Estimating conformal capacity using asymptotic matching

Abstract

Conformal capacity is a mathematical quantity relevant to a wide range of physical and mathematical problems and there has been a recent resurgence of interest in devising new methods for its computation. In this paper we show how ideas from matched asymptotics can be used to derive estimates for conformal capacity. The formulas derived here are explicit, and evidence is given that they provide excellent approximations to the exact capacity values even well outside the expected range of validity.

Going round the bend: reflection and transmission of long waves by waveguide corners and labyrinths

“…One of these concerns a parallel-walled waveguide with a patch of roughness on one of the walls. This is a good example because it permits comparison with an alternative method based on perturbation theory: this theory is given in appendix A. Interestingly, MAE have been used recently to extract good approximations to the electrostatic capacity for a variety of complicated two-dimensional geometries [7].…”