Laurent Bétermin

collaborators

3 papers

math.OC2019

On a lattice generalisation of the logarithm and a deformation of the Dedekind eta function

Laurent Bétermin

We consider a deformation $E_{L, Λ}^{(m)} (i t)$ of the Dedekind eta function depending on two $d$ -dimensional simple lattices $(L, Λ)$ and two parameters $(m, t) \in (0, \infty)$ , initia…

math.AP2019

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 $N$ particles to which we associate an energy of the form $E [V] (X) := 1 \leq i < j \leq N \sum V (∣ X (i) - X (j) ∣),$ where…

math-ph2019

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…