure equations in accordance with the principles of statistical mechanics. The formalism is cast in terms of a system of Stochastic Partial Differential Equations (SPDE's). Fast time scales introduced into the fluid dynamics by the thermal fluctuations pose a challenge for conventional approaches to numerical approximation. Using results from stochastic calculus, we are developing efficient stochastic numerical methods for the formalism. Additional work includes development of stochastic numerical methods for non-periodic and adaptive multilevel meshes, see Dr. Atzberger's [[http://www.math.ucsb.edu/~atzberg/index.html | papers.]]

are a numerical approaches for studying the mechanics of elastic structures which interact with a fluid in the presence of thermal fluctuations. The hydrodynamic interactions of the composite system are handled by an approximate treatment of the fluid-structure stresses in which a Lagrangian representation of the immersed structures is coupled to an Eulerian representation of the fluid. Thermal fluctuations are accounted for in the system by an appropriate stochastic forcing of the fluid-structure equations in accordance with the principles of statistical mechanics. The formalism is cast in terms of a system of Stochastic Partial Differential Equations (SPDE's). Fast time scales introduced into the fluid dynamics by the thermal fluctuations pose a challenge for conventional approaches to numerical approximation. Using results from stochastic calculus, we are developing efficient stochastic numerical methods for the formalism. Additional work includes development of stochastic numerical methods for non-periodic and adaptive multilevel meshes, see Dr. Atzberger's [[http://www.math.ucsb.edu/~atzberg/index.html | papers.]]

Changed line 44 from:

Immersed structures in SIB can be used to represent the mechanics of a variety of microscopic hydrodynamic systems, for example, in a complex fluid the structures could represent solute particles, polymers, or membrane structures. In the figure some simulations demonstrating the methodology for a few basic physical systems are shown. Click on the images to play the associated movies. From top to bottom are: (i) polymer knot simulations showing SIB preservation of knot topology without the need for excluded volume interactions, (ii) simulations demonstrating a tethered membrane model using SIB for the hydrodynamic coupling, (iii) simulations showing how the methodology may be used to simulate more complex mechanical systems subject to thermal fluctuations, in this case a basic model from biology of a motor protein transporting a cargo vesicle under an imposed hydrodynamic load. In collaboration with the Brown Group, Department of Chemistry, dynamic coarse-grained models of lipid bilayer membranes are being developed using the SIB formalism to account for molecular level interactions, lipid-lipid and lipid-solvent hydrodynamic coupling, and thermal fluctuations. For a more in-depth discussion see the publications section.

to:

Immersed structures in SIB can be used to represent the mechanics of a variety of microscopic hydrodynamic systems, for example, in a complex fluid the structures could represent solute particles, polymers, or membrane structures. In the figure some simulations demonstrating the methodology for a few basic physical systems are shown. Click on the images to play the associated movies. From top to bottom are: (i) polymer knot simulations showing SIB preservation of knot topology without the need for excluded volume interactions, (ii) simulations demonstrating a tethered membrane model using SIB for the hydrodynamic coupling, (iii) simulations showing how the methodology may be used to simulate more complex mechanical systems subject to thermal fluctuations, in this case a basic model from biology of a motor protein transporting a cargo vesicle under an imposed hydrodynamic load. In collaboration with the Brown Group, Department of Chemistry, Dr. Atzberger's group is developing dynamic coarse-grained models of lipid bilayer membranes are being developed using the SIB formalism to account for molecular level interactions, lipid-lipid and lipid-solvent hydrodynamic coupling, and thermal fluctuations. For a more in-depth discussion see the publications section.

Changed lines 37-39 from:

Dr. Paul J. Atzberger

\\

to:

'+Dr. Paul J. Atzberger+'

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%width=300px% Attach~~.~~SIB_Schematic.png

to:

%width=300px% Attach:SIB_Schematic.png

Changed lines 38-39 from:

(

to:

Dr. Paul J. Atzberger:

\\

\\

Changed lines 36-38 from:

!!Stochastic Immersed Boundary Methods / Computational Fluid Dynamics:\\

to:

!!Stochastic Immersed Boundary Methods / Computational Fluid Dynamics:

\\

\\

Added lines 32-46:

----

!!Stochastic Immersed Boundary Methods / Computational Fluid Dynamics:\\

(Dr. Paul J. Atzberger)

