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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 FluidStructure 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/20082009/W11.37.08/abstracts.html#AtzbergerPaul  [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 FluidStructure Dynamics at Microscopic Length Scales]] and [[http://dx.doi.org/10.1016/j.jcp.2010.12.028  Stochastic EulerianLangrain Methods for FluidStructure Interactions subject to Thermal Fluctuations.]].
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'+%color555555%Kozato Postdoctoral Fellowship in Quantitative Biology+'
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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]]\\
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[[http
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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 multiyear support comparable to the NSF Graduate Fellowship. The position is to begin in the Fall of 2011. The fellowship will support a student who has an interest in working on an interdisciplinary thesis project investigating a biological system using a combination of mathematical analysis and computational methods. It is envisioned the supported graduate student would have a primary adviser in mathematics, but would also interact closely with theoreticians and experimental biologists on campus at UCSB. The fellowship is funded by a generous donation from Hiro Kozato, a distinguished alumnus of the Department of Mathematics.
For those students interested in mathematics and biology, please see the following page for more information:
For those students interested in mathematics and biology, please see the following page for
to:
The University of California, Santa Barbara invites applications for the Kozato Postdoctoral Fellowship in Quantitative Biology. The fellowship will support research at the interface of the biological sciences with mathematics, computation, physics, or engineering. The postdoctoral appointment will be within the Department of Mathematics starting in September 2011, and is renewable for up to three years. UCSB offers a strong interdisciplinary environment for research with many opportunities for close interaction with both theoreticians and experimentalists on campus.
For more information:
For more information:
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'+%color555555%Kozato Graduate Fellowship in Quantitative Biology+'
%lfloat textalign=left margintop=5px marginright=5px marginbottom=10px marginleft=5px width=100px% Attach:UCSB_seal1.jpg
The Kozato Fellowship in Quantitative Biology will offer competitive multiyear 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 textalign=left margintop=5px marginright=5px marginbottom=10px marginleft=5px width=100px% Attach:UCSB_seal1.jpg
The Kozato Fellowship in Quantitative Biology will offer competitive multiyear 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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%lfloat textalign=left margintop=5px marginright=5px marginbottom=10px margin
The Kozato Fellowship in Quantitative Biology will offer competitive multiyear support comparable to the NSF Graduate Fellowship. The position is to begin in the Fall of 2011
For those students interested in mathematics and biology, please see the following page for more information:
to:
'+%color555555%Carlos GarciaCervera Wins NSF Faculty Early Career Development Award (NSF CAREER)+'
%lfloat textalign=left margintop=5px marginright=5px marginbottom=10px marginleft=5px width=100px% Attach:carlosSmiles.jpg
Professor Carlos GarciaCervera 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 teacherscholars who are most likely to become the academic leaders of the 21st century.
The awards are for a minimum of $400,000 and support his research for five years providing funding
for postdoctoral researchers and graduate students. The proposed research program has the potential
to impact fundamental computational approaches used in studying solid materials. This is the first
NSF CAREER award given to a faculty member of the department of mathematics.\\
[[http://www.ia.ucsb.edu/93106/2007/November19/math.html  Full Article]]
%lfloat textalign=left margintop=5px marginright=5px marginbottom=10px marginleft=5px width=100px% Attach:carlosSmiles.jpg
Professor Carlos GarciaCervera 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 teacherscholars 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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More information about Professor GarciaCervera'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 textalign=left margintop=5px marginright=5px marginbottom=10px marginleft=5px width=100px% Attach:UCSB_seal1.jpg
The Kozato Fellowship in Quantitative Biology will offer competitive multiyear support comparable to the NSF Graduate Fellowship. The position is to begin in the Fall of 2011. The fellowship will support a student who has an interest in working on an interdisciplinary thesis project investigating a biological system using a combination of mathematical analysis and computational methods. It is envisioned the supported graduate student would have a primary adviser in mathematics, but would also interact closely with theoreticians and experimental biologists on campus at UCSB. The fellowship is funded by a generous donation from Hiro Kozato, a distinguished alumnus of the Department of Mathematics.
For those students interested in mathematics and biology, please see the following page for more information:
\\
[[http://www.math.ucsb.edu/~atzberg/Kozato Fellowship/  Kozato Fellowship in Quantitative Biology]]\\
\\

%lfloat textalign=left margintop=5px marginright=5px marginbottom=10px marginleft=5px width=100px% Attach:UCSB_seal1.jpg
The Kozato Fellowship in Quantitative Biology will offer competitive multiyear 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 GarciaCervera Wins NSF Faculty Early Career Development Award (NSF CAREER)+'
%lfloat textalign=left margintop=5px marginright=5px marginbottom=10px marginleft=5px width=100px% Attach:carlosSmiles.jpg
Professor Carlos GarciaCervera 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 teacherscholars 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 GarciaCervera'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+'
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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.\\
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 multiyear 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] ]] \\
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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] ]] \\
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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] ]] \\
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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] ]] \\
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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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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 Atzberger's research be found on his [[http://www.math.ucsb.edu/~atzberg/index.html  website]]. \\
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More information about Professor GarciaCervera's research be found on his [[http://www.math.ucsb.edu/~cgarcia/index.html  homepage]]. \\
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More information about Professor GarciaCervera'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]]. \\
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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 GarciaCervera'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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More information about Professor GarciaCervera'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 GarciaCervera's research be found at [[http://www.math.ucsb.edu/~cgarcia/index.html  http://www.math.ucsb.edu/~cgarcia/index.html]]. \\
\\
More information about Professor GarciaCervera'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 textalign=left margintop=5px marginright=5px marginbottom=10px marginleft=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.\\
\\

%lfloat textalign=left margintop=5px marginright=5px marginbottom=10px marginleft=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 GarciaCervera receives the prestigious NSF Career Award for his proposal "Multilevel Physics in the Study of Solids: Modeling, Analysis and Simulations".
to:
Professor Carlos GarciaCervera receives the prestigious NSF Career Award for his proposal "Multilevel Physics in the Study of Solids: Modeling, Analysis and Simulations".
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!! Apply for Graduate Studies in Applied Mathematics at UCSB [[http://www.math.ucsb.edu/~applmath/pmwiki/pmwiki.php?n=Main.prospectiveGraduateStudents  [more info. here] ]] \\
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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] ]] \\
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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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!! Apply for Graduate Studies in Applied Mathematics at UCSB [[http://www.math.ucsb.edu/~applmath/pmwiki/pmwiki.php?n=Main.prospectiveGraduateStudents  [more info. here] ]] \\
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!! Apply to the UCSB Applied Mathematics Program [[http://www.math.ucsb.edu/~applmath/pmwiki/pmwiki.php?n=Main.prospectiveGraduateStudents  [more info. here] ]] \\
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and careers involving mathematics. From the Applied Math Group, [[http://www.math.ucsb.edu/~mbueno/index.html  Maribel Bueno Cachadina]] is playing a leading role in organizing the UCSB Math Circle. For more information see the Math Circle Website:\\
to:
and careers involving mathematics. From the Applied Mathematics Group, [[http://www.math.ucsb.edu/~mbueno/index.html  Maribel Bueno Cachadina]] is playing a leading role in organizing the UCSB Math Circle. For more information see the Math Circle Website:\\
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* complex fluids and softcondensed matter
* crystalline solids and liquid crystals
* density functional theory
* analysisof nonlinear evolutionary PDE's (existence results / finite time singularities)
* applied harmonic analysis
* stochastic analysis.
* crystalline solids
* analysis
to:
* Complex Fluids and SoftCondensed Matter Physics.
* Crystalline Solids and Liquid Crystals.
* Density Functional Theory.
* Analysis of Nonlinear Evolutionary PDE's (existence results / finite time singularities).
* Applied Harmonic Analysis.
* Stochastic Analysis.
* Crystalline Solids and Liquid Crystals.
* Density Functional Theory.
* Analysis of Nonlinear Evolutionary PDE's (existence results / finite time singularities).
* Applied Harmonic Analysis.
* Stochastic Analysis.
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and participate in collaborations with a diverse collection of faculty on campus.
Researchareas include: complex fluids, softcondensed matter, crystalline solids and
liquid crystals, density functional theory, analysis of nonlinear
evolutionary PDE's (existence results / finite time singularities),
applied harmonic analysis, and stochastic analysis.
Research
liquid crystals
evolutionary PDE's (existence results / finite time singularities)
applied harmonic analysis
to:
and participate in collaborations with many faculty on campus. Research areas include:
* complex fluids and softcondensed matter
* crystalline solids and liquid crystals
* density functional theory
* analysis of nonlinear evolutionary PDE's (existence results / finite time singularities)
* applied harmonic analysis
* stochastic analysis.
* complex fluids and softcondensed matter
* crystalline solids and liquid crystals
* density functional theory
* analysis of nonlinear 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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students from local high schools. The Math Circle offers a forum in which the discuss mathematical topics, mathematics education,
to:
students from local high schools. The UCSB Math Circle offers a forum for the discussion of mathematical topics, mathematics education,
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[[http://www.math.ucsb.edu/~mbueno/mathcircle/index.html  UCSB Math Circle Website]].
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[[http://www.math.ucsb.edu/~mbueno/mathcircle/index.html  UCSB Math Circle Website]].\\
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'+%color555555%Math Circle Started at UCSB+'
%lfloat textalign=left margintop=5px marginright=5px marginbottom=10px marginleft=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 precollege
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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%lfloat textalign=left margintop=5px marginright=5px marginbottom=10px marginleft=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 precollege
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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and careers involving mathematics. From the Applied Math Group, Maribel Bueno Cachadina is playing a leading role in
organizing the UCSB Math Circle. For more information see the Math Circle website:\\
[[  UCSB Math Circle Website]].
organizing the UCSB Math
[[
to:
and careers involving mathematics. From the Applied Math Group, [[http://www.math.ucsb.edu/~mbueno/index.html  Maribel Bueno Cachadina]] is playing a leading role in organizing the UCSB Math Circle. For more information see the Math Circle website:\\
[[http://www.math.ucsb.edu/~mbueno/mathcircle/index.html  UCSB Math Circle Website]].
[[http://www.math.ucsb.edu/~mbueno/mathcircle/index.html  UCSB Math Circle Website]].
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and careers involving mathematics. Maribel ... from the Applied Mathematics Group is play a leading role in organizing the UCSB Math Circle.
For more information see the Math Circle website:\\
[[  UCSB Math Circle Website]]
For more information see the Math Circle
[[  UCSB Math Circle Website]]
to:
and careers involving mathematics. From the Applied Math Group, Maribel Bueno Cachadina is playing a leading role in
organizing the UCSB Math Circle. For more information see the Math Circle website:\\
[[  UCSB Math Circle Website]].
organizing the UCSB Math Circle. For more information see the Math Circle website:\\
[[  UCSB Math Circle Website]].
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'+%color555555%UCSB Math Circle+'
%lfloat textalign=left margintop=5px marginright=5px marginbottom=10px marginleft=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 precollege
students from local high schools. The Math Circle offers a forum in which the discuss mathematical topics, mathematics education,
and careers involving mathematics. Maribel ... from the Applied Mathematics Group is play a leading role in organizing the UCSB Math Circle.
For more information see the Math Circle website:\\
[[  UCSB Math Circle Website]]
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and participate in collaborations with many departments on campus.
to:
and participate in collaborations with a diverse collection of faculty on campus.
September 07, 2009, at 03:47 PM
by  minor change
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Applied mathematics strives to integrate the development of core areas of mathematics with
to:
Applied mathematics integrates the development of core areas of mathematics with
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Applied mathematics refers to the branch of mathematics which strives
to integrate the development of core areas of mathematics with
to integrate the development of core areas of mathematics with
to:
Applied mathematics strives to integrate the development of core areas of mathematics with
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and participate in many collaborations with other departments on campus.
to:
and participate in collaborations with many departments on campus.
August 27, 2009, at 09:41 PM
by  restored the page...test....
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Another basic test of notifications....
August 27, 2009, at 09:41 PM
by  Please help review any suspicious changes by looking at author and clicking on links below....
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Another basic test of notifications....
Another basic test of notifications....
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Test of the notification system to make sure it works. Will send email summarizing changes made for the day, if any.
Test of the notification system to make sure it works. Will send email summarizing changes made for the day, if any.
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August 26, 2009, at 08:58 PM
by  Here is a summary of the changes made. This will send email summarizing changes made for the day...
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Test of the notification system to make sure it works. Will send email summarizing changes made for the day, if any.
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and participate in many collaborations with faculty from other departments on campus.
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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, softcondensed matter, crystalline solids and
including:
to:
or engineering. Faculty of the Applied Mathematics Group are active in diverse areas
and participate in many collaborations with faculty from other departments on campus.
Research areas include: complex fluids, softcondensed matter, crystalline solids and
and participate in many collaborations with faculty from other departments on campus.
Research areas include: complex fluids, softcondensed matter, crystalline solids and
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applied harmonic analysis, and stochastic analysis. Here you will find
information about our program in Applied Mathematics, current activities,
information about our program in Applied Mathematics, current activities,
to:
applied harmonic analysis, and stochastic analysis.
Here you will find information about our program in Applied Mathematics, current activities,
Here you will find information about our program in Applied Mathematics, current activities,
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!!Research Highlights (select subset of recent activities)
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!!Research Highlights
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or engineering. Faculyt of the Applied Mathematics Group are active in many areas
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or engineering. Faculty of the Applied Mathematics Group are active in many areas
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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 / softcondensed matter, computational fluid
dynamics, boundary integral methods, immersed boundary methods,
crystalline solids and liquid crystals, density functional theory,
analysis of nonlinear evolutionary PDE's, study of existence or
development of singularities in finite time, applied harmonic
analysis, and stochastic differential equations. Here you will
find researchhighlights, upcoming seminar talks, and information
concerning recent news or current activities of the applied mathematics group.
the study of
dynamics, boundary integral methods
crystalline solids and liquid crystals, density functional theory,
analysis of nonlinear evolutionary PDE's, study of existence or
analysis, and stochastic differential equations. Here you will
find research
concerning recent news or current activities of the applied mathematics group
to:
or engineering. Faculyt of the Applied Mathematics Group are active in many areas
including: complex fluids, softcondensed matter, crystalline solids and
liquid crystals, density functional theory, analysis of nonlinear
evolutionary PDE's (existence results / finite time singularities),
applied harmonic analysis, and stochastic analysis. Here you will find
information about our program in Applied Mathematics, current activities,
upcoming seminar talks, and highlights from recent research.
including: complex fluids, softcondensed matter, crystalline solids and
liquid crystals, density functional theory, analysis of nonlinear
evolutionary PDE's (existence results / finite time singularities),
applied harmonic analysis, and stochastic analysis. Here you will find
information about our program in Applied Mathematics, current activities,
upcoming seminar talks, and highlights from recent research.
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Provide conditions on initial data which ensure the existence, uniqueness, and continuous dependence of solutions to the initial value problem for nonlinear
evolutionary partial differential equations.
Determine whether solutions exist globally in time or develop singularities in finite time. Explore the regularity and asymptotic behavior of solutions.
Applications to nonlinear dispersive equations, hydro and elastodynamics.
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 elastodynamics.
Faculty members working in this area include:
* Dr. Sideris : [[http://www.math.ucsb.edu/~sideris/index.html  Research Website]].
* Dr. Ponce : [[http://www.math.ucsb.edu/~ponce/index.html  Research Website]].

