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Speakers:
Kaushik Bhattacharya
Applied Mechanics & Mechanical Engineering
Division of Engineering & Applied Science
California Institute of Technology
bhatta@cco.caltech.edu
http://mechmat.caltech.edu
Biography
Masao Doi
Department of Applied Physics
Tokyo University
doi@cse.nagoyau.ac.jp
http://www.stat.cse.nagoyau.ac.jp/~masao/
Biography
Qiang Du
Department of Mathematics
Pennsylvania State University
qdu@math.psu.edu
http://www.math.psu.edu/qdu/
Biography
Chun Liu
Department of Mathematics
Pennsylvania State University
liu@math.psu.edu
http://www.math.psu.edu/liu/
Biography
Ellad B. Tadmor
Faculty of Mechanical Engineering
Technion  Israel Institute of Technology
tadmor@technion.ac.il
http://tx.technion.ac.il/~tadmor
Biography
The 20042005 IMA thematic program on "Mathematics of Materials and Macromolecules: Multiple Scales, Disorder, and Singularities" will begin with a tutorial on "Mathematics and Materials," during the week September 2024, 2004. The tutorial week will consist of lectures by five distinguished researchers on background topics in methods to analytically and numerically address emerging modeling problems for materials. Applications will include multiscale methods for gels, liquid crystals, superconductivity, micromagnetics, elastomers, and crystalline solids.
The tutorial lectures are scheduled for 910 am, 10:3011:30 am, 1:302:30 pm and 3:004:30 pm, on Monday through Friday of the week of September 20 to 24 of 2004.




MONDAY,
SEPTEMBER 20 All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 


8:308:50  Coffee and Registration  Reception Room EE/CS 3176 

8:509:00  Directors and Organizers  Welcome and Introduction  
9:0010:00  Masao Doi Tokyo University 
Modeling of Gels (The Coupling Between Stress and Diffusion)
Slides: pdf 

10:3011:30  Chun Liu Pennsylvania State University 
Variational Approaches in Complex Fluids Slides: pdf 

1:302:30  Ellad B. Tadmor Technion  Israel Institute of Technology 
MultipleScale Modeling of Materials Using
the Quasicontinuum Method 1. Materials and Multiple Scales 

TUESDAY,
SEPTEMBER 21 All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 

8:459:00  Coffee  Reception Room EE/CS 3176  
9:0010:00  Masao Doi Tokyo University 
Modeling of Gels (The Coupling Between Stress and Diffusion)
Slides: pdf 

10:3011:30  Chun Liu Pennsylvania State University 
Variational Approaches in Complex Fluids Slides: pdf 

1:302:30  Ellad B. Tadmor Technion  Israel Institute of Technology 
MultipleScale Modeling of Materials Using
the Quasicontinuum Method 2. The Theoretical Foundations of the Quasicontinuum Method 

WEDNESDAY,
SEPTEMBER 22 All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 

8:459:00  Coffee  Reception Room EE/CS 3176  
9:0010:00  Chun Liu Pennsylvania State University 
Variational Approaches in Complex Fluids Slides: pdf 

10:3011:30  Qiang Du Pennsylvania State University 
Mathematical Models of Superconductivity, an Introduction  
1:302:30  Ellad B. Tadmor Technion  Israel Institute of Technology 
MultipleScale Modeling of Materials Using
the Quasicontinuum Method 3. Quasicontinuum Applications 

3:004:00  Kaushik Bhattacharya California Institute of Technology 
Energy Minimization and Microstructure Paper: pdf 

THURSDAY,
SEPTEMBER 23 All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 

8:459:00  Coffee  Reception Room EE/CS 3176  
9:0010:00  Masao Doi Tokyo University 
Modeling of Gels (The Coupling Between Stress and Diffusion)
Slides: pdf 

10:3011:30  Qiang Du Pennsylvania State University 
Mathematical Models of Superconductivity, an Introduction  
1:302:30  Kaushik Bhattacharya California Institute of Technology 
Energy Minimization and Microstructure Paper: pdf 

FRIDAY,
SEPTEMBER 24 All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 

8:459:00  Coffee  Reception Room EE/CS 3176  
9:0010:00  Masao Doi Tokyo University 
Modeling of Gels (The Coupling Between Stress and Diffusion)
Slides: pdf 

