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Some mathematical challenges in materials science


Author: Jean E. Taylor
Journal: Bull. Amer. Math. Soc. 40 (2003), 69-87
MSC (2000): Primary 74N20; Secondary 49Q20, 49Q15, 35R99, 53A17, 65K10
DOI: https://doi.org/10.1090/S0273-0979-02-00967-9
Published electronically: October 15, 2002
MathSciNet review: 1943134
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Abstract: Four challenges to mathematics research posed by the field of materials science are given, plus an additional challenge purely from the field of geometric measure theory. The problems all concern the effects of surface and grain boundary free energy: motion by weighted mean curvature and/or surface diffusion and/or other kinetics, proofs of minimality of soap bubble clusters and their anisotropic analogs, shapes of crystals in a gravitational or other field, incorporating data from simulations into mathematics, and understanding flat chains modulo $\nu$. The figures are selected copies of transparencies presented at the lecture on which this paper is based.


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Additional Information

Jean E. Taylor
Affiliation: Department of Mathematics, Rutgers University, Piscataway, New Jersey 08855
Email: taylor@math.rutgers.edu

DOI: https://doi.org/10.1090/S0273-0979-02-00967-9
Received by editor(s): November 6, 2000
Received by editor(s) in revised form: February 21, 2002
Published electronically: October 15, 2002
Article copyright: © Copyright 2002 American Mathematical Society

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