Geodesic
Percolation model of conductivity of two-phase lattice: theory and computer experiment
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 4 (2010), pp. 112-122

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The conductivity of percolation system is studied (the system consists of conductive and non-conducting phases). The connection of conductivity with probability is determined using the conception of Shklovskii–de Gennes on the topological structure of infinite cluster. The dependence lattice conductivity is obtained in a wide range of modification of conductive phase concentration. The concordance of theory and computer experiment is shown. Also the concordance of scaling dependence and conductivity for square and simple cubical lattice is shown using the critical index from the consequence of hypothesis of Alexander–Orbah.
Keywords: conductivity, lattice, percolation. 
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     author = {S. R. Gallyamov and S. A. Mel'chukov},
     title = {Percolation model of conductivity of two-phase lattice: theory and computer experiment},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {112--122},
     publisher = {mathdoc},
     number = {4},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2010_4_a12/}
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S. R. Gallyamov; S. A. Mel'chukov. Percolation model of conductivity of two-phase lattice: theory and computer experiment. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 4 (2010), pp. 112-122. http://geodesic.mathdoc.fr/item/VUU_2010_4_a12/