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.