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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 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]]].
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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://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.]]. 
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'+%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]].\\
\\
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'+%color555555%Kozato Graduate Fellowship in Quantitative Biology+'
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'+%color555555%Kozato Postdoctoral Fellowship in Quantitative Biology+'
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For more information:
\\
[[http
://www.math.ucsb.edu/~atzberg/KozatoFellowship/ | Kozato Fellowship in Quantitative Biology]]\\
to:
For more information see: [[http://www.math.ucsb.edu/~atzberg/KozatoFellowship/ | Kozato Fellowship in Quantitative Biology]].\\
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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:
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:
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'+%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]]\\
\\

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

%lfloat text
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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]]
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[[http://www.math.ucsb.edu/~atzberg/Kozato Fellowship/ | Kozato Fellowship in Quantitative Biology]]\\
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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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'+%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]]\\
\\

----

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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]]. \\
\\

\\

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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:
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\\
\\

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.\\

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'+%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

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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.\\
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----

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.

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!! 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] ]] \\
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!! 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] ]] \\
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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.\\
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. 
\\
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\\
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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]]. \\
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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]]. \\
\\

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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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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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\\
\\
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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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* Computational Fluid Dynamics.
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* 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
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
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and participate in collaborations with a diverse collection of faculty on campus.
Research
areas 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. 
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. 
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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://www.math.ucsb.edu/~mbueno/mathcircle/index.html |Attach:mathCircleLogo.gif]] %%
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[[http://www.math.ucsb.edu/~mbueno/mathcircle/index.html |Attach:mathCircleLogo.gif]]
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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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\\
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\\
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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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'+%color555555%UCSB Math Circle+'

%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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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]].
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]].
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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]]
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]].
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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 PJA - 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:
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.
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...
August 27, 2009, at 09:41 PM by atzberg - restored the page...test....
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Another basic test of notifications....
August 27, 2009, at 09:41 PM by atzberg - 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....
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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.
to:
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August 26, 2009, at 08:58 PM by atzberg - 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.
August 26, 2009, at 08:37 PM by 128.111.61.191 -
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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
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
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applied harmonic analysis, and stochastic analysis.  Here you will find
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,
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June 25, 2009, at 09:36 AM by 128.111.88.173 -
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June 23, 2009, at 09:13 AM by 128.111.88.173 -
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June 23, 2009, at 09:12 AM by 128.111.88.173 -
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June 23, 2009, at 09:10 AM by 128.111.88.173 -
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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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Welcome to the applied mathematics group's homepage.  Applied mathematics refers to the branch of mathematics which strives
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 research
highlights, upcoming seminar talks, and information
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.
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!!Research Gallery \\

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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]].

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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]].

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!!Research Gallery \\

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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]]].
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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 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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* [[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]].
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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]].
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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]].
June 04, 2009, at 05:35 PM by 98.182.20.139 -
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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]].
June 04, 2009, at 05:34 PM by 98.182.20.139 -
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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]].
June 04, 2009, at 05:32 PM by 98.182.20.139 -
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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]].
June 04, 2009, at 05:31 PM by 98.182.20.139 -
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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 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]].
June 04, 2009, at 05:30 PM by 98.182.20.139 -
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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:
* [[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]].
June 04, 2009, at 05:25 PM by 98.182.20.139 -
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the solution of
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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about news and current activities of the applied mathematics group.
to:
concerning recent news or current activities of the applied mathematics group.
June 04, 2009, at 05:23 PM by 98.182.20.139 -
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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:
* [[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]].
June 04, 2009, at 05:23 PM by 98.182.20.139 -
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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:
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]].
June 04, 2009, at 05:23 PM by 98.182.20.139 -
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* [[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:
* [[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]].
June 04, 2009, at 05:19 PM by 98.182.20.139 -
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* [[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]].
June 04, 2009, at 05:19 PM by 98.182.20.139 -
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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]].
June 04, 2009, at 05:18 PM by 98.182.20.139 -
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* 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]].
June 04, 2009, at 05:17 PM by 98.182.20.139 -
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* 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:
* 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]].
June 04, 2009, at 05:17 PM by 98.182.20.139 -
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* 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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!! Local and Global Wellposedness of Nonlinear Evolutionary Equations