The Stochastic Immersed Boundary Method (SIB) is a numerical approach for studying the mechanics of elastic structures which interact with a fluid in the presence of thermal fluctuations. The hydrodynamic interactions of the composite system are handled by an approximate treatment of the fluid-structure stresses in which a Lagrangian representation of the immersed structures is coupled to an Eulerian representation of the fluid. Thermal fluctuations are accounted for in the system by an appropriate stochastic forcing of the fluid-structure equations in accordance with the principles of statistical mechanics. The formalism is cast in terms of a system of Stochastic Partial Differential Equations (SPDE's). Fast time scales introduced into the fluid dynamics by the thermal fluctuations pose a challenge for conventional approaches to numerical approximation. Using results from stochastic calculus, we are developing efficient stochastic numerical methods for the formalism. Additional work includes development of stochastic numerical methods for non-periodic and adaptive multilevel meshes, see Dr. Atzberger's [[http://www.math.ucsb.edu/~atzberg/index.html | papers.]]

%width=300px% Attach.SIB_Schematic.png

Immersed structures in SIB can be used to represent the mechanics of a variety of microscopic hydrodynamic systems, for example, in a complex fluid the structures could represent solute particles, polymers, or membrane structures. In the figure some simulations demonstrating the methodology for a few basic physical systems are shown. Click on the images to play the associated movies. From top to bottom are: (i) polymer knot simulations showing SIB preservation of knot topology without the need for excluded volume interactions, (ii) simulations demonstrating a tethered membrane model using SIB for the hydrodynamic coupling, (iii) simulations showing how the methodology may be used to simulate more complex mechanical systems subject to thermal fluctuations, in this case a basic model from biology of a motor protein transporting a cargo vesicle under an imposed hydrodynamic load. In collaboration with the Brown Group, Department of Chemistry, dynamic coarse-grained models of lipid bilayer membranes are being developed using the SIB formalism to account for molecular level interactions, lipid-lipid and lipid-solvent hydrodynamic coupling, and thermal fluctuations. For a more in-depth discussion see the publications section.

A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found

[[http://www.ima.umn.edu/2008-2009/W11.3-7.08/abstracts.html#Atzberger-Paul | here.]]

Added line 5:

(please take a shot at writing this and we can collectively edit).

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%lfloat text-align=left margin-top=5px margin-right=5px margin-bottom=10px margin-left=5px width=100px% ~~ ~~

Attach:hectorImage.png

Attach:hectorImage.png

to:

%lfloat text-align=left margin-top=5px margin-right=5px margin-bottom=10px margin-left=5px width=100px% Attach:hectorImage.png

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%lfloat text-align=left margin-top=5px margin-right=5px margin-bottom=10px margin-left=5px width=100px% Attach:~~carlosImage~~.png~~ ~~

to:

%lfloat text-align=left margin-top=5px margin-right=5px margin-bottom=10px margin-left=5px width=100px%

Attach:hectorImage.png

Attach:hectorImage.png

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to:

%width=100px% Attach:carlosImage.png %width=100px% Attach:atzbergerImage.png

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to:

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%~~width=100px% Attach:carlosImage.png~~

to:

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%width=~~150px~~% Attach:carlosImage.png Carlos Garcia-Cervera receives the prestigious NSF Career Award for his proposal "Multilevel Physics in the Study of Solids: Modeling, Analysis and Simulations".

to:

%width=100px% Attach:carlosImage.png

Carlos Garcia-Cervera receives the prestigious NSF Career Award for his proposal "Multilevel Physics in the Study of Solids: Modeling, Analysis and Simulations".

Carlos Garcia-Cervera receives the prestigious NSF Career Award for his proposal "Multilevel Physics in the Study of Solids: Modeling, Analysis and Simulations".

Changed lines 14-17 from:

%width=~~100px~~% Attach:carlosImage.png

Carlos Garcia-Cervera receives the prestigious NSF Career Award for his proposal

"Multilevel Physics in the Study of Solids: Modeling, Analysis and Simulations".

Carlos

"Multilevel Physics in the Study of Solids: Modeling, Analysis and Simulations".

to:

%width=150px% Attach:carlosImage.png Carlos Garcia-Cervera receives the prestigious NSF Career Award for his proposal "Multilevel Physics in the Study of Solids: Modeling, Analysis and Simulations".

