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Microstructural Evolution and Metastability in Active Materials

Published online by Cambridge University Press:  10 February 2011

David Kinderlehrer
David Kinderlehrer*
Affiliation:
Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213-3890
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Abstract

Metastable systems pose significant problems in both analysis and simulation. We discuss here the evolution of microstructure in a shape-memory alloy where energetic contributions from disparate scales play determining roles. This is a challenge for modelling since the finest length scales cannot be ‘seen’ at macroscopic level. We then provide a mechanism for kinetics that gives a different notion metastability.

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References

[1] Abeyaratne, R, Chu, C, and James, R 1996, Phil. Mag. A, 73.2, 457–497 Google Scholar
[2] Jordan, R, Kinderlehrer, D, and Otto, F 1997, Physica D, 107, 265–271 Google Scholar
[3] Jordan, R, Kinderlehrer, D, and Otto, F 1998, Siam J Math Anal, 29, 1–17 Google Scholar
[4] Jordan, R, Kinderlehrer, D, and Otto, F in preparationGoogle Scholar
[5] Kinderlehrer, D 1997 in Mathematics and Control in Smart Structures, (Varadan, V.K. and Chandra, J, eds) Proc. SPIE 3039, 2–13 Google Scholar
[6] Bensousson, A, Lions, J-L., and Papinicolaou, G 1978 Asymptotic analysis for periodic structures, North Holland Google Scholar
[7] Ball, J.M. and James, R D. 1987, Arch. Rat. Mech. Anal. 100, 13–52, 1991, Phil. Trans. Roy. Soc. Lond. A338, 389–450Google Scholar
[8] James, R and Kinderlehrer, D 1989 in PDE's and continuum models of phase transitions, (M, Rascle, Serre, D, and Slemrod, M, eds.) Lecture Notes in Physics 344, Springer, 51–84.Google Scholar
[9] Bhattacharya, K 1992, Arch. Rat. Mech. Anal. 120, 201–244 Google Scholar
[10] Ericksen, J.L. 1987 in Metastability and Incompletely Posed Problems, (Antman, S. Ericksen, J.L. Kinderlehrer, D. Muillereds, I) IMA Vol. Math. Appl. 3, Springer, 77–96 Google Scholar
[11] Finnis, M W. and Sinclair, J E. 1984 Phil. Mag. A 50, 45 Google Scholar
[12] Sutton, A P. and Baluffi, R W. 1995 Interfaces in Crystalline Materials, Oxford 8 Google Scholar