The toposcopy, a new tool to probe the geometry of an irregular interface by measuring its transfer impedanceM. Filoche1, 2 and D. S. Grebenkov1
1 Physique de la Matière Condensée, Ecole Polytechnique, CNRS - F-91128 Palaiseau, France
2 CMLA, ENS Cachan, CNRS, UniverSud - 61 Avenue du President Wilson, F-94230 Cachan, France
received 20 September 2007; accepted in final form 21 December 2007; published February 2008
published online 24 January 2008
Semi-permeable interfaces of irregular geometry accessed by diffusion exhibit complex transfer properties. In particular, their transfer impedance is the non-trivial result of the interplay between their geometry and their physical properties. In this paper, we present a new method that we call toposcopy. Its aim is to solve the "inverse impedance spectroscopy problem", namely to retrieve the geometrical features of an irregular interface from a "black box" measurement of its transfer impedance only. From previous studies, one knows that all the possible information about the geometry of an interface that can be extracted from a measurement of its impedance consists in its harmonic geometrical spectrum, a set of spectral characteristics of the Dirichlet-to-Neumann operator of the same interface. Here, we first describe how the toposcopy technique permits to retrieve the main components of the harmonic geometrical spectrum and to deduce from them characteristic geometrical features of the interface. The toposcopy is then tested numerically for several irregular interfaces of either simple or complex shape. It is finally shown that this method gives access to the characteristics lengths of these interfaces and, when these lengths are sufficiently different, allows to separate and quantify their respective contributions to the interface impedance.
05.40.-a - Fluctuation phenomena, random processes, noise, and Brownian motion.
61.43.Hv - Fractals; macroscopic aggregates (including diffusion-limited aggregates).
41.20.Cv - Electrostatics; Poisson and Laplace equations, boundary-value problems.
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