Chaotic orbits for nonlocal equations, the Peierls-Nabarro model, and applications to atom dislocation dynamics in crystals
报告题目(Title)：Chaotic orbits for nonlocal equations, the Peierls-Nabarro model, and applications to atom dislocation dynamics in crystals
报告人(Speaker)：Enrico Valdinoci（University of Western Australia）
地点(Place)：ZOOM会议: 668 041 03984 密码: 123456
时间(Time)：2020年9月25日 14：00 - 15：00
邀请人(Inviter)：苏喜锋
报告摘要
In this talk we consider a nonlocal equation driven by a perturbed periodic potential. We
construct multibump solutions that connect one integer point to another one in a prescribed
way. In particular, heteroclinic, homoclinic and chaotic trajectories are constructed. This result
regarding symbolic dynamics in a fractional framework is part of a study of Peierls-Nabarro
model for crystal dislocations. The associated evolution equation can be studied in the
mesoscopic and macroscopic limits. Namely, the dislocation function has the tendency to
concentrate at single points of the crystal, where the size of the slip coincides with the natural
periodicity of the medium. These dislocation points evolve according to the external stress and
an interior potential, which can be either repulsive or attractive, depending on the relative
orientations of the dislocations. For opposite orientations, collisions occur, after which the
system relaxes exponentially fast.
主讲人简介
Enrico Valdinoci教授师从著名数学大师Luis Caffarelli，是《Nonlinear Analysis》杂志主编，发表论文200余篇。
