Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

For citation:

Buzmakova M. M. Percolation of spheres in continuum. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2012, vol. 12, iss. 2, pp. 48-56. DOI: 10.18500/1816-9791-2012-12-2-48-56

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
21.05.2012
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Language: 
Russian
Heading: 
Mechanics
UDC: 
519.68:[5/6+3]+004.94+544.015.4+544.022.822
DOI: 
10.18500/1816-9791-2012-12-2-48-56

Percolation of spheres in continuum

Autors: 
Buzmakova Mariya Mikhailovna, Astrakhan State University, Russia
Abstract: 

The model of the continuum percolation of hard spheres with permeable shells, which describes phase transition sol-gel, has been investigate. Spheres have hard parts in radii r, which can't be blocked with each other, and permeable shells in width d, which can be blocked. Such spheres of the equal size have been randomly packing in the cub with linear size L. The probability of joining the spheres in a cluster is proportional to the volume of overlapping of permeable shells. Spheres belong to a cluster, if a communication between spheres arises. The percolation cluster is the cluster connecting bottom and top sides of the cube. The packing fraction, at which probability of occurrence of the percolation cluster is 0.5, is called as the percolation threshold. The percolation threshold corresponds to the gel point. The dependency of the percolation threshold of the hard spheres with permeable shells from a thickness of the shell has been obtained. 

Key words: 
computer modeling
percolation
sol-gel phase transition
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