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Scattering from a random thin coating of nanoparticles

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MWSW03 - Computational methods for multiple scattering

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’s thickness are all of the same order but small compared to the wavelength of the incident wave. Solving numerically Maxwell’s equation in this context is very costly. To circumvent this, we propose, via a multi-scale asymptotic expansion of the solution, an effective model where the layer of particles is replaced by an equivalent boundary condition. The coefficients that appear in this equivalent boundary condition depend on the solutions to 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 behavior at inifinity of those solutions and well-posedness of the associated problems with both homogeneous Dirichlet and Neumann boundary conditions on the particles. We then establish quantitative error estimates for the effective model and present numerical simulations that illustrate our theoretical results. This is a joint work with Amandine Boucart (ENPC, Cermics) and Sonia Fliss (ENSTA Paris, Poems).

This talk is part of the Isaac Newton Institute Seminar Series series.

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