18 citations · 60 across the 6 of their papers we have counts for
11 papers
On energy ground states among crystal lattice structures with prescribed bonds
Laurent Bétermin
We consider pairwise interaction energies and we investigate their minimizers among lattices with prescribed minimal vectors (length and coordination number), i.e. the one correspo…
Effect of periodic arrays of defects on lattice energy minimizers
L. Bétermin
We consider interaction energies between a point , , and a lattice containing , where the interaction potential is assumed to be rad…
On a lattice generalisation of the logarithm and a deformation of the Dedekind eta function
Laurent Bétermin
We consider a deformation of the Dedekind eta function depending on two -dimensional simple lattices and two parameters , initia…
Crystallization to the square lattice for a two-body potential
Laurent Bétermin, Lucia De Luca, Mircea Petrache
We consider two-dimensional zero-temperature systems of particles to which we associate an energy of the form where…
Minimizing lattice structures for Morse potential energy in two and three dimensions
Laurent Bétermin
We investigate the local and global optimality of the triangular, square, simple cubic, face-centred-cubic (FCC), body-centred-cubic (BCC) lattices and the hexagonal-close-packing…
Optimal and non-optimal lattices for non-completely monotone interaction potentials
Laurent Bétermin, Mircea Petrache
We investigate the minimization of the energy per point among -dimensional Bravais lattices, depending on the choice of pairwise potential equal to a radially symmetric f…
Optimal lattice configurations for interacting spatially extended particles
Laurent Bétermin, Hans Knüpfer
We investigate lattice energies for radially symmetric, spatially extended particles interacting via a radial potential and arranged on the sites of a two-dimensional Bravais latti…
On Born's conjecture about optimal distribution of charges for an infinite ionic crystal
Laurent Bétermin, Hans Knüpfer
We study the problem for the optimal charge distribution on the sites of a fixed Bravais lattice. In particular, we prove Born's conjecture about the optimality of the rock-salt al…
Local variational study of 2d lattice energies and application to Lennard-Jones type interactions
Laurent Bétermin
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…
Local optimality of cubic lattices for interaction energies
Laurent Bétermin
We study the local optimality of Simple Cubic, Body-Centred-Cubic and Face-Centred-Cubic lattices among Bravais lattices of fixed density for some finite energy per point. Followin…
Renormalized Energy and Asymptotic Expansion of Optimal Logarithmic Energy on the Sphere
Laurent Bétermin, Etienne Sandier
We study the Hamiltonian of a two-dimensional log-gas with a confining potential satisfying the weak growth assumption -- is of the same order than near infinity…