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to:

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%width=

%width=

to:

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to:

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to:

%width=200px% (Attach:).carlosImage.png

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%width~~: ~~200px%

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Attach:carlosImage.png

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to:

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Attach.~~carlosImage.~~png

Attach~~.~~hectorImage.png

Attach

to:

Attach:carlosImage.png

Attach:hectorImage.png

Attach:hectorImage.png

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Attach.carlosImage.png

Attach.hectorImage.png

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(Attach~~)~~:carlosImage.png

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(Attach

(Attach

to:

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----

(these will be removed)

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For practice for when the site goes

public the "edit" and viewing the

"intranet" are now password protected.

The password for now is

"4coregroup." Once you type this in a

group your access should be presistent

so will not be required to be entered

too many times. This will give both

you and the administrator (for now me [Paul])

good practice.

\\

\\

We give some links to basic resources

which show how to make edits to the wiki

page. For each page look for the button

"edit" at the bottom to modify the page.\\

\\

Here are two tutorials on the basics of pmWiki syntax:

[[PmWiki/Text Formatting Rules]],

[[http://www.pmwiki.org/wiki/PmWiki/BasicEditing | Tutorial on Wiki Editing]]

Also see the Wiki-sandbox for a quick set of examples and to play around

with edits. [[Main/WikiSandbox | Wiki-Sandbox]].

----

!! Wiki Action Items [Please Perform Soon so We Can Launch]

* Enter faculty information and research description on the "Faculty Members" page. Also enter information for any graduate students (very brief name + dept. affiliations).

* Post below a few brief research highlights or resources for use on the website (upload images, movies, link to YouTube channel, etc...). Give brief description. (This is brainstorm for materials).

!! Feedback / Suggestions Concerning the Website

* Please enter any comments or suggestions concerning the Wiki website here.

----

to:

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Here ~~is a tutorial~~ on the basics of pmWiki syntax:

to:

Here are two tutorials on the basics of pmWiki syntax:

[[PmWiki/Text Formatting Rules]],

[[PmWiki/Text Formatting Rules]],

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to:

!! Welcome

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to:

!!Research Highlights \\

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to:

!!How to use and edit wiki-pages.

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to:

!! Wiki Action Items [Please Perform Soon so We Can Launch]

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!! Welcome

to:

!!! Welcome

Changed lines 9-10 from:

!!Research Highlights \\

to:

!!!Research Highlights \\

Changed lines 24-26 from:

Other highlights here...(images / movies, etc...) \\

to:

!!Other highlights here...(images / movies, etc...) \\

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!!How to use and edit wiki-pages.

to:

!!!How to use and edit wiki-pages.

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!! Wiki Action Items [Please Perform Soon so We Can Launch]

to:

!!! Wiki Action Items [Please Perform Soon so We Can Launch]

Changed lines 11-25 from:

to:

----

!!Carlos Garcia-Cervera Wins NSF Faculty Early Career Development Award (NSF CAREER)

Carlos Garcia-Cervera receives the prestigious NSF Career Award for his proposal

"Multilevel Physics in the Study of Solids: Modeling, Analysis and Simulations".

The award will .... and ... The proposed research program has the potential to

impact... This is the first NSF CAREER award given to a faculty member of the

department of mathematics.\\

[[http://www.ia.ucsb.edu/93106/2007/November19/math.html | Full Article]]

----

Other highlights here...(images / movies, etc...) \\

!!Carlos Garcia-Cervera Wins NSF Faculty Early Career Development Award (NSF CAREER)

Carlos Garcia-Cervera receives the prestigious NSF Career Award for his proposal

"Multilevel Physics in the Study of Solids: Modeling, Analysis and Simulations".

The award will .... and ... The proposed research program has the potential to

impact... This is the first NSF CAREER award given to a faculty member of the

department of mathematics.\\

[[http://www.ia.ucsb.edu/93106/2007/November19/math.html | Full Article]]

----

Other highlights here...(images / movies, etc...) \\

Changed line 48 from:

* Post a few brief research highlights or resources for use on the website (upload images, movies, link to YouTube channel, etc...). Give brief description. (This is brainstorm for materials).

to:

* Post below a few brief research highlights or resources for use on the website (upload images, movies, link to YouTube channel, etc...). Give brief description. (This is brainstorm for materials).

