THE POLARIZABILITY OF CYLINDER ARRAYS IN 2 DIMENSIONS

The technique of solving the two-dimensional Laplace equation by means of conformal transformations is a very useful one. Here we develop th is method into one which is applicable to chains and lattices in which the fundamental unit is a cylinder pair. An exact closed form express ion for the polarisability with explicit spectral weights is immediate once the appropriate transformation for the given cylinder arrangemen t is determined. The present formalism provides simple derivations of certain results, among which is a proof of Keller's theorem. We derive the polarisability formulae for a pair of separate cylinders and then determine the corresponding results for chains and lattices of cylind er pairs. (C) 1995 Academic Press, Inc.