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IMA Symposium:
Prospects for Mathematics and Mechanics upon the 80th Birthday of Jerry Ericksen
November 5-6, 2004


Mathematics of Materials and Macromolecules: Multiple Scales, Disorder, and Singularities, September 2004 - June 2005

Jerry Ericksen


Cosponsored with the Society for Natural Philosophy and the School of Mathematics, University of Minnesota

Organizers
Millard F. Beatty
   
res0guxi@verizon.net
Engineering Mechanics University of Nebraska-Lincoln
Yi-chao Chen
   chen@uh.edu
Department of Mechanical Engineering University of Houston
Richard D. James
   
james@aem.umn.edu
Department of Aerospace Engineering and Mechanics University of Minnesota
Mitchell Luskin
   
luskin@math.umn.edu
School of Mathematics University of Minnesota
Speakers
Kaushik Bhattacharya
   bhatta@cco.caltech.edu
Applied Mechanics & Mechanical Engineering
Division of Engineering & Applied Sciences
California Institute of Technology
Patricia E. Cladis
   cladis@alct.com
  Advanced Liquid Crystal Technologies, Inc.
Masao Doi
   doi@rheo.t.u-tokyo.ac.jp
Department of Applied Physics University of Tokyo
Richard D. James
   james@aem.umn.edu
Department of Aerospace Engineering & Mechanics University of Minnesota
David Kinderlehrer
   davidk@andrew.cmu.edu
Department of Mathematical Sciences Carnegie Mellon University
Fanghua Lin
   linf@courant.nyu.edu
Department of Mathematics Courant Institute of Mathematical Sciences
New York University
Lev Truskinovsky
   trusk@lms.polytechnique.fr
Laboratory of Solid Mechanics École Polytechnique

Abstract:

Jerry Ericksen pioneered the development of continuum theory for complex materials and laid the groundwork for theory that bridges continuum mechanics and molecular structure.

His research on nonlinear elasticity in the 1950s and 1960s gave a deep understanding of how principles of invariance served to identify special solutions. This body of work contains a landmark paper on the explicit classification of all deformations possible in every incompressible nonlinear elastic material, no matter what its free energy function. In the 1960s and 1970s he turned attention to the theory of liquid crystals, and, with Frank Leslie, gave the now accepted dynamical theory of liquid crystals. This theory featured completely nonstandard but physically necessary ingredients: nonsymmetric stresses, unusual kinetics, and an unconventional energy equation. He returned to the latter in the 1980s with his formulation of theory for liquid crystal polymers involving a variable degree of orientation.

Ericksen's work in the 1970s to the present, beginning with his influential paper on Equilibrium of Bars, has focused largely on phase transformations in crystals. His research on the Cauchy-Born rule and the the relation between lattice instabilities and the loss of ellipticity of free energy functions launched a line of research in the mechanics of crystals that continues to be one of the most vital in science and mathematics. A major advance was the reconciliation of the use of infinite symmetry groups of crystals with the finite symmetry groups used in nonlinear elasticity, achieved by his definition of the Ericksen-Pitteri neighborhood. Another major advance was the generalization of the Landau theory of second order phase transformations to first order transformations. There remain parts of this work, notably on defects in crystals and liquid crystals, and recent work on x-ray theory (elasticity theory without reference configurations or strains) that may well lead to major lines of research in the future.

Ericksen's work often made use of, and led to the development of, new lines of thought in mathematics, especially in pde and geometry. He inspired both scientists and mathematicians, his influence reaching deeply into both pure mathematics and materials science. This forward-looking symposium celebrates his accomplishments, and seeks to identify prospects for future research on nonlinear materials.

SCHEDULE
FRIDAY, NOVEMBER 5
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
9:50-10:00 Welcome and Introduction
10:00-10:45 Richard D. James
University of Minnesota
Hysteresis and geometry: a way to search for new materials with "unlikely" physical properties
10:45-11:15 coffee  
11:15-12:00 Kaushik Bhattacharya
California Institute of Technology
Ferroelectric ceramics
2:00-2:45 David Kinderlehrer
Carnegie Mellon University
Issues for interfaces in polycrystals
2:45-3:15 coffee  
3:15-4:00 Fanghua Lin
Courant Institute of Mathematical Sciences New York University
A mathematical journey on defects motions
4:00-4:30 coffee  
4:30 Round table 1: Jim Casey
University of California - Berkeley
A theory of pseudo-rigid bodies
5:00 Round table 2: Howard Brenner
Massachusetts Institute of Technology
Navier-Stokes-Fourier revisited
SATURDAY, NOVEMBER 6
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
10:00-10:45 Lev Truskinovsky
Ecole Polytechnique, Palaiseau
Thermodynamics of rate independent plasticity
10:45-11:15 coffee  
11:15-12:00 Masao Doi
University of Tokyo
A variational principle in dissipative systems
2:00-2:45 Patricia E. Cladis
Advanced Liquid Crystal Technologies
Hedgehog-antihedghog annihilation to a static soliton