Changed line 44 from:

!! Wiki Action Items [Please Perform]

to:

!! Wiki Action Items [Please Perform Soon so We Can Launch]

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with edits.

to:

with edits. [[Main/WikiSandbox | Wiki-Sandbox]].

Added lines 38-40:

Also see the Wiki-sandbox for a quick set of examples and to play around

with edits.

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Here is a tutorial on the ~~basic~~ of pmWiki syntax:

to:

Here is a tutorial on the basics of pmWiki syntax:

Changed lines 22-25 from:

The password ~~is ~~for now is

"4coregroup."

This will give both you and the

administrator for now (me) good practice.

"4coregroup."

This will give both you and the

administrator for now (me)

to:

The password for now is

"4coregroup." Once you type this in a

group your access should be presistent

so will not be required to be entered

too many times. This will give both

you and the administrator (for now me [Paul])

good practice.

"4coregroup." Once you type this in a

group your access should be presistent

so will not be required to be entered

too many times. This will give both

you and the administrator (for now me [Paul])

good practice.

Changed lines 17-18 from:

!!How to use and edit wiki-pages.~~\\~~

\\

\\

to:

!!How to use and edit wiki-pages.

Changed lines 17-26 from:

to:

!!How to use and edit wiki-pages.\\

\\

For practice for when the site goes

public the "edit" and viewing the

"intranet" are now password protected.

The password is for now is

"4coregroup."

This will give both you and the

administrator for now (me) good practice.

\\

\\

For practice for when the site goes

public the "edit" and viewing the

"intranet" are now password protected.

The password is for now is

"4coregroup."

This will give both you and the

administrator for now (me) good practice.

\\

Added lines 15-27:

----

'+How to use and edit wiki-pages.+'\\

\\

We give some links to basic resources

which show how to make edits to the wiki

page. For each page look for the button

"edit" at the bottom to modify the page.\\

\\

Here is a tutorial on the basic of pmWiki syntax:

[[http://www.pmwiki.org/wiki/PmWiki/BasicEditing | Tutorial on Wiki Editing]]

----

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to:

!!Research Highlights \\

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!! Wiki Action ~~Item (Group Members Please ~~Perform~~)~~

to:

!! Wiki Action Items [Please Perform]

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to:

(these will be removed)

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* Please enter any comments or suggestions concerning

the Wiki website here.

the Wiki website here.

to:

* Please enter any comments or suggestions concerning the Wiki website here.

Changed lines 17-21 from:

* Post a few brief research highlights or resources

for use on the website (upload images, movies, link

~~to~~ YouTube channel, etc...). Give brief description.

~~(This is brainstorm for~~ materials.

for use on the website (upload images, movies, link

to:

* Post a few brief research highlights or resources for use on the website (upload images, movies, link to YouTube channel, etc...). Give brief description. (This is brainstorm for materials).

Changed lines 15-16 from:

* Enter faculty information and research description on the "Faculty Members" page.

Also enter information for any graduate students (very brief name + dept. affiliations).

Also enter information for any graduate students (very brief name + dept. affiliations).

to:

* Enter faculty information and research description on the "Faculty Members" page. Also enter information for any graduate students (very brief name + dept. affiliations).

Added lines 10-28:

----

!! Wiki Action Item (Group Members Please Perform)

* Enter faculty information and research description on the "Faculty Members" page.

Also enter information for any graduate students (very brief name + dept. affiliations).

* Post a few brief research highlights or resources

for use on the website (upload images, movies, link

to YouTube channel, etc...). Give brief description.

(This is brainstorm for materials.

!! Feedback / Suggestions Concerning the Website

* Please enter any comments or suggestions concerning

the Wiki website here.

Changed lines 7-9 from:

Research Highlights here...(images / movies, etc...) \\

<a href="test"> test </a>

<a href="test"> test </a>

to:

'+Research Highlights+'\\

Highlights here...(images / movies, etc...) \\

Highlights here...(images / movies, etc...) \\

Changed lines 1-2 from:

!! Applied ~~Math and PDE Seminar~~

to:

!! Applied Mathematics Research at UCSB

Welcome to the applied mathematics group's homepage...

blurb about unifying themes and mission...

\\

Welcome to the applied mathematics group's homepage...

blurb about unifying themes and mission...

