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Equations for the self-consistent field in random medium

A. G. Ramm
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Abstract

An integral-differential equation is derived for the self-consistent (effective) field in the medium consisting of many small bodies randomly distributed in some region. Acoustic and electromagnetic fields are considered in such a medium. Each body has a characteristic dimension $a\ll\lambda$, where $\lambda$ is the wavelength in the free space. The minimal distance $d$ between any of the two bodies satisfies the condition $d\gg a$, but it may also satisfy the condition $d\ll\lambda$. Using Ramm's theory of wave scattering by small bodies of arbitrary shapes, the author derives an integral-differential equation for the self-consistent acoustic or electromagnetic fields in the above medium.

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A. G. Ramm. 2003-01-31. Equations for the self-consistent field in random medium. https://doi.org/10.1016/s0375-9601(03)00647-9

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