Asymptotic Approximation of the Dirichlet to Neumann Map of High Contrast Conductive Media

TL;DR

This paper provides an asymptotic analysis of the Dirichlet to Neumann map for high contrast composite media with nearly touching perfect conductors, offering explicit characterization as inclusions approach contact.

Contribution

It introduces a novel asymptotic approximation method for the Dirichlet to Neumann map in high contrast media with closely spaced conductors.

Findings

Explicit asymptotic formula for the Dirichlet to Neumann map.

Characterization of the map as inclusions nearly touch.

Insights into high contrast media behavior in limiting cases.

Abstract

We present an asymptotic study of the Dirichlet to Neumann map of high contrast composite media with perfectly conducting inclusions that are close to touching. The result is an explicit characterization of the map in the asymptotic limit of the distance between the particles tending to zero.