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!%color555555%Carlos Garcia-Cervera Wins NSF Faculty Early Career Development Award (NSF CAREER)
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!!%color555555%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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!!%blue%Research Areas (select subset of recent activities)
June 04, 2009, at 12:36 PM by 128.111.61.13 -
Changed line 68 from:
%width=400px% Attach:SIB_Schematic.png
to:
%width=300px% Attach:SIB_Schematic.png
June 04, 2009, at 12:36 PM by 128.111.61.13 -
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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
June 04, 2009, at 12:35 PM by 128.111.61.13 -
Changed lines 75-86 from:
* 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
]].
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]].
June 04, 2009, at 12:35 PM by 128.111.61.13 -
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!!%blue%Research Areas (Selected subset of activities)
to:
!!%blue%Research Areas (selected subset of activities)
June 04, 2009, at 12:34 PM by 128.111.61.13 -
Changed line 46 from:
!!%blue%Research Areas (Selected Subset of Activities)
to:
!!%blue%Research Areas (Selected subset of activities)
June 04, 2009, at 12:34 PM by 128.111.61.13 -
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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
June 04, 2009, at 12:34 PM by 128.111.61.13 -
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\\

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

%width=200px% Attach:carlosImage.png %width=200px% Attach:atzbergerImage.png
June 04, 2009, at 12:33 PM by 128.111.61.13 -
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%width=200px% Attach:carlosImage.png %width=200px% Attach:atzbergerImage.png %width=200px% Attach:carlosImage.png

(images / movies, here, etc...)
to:
%width=200px% Attach:carlosImage.png
%width=200px% Attach:atzbergerImage.png
June 04, 2009, at 12:32 PM by 128.111.61.13 -
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)

June 04, 2009, at 10:16 AM by 128.111.61.13 -
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
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
June 04, 2009, at 10:15 AM by 128.111.61.13 -
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)
Changed line 42 from:
!!Research Gallery \\
to:
!!%blue%Research Gallery \\
Changed line 49 from:
!!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
June 04, 2009, at 10:14 AM by 128.111.61.13 -
Changed lines 24-25 from:
!!Research Highlights \\
to:
!!%blue%Research Highlights \\
Changed line 29 from:
!!%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)
June 04, 2009, at 10:13 AM by 128.111.61.13 -
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%blue%
!!
Carlos Garcia-Cervera Wins NSF Faculty Early Career Development Award (NSF CAREER)
%black%
to:
!!%blue%Carlos Garcia-Cervera Wins NSF Faculty Early Career Development Award (NSF CAREER)
June 04, 2009, at 10:13 AM by 128.111.61.13 -
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%blue%
Added line 31:
%black%
June 04, 2009, at 10:12 AM by 128.111.61.13 -
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dynamics, boundary integral methods, immersed boundary methods),
to:
dynamics, boundary integral methods, immersed boundary methods,
June 04, 2009, at 10:11 AM by 128.111.61.13 -
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to:
%width=300px% Attach:southHallView1.jpg
June 04, 2009, at 10:10 AM by 128.111.61.13 -
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to:
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June 04, 2009, at 10:07 AM by 128.111.61.13 -
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%width=200px% Attach:southHallView1.jpg
South Hall
to:
%width=200px% Attach:southHallView2.jpg
June 04, 2009, at 10:07 AM by 128.111.61.13 -
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Department of Mathematics : South Hall [Image Credit:Statistics Homepage]
to:
South Hall
June 04, 2009, at 10:06 AM by 128.111.61.13 -
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to:
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June 04, 2009, at 10:05 AM by 128.111.61.13 -
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(Image from UCSB Statistics Homepage)
to:
Department of Mathematics : South Hall [Image Credit:Statistics Homepage]
June 04, 2009, at 10:05 AM by 128.111.61.13 -
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\\
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to:
(Image from UCSB Statistics Homepage)
June 04, 2009, at 10:03 AM by 128.111.61.13 -
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June 04, 2009, at 09:59 AM by 128.111.61.13 -
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June 04, 2009, at 09:58 AM by 128.111.61.13 -
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[[#ResearchHighlights]]
Deleted line 19:
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May 15, 2009, at 05:27 PM by 128.111.88.173 -
Deleted lines 35-41:
\\
\\
(Carlos: Please finish writing this synposis.)
\\
\\
\\
\\
May 15, 2009, at 05:27 PM by 128.111.88.173 -
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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 will
find research highlights, upcoming seminar talks, and information
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
May 15, 2009, at 05:26 PM by 128.111.88.173 -
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\\
May 15, 2009, at 05:26 PM by 128.111.88.173 -
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 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)
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.
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)

