Packing of monosized spheres in a cylindrical container of a fixed diameter is a frequently discussed subject in recent studies. It is motivated by the high applicability of these models, particularly by the advances in nanomaterial science and engineering, associated with the development of hierarchically ordered matters of specific structures and properties. Their features strongly depend on ...

The densest packings of n congruent circles in a circle are known for n 12 and n = 19. In this paper we exhibit the densest packings of 13 congruent circles in a circle. We show that the optimal con gurations are identical to Kravitz's [11] conjecture. We use a technique developed from a method of Bateman and Erd}os [1] which proved fruitful in investigating the cases n = 12 and 19 by the autho...

Two computer models were developed to realize the algorithms of random Apollonian and Apollonian packings of the spherical particles in a unit cube. A genetic algorithm was developed for the latter packing model. The upper and lower bounds of a fractal dimension were computed using various numerical methods. It was observed that for both models the fractal properties were not essentially affect...

When small numbers of colloidal microspheres are attached to the surfaces of liquid emulsion droplets, removing fluid from the droplets leads to packings of spheres that minimize the second moment of the mass distribution. The structures of the packings range from sphere doublets, triangles, and tetrahedra to exotic polyhedra not found in infinite lattice packings, molecules, or minimum-potenti...

A k-uniform hypergraph H contains a Hamilton `-cycle, if there is a cyclic ordering of the vertices of H such that the edges of the cycle are segments of length k in this ordering and any two consecutive edges fi, fi+1 share exactly ` vertices. We consider problems about packing and counting Hamilton `-cycles in hypergraphs of large minimum degree. Given a hypergraph H, for a d-subset A ⊆ V (H)...

Having sufficient and accurate understanding about kinetics of phenomena, could be an important reason for further technological progresses. Finding a white-box mathematical model for weight vs. time curves of Electrophoretic Deposition (EPD) using large and small signal analysis has been studied thoroughly in the present investigation. Weight-Time curves of nano-Mullite suspension have been tr...

In this paper, the effects of container size on the porosity of random loose packing of mono size particles have been investigated using an Event Dynamics (ED) based model. Simultaneous effects of square container walls on particles packing and their order are also investigated. Our simulation results indicate higher container size will increase the total packing factor and high density regions...