In this paper we consider the problem of packing a set of d-dimensional congruent cubes into a sphere of smallest radius. We describe and investigate an approach based on a function called the maximal inflation function. In the three-dimensional case, we localize the contact between two inflated cubes and we thus improve the efficiency of calculating . This approach and a stochastic algorithm a...

Several conditions are given when a packing of equal discs in a torus is locally maximally dense, where the torus is defined as the quotient of the plane by a two-dimensional lattice. Conjectures are presented that claim that the density of any collectively jammed packing, whose graph does not consist of all triangles, and the torus lattice is the standard triangular lattice, is at most (n/(n +...

The key features leading to low-energy grain boundaries in metals are discussed by reference to computersimulated structures and geometrical analysis in terms of atom packing. Low energy is found to be associated with boundary structures consisting of relatively dense packing, and this can in turn be expressed in terms of the space-filling packing of coordination polyhedra. The geometrical meth...

We show that geometric confinement dramatically affects the shear-induced configurations of dense monodisperse colloidal suspensions; a new structure emerges, where layers of particles buckle to stack in a more efficient packing. The volume fraction in the shear zone is controlled by a balance between the viscous stresses and the osmotic pressure of a contacting reservoir of unsheared particles...

We compute the dynamic structure factors of a dense binary liquid mixture. These describe dynamics on molecular length scales, where structural relaxation is important. We find that the presence of a few large particles in a dense fluid of small particles slows down the dynamics considerably. We also observe a deep narrowing of the spectrum for a disordered mixture composed of a nearly equal pa...

The Hungarian mathematician Farkas Bolyai (1775–1856) published in his principal work (‘Tentamen’, 1832–33 [Bol04]) a dense regular packing of equal circles in an equilateral triangle (see Fig. 1). He defined an infinite packing series and investigated the limit of vacuitas (in Latin, the gap in the triangle outside the circles). It is interesting that these packings are not always optimal in s...

In a recent paper, we showed that every sufficiently large regular digraph G on n vertices whose degree is linear in n and which is a robust outexpander has a decomposition into edge-disjoint Hamilton cycles. The main consequence of this theorem is that every regular tournament on n vertices can be decomposed into (n − 1)/2 edge-disjoint Hamilton cycles, whenever n is sufficiently large. This v...