!!Research Gallery \\
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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 FluidStructure 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/20082009/W11.37.08/abstracts.html#AtzbergerPaul  [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 FluidStructure 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/20082009/W11.37.08/abstracts.html#AtzbergerPaul  [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/index1.html Prof. Alexandre Roma]] (USP) has recently designed efficient implicit methods for the IBM formalisms significantly advancing the timescales 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, semiimplicit 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/index1.html Prof. Alexandre Roma]] (USP) has recently designed efficient implicit methods for the IBM formalisms significantly advancing the timescales 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, semiimplicit 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 FluidStructure 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/20082009/W11.37.08/abstracts.html#AtzbergerPaul  [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 FluidStructure 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/20082009/W11.37.08/abstracts.html#AtzbergerPaul  [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 FluidStructure 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/20082009/W11.37.08/abstracts.html#AtzbergerPaul  [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 FluidStructure 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/20082009/W11.37.08/abstracts.html#AtzbergerPaul  [Video of IMA Talk]]].
Changed lines 7172 from:
* [[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 FluidStructure 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/20082009/W11.37.08/abstracts.html#AtzbergerPaul  [Video of IMA Talk]]]. Additional papers can be found on his [[http://www.math.ucsb.edu/~atzberg/index.html  research website]].
[[http://www.math.ucsb.edu/~atzberg/publications/preprintStochIB.pdf  A Stochastic Immersed Boundary Method for FluidStructure 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/20082009/W11.37.08/abstracts.html#AtzbergerPaul  [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 FluidStructure 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/20082009/W11.37.08/abstracts.html#AtzbergerPaul  [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/20082009/W11.37.08/abstracts.html#AtzbergerPaul  [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 FluidStructure 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/20082009/W11.37.08/abstracts.html#AtzbergerPaul  [Video of IMA Talk]]]. Additional papers can be found on his [[http://www.math.ucsb.edu/~atzberg/index.html  research website]].
[[http://www.math.ucsb.edu/~atzberg/publications/preprintStochIB.pdf  A Stochastic Immersed Boundary Method for FluidStructure 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/20082009/W11.37.08/abstracts.html#AtzbergerPaul  [Video of IMA Talk]]]. Additional papers can be found on his [[http://www.math.ucsb.edu/~atzberg/index.html  research website]].
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* [[http://www.math.ucsb.edu/~atzberg/index.html  Dr. Atzberger]] : Prof. Atzberger has been working on utilizing immersed boundary methods to study properties of soft condensed matter. To account consistently for microstructure mechanics, hydrodynamic coupling, and thermal fluctuations he has extended the IBM formalism to incorporate stochastic driving fields consistent with statistical mechanics. Applications of the new methodology include the study of polymeric fluids, gels, and lipid bilayer membranes. The resulting stochastic partial differential equations (SPDEs) present many interesting challenges both for analysis and the development of numerical methods. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here [[http://www.ima.umn.edu/20082009/W11.37.08/abstracts.html#AtzbergerPaul  [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/20082009/W11.37.08/abstracts.html#AtzbergerPaul  [Video of IMA Talk]]]. Related papers can be found on his [[http://www.math.ucsb.edu/~atzberg/index.html  Research Website]].
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* [[http://www.math.ucsb.edu/~atzberg/index.html  Dr. Atzberger]] : Prof. Atzberger uses immersed boundary methods to study properties of soft condensed matter. To account consistently for microstructure mechanics, hydrodynamic coupling, and thermal fluctuations he has extended the immersed boundary method to incorporate stochastic driving fields consistent with statistical mechanics. The resulting stochastic partial differential equations (SPDEs) present many interesting challenges both for analysis and the development of numerical methods. His work is also concerned with applications of the methodology, in particular, to the study of polymeric fluids, gels, and lipid bilayer membranes. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here [[http://www.ima.umn.edu/20082009/W11.37.08/abstracts.html#AtzbergerPaul  [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/20082009/W11.37.08/abstracts.html#AtzbergerPaul  [Video of IMA Talk]]]. Related papers can be found on his [[http://www.math.ucsb.edu/~atzberg/index.html  Research Website]].
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* [[http://www.math.ucsb.edu/~atzberg/index.html  Dr. Atzberger]] : Prof. Atzberger is working on utilizing immersed boundary methods to study properties of soft condensed matter. To account consistently for microstructure mechanics, hydrodynamic coupling, and thermal fluctuations he has extended the immersed boundary method to incorporate stochastic driving fields consistent with statistical mechanics. The resulting stochastic partial differential equations (SPDEs) present many interesting challenges both for analysis and the development of numerical methods. His work is also concerned with applications of the methodology, in particular, to the study of polymeric fluids, gels, and lipid bilayer membranes. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here [[http://www.ima.umn.edu/20082009/W11.37.08/abstracts.html#AtzbergerPaul  [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/20082009/W11.37.08/abstracts.html#AtzbergerPaul  [Video of IMA Talk]]]. Related papers can be found on his [[http://www.math.ucsb.edu/~atzberg/index.html  Research Website]].
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* [[http://www.math.ucsb.edu/~atzberg/index.html  Dr. Atzberger]] : Prof. Atzberger is working on utilizing immersed boundary methods to study properties of soft condensed matter. To account consistently for microstructure mechanics, hydrodynamic coupling, and
thermal fluctuations he has extended the immersed boundary method to incorporate stochastic driving fields consistent with statistical mechanics. The resulting stochastic partial differential equations (SPDEs) present many interesting challenges both for analysis and the development of numerical methods. His work is also concerned with applications of the methodology, in particular, to the study of polymeric fluids, gels, and lipid bilayer membranes. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here [[http://www.ima.umn.edu/20082009/W11.37.08/abstracts.html#AtzbergerPaul  [Video of IMA Talk]]]. Related papers can be found on his [[http://www.math.ucsb.edu/~atzberg/index.html  Research Website]].
thermal fluctuations he has extended the immersed boundary method to incorporate stochastic driving fields consistent with statistical mechanics. The resulting stochastic partial differential equations (SPDEs) present many interesting challenges both for analysis and the development of numerical methods. His work is also concerned with applications of the methodology, in particular, to the study of polymeric fluids, gels, and lipid bilayer membranes. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here [[http://www.ima.umn.edu/20082009/W11.37.08/abstracts.html#AtzbergerPaul  [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/20082009/W11.37.08/abstracts.html#AtzbergerPaul  [Video of IMA Talk]]]. Related papers can be found on his [[http://www.math.ucsb.edu/~atzberg/index.html  Research Website]].
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* [[http://www.math.ucsb.edu/~atzberg/index.html  Dr. Atzberger]] : Prof. Atzberger is working on utilizing immersed boundary methods to study properties of soft matter materials, which contain hydrodynamically coupled microstructures subject to thermal fluctuations. To account for thermal fluctuations he has extended the immersed boundary method to incorporate stochastic driving fields which are consistent with statistical mechanics. The resulting formalism is cast in terms of a system of stochastic partial differential equations (SPDEs) which present interesting challenges both for analysis and the development of numerical methods. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here [[http://www.ima.umn.edu/20082009/W11.37.08/abstracts.html#AtzbergerPaul  [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/20082009/W11.37.08/abstracts.html#AtzbergerPaul  [Video of IMA Talk]]]. Related papers can be found on his [[http://www.math.ucsb.edu/~atzberg/index.html  Research Website]].
thermal fluctuations he has extended the immersed boundary method to incorporate stochastic driving fields consistent with statistical mechanics. The resulting stochastic partial differential equations (SPDEs) present many interesting challenges both for analysis and the development of numerical methods. His work is also concerned with applications of the methodology, in particular, to the study of polymeric fluids, gels, and lipid bilayer membranes. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here [[http://www.ima.umn.edu/20082009/W11.37.08/abstracts.html#AtzbergerPaul  [Video of IMA Talk]]]. Related papers can be found on his [[http://www.math.ucsb.edu/~atzberg/index.html  Research Website]].
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the solution of
specific problems arising in applications often in the basic sciences
specific problems arising in applications often in the basic sciences
to:
the solution of specific problems arising in applications, often in the basic sciences
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to:
concerning recent news or current activities of the applied mathematics group.
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* [[http://www.math.ucsb.edu/~atzberg/index.html  Dr. Atzberger]] : Prof. Atzberger is working on utilizing immersed boundary
methods to study properties of soft matter materials, which contain hydrodynamically coupled microstructures subject to thermal fluctuations. To account for thermal fluctuations he has extended the immersed boundary method to incorporate stochastic driving fields which are consistent with statistical mechanics. The resulting formalism is cast in terms of a system of stochastic partial differential equations (SPDEs) which present interesting challenges both for analysis and the development of numerical methods. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here [[http://www.ima.umn.edu/20082009/W11.37.08/abstracts.html#AtzbergerPaul  [Video of IMA Talk]]]. Related papers can be found on his [[http://www.math.ucsb.edu/~atzberg/index.html  Research Website]].
methods to study properties of soft matter materials, which contain hydrodynamically coupled microstructures subject to thermal fluctuations. To account for thermal fluctuations he has extended the immersed boundary method to incorporate stochastic driving fields which are consistent with statistical mechanics. The resulting formalism is cast in terms of a system of stochastic partial differential equations (SPDEs) which present interesting challenges both for analysis and the development of numerical methods. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here [[http://www.ima.umn.edu/20082009/W11.37.08/abstracts.html#AtzbergerPaul  [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/20082009/W11.37.08/abstracts.html#AtzbergerPaul  [Video of IMA Talk]]]. Related papers can be found on his [[http://www.math.ucsb.edu/~atzberg/index.html  Research Website]].
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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/20082009/W11.37.08/abstracts.html#AtzbergerPaul  [Video of IMA Talk]]]. Related papers can be found on his [[http://www.math.ucsb.edu/~atzberg/index.html  Research Website]].
stochastic driving fields which are consistent with statistical mechanics. The resulting formalism is cast in terms of a system of stochastic partial differential equations (SPDEs) which present interesting challenges both for analysis and the development of numerical methods. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here [[http://www.ima.umn.edu/20082009/W11.37.08/abstracts.html#AtzbergerPaul  [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/20082009/W11.37.08/abstracts.html#AtzbergerPaul  [Video of IMA Talk]]]. Related papers can be found on his [[http://www.math.ucsb.edu/~atzberg/index.html  Research Website]].
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* [[http://www.math.ucsb.edu/~atzberg/index.html  Dr. Atzberger]] : Prof. Atzberger 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/20082009/W11.37.08/abstracts.html#AtzbergerPaul  [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/20082009/W11.37.08/abstracts.html#AtzbergerPaul  [Video of IMA Talk]]]. Related papers can be found on his [[http://www.math.ucsb.edu/~atzberg/index.html  Research Website]].
methods to study properties of soft matter materials, which contain hydrodynamically coupled microstructures subject to thermal fluctuations. To account for thermal fluctuations he has extended the immersed boundary method to incorporate
stochastic driving fields which are consistent with statistical mechanics. The resulting formalism is cast in terms of a system of stochastic partial differential equations (SPDEs) which present interesting challenges both for analysis and the development of numerical methods. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here [[http://www.ima.umn.edu/20082009/W11.37.08/abstracts.html#AtzbergerPaul  [Video of IMA Talk]]]. Related papers can be found on his [[http://www.math.ucsb.edu/~atzberg/index.html  Research Website]].
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* [[http://www.math.ucsb.edu/~atzberg/index.html  Dr. Atzberger]] : Prof. Atzberger 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/20082009/W11.37.08/abstracts.html#AtzbergerPaul  [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/20082009/W11.37.08/abstracts.html#AtzbergerPaul  [Video of IMA Talk]]]. Related papers can be found on his [[http://www.math.ucsb.edu/~atzberg/index.html  Research Website]].
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* [[http://www.math.ucsb.edu/~hdc  Dr. Ceniceros]]) : Prof. Ceniceros in joint work with UCSB grad student Jordan Fisher and [[http://www.ime.usp.br/~roma/index1.html Prof. Alexandre Roma]] (USP) has recently designed efficient implicit methods for the IBM formalisms significantly advancing the timescales 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, semiimplicit 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/index1.html Prof. Alexandre Roma]] (USP) has recently designed efficient implicit methods for the IBM formalisms significantly advancing the timescales 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, semiimplicit discretizations of the Immersed Boundary Method]].
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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/20082009/W11.37.08/abstracts.html#AtzbergerPaul  [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/index1.html Prof. Alexandre Roma]] (USP) has recently designed efficient implicit methods for the IBM formalisms significantly advancing the timescales 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, semiimplicit 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/20082009/W11.37.08/abstracts.html#AtzbergerPaul  [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/index1.html Prof. Alexandre Roma]] (USP) has recently designed efficient implicit methods for the IBM formalisms significantly advancing the timescales 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, semiimplicit discretizations of the Immersed Boundary Method]].
* [[http://www.math.ucsb.edu/~hdc  Dr. Ceniceros]]) : Prof. Ceniceros in joint work with UCSB grad student Jordan Fisher and [[http://www.ime.usp.br/~roma/index1.html Prof. Alexandre Roma]] (USP) has recently designed efficient implicit methods for the IBM formalisms significantly advancing the timescales 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, semiimplicit discretizations of the Immersed Boundary Method]].
Changed lines 7274 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/20082009/W11.37.08/abstracts.html#AtzbergerPaul  [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/index1.html Prof. Alexandre Roma]] (USP) has recently designed efficient implicit methods for the IBM formalisms significantly advancing the timescales 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, semiimplicit discretizations of the Immersed Boundary Method]].
* Dr. Ceniceros :
to:
* Dr. Atzberger ([[http://www.math.ucsb.edu/~atzberg/index.html  Research Website]]) Prof. Atzberger has extended the immersed boundary method to incorporate thermal fluctuations consistent with statistical mechanics for applications involving microscopic mechanical systems. The resulting formalism is cast in terms of a system of stochastic partial differential equations (SPDEs) which present interesting challenges both for analysis and the development of numerical methods. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here [[http://www.ima.umn.edu/20082009/W11.37.08/abstracts.html#AtzbergerPaul  [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/index1.html Prof. Alexandre Roma]] (USP) has recently designed efficient implicit methods for the IBM formalisms significantly advancing the timescales 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, semiimplicit discretizations of the Immersed Boundary Method]].
* Dr. Ceniceros ([[http://www.math.ucsb.edu/~hdc  Research Website]]) Prof. Ceniceros in joint work with UCSB grad student Jordan Fisher and [[http://www.ime.usp.br/~roma/index1.html Prof. Alexandre Roma]] (USP) has recently designed efficient implicit methods for the IBM formalisms significantly advancing the timescales 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, semiimplicit discretizations of the Immersed Boundary Method]].
Changed line 72 from:
* Dr. Atzberger : [[http://www.math.ucsb.edu/~atzberg/index.html  Research Website]]. Prof. Atzberger has extended the immersed boundary method to incorporate thermal fluctuations consistent with statistical mechanics for applications involving microscopic mechanical systems. The resulting formalism is cast in terms of a system of stochastic partial differential equations (SPDEs) which present interesting challenges both for analysis and the development of numerical methods. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here : [[http://www.ima.umn.edu/20082009/W11.37.08/abstracts.html#AtzbergerPaul  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/20082009/W11.37.08/abstracts.html#AtzbergerPaul  [Video of IMA Talk]]]. Related papers can be found on his website [[http://www.math.ucsb.edu/~atzberg/index.html  publications]].
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%width=300px% Attach:southHallView1.jpg
to:
%width=300px% Attach:UCSBLagoon.jpg
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!!Research Highlights (select subset of activities)
to:
!!Research Highlights (select subset of recent activities)
Added lines 4445:
!!Research Highlights (select subset of activities)
Changed lines 4751 from:

