Méthodes asymptotiques pour le calcul des champs électromagnétiques dans des milieux à couches minces.
Application aux cellules biologiques.

Abstract : This thesis deals with asymptotic methods for electromagnetism in
heterogeneous domains with thin layer. The motivation is the
computation of electromagnetic fields in biological cells, which are
highly heterogeneous media. We replace the thin cytoplasmic
membrane with an appropriate condition on the boundary of the
cytoplasm and we estimate the error.
Two equations are considered: the steady state voltage equation and
Helmholtz equation. For the low frequency case, we suppose that
Neumann condition is imposed on the exterior boundary of the cell. We
build approximated boundary condition, which is valid for an
insulating (even perfectly insulating) thin membrane. For Helmholtz
equation, we suppose that the cell is embedded in an ambiant medium
and we build transmission conditions equivalent to the thin
membrane. All these results are proved and numerically computed.
For the high-frequency assumption (the frequency tends to infinity),
we build generalized impedance condition using pseudo-differential
approach equivalent to the membrane. We conclude this thesis with a
work with Michael Vogelius on the high frequency scattering by a small
circular inhomogeneity.
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Clair Poignard. Méthodes asymptotiques pour le calcul des champs électromagnétiques dans des milieux à couches minces.
Application aux cellules biologiques.. Mathématiques [math]. Université Claude Bernard - Lyon I, 2006. Français. 〈tel-00124110v2〉

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