LMA - Laboratoire de Mécanique et d’Acoustique

L. Giovangigli - Scattering from a random thin coating of nanoparticles : modeling, asymptotic analysis and numerical simulations

Amphithéâtre François Canac, LMA

Le 29 mars 2022 de 11h00 à 12h00

Laure Giovangigli / Associate Professor of Mathematics at ENSTA & POEMS, Palaiseau

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 Helmholtz’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 mixing random point process, we prove that those problems admit a unique solution in the proper spaces with both homogeneous Dirichlet (for d ≥ 2) and Neumann boundary conditions (for d = 3) on the inclusions. We then establish quantitative error estimates for the effective model and present numerical simulations that illustrate our theoretical results.

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