#### Vol. 5, No. 4, 2010

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Effective medium theories for wave propagation in two-dimensional random inhomogeneous media

### Jin-Yeon Kim

Vol. 5 (2010), No. 4, 567–581
##### Abstract

Two effective medium models for two-dimensional scalar wave propagation in random inhomogeneous media are examined in a single theoretical framework. It is shown how the hypotheses and self-consistency conditions in these models are mathematically formulated. As a special case, a two-phase composite in which circular cylindrical inclusions are embedded in a continuous matrix is considered. Numerical calculations are performed for such composites with different combinations of constituent properties in the frequency range up to $ka=10$, where geometric optic behavior starts appearing. The models mutually deviate when the motion of inclusions is relatively large, such as at the resonance scattering of the inclusions. Otherwise, deviations in the low-frequency regime ($ka<1$) are negligible and those at high frequencies are also strikingly small. The same facts are observed for two composites having very different constituent properties and in the high-frequency limit.

##### Keywords
effective medium theory, wave propagation, composite materials, multiple scattering