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Sonia Fliss (Ensta) nous parlera de
Scattering by a Random Thin Coating of Nanoparticles
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.
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G. Delay, V. Girault, F. Hecht, D. Lombardi, O. Pironneau, J. Salomon