Fractal-to-Euclidean crossover of the isotropy restoration feature in a family of fractal resistor networks

Xu, J. J., Lin, Z. F. and Wang, Z. (1998) Fractal-to-Euclidean crossover of the isotropy restoration feature in a family of fractal resistor networks. Physical Review E, 57 (6). pp. 7294-7296. ISSN 1539-3755 doi: 10.1103/PhysRevE.57.7294

Abstract/Summary

Fractal with microscopic anisotropy shows a unique type of macroscopic isotropy restoration phenomenon that is absent in Euclidean space [M. T. Barlow et al., Phys. Rev. Lett. 75, 3042]. In this paper the isotropy restoration feature is considered for a family of two-dimensional Sierpinski gasket type fractal resistor networks. A parameter xi is introduced to describe this phenomenon. Our numerical results show that xi satisfies the scaling law xi similar to l(-alpha), where l is the system size and alpha is an exponent independent of the degree of microscopic anisotropy, characterizing the isotropy restoration feature of the fractal systems. By changing the underlying fractal structure towards the Euclidean triangular lattice through increasing the side length b of the gasket generators, the fractal-to-Euclidean crossover behavior of the isotropy restoration feature is discussed.