26 citations · 56 across the 12 of their papers we have counts for
4 papers · 1 filter
Theta functions and optimal lattices for a grid cells model
Laurent Bétermin
Certain types of neurons, called "grid cells", have been shown to fire on a triangular grid when an animal is navigating on a two-dimensional environment, whereas recent studies su…
Stability of configurations in 3D
Laurent Bétermin, Manuel Friedrich, Ulisse Stefanelli
Inspired by the issue of stability of molecular structures, we investigate the strict minimality of point sets with respect to configurational energies featuring two- and three-bod…
Maximal Theta Functions -- Universal Optimality of the Hexagonal Lattice for Madelung-Like Lattice Energies
Laurent Bétermin, Markus Faulhuber
We present two families of lattice theta functions accompanying the family of lattice theta functions studied by Montgomery in [H.~Montgomery. Minimal theta functions. \textit{Glas…
On the optimality of the rock-salt structure among lattices with charge distributions
Laurent Bétermin, Markus Faulhuber, Hans Knüpfer
The goal of this work is to investigate the optimality of the -dimensional rock-salt structure, i.e., the cubic lattice of volume with an alternation o…