!! Local and Global Wellposedness of Nonlinear Evolutionary Equations
to:
'+Local and Global Wellposedness of Nonlinear Evolutionary Equations +'
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to:
'+FluidStructure Interactions : Immersed Boundary Methods and Boundary Integral Methods+'
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to:
'+%color555555%Carlos GarciaCervera Wins NSF Faculty Early Career Development Award (NSF CAREER)+'
Changed line 25 from:
to:
!%color555555%Carlos GarciaCervera Wins NSF Faculty Early Career Development Award (NSF CAREER)
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!!%blue%Research Gallery \\
to:
!!Research Gallery \\
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!!%blue%Research Highlights (select subset of activities)
to:
!!Research Highlights (select subset of activities)
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!!%color$555555%Carlos GarciaCervera Wins NSF Faculty Early Career Development Award (NSF CAREER)
to:
!!%color555555%Carlos GarciaCervera Wins NSF Faculty Early Career Development Award (NSF CAREER)
Changed line 25 from:
!!%red%Carlos GarciaCervera Wins NSF Faculty Early Career Development Award (NSF CAREER)
to:
!!%color$555555%Carlos GarciaCervera Wins NSF Faculty Early Career Development Award (NSF CAREER)
Changed lines 2223 from:
to:
!!News
Changed line 25 from:
!!Carlos GarciaCervera Wins NSF Faculty Early Career Development Award (NSF CAREER)
to:
!!%red%Carlos GarciaCervera Wins NSF Faculty Early Career Development Award (NSF CAREER)
Deleted lines 2021:

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to:
News
Deleted lines 2324:
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!!%blue%Research Areas (select subset of activities)
to:
[[#ResearchHighlights]]

!!%blue%Research Highlights (select subset of activities)
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!!%blue%Research Areas (select subset of recent activities)
to:
!!%blue%Research Areas (select subset of activities)
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!!%blue%Research Areas (selected subset of activities)
to:
!!%blue%Research Areas (select subset of recent activities)
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%width=400px% Attach:SIB_Schematic.png
to:
%width=300px% Attach:SIB_Schematic.png
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!!FluidStructure Dynamics : Immersed Boundary Methods and Boundary Integral Methods
to:
!!FluidStructure Interactions : Immersed Boundary Methods and Boundary Integral Methods
Changed lines 7586 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/index1.html Prof. Alexandre Roma]] (USP) has recently designed efficient implicit methods for the IBM formalisms significantly advancing the timescales 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, semiimplicit 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. GarciaCervera : [[http://www.math.ucsb.edu/~atzberg/index.html  Research Website]].
* Dr. Ceniceros : [[http://www.math.ucsb.edu/~hdc  Research Website]].
* Dr. Atzbeger : [[http://www.math.ucsb.edu/~atzberg/index.html  Research Website]].

!! Liquid Crystals / Lipid Bilayer Membranes / Complex Polymeric Fluids
Brief article outlining basic area of research, interesting math. issues...
Faculty members working in this area include:
* Dr. GarciaCervera : [[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/index1.html Prof. Alexandre Roma]] (USP) has recently designed efficient implicit methods for the IBM formalisms significantly advancing the timescales 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, semiimplicit discretizations of the Immersed Boundary Method]].
Changed line 46 from:
!!%blue%Research Areas (Selected subset of activities)
to:
!!%blue%Research Areas (selected subset of activities)
Changed line 46 from:
!!%blue%Research Areas (Selected Subset of Activities)
to:
!!%blue%Research Areas (Selected subset of activities)
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%width=200px% Attach:carlosImage.png %width=200px% Attach:atzbergerImage.png
to:
%width=100px% Attach:carlosImage.png %width=100px% Attach:atzbergerImage.png
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to:
%width=200px% Attach:carlosImage.png %width=200px% Attach:atzbergerImage.png
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%width=200px% Attach:carlosImage.png %width=200px% Attach:atzbergerImage.png %width=200px% Attach:carlosImage.png
(images / movies, here, etc...)
(images / movies, here, etc...)
to:
%width=200px% Attach:carlosImage.png
%width=200px% Attach:atzbergerImage.png
%width=200px% Attach:atzbergerImage.png
Deleted lines 89111:

!!%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 ongoing work both at the level of lightreading and in more detail. I wrote mostly about my own work, since I know the most about this activity presumably. :) I propose uptop we have short gallery style presentation of results for the lightofheart. 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 uptop 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 welldefined 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 writeup 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 underconstruction]
Please feel free to edit and taking a shot at writing these materials.
We can collectively edit over time until we get something we are
all happy with.
(will work on embedding some floating boxes on the right
to list in an accessible format "news items and current events",
see http://www.me.ucsb.edu/ for stylistic sense of what I
have in mind)
Changed lines 79 from:
Welcome to the applied mathematics group's homepage. Applied mathematics
refers to the branch of mathematics which strives to integrate the
development of core areas of mathematics with the solution of
refers to the branch of mathematics which strives to integrate the
development of core areas of mathematics with the solution of
to:
Welcome to the applied mathematics group's homepage. Applied mathematics refers to the branch of mathematics which strives
to integrate the development of core areas of mathematics with
the solution of
to integrate the development of core areas of mathematics with
the solution of
Changed lines 2930 from:
!!%grey%Carlos GarciaCervera Wins NSF Faculty Early Career Development Award (NSF CAREER)
to:
!!Carlos GarciaCervera Wins NSF Faculty Early Career Development Award (NSF CAREER)
Changed line 42 from:
!!Research Gallery \\
to:
!!%blue%Research Gallery \\
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!!Research Areas (Selected Subset of Activities)
to:
!!%blue%Research Areas (Selected Subset of Activities)
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!!Discussion of Above Items
to:
!!%blue%Discussion of Above Items
Changed lines 2425 from:
!!Research Highlights \\
to:
!!%blue%Research Highlights \\
Changed line 29 from:
!!%blue%Carlos GarciaCervera Wins NSF Faculty Early Career Development Award (NSF CAREER)
to:
!!%grey%Carlos GarciaCervera Wins NSF Faculty Early Career Development Award (NSF CAREER)
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%blue%
!!Carlos GarciaCervera Wins NSF Faculty Early Career Development Award (NSF CAREER)
%black%
!!
%black%
to:
!!%blue%Carlos GarciaCervera Wins NSF Faculty Early Career Development Award (NSF CAREER)
Changed line 13 from:
dynamics, boundary integral methods, immersed boundary methods),
to:
dynamics, boundary integral methods, immersed boundary methods,
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%width=200px% Attach:southHallView1.jpg
to:
%width=300px% Attach:southHallView1.jpg
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%width=200px% Attach:southHallView2.jpg
to:
%width=200px% Attach:southHallView1.jpg
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%width=200px% Attach:southHallView1.jpg
South Hall
South Hall
to:
%width=200px% Attach:southHallView2.jpg
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to:
South Hall
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%width=400px% Attach:southHallView1.jpg
to:
%width=200px% Attach:southHallView1.jpg
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to:
Department of Mathematics : South Hall [Image Credit:Statistics Homepage]
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\\
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to:
(Image from UCSB Statistics Homepage)
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[[#ResearchHighlights]]
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Deleted line 20:
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\\
(Carlos: Please finish writing this synposis.)
\\
\\
\\
\\
Changed lines 914 from:
dynamics for systems with moving boundaries (boundary integral methods
/ immersed boundary methods), crystalline solids and liquid crystals,
density functional theory, analysis of nonlinear evolutionary PDE's,
study of existence or development of singularities in finite time,
applied harmonic analysis, and stochastic differential equations. Here
you willfind research highlights, upcoming seminar talks, and information
study
applied harmonic analysis, and stochastic differential equations. Here
you will
to:
dynamics, boundary integral methods, immersed boundary methods),
crystalline solids and liquid crystals, density functional theory,
analysis of nonlinear evolutionary PDE's, study of existence or
development of singularities in finite time, applied harmonic
analysis, and stochastic differential equations. Here you will
find research highlights, upcoming seminar talks, and information
crystalline solids and liquid crystals, density functional theory,
analysis of nonlinear evolutionary PDE's, study of existence or
development of singularities in finite time, applied harmonic
analysis, and stochastic differential equations. Here you will
find research highlights, upcoming seminar talks, and information
Changed lines 925 from:
dynamics (boundary integral methods / immersed boundary methods),
crystalline solids and liquid crystals, density functional theory,
analysis of nonlinear 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 underconstruction]
Please feel free to editand taking a shot at writing these materials.
We can collectively edit over time until we get something we are
all happy with.
(will work on embedding some floating boxes on the right
to list in an accessible format "news items and current events",
see http://www.me.ucsb.edu/ for stylistic sense of what I
have in mind)
analysis of nonlinear hyperbolic PDE's (?), applied harmonic analysis
upcoming seminar talks
of the applied mathematics group.
test
[All pages are underconstruction]
Please feel free to edit
We can collectively edit over time until we get something we are
all happy with.
(will work on embedding some floating boxes on the right
to list in an accessible format "news items and current events",
see http://www.me.ucsb.edu/ for stylistic sense of what I
have in mind)
to:
dynamics for systems with moving boundaries (boundary integral methods
/ immersed boundary methods), crystalline solids and liquid crystals,
density functional theory, analysis of nonlinear evolutionary PDE's,
study of existence or development of singularities in finite time,
applied harmonic analysis, and stochastic differential equations. Here
you will find research highlights, upcoming seminar talks, and information
about news and current activities of the applied mathematics group.
/ immersed boundary methods), crystalline solids and liquid crystals,
density functional theory, analysis of nonlinear 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 105116:
test
[All pages are underconstruction]
Please feel free to edit and taking a shot at writing these materials.
We can collectively edit over time until we get something we are
all happy with.
(will work on embedding some floating boxes on the right
to list in an accessible format "news items and current events",
see http://www.me.ucsb.edu/ for stylistic sense of what I
have in mind)
Changed lines 4246 from:
The award will support his research for five years providing funding for postdoctoral researchers
and graduate students. The proposed research program has the potential to impact fundamental
computational approaches used in studying solid materials taking into account important
quantum effects. This is the first NSF CAREER award given to a faculty
member of the department of mathematics.\\
and graduate students.
computational approaches used in studying solid materials taking into account important
quantum effects.
member of the department of mathematics.\\
to:
The awards are for a minimum of $400,000 and support his research for five years providing funding
for postdoctoral researchers and graduate students. The proposed research program has the potential
to impact fundamental computational approaches used in studying solid materials. This is the first
NSF CAREER award given to a faculty member of the department of mathematics.\\
for postdoctoral researchers and graduate students. The proposed research program has the potential
to impact fundamental computational approaches used in studying solid materials. This is the first
NSF CAREER award given to a faculty member of the department of mathematics.\\
Added line 41:
The Faculty Early Career Development (CAREER) Program offers the NSF’s most prestigious awards in support of early career development activities of those teacherscholars who are most likely to become the academic leaders of the 21st century.
Changed lines 4344 from:
computational approaches used in studying quantum effects in a wide range of systems from
semiconductors to biological molecules. This is the first NSF CAREER award given to a faculty
semiconductors to biological molecules
to:
computational approaches used in studying solid materials taking into account important
quantum effects. This is the first NSF CAREER award given to a faculty
quantum effects. This is the first NSF CAREER award given to a faculty
Changed lines 4143 from:
The award will .... and ... The proposed research program has the potential to
impact... This is the first NSF CAREER award given to a faculty member of the
department of mathematics.\\
impact
department
to:
The award will support his research for five years providing funding for postdoctoral researchers
and graduate students. The proposed research program has the potential to impact fundamental
computational approaches used in studying quantum effects in a wide range of systems from
semiconductors to biological molecules. This is the first NSF CAREER award given to a faculty
member of the department of mathematics.\\
and graduate students. The proposed research program has the potential to impact fundamental
computational approaches used in studying quantum effects in a wide range of systems from
semiconductors to biological molecules. This is the first NSF CAREER award given to a faculty
member of the department of mathematics.\\
Deleted lines 111134:
Not sure if this is necessary (formal rules for editing the Wiki website):\\
\\
'''Applied math. group wiki bylaws:'''\\
\\
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 online
reflects the group consensus. Anything failing the vote and revisions process
will not be copied to the homepage [kind of like a journal peerreview process].
Basically, we will post on the hidden page content "approved PJA", "revise xyz PJA",
"donotapprove 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 online 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 bylaws for the pages
if this is required by university to avoid any formal objections being made
to how the pages are collectively managed.
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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 underconstruction]
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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/20082009/W11.37.08/abstracts.html#AtzbergerPaul  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/20082009/W11.37.08/abstracts.html#AtzbergerPaul  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/20082009/W11.37.08/abstracts.html#AtzbergerPaul  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/20082009/W11.37.08/abstracts.html#AtzbergerPaul  IMA Workshop on Multiscale Methods.]]
Changed lines 8687 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/20082009/W11.37.08/abstracts.html#AtzbergerPaul  IMA Workshop on Multiscale Methods.]]
mechanical systems. The formalism is cast in terms of a system of stochastic partial differential equations (SPDEs) obtained by introducing an appropriate stochastic driving field in the fluid equations. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here : [[http://www.ima.umn.edu/20082009/W11.37.08/abstracts.html#AtzbergerPaul  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/20082009/W11.37.08/abstracts.html#AtzbergerPaul  IMA Workshop on Multiscale Methods.]]
Changed lines 8788 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/20082009/W11.37.08/abstracts.html#AtzbergerPaul  IMA Workshop on Multiscale Methods.]]
obtained by introducing an appropriate stochastic driving field in the fluid equations. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here : [[http://www.ima.umn.edu/20082009/W11.37.08/abstracts.html#AtzbergerPaul  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/20082009/W11.37.08/abstracts.html#AtzbergerPaul  IMA Workshop on Multiscale Methods.]]
Changed lines 8687 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/20082009/W11.37.08/abstracts.html#AtzbergerPaul  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/20082009/W11.37.08/abstracts.html#AtzbergerPaul  IMA Workshop on Multiscale Methods.]]
mechanical systems. The formalism is cast in terms of a system of stochastic partial differential equations (SPDEs)
obtained by introducing an appropriate stochastic driving field in the fluid equations. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here : [[http://www.ima.umn.edu/20082009/W11.37.08/abstracts.html#AtzbergerPaul  IMA Workshop on Multiscale Methods.]]
Changed lines 8688 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/20082009/W11.37.08/abstracts.html#AtzbergerPaul  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/index1.html Prof. Alexandre Roma]](USP) has recently designed efficient implicit methods for the IBM formalisms significantly advancing the timescales 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, semiimplicit discretizations of the Immersed Boundary Method]]
* Dr. Ceniceros :
to:
* Dr. Atzberger : [[http://www.math.ucsb.edu/~atzberg/index.html  Research Website]]. Prof. Atzberger has worked on extending the immersed boundary method to incorporate thermal fluctuations for applications involving microscopic
mechanical systems. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here : [[http://www.ima.umn.edu/20082009/W11.37.08/abstracts.html#AtzbergerPaul  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/index1.html Prof. Alexandre Roma]] (USP) has recently designed efficient implicit methods for the IBM formalisms significantly advancing the timescales 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, semiimplicit discretizations of the Immersed Boundary Method]]
mechanical systems. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found here : [[http://www.ima.umn.edu/20082009/W11.37.08/abstracts.html#AtzbergerPaul  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/index1.html Prof. Alexandre Roma]] (USP) has recently designed efficient implicit methods for the IBM formalisms significantly advancing the timescales 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, semiimplicit discretizations of the Immersed Boundary Method]]
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!!Research Areas (Selected Subset for Highlights)
to:
!!Research Areas (Selected Subset of Activities)
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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 elastodynamics.
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 8597:

