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Cosponsored with the Society for Natural Philosophy
and the School of Mathematics, University of Minnesota
Organizers | ||
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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 | ||
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FRIDAY,
NOVEMBER 5 All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted. |
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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. |
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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 |
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. |
Name | Department | Affiliation |
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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 |