Percolation, statistical topography, and transport in random media
Year: 1992
Type: article
Abstract: A review of classical percolation theory is presented, with an emphasis on novel applications to statistical topography, turbulent diffusion, and heterogeneous media. Statistical topography involves the geometrical properties of the isosets (contour lines or surfaces) of a random potential $\ensuremath{\psi}(\mathrm{x})$. For rapidly decaying correlations of $\ensuremath{\psi}$, the isopotentials fall into the same universality class as the perimeters of percolation clusters. The topography of long-range correlated potentials involves many length scales and is associated either with the correlated percolation problem or with Mandelbrot's fractional Brownian reliefs. In all cases, the concept of fractal dimension is particularly fruitful in characterizing the geometry of random fields. The physical applications of statistical topography include diffusion in random velocity fields, heat and particle transport in turbulent plasmas, quantum Hall effect, magnetoresistance in inhomogeneous conductors with the classical Hall effect, and many others where random isopotentials are relevant. A geometrical approach to studying transport in random media, which captures essential qualitative features of the described phenomena, is advocated.
Source: Reviews of Modern Physics
Author: M. B. Isichenko
Institutions: Kurchatov Institute, The University of Texas at Austin
Language: English
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funder: U.S. Department of Energy
OpenAlex ID: W2073485865