26 citations · 56 across the 12 of their papers we have counts for
5 papers · 1 filter
A variational principle for Gaussian lattice sums
Laurent Bétermin, Markus Faulhuber, Stefan Steinerberger
We consider a two-dimensional analog of Jacobi theta functions and prove that, among all lattices with fixed density, the minimal value is maximized by the…
Three-dimensional lattice ground states for Riesz and Lennard-Jones type energies
Laurent Bétermin, Ladislav Šamaj, Igor Travěnec
The Riesz potential is known to be an important building block of many interactions, including Lennard-Jones type potentials $f_{n,m}^{\rm{LJ}}(r):=a r^{-n}-b r^{-m…
How well-conditioned can the eigenvalue problem be?
Carlos Beltrán, Laurent Bétermin, Peter Grabner +1
The condition number for eigenvalue computations is a well--studied quantity. But how small can we expect it to be? Namely, which is a perfectly conditioned matrix w.r.t. eigenvalu…
Optimality of the triangular lattice for Lennard-Jones type lattice energies: a computer-assisted method
Laurent Bétermin
It is well-known that any Lennard-Jones type potential energy must have a periodic ground state given by a triangular lattice in dimension 2. In this paper, we describe a computer-…
Lattice ground states for Embedded-Atom Models in 2D and 3D
Laurent Bétermin, Manuel Friedrich, Ulisse Stefanelli
The Embedded-Atom Model (EAM) provides a phenomenological description of atomic arrangements in metallic systems. It consists of a configurational energy depending on atomic positi…