NATURAL SCIENCES

Journal of fundamental
and
applied researches

Modeling of the continuum percolation of spheres and ellipsoids

2012. ¹4, pp. 126-134

Buzmakova Mariya M. - post-graduated student, Astrakhan State University, 20a Tatischev Str., Astrakhan, 414056, Russian Federation, òåëmariya_nazarova@mail.ru

The research work describes the algorithms and methods used for modeling the continuum percolation of spheres and ellipsoids. Both of these – spheres and ellipsoids – have hard parts and soft shells. The hard parts of the elements cannot be crossed, while the soft shells can. Crossing of the soft shells of two elements characterizes contact existence between them, and specifies that the two elements belong to one cluster. The system percolates when there is a cluster, stretching all the system (the percolation cluster). For the percolation of spheres, the paper considers two cases: in the first case, the bond between the spheres comes when the soft shells overlap; in the second case, the probability of a bond forming between the spheres is proportional to the volume of the soft shells’ overlapping. In case of ellipsoids, the bond would only come if the soft shells were to overlap.

Key words: modeling,percolation