10:3011:30  Qiang Du Pennsylvania State University 
Mathematical Models of Superconductivity, an Introduction  
1:302:30  Kaushik Bhattacharya California Institute of Technology 
Energy Minimization and Microstructure Paper: pdf 
Kaushik Bhattacharya (California Institute of Technology)
Biography: Kaushik Bhattacharya is a Professor of Mechanics and Materials Science at the California Institute of Technology. He received his Ph.D in Mechanics from the University of Minnesota in 1991 and his postdoctoral training at the Courant Institute for Mathematical Sciences during 19911993. He has held visiting positions at Cornell University, HeriotWatt University (Scotland), MaxPlanckInstitute (Leipzig, Germany), Cambridge University (England) and the Indian Institute of Science (Bangalore, India). He received the Young Investigator Award from the National Science Foundation (NSF) in 1994, Charles Lee Powell Award in 1997, the Young Investigator Prize from the Society of Engineering Science (SES) in 2003 and the Special Achievements Award in Applied Mechanics from the American Society of Mechanical Engineers in 2004. He is currently the Editor of the Journal of the Mechanics and Physics of Solids, and serves on the Editorial Board of three other journals. He has organized numerous international meetings including a fourmonth program at the Isaac Newton Institute, Cambridge, England on the mechanics of materials in 1999, and the recent SIAM Conference on the Mathematical Aspects of Materials Science in 2004. His research interest concerns modeling problems that arise in Materials Science, especially in the area of Active Materials.
Energy Minimization and Microstructure
Paper: pdf
Abstract. There are numerous phenomena in materials science where finescale microstructure is the result of the material seeking to optimize multiple incongruent objectives. Examples include alloy phase segregation, martensitic phase transformation, nematic elastomers, ferroelectrics and faceting of crystalline surfaces. Further the ability of a material to form microstructure and to change its microstructure depending on the macroscopic boundary conditions endow the materials with unusual macroscopic behavior like the shapememory effect, electrostriction and the liquidlike behavior of solids.
These series of lectures will describe selected examples of such phenomena and how such a phenomenon can naturally be modeled as a variational problem, specifically a minimization problem with nonconvex energy density. It will show that microstructure arises as an inevitable consequence of such a variational problem and that nontrivial aspects of the microstructure can be predicted from such a formulation. Finally, it will introduce the notion of effective behavior, i.e., the overall behavior of the material after it has formed microstructure, how microstructure gives rise to very unusual effective behavior and how one can describe it without having to resolve every fine detail of the microstructure. These lectures are intended to be accessible to a broad audience with a balance between phenomena, modeling and mathematical analysis.
Biography: Dr. Masao Doi is Professor of Computational Science and Engineering in Nagoya University. He was a Fellow of the Science Research Council at Cambridge University from 1976 through 1978. Professor Doi has received awards from the Polymer Society of the Japan and Rheology Society of Japan for his research on polymer dynamics and rheology. He is also the recipient of the Japan IBM Award of Science and doctor honoris causa of Katholic University Leuven, Belgium. His monograph, `The Theory of Polymer Dynamics` with Sam Edwards has become the standard reference on nonlinear rheology of flexible and rodlike polymers. Professor Doi received the Polymer Physics Prize in 2001 "For pioneering contributions to the theory of dynamics and rheology of entangled polymers and complex fluids."
Modeling of Gels (The Coupling Between Stress and Diffusion)
The lecture topics will be distributed as follows:
(1) What is a gel Slides: pdf
(2) Stress diffusion coupling: the phenomena and modeling Slides:
pdf
(3) Stressdiffusion coupling in polymer solutions Slides:
pdf
(4) Electroresponsive gels Slides:
pdf
