1:00 pm Wednesday, November 5, 2014
Analysis Seminar: Dyslocation dinamics and fractional equations by
Enrico Valdinoci (Weierstrass Institute, Berlin) in RLM 10.176
We consider a 1D evolution equation arising in the Peierls-Nabarro model for crystal dislocation. We study the evolution of the dislocation function using analytic techniques of fractional Laplace type. We show that, at a macroscopic scale, the dislocations have 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. The potential is either attractive or repulsive, according to the different orientations of the dislocations (in particular, collisions, and even multiple collisions, of the atom dislocation may occur). The results that will be presented have been obtained in some papers in collaboration with S. Dipierro, A. Figalli, G. Palatucci, S. Patrizi and extend previous works of R. Monneau and M.d.M. Gonzalez. Submitted by
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