Laboratoire de Physique Théorique

de la Matière Condensée

Compact packings of spheres

Thomas Fernique (LIPN, CNRS et U. Paris 13)

It is well known that the best way to pack oranges in a (very large) box is to place them on a face-centered cubic lattice (also known as checkerboard), although this has been formally demonstrated only in 1998 (with difficulty). This talk focuses on what happens when the dimension or number of different spheres change. In particular, so-called compact packings (the term will be defined properly) seem good candidates to maximize density. In this tallk, we propose : a) a non-technical survey of the known mathematical results ; b) an overview of the underlying computer problems (interval arithmetic, resolution of systems of polynomial equations, combinatorial exploration) ; (c) a discussion of possible applications in chemistry, including self-assembly of supercrystals ; d) a discussion of numerical simulations that may be of interest in this context.