!! 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 elastodynamics.
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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%lfloat textalign=left margintop=5px marginright=5px marginbottom=10px marginleft=5px width=100px% Attach:carlosSmiles.jpg Attach:boris.jpg
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%lfloat textalign=left margintop=5px marginright=5px marginbottom=10px marginleft=5px width=100px% Attach:carlosSmiles.jpg
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%lfloat textalign=left margintop=5px marginright=5px marginbottom=10px marginleft=5px width=100px% Attach:carlosSmiles.jpg Attach:boris.jpg
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!! Local and Global Wellposedness of Nonlinear Evolutionary Equations
(Tom and Gustavo, please write brief outline of research areas and edit URLs below)
Brief article outlining basic area of research, interesting math. issues.
Dr. Sideris's work and Dr. Ponce's work highlighted here...
Brief article outlining basic area of research, interesting math. issues
to:
!! Local and Global Wellposedness of Nonlinear Evolutionary Equations
Provide conditions on initial data which ensure the existence, uniqueness, and continuous dependence of solutions to the initial value problem for nonlinear
evolutionary partial differential equations.
Determine whether solutions exist globally in time or develop singularities in finite time. Explore the regularity and asymptotic behavior of solutions.
Applications to nonlinear dispersive equations, hydro and elastodynamics.
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 elastodynamics.
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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
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!! Analysis of XYZ... Nonlinear Elasticity.... Schrodinger Equ... (please edit)
to:
!! Local and Global Wellposedness of Nonlinear Evolutionary Equations
Changed lines 8184 from:
* Dr. Sideris : [[http://www.math.ucsb.edu/~atzberg/index.html  Research Website]].
* Dr. Ponce : [[http://www.math.ucsb.edu/~atzberg/index.html  Research Website]].
* Dr. Ponce : [[http://www.math.ucsb.edu/~
to:
* Dr. Sideris : [[http://www.math.ucsb.edu/~sideris/index.html  Research Website]].
* Dr. Ponce : [[http://www.math.ucsb.edu/~ponce/index.html  Research Website]].
* Dr. Ponce : [[http://www.math.ucsb.edu/~ponce/index.html  Research Website]].
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to:

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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
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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 %width=200px% Attach:/Users/sideris/Desktop/boris.jpg
Changed lines 6970 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 timescales 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, semiimplicit discretizations of the Immersed Boundary Method]]
[[http://www.math.ucsb.edu/~hdc/public/IBM_Implicit.pdf  Efficient solutions to robust, semiimplicit 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/index1.html Prof. Alexandre Roma]](USP) has recently designed efficient implicit methods for the IBM formalisms significantly advancing the timescales 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, semiimplicit discretizations of the Immersed Boundary Method]]
Changed lines 6970 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 timescales 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 timescales 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, semiimplicit discretizations of the Immersed Boundary Method]]
[[http://www.math.ucsb.edu/~hdc/public/IBM_Implicit.pdf  Efficient solutions to robust, semiimplicit 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 5960 from:
to:
The mechanics of many physical systems depends crucially on the interaction of flexible elastic
structures with a fluid flow. Examples of macroscopic systems include the pumping of the heart in which blood flow interacts with valves, lift general in insect flight, and wave propagation in the cochlea of the inner ear. Examples of microscopic systems include the rheology of complex fluids and softmatter which depends importantly on microstructures (such as colloids, lipids, polymers, vesicles) which interact with shear and extensional fluid flows serving through smallscale deformations to elastically store or dissipate energy. These microscopic processes often result macroscopically in material properties exhibiting interesting counterintuitive phenomena and features hard to predict a priori. Immersed Boundary Methods (IBM) and Boundary Integral Methods (BIM) are numerical approaches for studying the mechanics of elastic structures which interact with a fluid.
structures with a fluid flow. Examples of macroscopic systems include the pumping of the heart in which blood flow interacts with valves, lift general in insect flight, and wave propagation in the cochlea of the inner ear. Examples of microscopic systems include the rheology of complex fluids and softmatter which depends importantly on microstructures (such as colloids, lipids, polymers, vesicles) which interact with shear and extensional fluid flows serving through smallscale deformations to elastically store or dissipate energy. These microscopic processes often result macroscopically in material properties exhibiting interesting counterintuitive 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.
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if this is required by university to avoid any issues of "free speech" and
to guard against any formal objections being made to fairness.
to guard against any formal objections being made to fairness
to:
if this is required by university to avoid any formal objections being made
to how the pages are collectively managed.
to how the pages are collectively managed.
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'''Applied math. wikiedit bylaws:'''\\
to:
'''Applied math. group wiki bylaws:'''\\
Changed line 106 from:
'''Wikiedit ByLaws'''\\
to:
'''Applied math. wikiedit bylaws:'''\\
Changed lines 6869 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 timescales accessible in simulations of systems with stiff elastic structures, papers can be
found here [link]... (Hector please edit profile and above description as you see fit...)
found here [link]... (Hector please edit profile and above description as you see fit...)
to:
* Dr. Cinceros : [[http://www.math.ucsb.edu/~cinceros/index.html  Research Website]]. Dr. Cinceros has recently formulated efficient implicit methods for the IBM formalisms significantly advancing the timescales 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 6869 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 timescales 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 timescales accessible in simulations of systems with stiff elastic structures, papers can be
found here [link]... (Hector please edit profile and above description as you see fit...)
found here [link]... (Hector please edit profile and above description as you see fit...)
Changed line 57 from:
!!FluidStructure Dynamics: Immersed Boundary Methods and Boundary Integral Methods
to:
!!FluidStructure 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 softmatter which depends importantly on microstructures (such as colloids, lipids, polymers, vesicles) which interact with shear and extensional fluid flows serving through smallscale deformations to elastically store or dissipate energy. These microscopic processes often result macroscopically in material properties exhibiting interesting counterintuitive 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 softmatter which depends importantly on microstructures (such as colloids, lipids, polymers, vesicles) which interact with shear and extensional fluid flows serving through smallscale deformations to elastically store or dissipate energy. These microscopic processes often result macroscopically in material properties exhibiting interesting counterintuitive 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 softmatter which depends importantly on microstructures (such as colloids, lipids, polymers, vesicles) which interact with shear and extensional fluid flows serving through smallscale deformations to elastically store or dissipate energy. These microscopic processes often result macroscopically in material properties exhibiting interesting counterintuitive 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 softmatter which depends importantly on microstructures (such as colloids, lipids, polymers, vesicles) which interact with shear and extensional fluid flows serving through smallscale deformations to elastically store or dissipate energy. These microscopic processes often result macroscopically in material properties exhibiting interesting counterintuitive phenomena and a priori hard to predict features.
Changed lines 6670 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/20082009/W11.37.08/abstracts.html#AtzbergerPaul  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 timescales accessible in simulations of systems with stiff elastic structures... (Hector please edit profile and above description as you see fit...)
A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found
* Dr. Cinceros's : [[http://www.math.ucsb.edu/~cinceros/index.html  Research Website]].
Dr. Cinceros has recently formulated efficient implicit methods for the IBM formalisms significantly advancing the timescales 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/20082009/W11.37.08/abstracts.html#AtzbergerPaul  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 timescales accessible in simulations of systems with stiff elastic structures... (Hector please edit profile and above description as you see fit...)
* Dr. Cinceros's : [[http://www.math.ucsb.edu/~cinceros/index.html  Research Website]]. Dr. Cinceros has recently formulated efficient implicit methods for the IBM formalisms significantly advancing the timescales accessible in simulations of systems with stiff elastic structures... (Hector please edit profile and above description as you see fit...)
Changed lines 6668 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/20082009/W11.37.08/abstracts.html#AtzbergerPaul  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 timescales accessible in simulations of systems with stiff elastic structures... (Hector please edit profile and above description as you see fit...)
* Dr. Cinceros's : [[http://www.math.ucsb.edu/~cinceros/index.html  Research Website]]. Dr. Cinceros has recently formulated efficient implicit methods for the IBM formalisms significantly advancing the timescales 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/20082009/W11.37.08/abstracts.html#AtzbergerPaul  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 timescales accessible in simulations of systems with stiff elastic structures... (Hector please edit profile and above description as you see fit...)
A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found [[http://www.ima.umn.edu/20082009/W11.37.08/abstracts.html#AtzbergerPaul  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 timescales 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 6368 from:
In the IBM formalism the hydrodynamic interactions of the composite system are handled by an approximate treatment of the fluidstructure 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 nonlinear). The fluidstructure 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 fluidstructure 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 indepth 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/20082009/W11.37.08/abstracts.html#AtzbergerPaul  here.]]
* Dr. Cinceros's who has recently formulated efficient implicit methods for the IBM formalisms significantly advancing the timescales accessible in simulations of systems with stiff elastic structures...
* Dr. Atzberger who has extended the IB methodology to include thermal fluctuations
* Dr. Cinceros's who has recently formulated efficient implicit methods for the IBM formalisms significantly advancing the timescales 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 fluidstructure 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 nonlinear). The fluidstructure 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/20082009/W11.37.08/abstracts.html#AtzbergerPaul  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 timescales accessible in simulations of systems with stiff elastic structures... (Hector please edit profile and above description as you see fit...)
Faculty members working in this area include:
* Dr. Atzberger : [[http://www.math.ucsb.edu/~atzberg/index.html  Research Website]]. A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found [[http://www.ima.umn.edu/20082009/W11.37.08/abstracts.html#AtzbergerPaul  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 timescales accessible in simulations of systems with stiff elastic structures... (Hector please edit profile and above description as you see fit...)
Added lines 7374:
(Tom and Gustavo, please write brief outline of research areas and edit URLs below)
Changed lines 7778 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 8688 from:
Brief article outlining basic area of research, interesting math. issues.
Mention Dr. GarciaCervera's, Dr. Cinceros's, and
Dr. Atzbeger's specific work in this area...
Dr. Atzbeger's specific work in this area
to:
Brief article outlining basic area of research, interesting math. issues...
Faculty members working in this area include:
* Dr. GarciaCervera : [[http://www.math.ucsb.edu/~atzberg/index.html  Research Website]].
* Dr. Cinceros : [[http://www.math.ucsb.edu/~atzberg/index.html  Research Website]].
* Dr. Atzbeger : [[http://www.math.ucsb.edu/~atzberg/index.html  Research Website]].
Faculty members working in this area include:
* Dr. GarciaCervera : [[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 6367 from:
In the IBM formalism the hydrodynamic interactions of the composite system are handled by an approximate treatment of the fluidstructure 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 nonlinear). The fluidstructure 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 timescales introduced into the fluidstructure 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 fluidstructure systems and the development of efficient numerical methods.
Faculty members working on fluidstructure problems include:
* Dr. Atzberger who has extended the IB methodology to include thermal fluctuations, by an appropriate stochastic forcing of the fluidstructure 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 coarsegrained models of lipid bilayer membranes using the SIB formalism to account for molecular level interactions (lipidlipid and lipidsolvent) along with hydrodynamic coupling and thermal fluctuations. For a more indepth 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/20082009/W11.37.08/abstracts.html#AtzbergerPaul  here.]]
as a consequence of fast timescales introduced into the fluidstructure 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 fluidstructure systems and the development of efficient numerical methods.
Faculty members working on fluidstructure problems include:
* Dr. Atzberger who has extended the IB methodology to include thermal fluctuations, by an appropriate stochastic forcing of the fluidstructure 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 coarsegrained models of lipid bilayer membranes using the SIB formalism to account for molecular level interactions (lipidlipid and lipidsolvent) along with hydrodynamic coupling and
to:
In the IBM formalism the hydrodynamic interactions of the composite system are handled by an approximate treatment of the fluidstructure 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 nonlinear). The fluidstructure 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 fluidstructure 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 indepth 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/20082009/W11.37.08/abstracts.html#AtzbergerPaul  here.]]
* Dr. Atzberger who has extended the IB methodology to include thermal fluctuations. For a more indepth 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/20082009/W11.37.08/abstracts.html#AtzbergerPaul  here.]]
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!!Research Areas (Select Subset)
to:
!!Research Areas (Selected)
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!!Select Research Activities
to:
!!Research Areas (Select Subset)
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!!Research Activities (Subset)
to:
!!Select Research Activities
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!!Research Activities
to:
!!Research Activities (Subset)
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!!Highlighted Research Areas
to:
!!Research Activities
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!!Research Gallery (images / movies, here, etc...) \\
to:
!!Research Gallery \\
Added line 53:
(images / movies, here, etc...)
Changed lines 2021 from:
(will work on embedding some floating boxes that list news items and current events,
see http://www.me.ucsb.edu/ for some stylistic ideas)
see http://www.me.ucsb.edu/ for some stylistic ideas
to:
(will work on embedding some floating boxes on the right
to list in an accessible format "news items and current events",
see http://www.me.ucsb.edu/ for stylistic sense of what I
have in mind)
to list in an accessible format "news items and current events",
see http://www.me.ucsb.edu/ for stylistic sense of what I
have in mind)
Added lines 1921:
(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 8283 from:
Another model is not to have thematic articles, but to only have a few images uptop 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 welldefined 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 writeup some example or express your ideas.
to:
Another model is not to have thematic articles, but to only have a few images uptop 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 welldefined 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 writeup some example or express your ideas.
http://amath.unc.edu/]. In my opinion our group runs the risk of not presenting a welldefined 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 writeup 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 uptop 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 welldefined 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 uptop 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 welldefined 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 writeup 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 uptop 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 uptop 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 welldefined core and anchored research program communicated on the site to people when they visit if we only include a collection of images with captions.
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%lfloat textalign=left margintop=5px marginright=5px marginbottom=10px marginleft=5px width=100px% Attach:hectorImage.png
to:
%lfloat textalign=left margintop=5px marginright=5px marginbottom=10px marginleft=5px width=100px% Attach:carlosSmiles.jpg
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to:
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Mention Dr. GarciaCervera's group and Dr. Cinceros's group...
to:
Mention Dr. GarciaCervera's, Dr. Cinceros's, and
Dr. Atzbeger's specific work in this area...
Dr. Atzbeger's specific work in this area...
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!!Gallery of Recent Results (images / movies, here, etc...) \\
to:
!!Research Gallery (images / movies, here, etc...) \\
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!! Liquid Crystals / Lipid Bilayer Membranes / Complex Polymer Fluids
to:
!! Analysis of XYZ... Nonlinear Elasticity.... Schrodinger Equ... (please edit)
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to:
Dr. Sideris's work and Dr. Ponce's work highlighted here...
Changed lines 7071 from:
!! Analysis of XYZ... Nonlinear Elasticity.... Schrodinger Equ... (please edit)
to:
!! Liquid Crystals / Lipid Bilayer Membranes / Complex Polymeric Fluids
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Dr. Sideris's work and Dr. Ponce's work highlighted here...
to:
Mention Dr. GarciaCervera's group and Dr. Cinceros's group...
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!!Discussion of Above Items
Changed lines 7779 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 ongoing 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). Uptop we then include some short descriptions of "fresh work"
before these thematic shortarticles. This means people encounter what's new first, but can scroll down for a more detailed view of our group.
before these thematic shortarticles. This means people encounter what's new first, but can scroll down for a more detailed view of our
to:
Above is an experiment and rough draft / brainstorm. Idea is to give undergraduate / graduate students and general public and scientific audience sense of what types of work our group does. Above is meant to give an example of some themes and what we might post to highlight our specific research programs and ongoing work both at the level of lightreading and in more detail. I wrote mostly about my own work, since I know the most about this activity presumably. :) I propose uptop we have short gallery style presentation of results for the lightofheart. 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.
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if you think
Not sure if this is necessary
to:
Please take a shot at posting/editing the welcome message and some materials for discussion.
Not sure if this is necessary (formal rules for editing the Wiki website):\\
Not sure if this is necessary (formal rules for editing the Wiki website):\\
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%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
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%width=200px% Attach:carlosImage.png
%width=200px% Attach:atzbergerImage.png
%width=200px% Attach:carlosImage.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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%width=300px% Attach:carlosImage.png
%width=300px% Attach:atzbergerImage.png
%width=300px% Attach:carlosImage.png
%width=300px% Attach:atzbergerImage.png
%width=
%width=
%width=300px% Attach:atzbergerImage.png
to:
%width=200px% Attach:carlosImage.png
%width=200px% Attach:atzbergerImage.png
%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

