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 G⊂Rn and a small parameter ε>0, we denote
εZd∪G by Gε and, for a function u defined on Gε, consider the energy
Eε(u)=∑i,j∈Gεεd−1cij(ui−uj)2,cij⩾0,cij=0 if |i−j|≠ε.
Our goal is to study the limit behaviour of Eε as ε→0.