R. Cafiero et al., THEORY OF EXTREMAL DYNAMICS WITH QUENCHED DISORDER - SELF-ORGANIZATION, AVALANCHE DYNAMICS AND CRITICAL EXPONENTS, International journal of modern physics b, 12(12-13), 1998, pp. 1263-1275
In this paper we discuss a general theoretical scheme, that we have re
cently proposed, for a class of phenomena characterized by extremal dy
namics with quenched disorder. The approach is based on a transformati
on of the quenched dynamics into a stochastic dynamics with cognitive
memory. This transformation, together with other concepts, permits a m
athematical characterization of the self-organized nature of the avala
nche type dynamics. By combining the mapping with real space methods,
like the fixed scale transformation (FST), it is also possible to comp
ute the relevant critical exponents directly from the microscopic mode
l. A specific application to Invasion Percolation is presented but the
approach can be easily extended to various other problems with quench
ed disorder.