May 15, 2009, at 05:24 PM by 128.111.88.173 -
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.\\
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.\\
May 15, 2009, at 05:23 PM by 128.111.88.173 -
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.
May 15, 2009, at 05:22 PM by 128.111.88.173 -
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
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
May 15, 2009, at 05:20 PM by 128.111.88.173 -
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.\\
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.\\
May 14, 2009, at 10:28 PM by 98.182.20.139 -
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.
Added line 16:
test
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%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
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!! 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.]]
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.]]
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:
* 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 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]]
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]]
Deleted lines 51-52:
\\
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to:
\\
\\
\\
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\\
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\\
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!!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]].
April 27, 2009, at 03:14 PM by 128.111.88.151 -
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%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
April 27, 2009, at 03:14 PM by 128.111.88.151 -
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to:
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April 27, 2009, at 03:11 PM by 128.111.88.151 -
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...
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.
April 27, 2009, at 03:02 PM by 128.111.88.151 -
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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
April 27, 2009, at 03:00 PM by 128.111.88.151 -
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]].
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]].
Changed line 130 from:
----
to:
----
April 27, 2009, at 02:56 PM by 128.111.88.151 -
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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
April 27, 2009, at 02:48 PM by 128.111.88.68 -
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]]
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]]
April 27, 2009, at 02:46 PM by 128.111.88.68 -
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]]

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:
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.
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. 
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:
if this is required by university to avoid any formal objections being made
to how the pages are collectively managed
.
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'''Applied math. wiki-edit by-laws:'''\\
to:
'''Applied math. group wiki by-laws:'''\\
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'''Wiki-edit By-Laws'''\\
to:
'''Applied math. wiki-edit by-laws:'''\\
Added lines 105-106:
\\
'''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...)
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...)
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...)
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...)
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...)
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...)
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
...
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...)
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
...
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]]
.
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.]]
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.]]
Changed line 55 from:
!!Research Areas (Select Subset)
to:
!!Research Areas (Selected)
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!!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
Added lines 54-55:
----
!!Highlighted Research Areas
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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
)
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
)
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.
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
...
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:
Mention Dr. Garcia-Cervera's group and Dr. Cinceros's group...
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.
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:
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. 

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):\\
Changed lines 22-23 from:
to:
----
Added line 26:
----
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
to:
%width=200px% Attach:carlosImage.png %width=200px% Attach:atzbergerImage.png %width=200px% Attach:carlosImage.png
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
to:
%width=200px% Attach:carlosImage.png
%width=200px% Attach:atzbergerImage.png
%width=200px% Attach:carlosImage.png
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!!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

----
Changed lines 71-72 from:
!! Analysis of XYZ...
to:
!! Analysis of XYZ... Non-linear Elasticity.... Schrodinger Equ... (please edit)
Changed lines 74-76 from:
Mention Dr. Sideris's work and Dr. Ponce's work...

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].
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].
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.
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. 
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.   
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.  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. 
Changed lines 41-45 from:
!!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. 
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. 
Changed lines 47-54 from:
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]].

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.]]
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...