\\

Changed lines 7-34 from:

Tuesday, February 17th, 4:00pm - 5:00pm, SH 4607. \\

Peter R. Kramer, Dept. Mathematical Sciences, Rensselaer Polytechnic Institute.\\

\\

''Abstract:'' We study an all-to-all coupled network of identical excitatory

integrate-and-fire (I\&F) neurons driven by an external spike train

modeled as a Poisson process. Numerical simulations demonstrate that

over a broad range of parameters, the network enters a synchronized

state in which the neurons all fire together at regular intervals. We

identify mechanisms leading to this synchronization for two regimes of

the external driving current: superthreshold and subthreshold. In the

former, a probabilistic argument similar to the proof of the Central

Limit Theorem yields the oscillation period, while in the latter, this

period is analyzed via an exit time calculation utilizing a diffusion

approximation of the Kolmogorov forward equation. In both cases,

stochastic fluctuations play a central role in determining the

oscillation period. We also develop a criterion for

synchrony in the network through a probabilistic argument. This work

is in collaboration with Katherine Newhall, Gregor Kovacic, David Cai,

and Aaditya Rangan.

----

''''''+Something.+'''''' \\

Tuesday, February 17th, 4:00pm - 5:00pm, SH 4607. \\

Someone, Dept. Something, Somewhere.\\

\\

''Abstract:'' Some description of talk.

----

to:

Research Highlights here...(images / movies, etc...) \\

Changed lines 27-29 from:

'''~~Title:~~'''~~ Talking about something~~.~~ \\~~

''~~Some Speaker~~, ~~(University of Somewhere), Tuesday, April XX, 3:00pm - 4:00pm (South Hall 7777)''~~.~~ ~~\\

''~~'~~Abstract:''~~' A blurb about what to ~~talk~~ about~~.~~..\\~~

''

to:

----

''''''+Something.+'''''' \\

Tuesday, February 17th, 4:00pm - 5:00pm, SH 4607. \\

Someone, Dept. Something, Somewhere.\\

\\

''Abstract:'' Some description of talk.

----

''''''+Something.+'''''' \\

Tuesday, February 17th, 4:00pm - 5:00pm, SH 4607. \\

Someone, Dept. Something, Somewhere.\\

\\

''Abstract:'' Some description of talk.

----

Changed line 1 from:

to:

Added line 4:

----

Added line 26:

----

Added line 5:

Tuesday, February 17th, 4:00pm - 5:00pm, SH 4607. \\

Deleted line 6:

Changed line 7 from:

''~~'~~Abstract:~~'~~'' We study an all-to-all coupled network of identical excitatory

to:

''Abstract:'' We study an all-to-all coupled network of identical excitatory

Changed line 5 from:

to:

Peter R. Kramer, Dept. Mathematical Sciences, Rensselaer Polytechnic Institute.\\

Changed line 4 from:

''''+Dynamics of a Stochastically Driven Neuronal Network Model.+'''' \\

to:

''''''+Dynamics of a Stochastically Driven Neuronal Network Model.+'''''' \\

Changed line 4 from:

'+Dynamics of a Stochastically Driven Neuronal Network Model.+' \\

to:

''''+Dynamics of a Stochastically Driven Neuronal Network Model.+'''' \\

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+Dynamics of a Stochastically Driven Neuronal Network Model.+ \\

to:

'+Dynamics of a Stochastically Driven Neuronal Network Model.+' \\

Changed line 4 from:

to:

+Dynamics of a Stochastically Driven Neuronal Network Model.+ \\

Changed line 5 from:

+Peter R. Kramer, Dept. Mathematical Sciences, Rensselaer Polytechnic Institute.+\\

to:

'+Peter R. Kramer, Dept. Mathematical Sciences, Rensselaer Polytechnic Institute.+'\\

Changed line 5 from:

Peter R. Kramer, Dept. Mathematical Sciences, Rensselaer Polytechnic Institute.\\

to:

+Peter R. Kramer, Dept. Mathematical Sciences, Rensselaer Polytechnic Institute.+\\

Changed lines 4-6 from:

'''+Dynamics of a Stochastically Driven Neuronal Network Model.+'''~~'~~ \\

~~''~~Peter R. Kramer, Dept. Mathematical Sciences, Rensselaer Polytechnic Institute.~~''~~\\

~~''~~Tuesday, February 17th, 4:00pm - 5:00pm, SH 4607~~.''~~. \\

to:

'''+Dynamics of a Stochastically Driven Neuronal Network Model.+''' \\

Peter R. Kramer, Dept. Mathematical Sciences, Rensselaer Polytechnic Institute.\\