\\
%width=300px% Attach:carlosImage.png
%width=300px% Attach:atzbergerImage.png
%width=300px% Attach:carlosImage.png
%width=300px% Attach:atzbergerImage.png

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!! Analysis of XYZ...
to:
!! Analysis of XYZ... Nonlinear Elasticity.... Schrodinger Equ... (please edit)
Changed lines 7476 from:
to:
Dr. Sideris's work and Dr. Ponce's work highlighted here...
Changed lines 7881 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 ongoing work. I wrote about myself since I know the most about this activity presumably. :) We may have a few short articles and either leave in place for awhile or copy these to "hidden" pages and each month rotate through the content descriptions making modifications, new articles, and updates as research develops...
Another model is to have simply an image with a short caption and links to researchers webpages with more detailed into... [see UNC site].
Another model is to have simply an image with a short caption and links to researchers webpages with more detailed into...
to:
Above is an experiment and rough draft / brainstorm. Idea is to give newbie graduate students and general audience sense of what our group does. Above is meant to give an example of some themes and what we might post to highlight our specific research programs and ongoing 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). Uptop we then include some short descriptions of "fresh work"
before these thematic shortarticles. 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 uptop with a short caption and links to researchers webpages with more detailed info... [see UNC site].
before these thematic shortarticles. 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 uptop with a short caption and links to researchers webpages with more detailed info... [see UNC site].
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to:
Not sure if this is necessary:\\
\\
\\
Deleted lines 106111:
!!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 FluidStructure Dynamics:
to:
!!FluidStructure Dynamics: Immersed Boundary Methods and Boundary Integral Methods
Changed lines 4748 from:
In the IBM formalism the hydrodynamic interactions of the composite system are handled by an approximate treatment of the fluidstructure 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 nonlinear). The fluidstructure 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 fluidstructure 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 fluidstructure 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 nonlinear). The fluidstructure 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 timescales introduced into the fluidstructure 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 fluidstructure systems and the development of efficient numerical methods.
as a consequence of fast timescales introduced into the fluidstructure 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 fluidstructure systems and the development of efficient numerical methods.
Changed lines 4344 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 / softmatter which depends importantly on microstructures (such as colloids, lipids, polymers, vesicles) interact with shear and extensional fluid flows serving through smallscale 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 softmatter which depends importantly on microstructures (such as colloids, lipids, polymers, vesicles) which interact with shear and extensional fluid flows serving through smallscale deformations to elastically store or dissipate energy. These microscopic processes often result macroscopically in material properties exhibiting interesting counterintuitive 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 fluidstructure 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 nonlinear integral equations. The fluidstructure 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 fluidstructure 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 fluidstructure 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 nonlinear). The fluidstructure 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 fluidstructure 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 4144 from:
!!Immersed Boundary Methods for FluidStructure 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 / softmatter as a results of microstructures interacting with fluid flows at smallscales where immersed structures represent solute particles, polymers, or membrane structures.
Immersed Boundary Methods (IBM) are numerical approaches for studying the mechanics of elastic structures which interact with a fluid. Immersed
to:
!!Immersed Boundary Methods and Boundary Integral Methods for FluidStructure 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 / softmatter which depends importantly on microstructures (such as colloids, lipids, polymers, vesicles) interact with shear and extensional fluid flows serving through smallscale deformations to elastically store or dissipate energy.
Immersed Boundary Methods (IBM) and Boundary Integral Methods (BIM) are numerical approaches for studying the mechanics of elastic structures which interact with a fluid. Examples macroscopic systems include the pumping of the heart in which blood flow interacts with valves, lift general in insect flight, and wave propagation in the cochlea. In microscopic systems examples include the rheology of complex fluids / softmatter which depends importantly on microstructures (such as colloids, lipids, polymers, vesicles) interact with shear and extensional fluid flows serving through smallscale 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 fluidstructure 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 fluidstructure systems and in obtaining in general efficient numerical methods. In practice, fast time scales are often introduced into the fluidstructure 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 fluidstructure 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 nonlinear integral equations. The fluidstructure 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 fluidstructure 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 4145 from:
!!Stochastic Immersed Boundary Methods for FluidStructure Dynamics:
[[http://www.math.ucsb.edu/~atzberg/index.html  '+Paul J. Atzberger+']]
Stochastic Immersed Boundary Methods (SIB) are numerical approaches for studying the mechanics of elastic structures which interact with a fluid in microscopic systems where thermal fluctuations play an important role. Immersed structures in SIB can be used to represent the mechanics of a variety of microscopic hydrodynamic systems, for example, in a complex fluid the structures could represent solute particles, polymers, or membrane structures.
Stochastic Immersed Boundary Methods (SIB) are numerical approaches for studying the mechanics of elastic structures which interact with a fluid in microscopic systems where thermal fluctuations play an important role. Immersed structures in SIB can be used to represent the mechanics of a variety of microscopic hydrodynamic systems, for example, in a complex fluid the structures could
to:
!!Immersed Boundary Methods for FluidStructure 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 / softmatter as a results of microstructures interacting with fluid flows at smallscales where immersed structures represent solute particles, polymers, or membrane structures.
Immersed Boundary Methods (IBM) are numerical approaches for studying the mechanics of elastic structures which interact with a fluid. Immersed structures in IBM can be used to represent the mechanics of a variety of hydrodynamic systems from the macroscopic to microscopic. Examples include for macroscopic systems blood flow in the heart and interaction with valves, lift general in insect flight, and wave propagation in the cochlear. In microscopic systems examples include rheology of complex fluids / softmatter as a results of microstructures interacting with fluid flows at smallscales where immersed structures represent solute particles, polymers, or membrane structures.
Changed lines 4754 from:
In the SIB formalism the hydrodynamic interactions of the composite system are handled by an approximate treatment of the fluidstructure 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 fluidstructure equations in accordance with the principles of statistical mechanics. Mathematically, the formalism is cast in terms of a system of Stochastic Partial Differential Equations (SPDE's).
Many interesting mathematical challenges arise in obtaining efficient numerical methods as a result of fast time scales introduced into the fluid dynamics by the thermal fluctuations making the resulting system of equations stiff.
Dr. Atzberger's group uses results from stochastic calculus to develop efficient stochastic numerical methods forthe formalism. In collaboration with the Brown Group, Department of Chemistry, Dr. Atzberger's group is developing dynamic coarsegrained models of lipid bilayer membranes using the SIB formalism to account for molecular level interactions (lipidlipid and lipidsolvent) along with hydrodynamic coupling and thermal fluctuations. For a more indepth 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/20082009/W11.37.08/abstracts.html#AtzbergerPaul  here.]]
Many interesting mathematical challenges arise in obtaining efficient numerical methods as a result of fast time scales introduced into the fluid dynamics by
Dr. Atzberger's group uses results from stochastic calculus to develop efficient stochastic numerical methods for
A recent talk given by Dr. Atzberger on the Stochastic Immersed Boundary Method can be found
[[http://www
to:
In the IBM formalism the hydrodynamic interactions of the composite system are handled by an approximate treatment of the fluidstructure 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 fluidstructure systems and in obtaining in general efficient numerical methods. In practice, fast time scales are often introduced into the fluidstructure dynamics by the elastic structures or in microscopic system by thermal fluctuations making the resulting system of equations stiff.
Faculty members working on fluidstructure problems include:
* Dr. Atzberger who has extended the IB methodology to include thermal fluctuations, by an appropriate stochastic forcing of the fluidstructure 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 coarsegrained models of lipid bilayer membranes using the SIB formalism to account for molecular level interactions (lipidlipid and lipidsolvent) along with hydrodynamic coupling and thermal fluctuations. For a more indepth 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/20082009/W11.37.08/abstracts.html#AtzbergerPaul  here.]]
* Dr. Cinceros's who has recently formulated efficient implicit methods for the IBM formalisms significantly advancing the timescales accessible in simulations of systems with stiff elastic structures...
Faculty members working on fluidstructure problems include:
* Dr. Atzberger who has extended the IB methodology to include thermal fluctuations, by an appropriate stochastic forcing of the fluidstructure 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 coarsegrained models of lipid bilayer membranes using the SIB formalism to account for molecular level interactions (lipidlipid and lipidsolvent) along with hydrodynamic coupling and thermal fluctuations. For a more indepth 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/20082009/W11.37.08/abstracts.html#AtzbergerPaul  here.]]
* Dr. Cinceros's who has recently formulated efficient implicit methods for the IBM formalisms significantly advancing the timescales accessible in simulations of systems with stiff elastic structures...
Changed lines 5556 from:
!! Implicit Immersed Boundary Methods...
to:
!! Liquid Crystals / Lipid Bilayer Membranes / Complex Polymer Fluids
Changed lines 5860 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. GarciaCervera's group and Dr. Cinceros's group...
Changed lines 6162 from:
!! Liquid Crystals and XYZ
to:
!! Analysis of XYZ...
Changed lines 6470 from:
Mention Dr. GarciaCervera's group and Dr. Cinceros's group...

!! Analysis of XYZ...
Brief article outlining basic area of research, interesting math. issues.
Mention Dr. GarciaCervera's group and Dr. Cinceros's group...

