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 …

We investigate the minimization of the energy per point E_f E f among d-dimensional
Bravais lattices, depending on the choice of pairwise potential equal to a radially symmetric …

We consider two-dimensional zero-temperature systems of N particles to which we
associate an energy of the form EV (X):= ∑ _ 1\leqq i< j\leqq NV (| X (i)-X (j)|), EV (X):=∑ 1≦ …

In this paper, we focus on finite Bravais lattice energies per point in two dimensions. We
compute the first and second derivatives of these energies. We prove that the Hessian at the …

We investigate the local and global optimality of the triangular, square, simple cubic, face-
centered-cubic (fcc) and body-centered-cubic (bcc) lattices and the hexagonal-close …

We consider minimizers of the N-particle interaction potential energy and briefly review
numerical methods used to calculate them. We consider simple pair potentials which are …

We consider pairwise interaction energies and we investigate their minimizers among
lattices with prescribed minimal vectors (length and coordination number), ie the one …

We investigate the regularising effect of certain perturbations by noise in singular interacting
particle systems under the mean field scaling. In particular, we show that the addition of a …

We investigate the emergence of rigid polycrystalline structures from atomistic particle
systems. The atomic interaction is governed by a suitably normalized pair interaction energy …

The goal of this paper is to investigate the optimality of the d-dimensional rock-salt structure,
ie the cubic lattice V 1/d ℤ d of volume V with an alternation of charges±1 at lattice points …