Abstract: A gel is an elastic object swollen by solvent, so the force acting on the gel is coupled with the diffusion of the solvent. The stressdiffusion coupling is seen commonly in everyday life (water coming out of a squeezed gel) and is also important in many chemical engineering processes, soaking, drying and sedimentation. The stress diffusion coupling is also important in the study of artificial muscles, where the deformation of the gel is controlled by an electric field. Professor Doi will present equations for the stress diffusion coupling for an ionic gel and discuss electrochemical effects.
Qiang Du (Pennsylvania State University)
Biography: Qiang Du is a professor of mathematics at the Pennsylvania State University, University Park. He received his Ph.D. in 1988 under the direction of Max Gunzburger and then went on to do as a Dickson Instructor at the University of Chicago. He then served as assistant and associate professor in the Mathematics Department at Michigan State University from 19901996, before holding professorships at Iowa State University and the Hong Kong University of Science and Technology. Qiang Du's research interests span many areas but include numerical algorithms, partial differential equations, parallel and scientific computation and applications to the physical sciences. He is, in particular, internationally recognized as one of the world's leading researchers in the area of GinzburgLandau theory and superconductivity.
Mathematical Models of Superconductivity, an Introduction
Abstract: Superconductivity is one of the grand challenges identified as being crucial to future economic prosperity and scientific leadership. In recent years, the analysis and simulations of various mathematical models in superconductivity have attracted the interests of many mathematicians all over the world. Their works have helped us to understand the intriguing and complex phenomena in superconductivity.
With the recent award of the Nobel Prize in Physics, a renewed attention has been focused on theoretical foundations of superconductivity, for example, the popular GinzburgLandau theory was proclaimed as "being of great importance in physics ...". There are new and unresolved mathematical challenges be explored further. In this tutorial, we will briefly review the physical background of some interesting problems related to superconductivity, in particular, the problem of quantized vortices. Various mathematical models ranging from microscopic BCS theory to the macroscopic critical state models will then be described with the mesoscale GinzburgLandau model being our emphasis. Some recent analytical and numerical results will be surveyed. Connections to other relevant problems such as the vortices in BoseEinstein condensation will also be discussed.
Chun Liu (Department of Mathematics Pennsylvania State University)
Biography: Dr. Chun Liu is an Associate Professor of Mathematics in the Pennsylvania State University, University Park. He received his Ph.D. in Mathematics in 1995, from the Courant Institute of Mathematical Sciences, New York University. He was a postdoctoral research fellow in the Department of Mathematics, Carnegie Mellon University, Pittsburgh, during the academic year 19951996. In the following year, he held the Richard Duffin Visiting Assistant Professor position in the same department. Chun Liu research interests center around partial differential equations and calculus of variations, with applications to complex fluids, liquid crystals and polymeric materials, mixtures and interfaces, magnetohydrodynamics and electrokinetic flow, elasticity and grain growth. He is a very active researcher and speaker.
Variational Approaches in Complex Fluids
Lecture 1: Background and Liquid Crystals Slides pdfAbstract: Complex fluids such as polymeric solutions, liquid crystal solutions, pulmonary surfactant solutions, electrokinetic fluids, magnetorheological fluids and blood suspensions exhibit many intricate rheological and hydrodynamic features that are very important to biological and industrial processes.
The most common origin and manifestation of anomalous phenomena in complex fluids are different "elastic" effects. They can be the elasticity of deformable cells, elasticity of the molecule alignment in liquid crystals, polarized colloids or multicomponent phases, elasticity due to microstructures, or bulk elasticity endowed by polymer molecules in viscoelastic complex fluids. The physical properties are purely determined by the interplay of entropic and structural intermolecular elastic forces and interfacial interactions. These elastic effects can be represented in terms of certain internal variables, for example, the orientational order parameter in liquid crystals (related to their microstructures), the distribution density function in the dumbbell model for polymeric materials, the magnetic field in magnetohydrodynamic fluids, the volume fraction in mixture of different materials etc. The different rheological and hydrodynamic properties can be attributed to the special coupling between the transport of the internal variable and the induced elastic stress. From the point of the view of the energetic variational formulation, this represents a competition between the kinetic energy and the elastic energy.
