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.
Conducting nonoverlapping identical disks are embedded in a two-dimensional background. The set of disks is infinite. The disks are distributed in such a way that the obtained composite is macroscopically isotropic. Let the conductivity of inclusions be higher than the conductivity of the matrix. It is proved that the hexagonal (triangular) lattice of disks possess the minimal effective conductivity when the concentration is not high.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.