Invasion percolation between two sites in two, three, and four dimensions |
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Authors: | Sang Bub Lee |
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Affiliation: | Department of Physics, Kyungpook National University, Daegu 702-701, Republic of Korea |
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Abstract: | The mass distribution of invaded clusters in non-trapping invasion percolation between an injection site and an extraction site has been studied, in two, three, and four dimensions. This study is an extension of the recent study focused on two dimensions by Araújo et al. [A.D. Araújo, T.F. Vasconcelos, A.A. Moreira, L.S. Lucena, J.S. Andrade Jr., Phys. Rev. E 72 (2005) 041404] with respect to higher dimensions. The mass distribution exhibits a power-law behavior, P(m)∝m−α. It has been found that the index α for pe<pc, pc being the percolation threshold of a regular percolation, appears to be independent of the value of pe and is also independent of the lattice dimensionality. When pe=pc, α appears to depend marginally on the lattice dimensionality, and the relation α=τ−1, τ being the exponent associated with cluster size distribution of a regular percolation via ns∝s−τ, appears to be valid. |
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Keywords: | 64.60.Ak 47.55.Mh 61.43.Gt |
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