Changed lines 55-56 from:
!! Implicit Immersed Boundary Methods...
to:
!! Liquid Crystals / Lipid Bilayer Membranes / Complex Polymer Fluids
Changed lines 58-60 from:
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...
Changed lines 61-62 from:
!! Liquid Crystals and XYZ
to:
!! Analysis of XYZ...
Changed lines 64-70 from:
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...
Changed lines 44-46 from:
Dr. Atzberger's group works on Stochastic Immersed Boundary Methods (SIB) which
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.
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:
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]].
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]].
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...

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. 
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. 
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]].
Changed line 45 from:
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.
Changed line 45 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.
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.
Changed line 41 from:
!!Stochastic Immersed Boundary Methods for Computational Fluid-Structure Dynamics:
to:
!!Stochastic Immersed Boundary Methods for Fluid-Structure Dynamics:
Changed line 41 from:
!!Stochastic Immersed Boundary Methods for Computational Fluid Dynamics:
to:
!!Stochastic Immersed Boundary Methods for Computational Fluid-Structure Dynamics:
Changed lines 41-43 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 | '+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:
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.

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 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:
'+Dr. Paul J. Atzberger+'


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:
%width=400px% Attach:SIB_Schematic.png
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.
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.]]
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
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
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
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"
to:
core members).  To avoid abuse by any one group member.
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
.
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.
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,
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",
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",
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
.
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...].
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
...].
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...]
.
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.).
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.
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.
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
to:
development of core areas of mathematics with the solution of
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
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
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
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
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
).
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.
).
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
.
Changed lines 27-35 from:
!!Other highlights here...(images / movies, etc...) \\
\\

%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

----
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!!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:
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.]]
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.]]
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:

(
Dr. Paul J. Atzberger)
to:
Dr. Paul J. Atzberger:
\\
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!!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
to:
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to:
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Attach:hectorImage.png
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to:
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\\
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to:
\\
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to:
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\\
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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".
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".
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:
%width=100px% Attach:carlosImage.png
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(Attach):carlosImage.png

(Attach):hectorImage.png

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----
(these will be removed)

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!!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 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:

Changed lines 50-51 from:
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]],
Changed lines 1-2 from:
!!! Welcome
to:
!! Welcome
Changed lines 9-10 from:
!!!Research Highlights \\
to:
!!Research Highlights \\
Changed lines 31-32 from:
!!!How to use and edit wiki-pages.
to:
!!How to use and edit wiki-pages.
Changed line 58 from:
!!! Wiki Action Items [Please Perform Soon so We Can Launch]
to:
!! Wiki Action Items [Please Perform Soon so We Can Launch]
Changed lines 1-2 from:
!! 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...) \\

Changed lines 31-32 from:
!!How to use and edit wiki-pages.
to:
!!!How to use and edit wiki-pages.
Changed line 58 from:
!! 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:
Highlights here...(images / movies, etc...) \\
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...) \\

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.
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.
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:
'+How to use and edit wiki-pages.+'\\
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.

\\
April 23, 2009, at 08:31 PM by 98.182.20.139 -
April 23, 2009, at 08:30 PM by 98.182.20.139 -
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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----
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'+Research Highlights+'\\
to:
!!Research Highlights \\
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!! Welcome
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!! Wiki Action Item (Group Members Please Perform)
to:
!! Wiki Action Items [Please Perform]
Changed lines 12-13 from:
to:
(these will be removed)
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* Please enter any comments or suggestions concerning
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.
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).
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>
to:
'+Research Highlights+'\\

Highlights
here...(images / movies, etc...) \\
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<a href="test"> test </a>
Deleted lines 0-1:
!! Applied Mathematics Research at UCSB
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!! 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...
\\
Changed lines 7-34 from:
''''''+Dynamics of a Stochastically Driven Neuronal Network Model.+'''''' \\
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...) \\
Deleted lines 25-26:

----
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. 
----

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\\
Deleted line 0:
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\\
to:
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----
to:
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\\
Added line 5:
Tuesday, February 17th, 4:00pm - 5:00pm, SH 4607. \\
Deleted line 6:
Tuesday, February 17th, 4:00pm - 5:00pm, SH 4607. \\
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'''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:
'+Peter R. Kramer, Dept. Mathematical Sciences, Rensselaer Polytechnic Institute.+'\\
to:
Peter R. Kramer, Dept. Mathematical Sciences, Rensselaer Polytechnic Institute.\\
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''''+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.+'''' \\
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+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 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. \\
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...\\
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.
Added lines 24-25:
\\
Deleted lines 2-4:

/* http://pmichaud.com/img/misc/gem.jpg  */

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http://pmichaud.com/img/misc/gem.jpg
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)''. \\
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to:
\\
'''Title:''' Talking about something. \\
Deleted line 12:
'''Title:''' Talking about something. \\
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''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:
* ''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 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...
\\
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).


to:
* ''Some Speaker, (University of Somewhere), Tuesday, April XX, 3:00pm - 4:00pm (South Hall 7777)''.
'''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:
Research project will be discussed here...
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).

April 08, 2009, at 11:25 AM by 128.111.88.51 -
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
April 08, 2009, at 11:25 AM by 128.111.88.51 -
Changed lines 2-3 from:
!! Research Project I
to:
!! Research Project I http://pmichaud.com/img/misc/gem.jpg
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http://pmichaud.com/img/misc/gem.jpg
to:
April 08, 2009, at 11:24 AM by 128.111.88.51 -
Changed line 6 from:
%http://pmichaud.com/img/misc/gem.jpg
to:
http://pmichaud.com/img/misc/gem.jpg
April 08, 2009, at 11:23 AM by 128.111.88.51 -
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%lfloat%http://pmichaud.com/img/misc/gem.jpg
to:
%http://pmichaud.com/img/misc/gem.jpg
April 08, 2009, at 11:23 AM by 128.111.88.51 -
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April 08, 2009, at 11:23 AM by 128.111.88.51 -
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to:
\\
April 08, 2009, at 11:23 AM by 128.111.88.51 -
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%lfloat %http://pmichaud.com/img/misc/gem.jpg
to:
%lfloat%http://pmichaud.com/img/misc/gem.jpg
April 08, 2009, at 11:22 AM by 128.111.88.51 -
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April 08, 2009, at 11:22 AM by 128.111.88.51 -
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%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
April 08, 2009, at 11:22 AM by 128.111.88.51 -
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----

%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.'''
to:
%lfloat text-align=left margin-top=0px margin-right=0px margin-bottom=10px margin-left=0px %http://pmichaud.com/img/misc/gem.jpg
April 08, 2009, at 11:22 AM by 128.111.88.51 -
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----
April 08, 2009, at 11:21 AM by 128.111.88.51 -
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%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.'''

March 04, 2008, at 10:17 PM by 169.231.32.102 -
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----
March 04, 2008, at 10:17 PM by 169.231.32.102 -
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-
to:
----
March 04, 2008, at 10:17 PM by 169.231.32.102 -
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First research project will be discussed here...
to:
Research project will be discussed here...
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First research project will be discussed here...
to:
Research project will be discussed here...
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First research project will be discussed here...
to:
Research project will be discussed here...
March 04, 2008, at 10:16 PM by 169.231.32.102 -
Changed lines 5-6 from:
to:
Image and some links
Changed lines 9-12 from:
http://pmichaud.com/img/misc/pc.jpg"Image Description"

[[(http://www.math.ucsb.edu/~atzberg/movies4IGERT/trefoilKnot.avi | Trefoil knot ]]

to:
!! Research Project II

First research project will be discussed here...
Image and some links

Changed lines 15-75 from:
http://pmichaud.com/img/misc/pc.jpg"Paper clips" | '''Figure 1'''

----

%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.'''


Welcome to PmWiki!

A local copy of PmWiki's
documentation has been installed along with the software,
and is available via the [[PmWiki/documentation index]]. 

To continue setting up PmWiki, see [[PmWiki/initial setup tasks]].

The [[PmWiki/basic editing]] page describes how to create pages
in PmWiki.  You can practice editing in the [[wiki sandbox]].

More information about PmWiki is available from http://www.pmwiki.org .



----
This is my first test.

pretty cool.

