Wave scattering by many small bodies: transmission boundary conditions

Abstract

Wave scattering by many (M = M(a)) small bodies, at the boundary of which transmission boundary conditions are imposed, is studied. Smallness of the bodies means that ka << 1, where a is the characteristic dimension of the body and k = [2π/λ] is the wave number in the medium in which small bodies are embedded. Explicit asymptotic formulas are derived for the field scattered by a single small scatterer of an arbitrary shape. Equation for the effective field is derived in the limit as a → 0 while M(a) → ∞ at a suitable rate.