On universality of conductivity of planar random self-dual systems

dc.creatorBulgadaev, S. A.
dc.date2004-10-03
dc.date.accessioned2026-07-07T03:01:13Z
dc.date.available2026-07-07T03:01:13Z
dc.descriptionGeneral properties of the effective conductivity sigma_e of planar isotropic randomly inhomogeneous two-phase self-dual systems are investigated. A new approach for finding out sigma_e of random systems based on a duality, a series expansion in the inhomogeneous parameter z and additional assumptions, is proposed. Two new approximate expressions for sigma_e at arbitrary values of phase concentrations are found. They satisfy all necessary inequalities, symmetries, including a dual one, and reproduce known results in various limiting cases. Two corresponding models with different inhomogeneity structures, whose sigma_e coincide with these expressions, are constructed. First model describes systems with a finite maximal characteristic scale of the inhomogeneities. In this model sigma_e is a solution of the approximate functional equation, generalizing the duality relation. The second model is constructed from squares with random layered structure. The difference of sigma_e for these models means a nonuniversality of the effective conductivity even for binary random self-dual systems. The first explicit expression for sigma_e can be used also for approximate description of various inhomogeneous systems with compact inclusions of the second phase. The percolation problem of these models is briefly discussed.
dc.description25 pages, 5 figures, Latex2e
dc.identifierhttps://arxiv.org/abs/cond-mat/0410058
dc.identifierhttp://arxiv.org/abs/cond-mat/0410058
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/24991
dc.subjectDisordered Systems and Neural Networks
dc.subjectStatistical Mechanics
dc.titleOn universality of conductivity of planar random self-dual systems
dc.typetext

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