[[WikiStyles]] allow %red% text
%blue% to %green% be in
%color=#ff7f00% different %%colors

!! Major Subheading
!! [-Major Subheading With Smaller

----

http://pmichaud.com/img/misc/pc.jpg"Paper clips" |
[- %newwin% [[
(Wikipedia:Paper_clips | Paper clips ]] are ''fun'' to work with. -]
Text-]
!!! Minor Subheading
!!!! And More
!!!!! Subheadings

||border=1 width=50%
||!Table||!Heading||!Example||
||!Left  || Center || Right||
||A      ||!  a B  ||    C||
||        || single ||      ||
||        || multi span  ||||



%lfloat text-align=center margin-top=5px margin-right=25px
margin-bottom=5px margin-left=25px
% http://pmichaud.com/img/misc/gem.jpg |
'''Rock on!'''
'''The image is left-aligned, with margins set;
the caption is centered;
the text wraps on the right side of the image.'''

to:

!! Research Project III

First research project will be discussed here...
Image and some links

-
March 04, 2008, at 09:57 PM by 169.231.32.102 -
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!! Major Subheading
to:
!! Research Project I
March 04, 2008, at 09:57 PM by 169.231.32.102 -
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!! Major Subheading
March 04, 2008, at 06:12 PM by 128.111.88.51 -
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%lfloat text-align=left margin-top=0px margin-right=0px margin-bottom=0px 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.'''
to:
%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.'''
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%lfloat text-align=left margin-top=0px margin-right=0px margin-bottom=5px margin-left=25px %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.'''
to:
%lfloat text-align=left margin-top=0px margin-right=0px margin-bottom=0px 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.'''
March 04, 2008, at 06:12 PM by 128.111.88.51 -
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%lfloat text-align=left margin-top=2px margin-right=5px margin-bottom=5px margin-left=25px %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.'''
to:
%lfloat text-align=left margin-top=0px margin-right=0px margin-bottom=5px margin-left=25px %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.'''
March 04, 2008, at 06:12 PM by 128.111.88.51 -
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%lfloat text-align=center margin-top=2px margin-right=5px margin-bottom=5px margin-left=25px %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.'''
to:
%lfloat text-align=left margin-top=2px margin-right=5px margin-bottom=5px margin-left=25px %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.'''
March 04, 2008, at 06:12 PM by 128.111.88.51 -
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%lfloat text-align=center margin-top=2px margin-right=5px margin-bottom=5px margin-left=25px %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.
to:
%lfloat text-align=center margin-top=2px margin-right=5px margin-bottom=5px margin-left=25px %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.'''
March 04, 2008, at 06:11 PM by 128.111.88.51 -
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%lfloat text-align=center margin-top=2px margin-right=5px margin-bottom=5px margin-left=25px %http://pmichaud.com/img/misc/gem.jpg '''Look!''' '''The image is left-aligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''
to:
%lfloat text-align=center margin-top=2px margin-right=5px margin-bottom=5px margin-left=25px %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.
March 04, 2008, at 06:11 PM by 128.111.88.51 -
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%lfloat text-align=left margin-top=2px margin-right=5px margin-bottom=5px margin-left=25px %http://pmichaud.com/img/misc/gem.jpg '''Look!''' '''The image is left-aligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''
to:
%lfloat text-align=center margin-top=2px margin-right=5px margin-bottom=5px margin-left=25px %http://pmichaud.com/img/misc/gem.jpg '''Look!''' '''The image is left-aligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''
March 04, 2008, at 06:11 PM by 128.111.88.51 -
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%lfloat text-align=left margin-top=2px margin-right=5px margin-bottom=5px margin-left=25px %http://pmichaud.com/img/misc/gem.jpg '''Rock on!''' '''The image is left-aligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''
to:
%lfloat text-align=left margin-top=2px margin-right=5px margin-bottom=5px margin-left=25px %http://pmichaud.com/img/misc/gem.jpg '''Look!''' '''The image is left-aligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''
March 04, 2008, at 06:11 PM by 128.111.88.51 -
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%lfloat text-align=left margin-top=0px margin-right=25px margin-bottom=5px margin-left=25px %http://pmichaud.com/img/misc/gem.jpg '''Rock on!''' '''The image is left-aligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''
to:
%lfloat text-align=left margin-top=2px margin-right=5px margin-bottom=5px margin-left=25px %http://pmichaud.com/img/misc/gem.jpg '''Rock on!''' '''The image is left-aligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''
March 04, 2008, at 06:10 PM by 128.111.88.51 -
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%lfloat text-align=left margin-top=2px margin-right=25px margin-bottom=5px margin-left=25px %http://pmichaud.com/img/misc/gem.jpg '''Rock on!''' '''The image is left-aligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''
to:
%lfloat text-align=left margin-top=0px margin-right=25px margin-bottom=5px margin-left=25px %http://pmichaud.com/img/misc/gem.jpg '''Rock on!''' '''The image is left-aligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''
March 04, 2008, at 06:10 PM by 128.111.88.51 -
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%lfloat text-align=left margin-top=2px margin-right=25px margin-bottom=5px margin-left=25px %http://pmichaud.com/img/misc/gem.jpg '''Rock on!''' '''The image is left-aligned, with margins set; the caption is centered; the text wraps on the right side of the image.
to:
%lfloat text-align=left margin-top=2px margin-right=25px margin-bottom=5px margin-left=25px %http://pmichaud.com/img/misc/gem.jpg '''Rock on!''' '''The image is left-aligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''
March 04, 2008, at 06:10 PM by 128.111.88.51 -
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----
March 04, 2008, at 06:10 PM by 128.111.88.51 -
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%lfloat text-align=left margin-top=2px margin-right=25px margin-bottom=5px margin-left=25px %http://pmichaud.com/img/misc/gem.jpg '''Rock on!''' '''The image is left-aligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''
to:
%lfloat text-align=left margin-top=2px margin-right=25px margin-bottom=5px margin-left=25px %http://pmichaud.com/img/misc/gem.jpg '''Rock on!''' '''The image is left-aligned, with margins set; the caption is centered; the text wraps on the right side of the image.

