Percolation, statistical topography, and transport in random media

摘要: 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 isosets (contour lines or surfaces) a random potential $\ensuremath{\psi}(\mathrm{x})$. For rapidly decaying correlations $\ensuremath{\psi}$, isopotentials fall into same universality class as perimeters clusters. The long-range correlated potentials many length scales associated either problem Mandelbrot's fractional Brownian reliefs. In all cases, concept fractal dimension particularly fruitful in characterizing geometry fields. physical include diffusion velocity fields, heat particle transport plasmas, quantum Hall effect, magnetoresistance inhomogeneous conductors others where are relevant. approach studying media, which captures essential qualitative features described phenomena, advocated.