Title: Scattering by a Random Thin Coating of Nanoparticles
Abstract
This is a joint work with Laure Giovangigli and Amandine Boucart.
We study the time-harmonic scattering by a heterogeneous object covered with a thin layer of randomly distributed nanoparticles. The size of the particles, their distance between each other and the layer thickness are all of the same order but small compared to the wavelength of the incident wave. The computational cost to solve numerically Maxwells equations in such domain is tremendous. To circumvent this direct computation, we propose via a multi-scale asymptotic expansion of the solution, an effective model where the layer of particles and the object are replaced by an equivalent boundary condition. The coefficients in this equivalent boundary condition depend on the solutions of so-called corrector problems of Laplace-type defined on unbounded random domains. Under the assumption that the particles are distributed given a stationary and ergodic random point process, we study the well-posedness of the corrector problems and the behaviour at infinity of the associated solutions. We then establish quantitative error estimates for the effective model and present numerical simulations that illustrate our theoretical results.