March 04, 2008, at 06:09 PM by 128.111.88.51 -
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%lfloat text-align=left margin-top=2px margin-right=25px margin-bottom=5px margin-left=25px %http://pmichaud.com/img/misc/gem.jpg | '''Rock on!''' '''The image is left-aligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''
to:
%lfloat text-align=left margin-top=2px margin-right=25px margin-bottom=5px margin-left=25px %http://pmichaud.com/img/misc/gem.jpg '''Rock on!''' '''The image is left-aligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''
March 04, 2008, at 06:09 PM by 128.111.88.51 -
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%lfloat text-align=right margin-top=5px margin-right=25px margin-bottom=5px margin-left=25px %http://pmichaud.com/img/misc/gem.jpg | '''Rock on!''' '''The image is left-aligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''
to:
%lfloat text-align=left margin-top=2px margin-right=25px margin-bottom=5px margin-left=25px %http://pmichaud.com/img/misc/gem.jpg | '''Rock on!''' '''The image is left-aligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''
March 04, 2008, at 06:09 PM by 128.111.88.51 -
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%lfloat text-align=left margin-top=5px margin-right=25px margin-bottom=5px margin-left=25px %http://pmichaud.com/img/misc/gem.jpg | '''Rock on!''' '''The image is left-aligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''
to:
%lfloat text-align=right margin-top=5px margin-right=25px margin-bottom=5px margin-left=25px %http://pmichaud.com/img/misc/gem.jpg | '''Rock on!''' '''The image is left-aligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''
March 04, 2008, at 06:09 PM by 128.111.88.51 -
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%lfloat text-align=center margin-top=5px margin-right=25px margin-bottom=5px margin-left=25px %http://pmichaud.com/img/misc/gem.jpg | '''Rock on!''' '''The image is left-aligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''
to:
%lfloat text-align=left margin-top=5px margin-right=25px margin-bottom=5px margin-left=25px %http://pmichaud.com/img/misc/gem.jpg | '''Rock on!''' '''The image is left-aligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''
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%lfloat text-align=center margin-top=5px margin-right=25px margin-bottom=5px margin-left=25px
%http://pmichaud.com/img/misc/gem.jpg |'''Rock on!''' '''The image is left-aligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''
to:
%lfloat text-align=center margin-top=5px margin-right=25px margin-bottom=5px margin-left=25px %http://pmichaud.com/img/misc/gem.jpg | '''Rock on!''' '''The image is left-aligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''
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%lfloat text-align=center margin-top=5px margin-right=25pxmargin-bottom=5px margin-left=25px%http://pmichaud.com/img/misc/gem.jpg |'''Rock on!''' '''The image is left-aligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''
to:
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%lfloat text
-align=center margin-top=5px margin-right=25pxmargin-bottom=5px margin-left=25px
%http://pmichaud.com/img/misc/gem.jpg |'''Rock on!''' '''The image is left-aligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''
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%lfloat text-align=center margin-top=5px margin-right=25pxmargin-bottom=5px margin-left=25px%http://pmichaud.com/img/misc/gem.jpg |'''Rock on!''' '''The image is left-aligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''
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"Image Description"
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http://pmichaud.com/img/misc/pc.jpg"Image Description"
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http://pmichaud.com/img/misc/pc.jpg
"Paper clips" | '''Figure 1'''
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http://pmichaud.com/img/misc/pc.jpg"Paper clips" | '''Figure 1'''
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http://pmichaud.com/img/misc/pc.jpg"
Paper clips" | '''Figure 1'''
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"Paper clips" | '''Figure 1'''
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http://pmichaud.com/img/misc/pc.jpg"
Paper clips" | '''Figure 1'''
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% http://pmichaud.com/img/misc/gem.jpg |
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'''The image is left-aligned, with margins set; the caption is centered;
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'''The image is left-aligned, with margins set;
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[[(http://www.math.ucsb.edu/~atzberg/index.html | trefoilKnot.avi ]]
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[[(http://www.math.ucsb.edu/~atzberg/movies4IGERT/trefoilKnot.avi | Trefoil knot ]]
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[[(http://www.math.ucsb.edu/~atzberg/index.html | Clips ]]
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[[(http://www.math.ucsb.edu/~atzberg/index.html | Clips ]]
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[[(Wikipedia:Paper_clips | Clips ]]
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[[(Wikipedia:Paper_clips | Paper clips ]]
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http://pmichaud.com/img/misc/pc.jpg"Paper clips"

