We study dense packings of a large number congruent non-overlapping circles inside square by looking for configurations which maximize the packing density, defined as ratio between area occupied disks and container. The search these is carried out with help two algorithms that we have devised: first algorithm in charge obtaining sufficiently starting from random guess, while second improves obt...

This paper proposes a new expression of discrete-mechanical quantities in a granular assembly and a new formulation of the graph-theoretical approach in the mechanics of granular materials. New mechanical quantities for void, i.e., void force, void displacement, etc., are introduced and relations between discrete-mechanical quantities of particle, contact and void are given in a very simple for...

Dynamic simulations with discrete elements are used to obtain more insight into the wave propagation in dense granular media. A small perturbation is created on one side of a dense, static packing and examined during its propagation until it arrives at the opposite side. The influence of polydispersity is studied by randomly varying the particle sizes by a tiny amount. A size variation comparab...

It is well known that a graph with m edges can be made triangle-free by removing (slightly less than) m/2 edges. On the other hand, there are many classes of graphs which are hard to make triangle-free in the sense that it is necessary to remove roughly m/2 edges in order to eliminate all triangles. We prove that dense graphs that are hard to make triangle-free have a large packing of pairwise ...

Vertical silos are large cylinders used for material storage in agriculture and mineral industries. One of the silo problems is its obstruction due to dome and dense packing. Depend on the material properties and silo dimensions several techniques are used to solve this problem. In the present work, possibility of obstruction solution of a laboratory silo by ball impact is investigated. Test ma...

Random dense packing of poly-disperse discs and spheres generated under the infinitesimal gravity protocol is investigated by a Monte Carlo simulation. For the binary discs packed in two dimensions, the packing fraction of disc assembly becomes lower than that of the monodisperse system when the size ratio is close to unity. We show that the suppressed packing fraction is caused by an increase ...

Recent simulations indicate that ellipsoids can pack randomly more densely than spheres and, remarkably, for axes ratios near 1.25:1:0.8 can approach the densest crystal packing (fcc) of spheres, with a packing fraction of 74%. We demonstrate that such dense packings are realizable. We introduce a novel way of determining packing density for a finite sample that minimizes surface effects. We ha...