Tuesday, February 17th, 4:00pm - 5:00pm, SH 4607. \\

Peter R. Kramer, Dept. Mathematical Sciences, Rensselaer Polytechnic Institute.\\

Tuesday, February 17th, 4:00pm - 5:00pm, SH 4607. \\

Changed line 4 from:

'''~~Title:''' ~~Dynamics of a Stochastically Driven Neuronal Network Model. \\

to:

'''+Dynamics of a Stochastically Driven Neuronal Network Model.+'''' \\

Changed lines 4-6 from:

'''Title:''' ~~Talking about something. \\~~

''Some Speaker, (University of Somewhere), Tuesday, April XX, ~~3:00pm - 4:00pm (South Hall 7777)~~''~~. ~~\\

''~~'Abstract:''' A blurb about what to talk about~~..~~.~~\\

''Some Speaker, (University of Somewhere), Tuesday, April XX

''

to:

'''Title:''' Dynamics of a Stochastically Driven Neuronal Network Model. \\

''Peter R. Kramer, Dept. Mathematical Sciences, Rensselaer Polytechnic Institute.''\\

''Tuesday, February 17th, 4:00pm - 5:00pm, SH 4607.''. \\

'''Abstract:''' We study an all-to-all coupled network of identical excitatory

integrate-and-fire (I\&F) neurons driven by an external spike train

modeled as a Poisson process. Numerical simulations demonstrate that

over a broad range of parameters, the network enters a synchronized

state in which the neurons all fire together at regular intervals. We

identify mechanisms leading to this synchronization for two regimes of

the external driving current: superthreshold and subthreshold. In the

former, a probabilistic argument similar to the proof of the Central

Limit Theorem yields the oscillation period, while in the latter, this

period is analyzed via an exit time calculation utilizing a diffusion

approximation of the Kolmogorov forward equation. In both cases,

stochastic fluctuations play a central role in determining the

oscillation period. We also develop a criterion for

synchrony in the network through a probabilistic argument. This work

is in collaboration with Katherine Newhall, Gregor Kovacic, David Cai,

and Aaditya Rangan.

''Peter R. Kramer, Dept. Mathematical Sciences, Rensselaer Polytechnic Institute.''\\

''Tuesday, February 17th, 4:00pm - 5:00pm, SH 4607.''. \\

'''Abstract:''' We study an all-to-all coupled network of identical excitatory

integrate-and-fire (I\&F) neurons driven by an external spike train

modeled as a Poisson process. Numerical simulations demonstrate that

over a broad range of parameters, the network enters a synchronized

state in which the neurons all fire together at regular intervals. We

identify mechanisms leading to this synchronization for two regimes of

the external driving current: superthreshold and subthreshold. In the

former, a probabilistic argument similar to the proof of the Central

Limit Theorem yields the oscillation period, while in the latter, this

period is analyzed via an exit time calculation utilizing a diffusion

approximation of the Kolmogorov forward equation. In both cases,

stochastic fluctuations play a central role in determining the

oscillation period. We also develop a criterion for

synchrony in the network through a probabilistic argument. This work

is in collaboration with Katherine Newhall, Gregor Kovacic, David Cai,

and Aaditya Rangan.

Added lines 24-25:

\\

Changed line 4 from:

to:

/* http://pmichaud.com/img/misc/gem.jpg */

Deleted lines 6-7:

''Some Speaker, (University of Somewhere), Tuesday, April XX, 3:00pm - 4:00pm (South Hall 7777)''. \\

Added line 8:

''Some Speaker, (University of Somewhere), Tuesday, April XX, 3:00pm - 4:00pm (South Hall 7777)''. \\

Changed lines 10-11 from:

to:

\\

'''Title:''' Talking about something. \\

'''Title:''' Talking about something. \\

Deleted line 12:

Changed line 8 from:

''Some Speaker, (University of Somewhere), Tuesday, April XX, 3:00pm - 4:00pm (South Hall 7777)''.

to:

''Some Speaker, (University of Somewhere), Tuesday, April XX, 3:00pm - 4:00pm (South Hall 7777)''. \\

Changed line 12 from:

''Some Speaker, (University of Somewhere), Tuesday, April XX, 3:00pm - 4:00pm (South Hall 7777)''.

to:

''Some Speaker, (University of Somewhere), Tuesday, April XX, 3:00pm - 4:00pm (South Hall 7777)''. \\

Changed line 8 from:

to:

''Some Speaker, (University of Somewhere), Tuesday, April XX, 3:00pm - 4:00pm (South Hall 7777)''.