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http://pmichaud.com/img/misc/pc.jpg"Paper clips" | [- %newwin% [[
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[- %newwin% [[
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First research project will be discussed here...

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First research project to discuss here...
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First research project to discuss here...

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March 04, 2008, at 05:16 PM by 128.111.88.51 -
March 04, 2008, at 04:47 PM by 128.111.88.51 -
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$Skin = 'xyz';
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$Skin = 'xyz';
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%lfloat text-align=center margin-top=5px margin-right=25px
margin-bottom=5px margin-left=25px% http://pmichaud.com/img/misc/gem.jpg |
'''Rock on!'''
'''The image is left-aligned, with margins set; the caption is centered;
the text wraps on the right side of the image.'''
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http://pmichaud.com/img/misc/pc.jpg"Paper clips" | [- %newwin% [[
(Wikipedia:Paper_clips | Paper clips ]] are ''fun'' to work with. -]
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[[WikiStyles]] allow %red% text
%blue% to %green% be in
%color=#ff7f00% different %%colors

!! Major Subheading
!! [-Major Subheading With Smaller
Text-]
!!! Minor Subheading
!!!! And More
!!!!! Subheadings

||border=1 width=50%
||!Table||!Heading||!Example||
||!Left  || Center || Right||
||A      ||!  a B  ||    C||
||        || single ||      ||
||        || multi span  ||||
March 04, 2008, at 04:38 PM by 128.111.88.51 -
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pretty cool.


March 04, 2008, at 04:38 PM by 128.111.88.51 -
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This is my first test.