Wave Scattering by Many Small Bodies: Transmission Boundary Conditions

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 formula is 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.