Mathematical Theory of Solids: From Atomic to Macroscopic
How do we build a mathematical theory for the
macroscopic deformation of solids starting from atomistic models?
This talk will present a review of current work on this problem at
zero temperature. It will cover the following topics: (1) Stability of
crystals and the validity of Cauchy-Born rule for the elastic regime;
(2) instability of crystals and mechanisms of defect formation; (3)
generalized Peierls-Nabarro models for defect structure and dynamics.