Tuesday, June 5, 2012

1206.0268 (Michael Herrmann et al.)

Subsonic phase transition waves in bistable lattice models with small
spinodal region

Michael Herrmann, Karsten Matthies, Hartmut Schwetlick, Johannes Zimmer
Phase transitions waves in atomic chains with double-well potential play a fundamental role in materials science, but very little is known about their mathematical properties. In particular, the only available results about waves with large amplitudes concern chains with piecewise-quadratic pair potential. In this paper we consider perturbations of a bi-quadratic potential and prove that the corresponding three-parameter family of waves persists as long as the perturbation is small and localised with respect to the strain variable. More precisely, we introduce an anchor-corrector ansatz, characterise the corrector as a fixed point of a nonlinear and nonlocal operator, and show that this operator is contractive in a small ball of a certain function space.
View original: http://arxiv.org/abs/1206.0268

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