Duruflé, Marc; Péron, Victor; Poignard, Clair Time-harmonic Maxwell equations in biological cells-the differential form formalism to treat the thin layer. (English) Zbl 1235.78035 Confluentes Math. 3, No. 2, 325-357 (2011). The authors study the behavior of the electromagnetic field in a biological cell modelled by a medium surrounded by a thin layer embedded in an ambient medium. In the first part, the authors present the problem in a differential calculus formalism and state the main results. In the next section, they give numerical simulations that validate the theoretical results. In particular, it is argued that for biological cells, the membrane’s behaviour dramatically changes with respect to the frequency. More precisely, it is established that if the “thin-layer” model is valid for quite large frequencies, then a very resistive thin layer model must be studied for low frequencies. The proofs combine related estimates with recurrence formulae in order to deduce the asymptotic expansion at any order. Reviewer: Teodora-Liliana Rădulescu (Craiova) Cited in 5 Documents MSC: 78A70 Biological applications of optics and electromagnetic theory 78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory 78M30 Variational methods applied to problems in optics and electromagnetic theory 78M35 Asymptotic analysis in optics and electromagnetic theory Keywords:asymptotic expansion; time-harmonic Maxwell’s equations; differential forms on manifolds; finite element method; edge elements PDFBibTeX XMLCite \textit{M. Duruflé} et al., Confluentes Math. 3, No. 2, 325--357 (2011; Zbl 1235.78035) Full Text: DOI