We study the phenomenon of internal avalanching within the context of recently introduced lattice models of granular media. The avalanche is produced by pulling out a grain at the base of the packing and then studying the number of grains to be rearranged before the packing is stable again. We find that the avalanches are long-ranged, decaying as a power law. We study the distribution of avalan...

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 +...

We investigate the morphologies and maximum packing density of thin wires packed into spherical cavities. Using simulations and experiments, we find that ordered as well as disordered structures emerge, depending on the amount of internal torsion. We find that the highest packing densities are achieved in low torsion packings for large systems, but in high torsion packings for small systems. An...

The bubble packing method is implemented for adaptive mesh generation in two and three dimensions. Bubbles on the boundary of a three-dimensional domain are controlled independently of the interior bubbles in the domain, and a modified octree technique is employed to place initial bubbles in the three-dimensional zone. Numerical comparisons are made with other mesh generation techniques to demo...

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...

Previous attempts to simulate disordered binary sphere packings have been limited in producing mechanically stable, isostatic packings across a broad spectrum of packing fractions. Here we report that disordered strictly jammed binary packings (packings that remain mechanically stable under general shear deformations and compressions) can be produced with an anomalously large range of average p...

Apollonian circle packings arise by repeatedly filling the interstices between mutually tangent circles with further tangent circles. It is possible for every circle in such a packing to have integer radius of curvature, and we call such a packing an integral Apollonian circle packing. This paper studies number-theoretic properties of the set of integer curvatures appearing in such packings. Ea...

in a graph g = (v,e), a subset s  v is said to be an open packing set if no two vertices of s have a common neighbour in g. the maximum cardinality of an open packing set is called the open packing number and is denoted by rho^o. this paper further studies on this parameter by obtaining some new bounds.