[CvGmt News] [cvgmt seminar] Crystal dislocation, nonlocal equations and fractional dynamical systems
matteo.novaga at unipi.it
matteo.novaga at unipi.it
Wed Sep 20 11:08:21 CEST 2017
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Matteo
Crystal dislocation, nonlocal equations and fractional dynamical systems
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http://cvgmt.sns.it/seminar/595/
Date: Friday, Sep 22, 2017
Time: 14:00
Place: Scuola Normale Superiore, Aula Bianchi
Speaker: Serena Dipierro (Univ. di Milano)
Abstract. We study heteroclinic and multibump orbits for a system of equations driven by a nonlocal operator. Our motivation comes from the study of the atom dislocation function in a periodic crystal, according to the Peierls-Nabarro model. The evolution of the dislocation function can be studied by analytic techniques of fractional Laplace type. 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.
Such potential turns out to be either attractive or repulsive, depending on the mutual orientation of the dislocations, and the attractive potentials generate "particle collisions" in finite time. After the collisions, the system relaxes to the equilibrium exponentially fast, and the associated steady states provide a natural setting for the study of dynamics and chaos in a fractional framework.
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