Hierarchical lattice constructions (Q1311069)

The paper is devoted to the study of methods of construction of hierarchical lattices which do not satisfy the assumption of the dispersivity of nonhomogeneity, used in [\textit{D. A. G. Bruggeman}, Ann. Phys. 24, 636-664 (1935)]. The principal result states the existence of the limit \(\widehat \sigma = \lim \widehat \sigma_ j\) of the effective conductivities \(\widehat \sigma_ j\) of hierarchical lattice constructions, where \(j,n \to \infty\) and \(j/n \to t\). It turns out that the Maxwell classical formula is precisely valid in a two-dimensional hierarchical lattice (``lattice of lattices'').