Effective coefficients of quasi-steady Maxwell’s equations with multiscale isotropic log-stable conductivity

M. I. Epov, E. P. Kurochkina, O. N. Soboleva

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Abstract

The effective coefficients in the quasi-steady Maxwell’s equations are calculated for a multiscale isotropic medium by using a subgrid modeling approach.The conductivity is mathematically represented by a Kolmogorov multiplicative cascade with a log-stable probability distribution. The skewness of the stable probability distribution (Formula presented.) is equal to one. The parameter (Formula presented.) is such that (Formula presented.), where the situation (Formula presented.) corresponds to the Gaussian distribution. Thus, the variance of the stable probability distribution is infinite, but the mean is finite. The scale of a solution domain is assumed to be large as compared with the scale of heterogeneities of the medium. The theoretical results obtained in the paper are compared with the results of a direct 3D numerical simulation.

Original language English 850-866 17 Journal of Electromagnetic Waves and Applications 31 8 https://doi.org/10.1080/09205071.2017.1319301 Published - 24 May 2017

Keywords

• effective coefficients
• log-stable random conductivity