The spheropolyhedra method has been used earlier for efficient and accurate molecular dynamics simulations of granular matter with particles with complex shapes. Also the Voronoi construction is a tool of proved utility for the virtual representation of powders and grains. In this paper a technique that combines the two methods and provides a framework for the study of the three-dimensional mec...

Structural transitions involving shape changes play an important role in cellular physiology. Such transition can be conveniently induced in charged micelles by increasing ionic strength of the medium. Shape changes have recently been shown to result in altered packing and lowering of micellar polarity. As a consequence of reduced polarity, the ionization states of micelle-bound molecules vary ...

This paper addresses the packing and void fraction of polydisperse particles with a lognormal size distribution. It is demonstrated that a binomial particle size distribution can be transformed into a continuous particle-size distribution of the lognormal type. Furthermore, an original and exact expression is derived that predicts the packing fraction of mixtures of particles with a lognormal d...

We consider nite lattice packings C n + K of n copies of some centrally symmetric convex body K in E d for large n. Assume that C n is a subset of a lattice , and % is at least the covering radius; namely, + %K covers the space. The parametric density (C n ; %) is deened by (C n ; %) = n V (K)=V (conv C n + %K). We show that if (C n ; %) is minimal for n large then the shape of conv C n is appr...

We recently described general principles for designing ideal protein structures stabilized by completely consistent local and nonlocal interactions. The principles relate secondary structure patterns to tertiary packing motifs and enable design of different protein topologies. To achieve fine control over protein shape and size within a particular topology, we have extended the design rules by ...

Leaves are packed in a bud in different ways, being flat, enrolled, or folded, but always filling the whole bud volume. This « filling law » has many consequences, in particular on the shape of growing folded leaves. This is shown here for different types of folding and packing. The folded volume is always part of an ellipsoid, with the veins on the outside rounded face, and the lamina margin o...

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...

The influence of atom packing and the geometric arrangement of atoms on the coordination number(s) and resultant simulated EXAFS spectra for face centrered cubic (fcc), hexagonal close packed (hcp) and body centered cubic (bcc) monometallic structures and fcc bimetallic structures, has been examined for metal clusters with an isotropic diameter up to 3 nm. We observe clear differences as a func...