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Sixth International Conference on Differential and Functional Differential Equations DFDE-2011
August 16, 2011 12:55, Moscow
 


Homogenization of spin energies

A. L. Piatnitskiab

a Lebedev Physical Institute, Moscow, Russia
b Narvik University College, Narvik, Norway
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A. L. Piatnitski



Abstract: The talk will focus on homogenization and Γ-convergence of surface and line energies defined on lattice (spin) systems in Zd through bond interactions. We will dwell on nearest neighbours interaction systems and consider both periodic and random statistically homogeneous ergodic cases.
Given a smooth bounded domain GRn and a small parameter ε>0, we denote εZdG by Gε and, for a function u defined on Gε, consider the energy
Eε(u)=i,jGεεd1cij(uiuj)2,cij0,cij=0 if |ij|ε.
Our goal is to study the limit behaviour of Eε as ε0.

Language: English
 
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