Many materials can be modeled either as discrete systems or as continua, depending on the
scale. At intermediate scales it is necessary to understand the transition from discrete to …

The effective large-scale properties of materials with random heterogeneities on a small
scale are typically determined by the method of representative volumes: a sample of the …

We study the limit behaviour of singularly-perturbed elliptic functionals of the form F k (u,
v)=∫ A v 2 fk (x,∇ u) dx+ 1 ε k∫ A gk (x, v, ε k∇ v) dx, where u is a vector-valued Sobolev …

We propose a new Γ-convergent discrete approximation of the Mumford–Shah functional.
The discrete functionals act on functions defined on stationary stochastic lattices and take …

We prove a homogenization theorem for a class of quadratic convolution energies with
random coefficients. Under suitably stated hypotheses of ergodicity and stationarity, we …

We study the atomistic-to-continuum limit of a class of energy functionals for crystalline
materials via Gamma-convergence. We consider energy densities that may depend on …

In this paper, we study the asymptotics of singularly perturbed phase-transition functionals of
the formℱ k (u)= 1/ε k∫ A fk (𝑥, u, ε k∇ u) d𝑥, where u∈[0, 1] is a phase-field variable, ε k> …

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 …

We discuss the discrete-to-continuum transition in the description of matter, starting from a
cluster of flowing molecules with equal mass and ending up with a non-simple fluid. We …

We prove that by scaling nearest-neighbour ferromagnetic energies defined on Poisson
random sets in the plane one obtains an isotropic perimeter energy with a surface tension …