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Michigan Institute for Computational Discovery and Engineering pres.

Anna Vainchtein: Strictly supersonic solitary waves in lattices

MICDE Seminar Series

A. Vainchtein A. Vainchtein
A. Vainchtein
Abstract:We consider a nonlinear mass-spring chain with first and second-neighbor interactions and show that there is a parameter range where solitary waves in this system are strictly supersonic. In these regimes standard quasicontinuum theories, targeting long-wave limits of lattice models, are not adequate since even weak strictly supersonic solitary waves are of envelope type and crucially involve a microscopic scale in addition to the mesoscopic scale of the envelope. To capture this effect in a continuum setting it is necessary to employ unconventional, higher-order quasicontinuum approximations carrying more than one length scale. This talk is based on recent joint work with Lev Truskinovsky (ESPCI).

Bio: Anna Vainchtein is a professor in the Department of Mathematics at the University of Pittsburgh. She is generally interested in mathematical modeling and analysis of nonlinear phenomena in materials science, physics and biology.
A. Vainchtein A. Vainchtein
A. Vainchtein

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