Singularities in nonlinear evolution phenomena and applications

seminar: Multiscale decomposition of microstructure in a model of dislocations in crystals

speaker: Sergio Conti (Universität Bonn)

abstract: We consider a model for dislocations in crystals proposed by Koslowski and Ortiz, in the limit of small lattice spacing. The elastic interactions are represented in the model via a singular kernel, which results in a regularizing term behaving as the H^{12} norm of the slip. Building upon pervious work by Cacace, Garroni and Müller we obtain a sharp-interface limit via Gamma convergence. The key ingredient of our work is a proof of the fact that the presence of infinitely many equivalent length scales gives strong restrictions on the geometry of the microstructure, and hence permits to derive a simple relaxation formula. This talk is based on joint work with Adriana Garroni and Stefan Müller.

timetable:
Mon 26 May, 15:30 - 16:30, Aula Dini
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