In these lectures, I will study three different but related types of problems to illustrate this unified energetic variational approach. All the systems are related and have common structures. However, each one posses its own distinct features (difficulties). I will present some modeling and analytical results, as well as those problems that remain to be solved.
Ellad B. Tadmor (Faculty of Mechanical Engineering, Technion  Israel Institute of Technology)
Biography: Dr. Ellad B. Tadmor is a senior lecturer in the Department of Mechanical Engineering at the Technion  Israel Institute of Technology in Haifa, Israel. Dr. Tadmor's research focuses on understanding material response from fundamental principles rather than phenomenology. He studies microscopic processes that lead to macroscopic phenomena such as fracture and plasticity using atomicscale modeling and multiplescale techniques. Prior to his current position, Dr. Tadmor was a postdoctoral research fellow in the Division of Engineering and Applied Sciences at Harvard University working with Prof. Efthimios Kaxiras on incorporating ab initio models into multiscale methods. In 1996 Dr. Tadmor received his Ph.D. in Engineering from Brown University in Providence, RI. His doctoral research with Prof. Michael Ortiz and Prof. Rob Phillips focused on the development of the Quasicontinuum Method, a mixed continuum and atomistic formulation for describing the mechanical response of materials at the atomic scale. Dr. Tadmor has received a number of awards including several Technion Awards for Excellence in Teaching, the Salomon Simon Mani Award for Excellence in Teaching, and the Materials Research Society (MRS) Graduate Student Award for his Ph.D. work.
MultipleScale Modeling of Materials using the Quasicontinuum Method
Tentative titles for the three lectures are:
1. Materials and Multiple Scales
2. The Theoretical Foundations of the Quasicontinuum Method
3. Quasicontinuum Applications
Abstract: Atomistic and continuum methods alike are often confounded when faced with mesoscopic problems in which multiple scales operate simultaneously. In many cases, both the finite dimensions of the system as well as the microscopic atomicscale interactions contribute equally to the overall response. This makes modeling difficult since continuum tools appropriate to the larger scales are unaware of atomic detail and atomistic models are too computationally intensive to treat the system as a whole.
We present an alternative methodology referred to as the "quasicontiuum method" which draws upon the strengths of both approaches. The key idea is that of selective representation of atomic degrees of freedom. Instead of treating all atoms making up the system, a small relevant subset of atoms is selected to represent, by appropriate weighting, the energetics of the system as a whole. Based on their kinematic environment, the energies of individual "representative atoms" are computed either in nonlocal fashion in correspondence with straightforward atomistic methodology or within a local approximation as befitting a continuum model. The representation is of varying density with more atoms sampled in highly deformed regions (such as near defect cores) and correspondingly fewer in the less deformed regions further away and is adaptively updated as the deformation evolves.
The method has been successfully applied to a number of atomicscale mechanics problems including nanoindentation into thin aluminum films, microcracking of nickel bicrystals, interactions of dislocations with grain boundaries in nickel, junction formation of dislocations in aluminum, crossslip and jogdrag of screw dislocations in copper, stressinduced phase transformations in silicon due to nanoindentation, polarization switching in ferroelectric leadtitanate and deformation twinning at aluminum crack tips. An overview of the methodology and selected examples from these applications will be presented.
Name  Department  Affiliation 

