Transport properties of arrays of elliptical cylinders

We apply the Rayleigh method to derive a formulation yielding the effective dielectric tensor of a periodic composite consisting of an array of elliptical cylinders placed in a matrix bf unit dielectric constant. We consider three types of composites having this structure: dilute noncritical, dilute critical, and concentrated composites. For dilute noncritical composites we comment on our result in relation to the competing forms of the Maxwell-Garnett formula, which have been proposed previously. We also discuss the case of dilute critical and concentrated composites of solid elliptical inclusions, and comment on geometrical constraints on the validity of the Rayleigh equations.