Changed line 12 from:

to:

''Some Speaker, (University of Somewhere), Tuesday, April XX, 3:00pm - 4:00pm (South Hall 7777)''.

Changed lines 9-12 from:

'''Title:'''

'''Abstract:'''

\\

to:

'''Title:''' Talking about something. \\

'''Abstract:''' A blurb about what to talk about...\\

* ''Some Speaker, (University of Somewhere), Tuesday, April XX, 3:00pm - 4:00pm (South Hall 7777)''.

'''Title:''' Talking about something. \\

'''Abstract:''' A blurb about what to talk about...\\

'''Abstract:''' A blurb about what to talk about...\\

* ''Some Speaker, (University of Somewhere), Tuesday, April XX, 3:00pm - 4:00pm (South Hall 7777)''.

'''Title:''' Talking about something. \\

'''Abstract:''' A blurb about what to talk about...\\

Changed lines 8-12 from:

* Some Speaker, (University of Somewhere), Tuesday, April XX, 3:00pm - 4:00pm (South Hall 7777).

~~* Some Speaker, (University of Somewhere), Tuesday, April XX, 3~~:~~00pm - 4~~:~~00pm (South Hall 7777).~~

* Some Speaker, (University of Somewhere), Tuesday, April XX, 3:00pm - 4:00pm (South Hall 7777).

* Some Speaker, (University of Somewhere), Tuesday, April XX, 3:00pm - 4:00pm (South Hall 7777).

to:

* ''Some Speaker, (University of Somewhere), Tuesday, April XX, 3:00pm - 4:00pm (South Hall 7777)''.

'''Title:'''

'''Abstract:'''

'''Title:'''

'''Abstract:'''

Deleted lines 12-28:

----

!! Research Project II

Research project will be discussed here...

Image and some links

----

!! Research Project III

Research project will be discussed here...

Image and some links

Changed lines 2-3 from:

!! ~~Research Project I ~~

to:

!! Applied Math and PDE Seminar

Changed lines 6-7 from:

Image and some links

to:

* Some Speaker, (University of Somewhere), Tuesday, April XX, 3:00pm - 4:00pm (South Hall 7777).

* Some Speaker, (University of Somewhere), Tuesday, April XX, 3:00pm - 4:00pm (South Hall 7777).

* Some Speaker, (University of Somewhere), Tuesday, April XX, 3:00pm - 4:00pm (South Hall 7777).

Changed lines 2-4 from:

!! Research Project I http://pmichaud.com/img/misc/gem.jpg

to:

!! Research Project I

http://pmichaud.com/img/misc/gem.jpg

http://pmichaud.com/img/misc/gem.jpg

Changed lines 2-3 from:

!! Research Project I

to:

!! Research Project I http://pmichaud.com/img/misc/gem.jpg

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to:

Changed line 6 from:

to:

http://pmichaud.com/img/misc/gem.jpg

Changed line 6 from:

to:

%http://pmichaud.com/img/misc/gem.jpg

Changed line 6 from:

%lfloat~~ ~~%http://pmichaud.com/img/misc/gem.jpg

to:

%lfloat%http://pmichaud.com/img/misc/gem.jpg

Changed line 7 from:

%lfloat~~ text-align=left margin-top=0px margin-right=0px margin-bottom=10px margin-left=0px~~ %http://pmichaud.com/img/misc/gem.jpg

to:

%lfloat %http://pmichaud.com/img/misc/gem.jpg

Changed lines 7-10 from:

----

%lfloat text-~~align=~~left ~~margin-top=0px margin-right=0px margin-bottom=10px margin-left=0px %http://pmichaud.com/img/misc/gem.jpg '''The image is left-aligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''~~

%lfloat text

to:

%lfloat text-align=left margin-top=0px margin-right=0px margin-bottom=10px margin-left=0px %http://pmichaud.com/img/misc/gem.jpg

Added lines 6-8:

%lfloat text-align=left margin-top=0px margin-right=0px margin-bottom=10px margin-left=0px %http://pmichaud.com/img/misc/gem.jpg '''The image is left-aligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''