Douglas N. Arnold  Institute for Mathematics and its Applications  University of Minnesota 
Donald G. Aronson  Institute for Mathematics and its Applications  University of Minnesota 
Gerard Awanou  Institute for Mathematics and its Applications  University of Minnesota 
Martin Z. Bazant  Department of Mathematics  Massachusetts Institute of Technology 
Josef Bemelmans  Institute for Mathematics  Aachen University of Technology 
Daniel E. Bentil  Department of Mathematics & Statistics  University of Vermont 
Ali Berker  Corporate Research Materials Lab  3M 
Keith Berrier  Rice University  
Amardeep Bhalla  Department of Pharmaceutics  University of Minnesota 
Kaushik Bhattacharya  Division of Eng. & Applied Sci.  California Institute of Technology 
Helmut Brand  Physikalisches Institut  Universität Bayreuth 
MariaCarme Calderer  School of Mathematics  University of Minnesota 
Brandon Chabaud  Department of Mathematics  University of Minnesota 
Purnendu Chakraborty  Department of Applied Mathematics & Scientific Computation  University of Maryland 
Athonu Chatterjee  Dept. of Science & Technology, Modeling & Simulation  Corning Incorporated 
Qianyong Chen  Institute for Mathematics and its Applications  University of Minnesota 
L. Pamela Cook  Department of Mathematical Science  University of Delaware 
Bentao Cui  Department of Chemical Engineering and Materials Science  University of Minnesota 
Brian DiDonna  Institute for Mathematics and its Applications  University of Minnesota 
Masao Doi  Department of Applied Physics  University of Tokyo 
Georg Dolzmann  Department of Applied Mathematics  University of Maryland 
Qiang Du  Department of Mathematics  Pennsylvania State University 
Maria Emelianenko  Department of Mathematics  Pennsylvania State University 
Laura JD Frink  Computational Biology  Sandia National Laboratories 
Tim Garoni  Institute for Mathematics and its Applications  University of Minnesota 
Matthias Gobbert  Department of Mathematics and Statistics  University of Maryland  Baltimore County 
Robert Gulliver  School of Mathematics  University of Minnesota 
ChuanHsiang Han  Ford Company  University of Minnesota 
Thomas J. Hatch  ECE/ME  University of Minnesota 
Manish Jain  Corporate Research3M  3M 
Richard D. James  Aerospace Engineering and Mechanics  University of Minnesota 
Sookyung Joo  Institute for Mathematics and its Applications  University of Minnesota 
Chiu Yen Kao  Institute for Mathematics and its Applications  University of Minnesota 
YunHui Kim  Department of Mathematics  Indiana University 
Bernhard Klampfl  Department of Materials Science  Klaiss Inc. 
Richard Kollar  Institute of Mathematics and its Applications  University of Minnesota 
Matthias Kurzke  Institute for Mathematics and its Applications  University of Minnesota 
Frederic Legoll  Institute for Mathematics and its Applications  University of Minnesota 
Benedict Leimkuhler  Department of Mathematics and Computer Science  University of Leicester 
Debra Lewis  Institute for Mathematics and its Applications  University of Minnesota 
Huan Li  Department of Mathematics  University of Maryland 
Xiantao Li  Institute for Mathematics and its Applications  University of Minnesota 
Fanghua Lin  Department of Mathematics  New York University 
Chun Liu  Department of Mathematics  Pennsylvania State University 
Zuhan Liu  Xuzhou Normal University  
Gang Lu  Department of Physics and Astronomy  California State University  Northridge 
Mitchell Luskin  School of Mathematics  University of Minnesota 
Suping Lyu  Materials and Biosciences Center  Medtronic, Inc. 
Qingfeng Ma  Department of Mathematics  Indiana University 
Govind Menon  University of Wisconsin  
Michael Mlejnek  Department of Modeling and Simulation  Corning Incorporated 
Sanat Mohanty  CRL  3M 
Siddharthya Mujumdar  Department of Biomedical  University of Minnesota 
MiaoJung Yvonne Ou  Department of Mathematics  University of Central Florida 
Jinhae Park  School of Mathematics  University of Minnesota 
Lyudmila Pekurousky  CMRL  3M 
Peter Philip  Institute for Mathematics and its Application  University of Minnesota 
Petr Plechac  Mathematics Institute  University of Warwick 
Harald Pleiner  Max Planck Institute for Polymer Research  
Lea Popovic  Institute for Mathematics and its Applications  University of Minnesota 
Yitzhak Rabin  Department of Physics  BarIlan University 
Amit Ranjan  Department of Chemical Engineering and Material Sciences  University of Minnesota 
Rolf Ryham  Department of Mathematics  Pennsylvania State University 
Arnd Scheel  Institute for Mathematics and its Applications  University of Minnesota 
George R Sell  School of Math  University of Minnesota 
Jackie Shen  School of Mathematics  University of Minnesota 
TienTsan Shieh  Department of Mathematics  Indiana University 
Tiffany Shih  Department of Chemicial Engineering and Materials Sciences  University of Minnesota 
Daniel Spirn  University of Minnesota  
Peter J. Sternberg  Department of Mathematics  Indiana University 
Vladimir Sverak  Department of Mathematics  University of Minnesota 
Ellad Tadmor  Department of Mechanical Engineering  Technion  Israel Institute of Technology 
Eugene Terentjev  Cavendish Laboratory  Cambridge University 
Raul Velasquez  Department of Civil Engineering  University of Minnesota 
Epifanio G. Virga  Dipartimento di Matematica  Universita di Pavia 
Jimmy Wang  Aerospace Engineering and Mechanics  University of Minnesota 
Xiaoqiang Wang  Pennsylvania State University  
ZhiQiang Wang  Department of Mathematics & Statistics  Utah State University 
Stephen J. Watson  ESAM  Northwestern University 
Olaf Weckner  Department of Mechanical Engineering  Massachusetts Institute of Technology 
Baisheng Yan  Department of Mathematics  Michigan State University 
Xiaofeng Yang  Department of Mathematics  Purdue University 
Toshio Yoshikawa  Liu Bie Ju Centre for Mathematical Sciences  City University of Hong Kong 
Arghir Dani Zarnescu  Department of Mathematics  University of Chicago 