Structure of the scalar field around unidirectional circular cylinders
Natalia Ryłko · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · 2007
We study transport properties of equal infinite unidirectional circular cylinders that are arbitrarily distributed in a uniform host. The problem is reduced to a conjugation problem for the two-dimensional Laplace equation. The flux is written exactly in the form of a power series in Bergman's contrast parameter. Asymptotic formulae for the flux are deduced for densely packed inclusions. These formulae involve two small parameters: the ratio of the distance between the close discs to their radius and a dimensionless parameter that characterizes the degree of perfect conductor/isolator. Validity of the structural approximation is discussed.