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math-ph2021
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…
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…
math-ph2018
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…