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CNA Seminar/Colloquium/Joint Pitt-CNA Colloquium
Hartmut Schwetlick
University of Bath
Title: On non propagating waves in an edge dislocation transport problem

Abstract: We present an equation of field dislocation mechanics, which is based on earlier work of Acharya, Zhang [CAM 2015]. With plasticity restricted to motion of straight edge dislocations within a single horizontal interatomic layer, a local averaging approximation across the vertical axis yields a 1D nonlocal quasilinear parabolic p.d.e. which contains in highest order a p-Laplacian. Numerical investigations by Zhang e.a. suggest the existence of a rich and nontrivial set of equilibria, which governs the long time behaviour for physically interesting initial data. The talk will focus on results relating to non-trivial stationary solutions as well as related travelling wave behaviour. The physical relevance of this problem rests on the possibility of demonstrating the existence of a Peierls threshold in a translationally-invariant p.d.e. model.

This is joint work with Acharya (Carnegie Mellon) and Matthies, Zimmer (Bath).

Date: Thursday, January 25, 2018
Time: 1:30 pm
Location: Wean Hall 7218
Submitted by:  Ian Tice