The toposcopy: how to deduce the shape of an electrode from a black box measurement

Marcel Filoche
École Polytechnique

The transfer across an irregular electrode of a current driven by a Laplacian field is a complex interplay between the physical characteristics of the electrode and its geometry. In the case of a linear resistive or capacitive electrode, the current continuity translates into a real or complex Robin boundary
condition on the field. We show that the response of the system can be described in terms of the eigenfunctions of the Dirichlet-to-Neumann operator of the domain, which are directly related to the sizes of the geometrical features of the electrode. Moreover, only a very small number of these eigenfunctions are necessary to reproduce the total response of the electrode. Finally, numerical computations and real experiments on model electrodes will be presented, to evaluate the efficiency of the method.

Presentation (PDF File)

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