!! Analysis of XYZ...
Brief article outlining basic area of research, interesting math. issues.
Mention Dr. GarciaCervera's group and Dr. Cinceros's group
to:
Mention Dr. Sideris's work and Dr. Ponce's work...
Changed lines 4446 from:
are numerical approaches for studying the mechanics of elastic structures which interact with a fluid in systems at small lengthscales where thermal fluctuations play an important role. The hydrodynamic interactions
to:
Stochastic Immersed Boundary Methods (SIB) are numerical approaches for studying the mechanics of elastic structures which interact with a fluid in microscopic systems where thermal fluctuations play an important role. Immersed structures in SIB can be used to represent the mechanics of a variety of microscopic hydrodynamic systems, for example, in a complex fluid the structures could represent solute particles, polymers, or membrane structures.
Changed lines 4849 from:
to:
In the SIB formalism the hydrodynamic interactions of the composite system are handled by an approximate treatment of the fluidstructure 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 fluidstructure 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 coarsegrained models of lipid bilayer membranes using the SIB formalism to account for molecular level interactions (lipidlipid and lipidsolvent) along with hydrodynamic coupling and thermal fluctuations. For a more indepth discussion see Dr. Atzberger's [[http://www.math.ucsb.edu/~atzberg/index.html  research website]].
Many interesting mathematical challenges arise in obtaining efficient numerical methods as a result of fast time scales introduced into the fluid dynamics by the thermal fluctuations making the resulting system of equations stiff.
Dr. Atzberger's group uses results from stochastic calculus to develop efficient stochastic numerical methods for the formalism. In collaboration with the Brown Group, Department of Chemistry, Dr. Atzberger's group is developing dynamic coarsegrained models of lipid bilayer membranes using the SIB formalism to account for molecular level interactions (lipidlipid and lipidsolvent) along with hydrodynamic coupling and thermal fluctuations. For a more indepth discussion see Dr. Atzberger's [[http://www.math.ucsb.edu/~atzberg/index.html  research website]].
Added lines 5675:

!! 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. GarciaCervera's group and Dr. Cinceros's group...

!! Analysis of XYZ...
Brief article outlining basic area of research, interesting math. issues.
Mention Dr. GarciaCervera's group and Dr. Cinceros's group...
!! Implicit Immersed Boundary Methods...
Brief article outlining basic area of research, interesting math. issues.
Mention Dr. Cinceros's group... (maybe merge SIB and IIBM approaches into one article on IB methods and boundary integral methods and then reference group members.)

!! Liquid Crystals and XYZ
Brief article outlining basic area of research, interesting math. issues.
Mention Dr. GarciaCervera's group and Dr. Cinceros's group...

!! Analysis of XYZ...
Brief article outlining basic area of research, interesting math. issues.
Mention Dr. GarciaCervera's group and Dr. Cinceros's group...
Changed lines 7783 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 nearfinal form].
The working process will eventually be to have a "hidden" page we can all edit
where we write the materials and review before copying to the homepage.
our work. We can discuss style of the research highlights and how we present things
if you think this is too much
we go public to discuss overall theme and criteria for content... Please also take
a shot at posting some materials for discussion [present in nearfinal form].
where
to:
Above is an experiment and rough draft / brainstorm. Above is meant to give an example of what we might post to highlight our research programs and ongoing 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 nearfinal form]. The working process will eventually be to have a "hidden" page we can all edit where we write the materials and review before copying to the homepage.
Another model is to have simply an image with a short caption and links to researchers webpages with more detailed into... [see UNC site].
We can discuss style of the research highlights and how we present things
if you think this is too much... In any case, the idea is to post things here before we go public to discuss overall theme and criteria for content... Please also take a shot at posting some materials for discussion [present in nearfinal 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 4546 from:
are numerical approaches for studying the mechanics of elastic structures which interact with a fluid in systems at small lengthscales where thermal fluctuations play an important role. The hydrodynamic interactions of the composite system are handled by an approximate treatment of the fluidstructure 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 fluidstructure 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 lengthscales where thermal fluctuations play an important role. The hydrodynamic interactions of the composite system are handled by an approximate treatment of the fluidstructure 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 fluidstructure 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 coarsegrained models of lipid bilayer membranes are being developed using the SIB formalism to account for molecular level interactions, lipidlipid and lipidsolvent hydrodynamic coupling, and thermal fluctuations. For a more indepth 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 coarsegrained models of lipid bilayer membranes using the SIB formalism to account for molecular level interactions (lipidlipid and lipidsolvent) along with hydrodynamic coupling and thermal fluctuations. For a more indepth 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 fluidstructure 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 fluidstructure 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 lengthscales where thermal fluctuations play an important role. The hydrodynamic interactions of the composite system are handled by an approximate treatment of the fluidstructure 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 fluidstructure 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 fluidstructure 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 fluidstructure 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 fluidstructure 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 fluidstructure 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 FluidStructure Dynamics:
to:
!!Stochastic Immersed Boundary Methods for FluidStructure Dynamics:
Changed line 41 from:
!!Stochastic Immersed Boundary Methods for Computational Fluid Dynamics:
to:
!!Stochastic Immersed Boundary Methods for Computational FluidStructure Dynamics:
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!!Stochastic Immersed Boundary Methods for Computational Fluid Dynamics: [[http://www.math.ucsb.edu/~atzberg/index.html  '+Dr. Paul J. Atzberger+']]
to:
!!Stochastic Immersed Boundary Methods for Computational Fluid Dynamics:
[[http://www.math.ucsb.edu/~atzberg/index.html  '+Paul J. Atzberger+']]
[[http://www.math.ucsb.edu/~atzberg/index.html  '+Paul J. Atzberger+']]
Changed lines 4546 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 fluidstructure 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 fluidstructure 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 fluidstructure 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 fluidstructure 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 4951 from:
Immersed structures in SIB can be used to represent the mechanics of a variety of microscopic hydrodynamic systems, for example, in a complex fluid the structures could represent solute particles, polymers, or membrane structures
to:
Immersed structures in SIB can be used to represent the mechanics of a variety of microscopic hydrodynamic systems, for example, in a complex fluid the structures could represent solute particles, polymers, or membrane structures. In collaboration with the Brown Group, Department of Chemistry, Dr. Atzberger's group is developing dynamic coarsegrained models of lipid bilayer membranes are being developed using the SIB formalism to account for molecular level interactions, lipidlipid and lipidsolvent hydrodynamic coupling, and thermal fluctuations. For a more indepth discussion see Dr. Atzberger's [[http://www.math.ucsb.edu/~atzberg/index.html  research website]].
Changed lines 4144 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 4245 from:
to:
[[http://www.math.ucsb.edu/~atzberg/index.html  '+Dr. Paul J. Atzberger+']]
Changed line 52 from:
The formalism is cast in terms of a system of Stochastic Partial Differential Equations (SPDE's). Fast time scales introduced into the fluid dynamics by the thermal fluctuations pose a challenge for conventional approaches to numerical approximation. Using results from stochastic calculus, we are developing efficient stochastic numerical methods for the formalism. Additional work includes development of stochastic numerical methods for nonperiodic 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 nonperiodic and adaptive multilevel meshes.
Changed lines 4445 from:
to:
Added lines 4849:
%width=400px% Attach:SIB_Schematic.png
Added lines 4445:
%width=400px% Attach:SIB_Schematic.png
Changed lines 4751 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 fluidstructure 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 fluidstructure 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 nonperiodic 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 coarsegrained models of lipid bilayer membranes are being developed using the SIB formalism to account for molecular level interactions, lipidlipid and lipidsolvent hydrodynamic coupling, and thermal fluctuations. For a more indepth discussion see the publications section.
Immersed structures in SIB can be used to represent the mechanics
to:
are numerical approaches for studying the mechanics of elastic structures which interact with a fluid in the presence of thermal fluctuations. The hydrodynamic interactions of the composite system are handled by an approximate treatment of the fluidstructure 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 fluidstructure 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 nonperiodic 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 coarsegrained models of lipid bilayer membranes are being developed using the SIB formalism to account for molecular level interactions, lipidlipid and lipidsolvent hydrodynamic coupling, and thermal fluctuations. For a more indepth discussion see Dr. Atzberger's [[http://www.math.ucsb.edu/~atzberg/index.html  research website.]]
The formalism is cast in terms of a system of Stochastic Partial Differential Equations (SPDE's). Fast time scales introduced into the fluid dynamics by the thermal fluctuations pose a challenge for conventional approaches to numerical approximation. Using results from stochastic calculus, we are developing efficient stochastic numerical methods for the formalism. Additional work includes development of stochastic numerical methods for nonperiodic 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 coarsegrained models of lipid bilayer membranes are being developed using the SIB formalism to account for molecular level interactions, lipidlipid and lipidsolvent hydrodynamic coupling, and thermal fluctuations. For a more indepth discussion see Dr. Atzberger's [[http://www.math.ucsb.edu/~atzberg/index.html  research website.]]
Changed lines 5455 from:
(rough draft / brainstorm) Above is meant to give an example of what we might post about
to:

Above is (rough draft / brainstorm) Above is meant to give an example of what we might post about
Above is (rough draft / brainstorm) Above is meant to give an example of what we might post about
Changed line 64 from:
the website all content editing will be password protected (admin or
to:
the public part of the website all content editing will be password protected (admin or
Changed lines 7476 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 bylaws for the pages
remove anything
These
to:
also agree to authorize certain individuals (by majority vote) to have the
right to post content online 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 bylaws for the pages
right to post content online 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 bylaws 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 6566 from:
core members). To avoid abuse by any group members, mainly the usual one,
we shall have the convention that all core members "vote"
we shall have the
to:
core members). To avoid abuse by any one group member.
I propose we shall have the official convention that all core members "vote"
I propose we shall have the official convention that all core members "vote"
Changed lines 7379 from:
"donotapprove PJA", after all members post the admin will copy...
[This paragraph will be copied to our manual of bylaws 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 "OffCenter" around Applied and Computational Analysis
and make the pages based on that group to avoid having to deal with
certain members. In any case, the group should brainstorm here.
avoid any university issues if anyone formally objects to not being able
to post anything they like...]. Another work around might be to start out
own "Center" or "OffCenter" around Applied and Computational Analysis
certain members. In any case, the group should brainstorm here
to:
"donotapprove 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 bylaws for the pages
if this is required by university to avoid any issues of "free speech" and
to guard against any formal objections being made to fairness.
also agree to authorize certain individuals to post content with provision they
remove anything to which a majority in the group objects.
These paragraphs could be copied to a formal manual on bylaws 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 6365 from:
To avoid the alltoo common wackyness from occuring by some appl. members,
to:
To handle the issue of any members putting in appropriate things on
the website all content editing will be password protected (admin or
core members). To avoid abuse by any group members, mainly the usual one,
the website all content editing will be password protected (admin or
core members). To avoid abuse by any group members, mainly the usual one,
Changed lines 6972 from:
in fairness his wackiness to post material, but everything online reflects
the group consensus. Anything failing the vote and revisions process will not
be copied to the homepage [kind of like a journal peerreview process]. Basically,
we will post on the hidden page content "approved PJA", "revise xyz PJA",
the group consensus. Anything failing the vote and revisions process will not
be copied to the homepage [kind of like a journal peerreview 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 online
reflects the group consensus. Anything failing the vote and revisions process
will not be copied to the homepage [kind of like a journal peerreview process].
Basically, we will post on the hidden page content "approved PJA", "revise xyz PJA",
reflects the group consensus. Anything failing the vote and revisions process
will not be copied to the homepage [kind of like a journal peerreview process].
Basically, we will post on the hidden page content "approved PJA", "revise xyz PJA",
Changed lines 7679 from:
to post anything they like...].
to:
to post anything they like...]. Another work around might be to start out
own "Center" or "OffCenter" around Applied and Computational Analysis
and make the pages based on that group to avoid having to deal with
certain members. In any case, the group should brainstorm here.
own "Center" or "OffCenter" 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 7273 from:
[This paragraph will be copied to our manual on bylaws for the pages to
avoid any university issues ifany wacko's object...].
avoid any university issues if
to:
[This paragraph will be copied to our manual of bylaws for the pages to
avoid any university issues if anyone formally objects to not being able
to post anything they like...].
avoid any university issues if anyone formally objects to not being able
to post anything they like...].
Changed lines 6073 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 alltoo common wackyness 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 wackiness to post material, but everything online reflects
the group consensus. Anything failing the vote and revisions process will not
be copied to the homepage [kind of like a journal peerreview process]. Basically,
we will post on the hidden page content "approved PJA", "revise xyz PJA",
"donotapprove PJA", after all members post the admin will copy...
[This paragraph will be copied to our manual on bylaws for the pages to
avoid any university issues if any wacko's object...].
To avoid the alltoo common wackyness 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 wackiness to post material, but everything online reflects
the group consensus. Anything failing the vote and revisions process will not
be copied to the homepage [kind of like a journal peerreview process]. Basically,
we will post on the hidden page content "approved PJA", "revise xyz PJA",
"donotapprove PJA", after all members post the admin will copy...
[This paragraph will be copied to our manual on bylaws 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 / softcondensed matter, computational fluid
Changed lines 1117 from:
analysis of nonlinear hyperbolic PDE's (?), applied harmonic analysis.
Here you will find research highlights, upcoming seminar talks, and
information about news and current activities of the applied mathematics
group.
(Please edit and take a shot at writing this materials. We can collectively edit
over time until we get something we are all happy with.).
Here you will find research highlights, upcoming seminar talks, and
group.
over time until we get something
to:
analysis of nonlinear hyperbolic PDE's (?), applied harmonic analysis,
stochastic differential equations. Here you will find research highlights,
upcoming seminar talks, and information about news and current activities
of the applied mathematics group.
Please feel free to edit and taking a shot at writing these materials.
We can collectively edit over time until we get something we are
all happy with.
stochastic differential equations. Here you will find research highlights,
upcoming seminar talks, and information about news and current activities
of the applied mathematics group.
Please feel free to edit and taking a shot at writing these materials.
We can collectively edit over time until we get something we are
all happy with.
Changed lines 5460 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 nearfinal 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 nearfinal form].
The working process will eventually be to have a "hidden" page we can all edit
where we write the materials and review before copying to the homepage.
our work. We can discuss style of the research highlights and how we present things
if you think this is too much... In any case, the idea is to post things here before
we go public to discuss overall theme and criteria for content... Please also take
a shot at posting some materials for discussion [present in nearfinal 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 56 from:
development of core areas of mathematics motivated by the solution to
specific problems arising in applications, such as arise in the basic sciences
specific problems arising in applications
to:
development of core areas of mathematics with the solution of
specific problems arising in applications often in the basic sciences
specific problems arising in applications often in the basic sciences
Changed line 6 from:
problems arising in applications, such as arise in the basic sciences
to:
specific problems arising in applications, such as arise in the basic sciences
Changed lines 57 from:
development of core areas of mathematics while motivated by the solution to
problems arising in applications, such as arise in the sciences
and engineering. Specific areas in which faculty are involved include
problems arising in applications, such as arise in the sciences
to:
development of core areas of mathematics motivated by the solution to
problems arising in applications, such as arise in the basic sciences
or engineering. Specific areas in which faculty are involved include
problems arising in applications, such as arise in the basic sciences
or engineering. Specific areas in which faculty are involved include
Changed lines 37 from:
Welcome to the applied mathematics group's homepage. Here you will find
information about current research activities and events around campus
related to applied mathematics. Applied mathematics refers to the
branch of mathematics which strives to integrate the development of
core areas of mathematics while motivated by the solution to
information about current research activities and events around campus
related to applied mathematics. Applied mathematics refers to the
branch of mathematics which strives to integrate the development of
core areas of mathematics while motivated by the solution to
to:
Welcome to the applied mathematics group's homepage. Applied mathematics
refers to the branch of mathematics which strives to integrate the
development of core areas of mathematics while motivated by the solution to
refers to the branch of mathematics which strives to integrate the
development of core areas of mathematics while motivated by the solution to
Changed lines 711 from:
and engineering. Here you will find research highlights, upcoming
seminar talks, and information about news and current activities of
the applied mathematics group.
(please take a shot at writing this and we can collectively edit).
seminar talks, and information about news and current activities of
the applied mathematics group.
(please take a shot at writing this and we can collectively edit
to:
and engineering. Specific areas in which faculty are involved include
the study of complex fluids / soft condense matter, computational fluid
dynamics (boundary integral methods / immersed boundary methods),
crystalline solids and liquid crystals, density functional theory,
analysis of nonlinear hyperbolic PDE's (?), applied harmonic analysis.
Here you will find research highlights, upcoming seminar talks, and
information about news and current activities of the applied mathematics
group.
(Please edit and take a shot at writing this materials. We can collectively edit
over time until we get something we are all happy with.).
the study of complex fluids / soft condense matter, computational fluid
dynamics (boundary integral methods / immersed boundary methods),
crystalline solids and liquid crystals, density functional theory,
analysis of nonlinear 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 34 from:
Welcome to the applied mathematics group's homepage...
blurb about unifying themes and mission...
to:
Welcome to the applied mathematics group's homepage. Here you will find
information about current research activities and events around campus
related to applied mathematics. Applied mathematics refers to the
branch of mathematics which strives to integrate the development of
core areas of mathematics while motivated by the solution to
problems arising in applications, such as arise in the sciences
and engineering. Here you will find research highlights, upcoming
seminar talks, and information about news and current activities of
the applied mathematics group.
information about current research activities and events around campus
related to applied mathematics. Applied mathematics refers to the
branch of mathematics which strives to integrate the development of
core areas of mathematics while motivated by the solution to
problems arising in applications, such as arise in the sciences
and engineering. Here you will find research highlights, upcoming
seminar talks, and information about news and current activities of
the applied mathematics group.
Changed lines 2735 from:
\\
%width=100px% Attach:carlosImage.png %width=100px% Attach:atzbergerImage.png