Slides:  pdf

2:45-3:30 coffee  
3:30 Round table 3: Anna Vainchtein
University of Pittsburgh
Kinetics of lattice phase transitions
4:00 Round table 4: Gianni Royer-Carfagni
Universita di Parma (CNR
The role of stress on chemical transformations in an elastic bar with nonconvex chemomechanical free energy
4:30 Round table 5: Anja Schlömerkemper
Universität Stuttgart
About magnetic force formulae
5:00 Weisman Art Museum open for viewing
6:00 Reception at Weisman Art Museum
6:30 Seating for Dinner at Weisman Art Museum
Note: The gallery, reception, and dinner are open only for those who have purchased banquet tickets.If you come during the reception hour and would like to view the gallery, you should do the viewing first and then participate in the reception. No one is permitted to view the the gallery with any drink or food in their hands.

LIST OF CONFIRMED PARTICIPANTS

Name Department Affiliation
Rohan Abeyaratne Mechanical Engineering Massachusetts Institute of Technology
Douglas N. Arnold Institute for Mathematics and its Applications University of Minnesota
Donald G. Aronson Institute for Mathematics and its Applications University of Minnesota
Enrico Babilio Mathematics University of Pittsburgh
Millard Beatty Department of Engineering Mechanics University of Nebraska-Lincoln
Kaushik Bhattacharya Division of Eng. & Applied Sci. California Institute of Technology
Howard Brenner Department of Chemical Engineering Massachusetts Institute of Technology
Maria-Carme Calderer School of Mathematics University of Minnesota
Donald Carlson Dept.of Theoretical and Applied Mechanics University of Illinois - Urbana-Champaign
Jim Casey Department of Mechanical engineering University of California - Berkeley
Yi-Chao Chen Department of Aerospace Engineering and Mechanics University of Houston
Patricia Cladis   Advanced Liquid Crystal Technologies
L. Pamela Cook Department of Mathematical Science University of Delaware
Cesare Davini   University of Udine
Raffaella De Vita Department of Mechanical Engineering University of Pittsburgh
Masao Doi Department of Applied Physics University of Tokyo
Hongjie Dong Mathematics University of Minnesota
Jerald Ericksen    
Roger Fosdick Dept. of Aerospace Eng. and Mech. University of Minnesota
Robert Gulliver School of Mathematics University of Minnesota
Robert Hardt Mathematics Rice University
Richard D. James Aerospace Engineering and Mechanics University of Minnesota
Huiqiang Jiang School of Mathematics University of Minnesota
Sookyung Joo Institute for Mathematics and its Applications University of Minnesota
Daniel Joseph Aerospace Engineering/Mechanics University of Minnesota
Abdul M. Khaliq Department of Mathematics University of Wisconsin - La Crosse
David Kinderlehrer Department of Mathematics Carnegie Mellon University
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
Debra Lewis Institute for Mathematics and its Applications University of Minnesota
Yi Li Department of Mathematics University of Iowa
Fanghua Lin Department of Mathematics New York University
Chun Liu Department of Mathematics Pennsylvania State University
Mitchell Luskin School of Mathematics University of Minnesota
Gearoid P. Mac Sithigh Department of Mechanical and Aerospace Engineering University of Missouri - Rolla
Chi-Sing Man DEPARTMENT OF MATHEMATICS University of Kentucky
Christof Melcher Institut fuer Mathematik Humboldt-Universitaet zu Berlin
Govind Menon   University of Wisconsin
Willard Jr. Miller IMA University of Minnesota
Nilima Nigam Department of Mathematics and Statistics McGill University
Peter J. Olver Department of Mathematics University of Minnesota
David Owen Mathematical Sciences Carnegie Mellon University
Jinhae Park School of Mathematics University of Minnesota
Eric Petersen   United Defense LP
Peter Philip Institute for Mathematics and its Application University of Minnesota
Gianni Royer-Carfagni Civil-Environmental Engineering and Architecture Universita di Parma (CNR)
Arnd Scheel Institute for Mathematics and its Applications University of Minnesota
Anja Schloemerkemper   University of Stuttgart
George R Sell School of Math University of Minnesota
James P. Sethna Department of Physics Cornell University
Tiffany Shih Department of Chemicial Engineering and Materials Sciences University of Minnesota
Scott Spector Department of Mathematics Southern Illinois University
Vladimir Sverak Department of Mathematics University of Minnesota
Peter Takac Fachbereich Mathematik Universitaet Rostock
Lev Truskinovsky Laboratory of Solid Mechanics Ecole Polytechnique, Palaiseau
Anna Vainchtein Department of Mathematics University of Pittsburgh
Zhi-Qiang Wang Department of Mathematics & Statistics Utah State University
Stephen J. Watson ESAM Northwestern University
Hans Weinberger School of Mathematics University of Minnesota
Baisheng Yan Department of Mathematics Michigan State University
Giovanni Zanzotto DMSA University of Padua
Tianyu Zhang Department of Mathematics University of Minnesota
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