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

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 is equal to one. The parameter is such that , where the situation 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.

Keywords:

• Quasi-steady Maxwell’s equations
• effective coefficients
• Kolmogorov multiplicativecascades
• log-stable random conductivity
• subgrid modeling

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work was supported by the Russian Fund of Basic Researchers (RFBR) [number 15-01-01458].