Applications of statistical mechanics to natural hazards and landforms

The concept of self-organized criticality was introduced to explain the beh avior of the cellular-automata sandpile model. A variety of multiple slider -block and forest-fire models have been introduced which are also said to e xhibit self-organized critical behavior. It has been argued that earthquake s, landslides, forest-fires, and extinctions are examples of self-organized criticality in nature. The basic forest-fire model is particularly interes ting in terms of its relation to the critical-point behavior of the site-pe rcolation model. In the basic forest-fire model trees are randomly planted on a grid of points, periodically sparks are randomly dropped on the grid a nd if a spark drops on a tree that tree and the adjacent trees burn in a mo del fire. In the forest-lire model there is an inverse cascade of trees fro m small clusters to large clusters, trees are lost primarily from model fir es that destroy the largest clusters, This quasi-steady-state cascade gives a power-law frequency-area distribution for both clusters of trees and sma ller fires. The site-percolation model is equivalent to the forest-fire mod el without fires. In this case there is a transient cascade of trees from s mall to large clusters and a power-law distribution is found only at a crit ical density of trees. The earth's topography is an example of both statist ically self-similar and self-affine fractals. Landforms are also associated with drainage networks, which are statistical fractal trees. A universal f eature of drainage networks and other growth networks is side branching. De terministic space-filling networks with side-branching symmetries are illus trated. It is shown that naturally occurring drainage networks have symmetr ies similar to diffusion-limited aggregation clusters. (C) 1999 Elsevier Sc ience B.V, All rights reserved.