Mathematical Modeling

Percolation of the prolate ellipsoids of rotation in the continuum

M. M. Buzmakova

Astrakhan State University, Astrakhan, Russia

Abstract: Continuum percolation of the hard prolate ellipsoids of rotation with permeable shell has been investigated. It is the model of phase transition sol–gel. Ellipsoids are located in the cube randomly. For each set of parameters 100 tests are spent. For each test the finding of the percolation cluster is the main task. The fraction of the packing for which the probability of the percolation cluster appearance is equal 0.5, is called a percolation threshold. Value of the percolation threshold corresponds to the gel point. Dependence of value of the percolation threshold on thickness of permeable shell and aspect ratio has been obtained. In addition to the percolation threshold the other characteristics of the model have been obtained, such as: the size distribution of clusters, the average cluster size, the strength and the fractal dimension of the percolation cluster, the average value and the distribution of neighbors of an element, the critical exponents.

Keywords: percolation, gelation, phase transitions.

UDC: 519.68:[5/6+3]+004.94+544.015.4+544.022.822

MSC: Primary 60K35; Secondary 82B43, 82B26, 82B21

Original article submitted 09/VI/2012
revision submitted – 25/IX/2012

DOI: 10.14498/vsgtu1095

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