Consider the wave equation with heterogeneous coefficients in the homogenization regime. At large times, the wave interacts in a nontrivial way with the heterogeneities, giving rise to effective dispersive effects. The main achievement of the present wor ...
We study stochastic homogenization for convex integral functionals|u bar right arrow integral(D) W(omega, x/epsilon, del u) dx, where u : D subset of R-d -> R-m,|defined on Sobolev spaces. Assuming only stochastic integrability of the map omega bar right a ...
We prove a stochastic homogenization result for integral functionals defined on finite partitions assuming the surface tension to be stationary and possibly ergodic. We also consider the convergence of boundary value problems when we impose a boundary valu ...
We study the limit behaviour of sequences of non-convex, vectorial, random integral functionals, defined on W1,1, whose integrands are ergodic and satisfy degenerate linear growth conditions. The latter involve suitable random, scale-dependent weight-funct ...
We consider a classical Heisenberg system of S-2 spins on a square lattice of spacing epsilon. We introduce a magnetic anisotropy by constraining the out-of-plane component of each spin to take only finitely many values. Computing the Gamma-limit of a suit ...
We study a nearest neighbors ferromagnetic classical spin system on the square lattice in which the spin field is constrained to take values in a discretization of the unit circle consisting of N equi-spaced vectors, also known as the N-clock model. We fin ...
We propose and analyze a finite-difference discretization of the Ambrosio-Tortorelli functional. It is known that if the discretization is made with respect to an underlying periodic lattice of spacing ffi, the discretized functionals Gamma-converge to the ...
We study the asymptotic behavior of the N-clock model, a nearest neighbors ferromagnetic spin model on the d-dimensional cubic epsilon-lattice in which the spin field is constrained to take values in a discretization S-N of the unit circle S-1 consisting o ...
We prove stochastic homogenization for integral functionals defined on Sobolev spaces, where the stationary, ergodic integrand satisfies a degenerate growth condition of the form c|xi A(w, x)|p 5 f (w, x, xi) 5 |xi A(w, x)|p + A(w, x) for some p is an elem ...
We investigate the relationship between the N-clock model (also known as planar Potts model or DOUBLE-STRUCK CAPITAL ZN-model) and the XY model (at zero temperature) through a Gamma-convergence analysis of a suitable rescaling of the energy as both the num ...
