Email this article Percolation of the prolate ellipsoids of rotation in the continuum
- Authors: Buzmakova M.M1
-
Affiliations:
- Astrakhan State University
- Issue: Vol 16, No 4 (2012)
- Pages: 146-153
- Section: Articles
- URL: https://journal-vniispk.ru/1991-8615/article/view/20830
- ID: 20830
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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.
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##article.viewOnOriginalSite##About the authors
Mariya M Buzmakova
Astrakhan State University
Email: mariya_nazarova@mail.ru
Assistant, Dept. of Applied Mathematics & Computer Science 20 а, Tatishcheva st., Astrakhan, Russia, 414056
References
- Stauffer D., Aharony A. Introduction to Percolation Theory. London: Taylor & Francis, 1992. 181 pp.
- Sahimi M. Application of Percolation Theory. London: Taylor & Francis, 1994. 258 pp.
- Ohira K., Sato M., Kohmoto M. Fluctuations in chemical gelation // Phys. Rev. E, 2007. Vol. 75, no. 4, 041402. 6 pp., arXiv: cond-mat/0510106 [cond-mat.soft].
- Del Gado E., Fierro A., de Arcangelis L., Coniglio A. Slow dynamics in gelation phenomena: From chemical gels to colloidal glasses // Phys. Rev. E, 2004. Vol. 69, no. 5, 051103. 9 pp., arXiv: cond-mat/0310776 [cond-mat.soft].
- Plischke M., Vernon D. C., Joóc B. Model for gelation with explicit solvent effects: Structure and dynamics // Phys. Rev. E, 2003. Vol. 67, no. 1, 011401. 6 pp., arXiv: cond-mat/0207304 [cond-mat.soft].
- Garboczi E. J., Snyder K. A., Douglas J. F., Thorpe M. F. Geometrical percolation threshold of overlapping ellipsoids // Phys. Rev. E, 1995. Vol. 52, no. 1. Pp. 819–828.
- Yi. Y. B. Void percolation and conduction of overlapping ellipsoids // Phys. Rev. E, 2006. Vol. 74, no. 3, 031112. 6 pp.
- Akagawa S., Odagaki T. Geometrical percolation of hard-core ellipsoids of revolution in the continuum // Phys. Rev. E, 2007. Vol. 76, no. 5, 051402. 5 pp.
- Ambrosetti G., Johner N. , Grimaldi C., Danani A., Ryser P. Percolative properties of hard oblate ellipsoids of revolution witha soft shell // Phys. Rev. E, 2008. Vol. 78, no. 6, 061126. 11 pp., arXiv: 0805.1181 [cond-mat.stat-mech].
- Matsumoto M., Nishimura T. Mersenne twister: A 623-dimensionally equidistributed uniform pseudo-random number generator // ACM Trans. Model. Comput. Simul., 1998. Vol. 8, no. 1. Pp. 3–30.
- Hoshen J., Kopelman R. Percolation and cluster distribution. I. Cluster multiple labeling technique and critical concentration algorithm // Phys. Rev. B, 1976. Vol. 14, no. 8. Pp. 3438–3445.
- Rubin F. The Lee path connection algorithm // IEEE Trans. Computers, 1974. Vol. C-23, no. 9. Pp. 907–914.
- Тарасевич Ю. Ю. Перколяция: теория, приложения, алгоритмы. M.: Едиториал УРСС, 2002. 112 с.
- Balberg I., Binenbaum N. Invariant properties of the percolation thresholds in the softcore–hard-core transition // Phys. Rev. A, 1987. Vol. 35, no. 12. Pp. 5174–5177.
- Goncharuk A. I., Lebovka N. I., Lisetski L. N., Minenko S. S. Aggregation, percolation and phase transitions in nematic liquid crystal EBBA doped with carbon nanotubes // J. Phys. D: Appl. Phys., 2009. Vol. 42, no. 16, 165411. 8 pp.
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