An asymptotic homogenization formula for complex permittivity and its application

Abstract

The R-linear boundary value problem in a multiply con-nected domain on a flat torus is considered. This problem is closely related to the Riemann-Hilbert problem on analytic functions. The considered problem arises in the homogenization procedure of random media with complex constants which express the permittivity of compo-nents. A new asymptotic formula for the effective permittivity tensor is derived. The formula contains location of inclusions in symbolic form. The application of the derived formula to investigation of the morphol-ogy of the tumor cells in disordered biological media is discussed.