Spectral properties of the Brownian self-transport operator

Abstract

The problem of the Laplacian transfer across an irregular resistive interface (a membrane or an electrode) is investigated with use of the Brownian self-transport operator. This operator describes the transfer probability between two points of a surface, through Brownian motion in the medium neighbouring the surface. This operator governs the flux across a semi-permeable membrane as diffusing particles repetitively hit the surface until they are finally absorbed. In this paper, we first give a theoretical study of the properties of this operator for a planar membrane. It is found that the net effect of a decrease of the surface permeability is to induce a broadening of the region where a particle, first hitting the surface on one point, is finally absorbed. This result constitutes the first analytical justification of the Land Surveyor Approximation, a formerly developed method used to compute the overall impedance of a semi-permeable membrane. In a second step, we study numerically the properties of the Brownian self-transport operator for selected irregular shapes. Copyright Springer-Verlag Berlin/Heidelberg 2003

Similar works

Full text

thumbnail-image

Research Papers in Economics

redirect
Last time updated on 06/07/2012

This paper was published in Research Papers in Economics.

Having an issue?

Is data on this page outdated, violates copyrights or anything else? Report the problem now and we will take corresponding actions after reviewing your request.