to:
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to:
!!Other highlights here...(images / movies, etc...) \\
\\
%width=100px% Attach:carlosImage.png %width=100px% Attach:atzbergerImage.png

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

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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 fluidstructure 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 fluidstructure 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 nonperiodic 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 fluidstructure 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 fluidstructure 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 nonperiodic and adaptive multilevel meshes, see Dr. Atzberger's [[http://www.math.ucsb.edu/~atzberg/index.html  papers.]]
Changed lines 4243 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 nearfinal form].)
Changed lines 3940 from:
to:
Dr. Atzberger's group works on Stochastic Immersed Boundary Methods (SIB) which
are a numerical approaches for studying the mechanics of elastic structures which interact with a fluid in the presence of thermal fluctuations. The hydrodynamic interactions of the composite system are handled by an approximate treatment of the fluidstructure 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 fluidstructure 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 nonperiodic and adaptive multilevel meshes, see Dr. Atzberger's [[http://www.math.ucsb.edu/~atzberg/index.html  papers.]]
are a numerical approaches for studying the mechanics of elastic structures which interact with a fluid in the presence of thermal fluctuations. The hydrodynamic interactions of the composite system are handled by an approximate treatment of the fluidstructure 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 fluidstructure 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 nonperiodic and adaptive multilevel meshes, see Dr. Atzberger's [[http://www.math.ucsb.edu/~atzberg/index.html  papers.]]
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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 coarsegrained models of lipid bilayer membranes are being developed using the SIB formalism to account for molecular level interactions, lipidlipid and lipidsolvent hydrodynamic coupling, and thermal fluctuations. For a more indepth 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 coarsegrained models of lipid bilayer membranes are being developed using the SIB formalism to account for molecular level interactions, lipidlipid and lipidsolvent hydrodynamic coupling, and thermal fluctuations. For a more indepth discussion see the publications section.
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Dr. Paul J. Atzberger
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!!Stochastic Immersed Boundary Methods / Computational Fluid Dynamics:\\
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!!Stochastic Immersed Boundary Methods / Computational Fluid Dynamics:
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!!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 fluidstructure 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 fluidstructure 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 nonperiodic 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 coarsegrained models of lipid bilayer membranes are being developed using the SIB formalism to account for molecular level interactions, lipidlipid and lipidsolvent hydrodynamic coupling, and thermal fluctuations. For a more indepth 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/20082009/W11.37.08/abstracts.html#AtzbergerPaul  here.]]
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(please take a shot at writing this and we can collectively edit).
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Carlos GarciaCervera receives the prestigious NSF Career Award for his proposal "Multilevel Physics in the Study of Solids: Modeling, Analysis and Simulations".
Carlos GarciaCervera receives the prestigious NSF Career Award for his proposal "Multilevel Physics in the Study of Solids: Modeling, Analysis and Simulations".
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Carlos GarciaCervera receives the prestigious NSF Career Award for his proposal
"Multilevel Physics in the Study of Solids: Modeling, Analysis and Simulations".
Carlos
"Multilevel Physics in the Study of Solids: Modeling, Analysis and Simulations".
to:
%width=150px% Attach:carlosImage.png Carlos GarciaCervera receives the prestigious NSF Career Award for his proposal "Multilevel Physics in the Study of Solids: Modeling, Analysis and Simulations".
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For practice for when the site goes
public the "edit" and viewing the
"intranet" are now password protected.
The password for now is
"4coregroup." Once you type this in a
group your access should be presistent
so will not be required to be entered
too many times. This will give both
you and the administrator (for now me [Paul])
good practice.
\\
\\
We give some links to basic resources
which show how to make edits to the wiki
page. For each page look for the button
"edit" at the bottom to modify the page.\\
\\
Here are two tutorials on the basics of pmWiki syntax:
[[PmWiki/Text Formatting Rules]],
[[http://www.pmwiki.org/wiki/PmWiki/BasicEditing  Tutorial on Wiki Editing]]
Also see the Wikisandbox for a quick set of examples and to play around
with edits. [[Main/WikiSandbox  WikiSandbox]].

!! Wiki Action Items [Please Perform Soon so We Can Launch]
* Enter faculty information and research description on the "Faculty Members" page. Also enter information for any graduate students (very brief name + dept. affiliations).
* Post below a few brief research highlights or resources for use on the website (upload images, movies, link to YouTube channel, etc...). Give brief description. (This is brainstorm for materials).
!! Feedback / Suggestions Concerning the Website
* Please enter any comments or suggestions concerning the Wiki website here.

to:
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Here is a tutorial on the basics of pmWiki syntax:
to:
Here are two tutorials on the basics of pmWiki syntax:
[[PmWiki/Text Formatting Rules]],
[[PmWiki/Text Formatting Rules]],
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!! Welcome
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!!Research Highlights \\
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!!How to use and edit wikipages.
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!! Wiki Action Items [Please Perform Soon so We Can Launch]
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!! Welcome
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!!! Welcome
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!!Research Highlights \\
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!!!Research Highlights \\
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Other highlights here...(images / movies, etc...) \\
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!!Other highlights here...(images / movies, etc...) \\
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!!How to use and edit wikipages.
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!!!How to use and edit wikipages.
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!! Wiki Action Items [Please Perform Soon so We Can Launch]
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!!! Wiki Action Items [Please Perform Soon so We Can Launch]
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!!Carlos GarciaCervera Wins NSF Faculty Early Career Development Award (NSF CAREER)
Carlos GarciaCervera receives the prestigious NSF Career Award for his proposal
"Multilevel Physics in the Study of Solids: Modeling, Analysis and Simulations".
The award will .... and ... The proposed research program has the potential to
impact... This is the first NSF CAREER award given to a faculty member of the
department of mathematics.\\
[[http://www.ia.ucsb.edu/93106/2007/November19/math.html  Full Article]]

Other highlights here...(images / movies, etc...) \\
!!Carlos GarciaCervera Wins NSF Faculty Early Career Development Award (NSF CAREER)
Carlos GarciaCervera 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...) \\
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* 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).
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!! 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  WikiSandbox]].
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Also see the Wikisandbox 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:
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The password is for now is
"4coregroup."
This will give both you and the
administrator for now (me) good practice.
"4coregroup."
This will give both you and the
administrator for now (me)
to:
The password for now is
"4coregroup." Once you type this in a
group your access should be presistent
so will not be required to be entered
too many times. This will give both
you and the administrator (for now me [Paul])
good practice.
"4coregroup." Once you type this in a
group your access should be presistent
so will not be required to be entered
too many times. This will give both
you and the administrator (for now me [Paul])
good practice.
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!!How to use and edit wikipages.\\
\\
\\
to:
!!How to use and edit wikipages.
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to:
!!How to use and edit wikipages.\\
\\
For practice for when the site goes
public the "edit" and viewing the
"intranet" are now password protected.
The password is for now is
"4coregroup."
This will give both you and the
administrator for now (me) good practice.
\\
\\
For practice for when the site goes
public the "edit" and viewing the
"intranet" are now password protected.
The password is for now is
"4coregroup."
This will give both you and the
administrator for now (me) good practice.
\\
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'+How to use and edit wikipages.+'\\
\\
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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!!Research Highlights \\
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!! Wiki Action Item (Group Members Please Perform)
to:
!! Wiki Action Items [Please Perform]
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(these will be removed)
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* Please enter any comments or suggestions concerning
the Wiki website here.
the Wiki website here.
to:
* Please enter any comments or suggestions concerning the Wiki website here.
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* Post a few brief research highlights or resources
for use on the website (upload images, movies, link
to YouTube channel, etc...). Give brief description.
(This is brainstorm for materials.
for use on the website (upload images, movies, link
to:
* Post a few brief research highlights or resources for use on the website (upload images, movies, link to YouTube channel, etc...). Give brief description. (This is brainstorm for materials).
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* Enter faculty information and research description on the "Faculty Members" page.
Also enter information for any graduate students (very brief name + dept. affiliations).
Also enter information for any graduate students (very brief name + dept. affiliations).
to:
* Enter faculty information and research description on the "Faculty Members" page. Also enter information for any graduate students (very brief name + dept. affiliations).
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!! 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.
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Research Highlights here...(images / movies, etc...) \\
<a href="test"> test </a>
<a href="test"> test </a>
to:
'+Research Highlights+'\\
Highlights here...(images / movies, etc...) \\
Highlights here...(images / movies, etc...) \\
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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...
\\
Welcome to the applied mathematics group's homepage...
blurb about unifying themes and mission...
\\
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Tuesday, February 17th, 4:00pm  5:00pm, SH 4607. \\
Peter R. Kramer, Dept. Mathematical Sciences, Rensselaer Polytechnic Institute.\\
\\
''Abstract:'' We study an alltoall coupled network of identical excitatory
integrateandfire (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...) \\
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'''Title:''' Talking about something. \\
''Some Speaker, (University of Somewhere), Tuesday, April XX, 3:00pm  4:00pm (South Hall 7777)''. \\
'''Abstract:''' A blurb about what to talk about...\\
''
to:

''''''+Something.+'''''' \\
Tuesday, February 17th, 4:00pm  5:00pm, SH 4607. \\
Someone, Dept. Something, Somewhere.\\
\\
''Abstract:'' Some description of talk.

''''''+Something.+'''''' \\
Tuesday, February 17th, 4:00pm  5:00pm, SH 4607. \\
Someone, Dept. Something, Somewhere.\\
\\
''Abstract:'' Some description of talk.

