In this article we describe the crystallization conjecture. It states that, in appropriate physical
conditions, interacting particles always place themselves into periodic configurations …

The first systematic overviews on global optimization appeared in 1975–1978 thanks to two
fundamental volumes titled Towards Global Optimization (Dixon & Szegö, 1975, 1978). At …

We present a direct method for solving the inverse problem of designing isotropic potentials
that cause self-assembly into target lattices. Each potential is constructed by matching its …

We present a scalable and distributed control strategy for swarms of satellites to
autonomously form an hexagonal lattice in space around a predefined meeting point. The …

We prove in this paper that the minimizer of Lennard–Jones energy per particle among
Bravais lattices is a triangular lattice, ie composed of equilateral triangles, in ℝ2 for large …

This note establishes, first of all, the monotonic increase with N of the average K-body
energy of classical N-body ground state configurations with N≥ K monomers that interact …

Very hard optimization problems, ie, problems with a large number of variables and local
minima, have been effectively attacked with algorithms which mix local searches with …

Finding good solutions to large scale, hard, global optimization problems, is a demanding
task with many relevant applications. It is well known that, in order to tackle a difficult …

We show that the stability constant of the Lennard-Jones potential in R^ 3 R 3, Φ (x)= ‖ x ‖
_2^-12-2 ‖ x ‖ _2^-6 Φ (x)=‖ x‖ 2-12-2‖ x‖ 2-6, is smaller than 14.316. This is …

We provide a lower bound for the convergence radius of the Mayer series of the Lennard–
Jones gas which strongly improves on the classical bound obtained by Penrose and Ruelle …