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'''Abstract:''' We study an alltoall coupled network of identical excitatory
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''Abstract:'' We study an alltoall coupled network of identical excitatory
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Peter R. Kramer, Dept. Mathematical Sciences, Rensselaer Polytechnic Institute.\\
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''''''+Dynamics of a Stochastically Driven Neuronal Network Model.+'''''' \\
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'+Peter R. Kramer, Dept. Mathematical Sciences, Rensselaer Polytechnic Institute.+'\\
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Peter R. Kramer, Dept. Mathematical Sciences, Rensselaer Polytechnic Institute.\\
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+Peter R. Kramer, Dept. Mathematical Sciences, Rensselaer Polytechnic Institute.+\\
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'''+Dynamics of a Stochastically Driven Neuronal Network Model.+'''' \\
''Peter R. Kramer, Dept. Mathematical Sciences, Rensselaer Polytechnic Institute.''\\
''Tuesday, February 17th, 4:00pm  5:00pm, SH 4607.''. \\
to:
'''+Dynamics of a Stochastically Driven Neuronal Network Model.+''' \\
Peter R. Kramer, Dept. Mathematical Sciences, Rensselaer Polytechnic Institute.\\
Tuesday, February 17th, 4:00pm  5:00pm, SH 4607. \\
Peter R. Kramer, Dept. Mathematical Sciences, Rensselaer Polytechnic Institute.\\
Tuesday, February 17th, 4:00pm  5:00pm, SH 4607. \\
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to:
'''+Dynamics of a Stochastically Driven Neuronal Network Model.+'''' \\
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'''Title:''' Talking about something. \\
''Some Speaker, (University of Somewhere), Tuesday, April XX, 3:00pm  4:00pm (South Hall 7777)''. \\
'''Abstract:''' A blurb about what to talk about...\\
''Some Speaker, (University of Somewhere), Tuesday, April XX
''
to:
'''Title:''' Dynamics of a Stochastically Driven Neuronal Network Model. \\
''Peter R. Kramer, Dept. Mathematical Sciences, Rensselaer Polytechnic Institute.''\\
''Tuesday, February 17th, 4:00pm  5:00pm, SH 4607.''. \\
'''Abstract:''' We study an alltoall coupled network of identical excitatory
integrateandfire (I\&F) neurons driven by an external spike train
modeled as a Poisson process. Numerical simulations demonstrate that
over a broad range of parameters, the network enters a synchronized
state in which the neurons all fire together at regular intervals. We
identify mechanisms leading to this synchronization for two regimes of
the external driving current: superthreshold and subthreshold. In the
former, a probabilistic argument similar to the proof of the Central
Limit Theorem yields the oscillation period, while in the latter, this
period is analyzed via an exit time calculation utilizing a diffusion
approximation of the Kolmogorov forward equation. In both cases,
stochastic fluctuations play a central role in determining the
oscillation period. We also develop a criterion for
synchrony in the network through a probabilistic argument. This work
is in collaboration with Katherine Newhall, Gregor Kovacic, David Cai,
and Aaditya Rangan.
''Peter R. Kramer, Dept. Mathematical Sciences, Rensselaer Polytechnic Institute.''\\
''Tuesday, February 17th, 4:00pm  5:00pm, SH 4607.''. \\
'''Abstract:''' We study an alltoall coupled network of identical excitatory
integrateandfire (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.
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\\
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/* http://pmichaud.com/img/misc/gem.jpg */
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''Some Speaker, (University of Somewhere), Tuesday, April XX, 3:00pm  4:00pm (South Hall 7777)''. \\
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''Some Speaker, (University of Somewhere), Tuesday, April XX, 3:00pm  4:00pm (South Hall 7777)''. \\
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\\
'''Title:''' Talking about something. \\
'''Title:''' Talking about something. \\
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''Some Speaker, (University of Somewhere), Tuesday, April XX, 3:00pm  4:00pm (South Hall 7777)''.
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''Some Speaker, (University of Somewhere), Tuesday, April XX, 3:00pm  4:00pm (South Hall 7777)''. \\
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''Some Speaker, (University of Somewhere), Tuesday, April XX, 3:00pm  4:00pm (South Hall 7777)''.
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''Some Speaker, (University of Somewhere), Tuesday, April XX, 3:00pm  4:00pm (South Hall 7777)''. \\
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''Some Speaker, (University of Somewhere), Tuesday, April XX, 3:00pm  4:00pm (South Hall 7777)''.
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''Some Speaker, (University of Somewhere), Tuesday, April XX, 3:00pm  4:00pm (South Hall 7777)''.
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'''Title:'''
'''Abstract:'''
\\
to:
'''Title:''' Talking about something. \\
'''Abstract:''' A blurb about what to talk about...\\
* ''Some Speaker, (University of Somewhere), Tuesday, April XX, 3:00pm  4:00pm (South Hall 7777)''.
'''Title:''' Talking about something. \\
'''Abstract:''' A blurb about what to talk about...\\
'''Abstract:''' A blurb about what to talk about...\\
* ''Some Speaker, (University of Somewhere), Tuesday, April XX, 3:00pm  4:00pm (South Hall 7777)''.
'''Title:''' Talking about something. \\
'''Abstract:''' A blurb about what to talk about...\\
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* Some Speaker, (University of Somewhere), Tuesday, April XX, 3:00pm  4:00pm (South Hall 7777).
* Some Speaker, (University of Somewhere), Tuesday, April XX, 3:00pm  4:00pm (South Hall 7777).
* Some Speaker, (University of Somewhere), Tuesday, April XX, 3:00pm  4:00pm (South Hall 7777).
* Some Speaker, (University of Somewhere), Tuesday, April XX, 3:00pm  4:00pm (South Hall 7777).
to:
* ''Some Speaker, (University of Somewhere), Tuesday, April XX, 3:00pm  4:00pm (South Hall 7777)''.
'''Title:'''
'''Abstract:'''
'''Title:'''
'''Abstract:'''
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!! 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
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!! Research Project I
to:
!! Applied Math and PDE Seminar
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Image and some links
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* 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).
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!! Research Project I http://pmichaud.com/img/misc/gem.jpg
to:
!! Research Project I
http://pmichaud.com/img/misc/gem.jpg
http://pmichaud.com/img/misc/gem.jpg
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!! Research Project I
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!! Research Project I http://pmichaud.com/img/misc/gem.jpg
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http://pmichaud.com/img/misc/gem.jpg
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%http://pmichaud.com/img/misc/gem.jpg
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%lfloat %http://pmichaud.com/img/misc/gem.jpg
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%lfloat%http://pmichaud.com/img/misc/gem.jpg
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%lfloat textalign=left margintop=0px marginright=0px marginbottom=10px marginleft=0px %http://pmichaud.com/img/misc/gem.jpg
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%lfloat %http://pmichaud.com/img/misc/gem.jpg
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%lfloat textalign=left margintop=0px marginright=0px marginbottom=10px marginleft=0px %http://pmichaud.com/img/misc/gem.jpg '''The image is leftaligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''
%lfloat text
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%lfloat textalign=left margintop=0px marginright=0px marginbottom=10px marginleft=0px %http://pmichaud.com/img/misc/gem.jpg
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%lfloat textalign=left margintop=0px marginright=0px marginbottom=10px marginleft=0px %http://pmichaud.com/img/misc/gem.jpg '''The image is leftaligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''
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Research project will be discussed here...
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Research project will be discussed here...
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Research project will be discussed here...
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Image and some links
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[[(http://www.math.ucsb.edu/~atzberg/movies4IGERT/trefoilKnot.avi  Trefoil knot ]]
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!! Research Project II
First research project will be discussed here...
Image and some links
First research project will be discussed here...
Image and some links
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%lfloat textalign=left margintop=0px marginright=0px marginbottom=10px marginleft=0px %http://pmichaud.com/img/misc/gem.jpg '''The image is leftaligned, 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 textalign=center margintop=5px marginright=25px
marginbottom=5px marginleft=25px
% http://pmichaud.com/img/misc/gem.jpg 
'''Rock on!'''
'''The image is leftaligned, 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

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!! Major Subheading
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!! Research Project I
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%lfloat textalign=left margintop=0px marginright=0px marginbottom=0px marginleft=0px %http://pmichaud.com/img/misc/gem.jpg '''The image is leftaligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''
to:
%lfloat textalign=left margintop=0px marginright=0px marginbottom=10px marginleft=0px %http://pmichaud.com/img/misc/gem.jpg '''The image is leftaligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''
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%lfloat textalign=left margintop=0px marginright=0px marginbottom=5px marginleft=25px %http://pmichaud.com/img/misc/gem.jpg '''The image is leftaligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''
to:
%lfloat textalign=left margintop=0px marginright=0px marginbottom=0px marginleft=0px %http://pmichaud.com/img/misc/gem.jpg '''The image is leftaligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''
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%lfloat textalign=left margintop=2px marginright=5px marginbottom=5px marginleft=25px %http://pmichaud.com/img/misc/gem.jpg '''The image is leftaligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''
to:
%lfloat textalign=left margintop=0px marginright=0px marginbottom=5px marginleft=25px %http://pmichaud.com/img/misc/gem.jpg '''The image is leftaligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''
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%lfloat textalign=center margintop=2px marginright=5px marginbottom=5px marginleft=25px %http://pmichaud.com/img/misc/gem.jpg '''The image is leftaligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''
to:
%lfloat textalign=left margintop=2px marginright=5px marginbottom=5px marginleft=25px %http://pmichaud.com/img/misc/gem.jpg '''The image is leftaligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''
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%lfloat textalign=center margintop=2px marginright=5px marginbottom=5px marginleft=25px %http://pmichaud.com/img/misc/gem.jpg The image is leftaligned, with margins set; the caption is centered; the text wraps on the right side of the image.
to:
%lfloat textalign=center margintop=2px marginright=5px marginbottom=5px marginleft=25px %http://pmichaud.com/img/misc/gem.jpg '''The image is leftaligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''
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%lfloat textalign=center margintop=2px marginright=5px marginbottom=5px marginleft=25px %http://pmichaud.com/img/misc/gem.jpg '''Look!''' '''The image is leftaligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''
to:
%lfloat textalign=center margintop=2px marginright=5px marginbottom=5px marginleft=25px %http://pmichaud.com/img/misc/gem.jpg The image is leftaligned, with margins set; the caption is centered; the text wraps on the right side of the image.
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%lfloat textalign=left margintop=2px marginright=5px marginbottom=5px marginleft=25px %http://pmichaud.com/img/misc/gem.jpg '''Look!''' '''The image is leftaligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''
to:
%lfloat textalign=center margintop=2px marginright=5px marginbottom=5px marginleft=25px %http://pmichaud.com/img/misc/gem.jpg '''Look!''' '''The image is leftaligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''
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%lfloat textalign=left margintop=2px marginright=5px marginbottom=5px marginleft=25px %http://pmichaud.com/img/misc/gem.jpg '''Rock on!''' '''The image is leftaligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''
to:
%lfloat textalign=left margintop=2px marginright=5px marginbottom=5px marginleft=25px %http://pmichaud.com/img/misc/gem.jpg '''Look!''' '''The image is leftaligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''
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%lfloat textalign=left margintop=0px marginright=25px marginbottom=5px marginleft=25px %http://pmichaud.com/img/misc/gem.jpg '''Rock on!''' '''The image is leftaligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''
to:
%lfloat textalign=left margintop=2px marginright=5px marginbottom=5px marginleft=25px %http://pmichaud.com/img/misc/gem.jpg '''Rock on!''' '''The image is leftaligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''
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%lfloat textalign=left margintop=2px marginright=25px marginbottom=5px marginleft=25px %http://pmichaud.com/img/misc/gem.jpg '''Rock on!''' '''The image is leftaligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''
to:
%lfloat textalign=left margintop=0px marginright=25px marginbottom=5px marginleft=25px %http://pmichaud.com/img/misc/gem.jpg '''Rock on!''' '''The image is leftaligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''
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%lfloat textalign=left margintop=2px marginright=25px marginbottom=5px marginleft=25px %http://pmichaud.com/img/misc/gem.jpg '''Rock on!''' '''The image is leftaligned, with margins set; the caption is centered; the text wraps on the right side of the image.
to:
%lfloat textalign=left margintop=2px marginright=25px marginbottom=5px marginleft=25px %http://pmichaud.com/img/misc/gem.jpg '''Rock on!''' '''The image is leftaligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''
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%lfloat textalign=left margintop=2px marginright=25px marginbottom=5px marginleft=25px %http://pmichaud.com/img/misc/gem.jpg '''Rock on!''' '''The image is leftaligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''
to:
%lfloat textalign=left margintop=2px marginright=25px marginbottom=5px marginleft=25px %http://pmichaud.com/img/misc/gem.jpg '''Rock on!''' '''The image is leftaligned, with margins set; the caption is centered; the text wraps on the right side of the image.
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%lfloat textalign=left margintop=2px marginright=25px marginbottom=5px marginleft=25px %http://pmichaud.com/img/misc/gem.jpg  '''Rock on!''' '''The image is leftaligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''
to:
%lfloat textalign=left margintop=2px marginright=25px marginbottom=5px marginleft=25px %http://pmichaud.com/img/misc/gem.jpg '''Rock on!''' '''The image is leftaligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''
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%lfloat textalign=right margintop=5px marginright=25px marginbottom=5px marginleft=25px %http://pmichaud.com/img/misc/gem.jpg  '''Rock on!''' '''The image is leftaligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''
to:
%lfloat textalign=left margintop=2px marginright=25px marginbottom=5px marginleft=25px %http://pmichaud.com/img/misc/gem.jpg  '''Rock on!''' '''The image is leftaligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''
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%lfloat textalign=left margintop=5px marginright=25px marginbottom=5px marginleft=25px %http://pmichaud.com/img/misc/gem.jpg  '''Rock on!''' '''The image is leftaligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''
to:
%lfloat textalign=right margintop=5px marginright=25px marginbottom=5px marginleft=25px %http://pmichaud.com/img/misc/gem.jpg  '''Rock on!''' '''The image is leftaligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''
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%lfloat textalign=center margintop=5px marginright=25px marginbottom=5px marginleft=25px %http://pmichaud.com/img/misc/gem.jpg  '''Rock on!''' '''The image is leftaligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''
to:
%lfloat textalign=left margintop=5px marginright=25px marginbottom=5px marginleft=25px %http://pmichaud.com/img/misc/gem.jpg  '''Rock on!''' '''The image is leftaligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''
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%lfloat textalign=center margintop=5px marginright=25px marginbottom=5px marginleft=25px
%http://pmichaud.com/img/misc/gem.jpg '''Rock on!''' '''The image is leftaligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''
to:
%lfloat textalign=center margintop=5px marginright=25px marginbottom=5px marginleft=25px %http://pmichaud.com/img/misc/gem.jpg  '''Rock on!''' '''The image is leftaligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''
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%lfloat textalign=center margintop=5pxmarginright=25pxmarginbottom=5px marginleft=25px
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%lfloat textalign=center margintop=5px marginright=25px marginbottom=5px marginleft=25px
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%lfloat textalign=center margintop=5px marginright=25pxmarginbottom=5px marginleft=25px
%http://pmichaud.com/img/misc/gem.jpg '''Rock on!''' '''The image is leftaligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''
%lfloat textalign=center margintop=5px marginright=25pxmarginbottom=5px marginleft=25px
%http://pmichaud.com/img/misc/gem.jpg '''Rock on!''' '''The image is leftaligned, with margins set; the caption is centered; the text wraps on the right side of the image.'''
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%lfloat textalign=center margintop=5px marginright=25pxmarginbottom=5px marginleft=25px%http://pmichaud.com/img/misc/gem.jpg '''Rock on!''' '''The image is leftaligned, 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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"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'''
Paper clips"  '''Figure 1'''
to:
http://pmichaud.com/img/misc/pc.jpg
"Paper clips"  '''Figure 1'''
"Paper clips"  '''Figure 1'''
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http://pmichaud.com/img/misc/pc.jpg"
Paper clips"  '''Figure 1'''
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marginbottom=5px marginleft=25px
% http://pmichaud.com/img/misc/gem.jpg 
% http://pmichaud.com/img/misc/gem.jpg 
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'''The image is leftaligned, with margins set; the caption is centered;
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'''The image is leftaligned, with margins set;
the caption is centered;
the caption is centered;
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[[(http://www.math.ucsb.edu/~atzberg/index.html  trefoilKnot.avi ]]
to:
[[(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  trefoilKnot.avi ]]
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[[(http://pmichaud.com/  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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[[(http://pmichaud.com/  Clips ]]
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[[(Wikipedia:Paper_clips  Clips ]]
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"Image Description"
"Image Description"
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http://pmichaud.com/img/misc/pc.jpg"Paper clips"  [ %newwin% [[
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http://pmichaud.com/img/misc/pc.jpg"Paper clips" 
[ %newwin% [[
[ %newwin% [[
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First research project will be discussed here...

First research project will be discussed here...

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First research project to discuss here...
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%lfloat textalign=center margintop=5px marginright=25px
marginbottom=5px marginleft=25px% http://pmichaud.com/img/misc/gem.jpg 
'''Rock on!'''
'''The image is leftaligned, with margins set; the caption is centered;
the text wraps on the right side of the image.'''
marginbottom=5px marginleft=25px% http://pmichaud.com/img/misc/gem.jpg 
'''Rock on!'''
'''The image is leftaligned, 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 