MAPPING OF A DETERMINISTIC DYNAMICS WITH QUENCHED VARIABLES INTO A STOCHASTIC PROBLEM WITH COGNITIVE MEMORY

Irreversible dynamics in media with quenched disorder seems to be the essential mechanism for a variety of phenomena like fracture propagati on or displacement of immiscible fluids in disordered porous media. Th is problem does not seem to be treatable along the standard theoretica l schemes. Recently a new approach has been introduced that allows map ping of a deterministic dynamics with quenched disorder like that of I nvasion Percolation into a stochastic dynamics with memory. This memor y consists essentially in a cognitive process that modifies the probab ility distribution of quenched variables conditionally to all previous events. This approach, together with the FST and the corresponding an alysis of the scale invariant dynamics, provides a new framework to un derstand the self organization and to compute the critical exponents o f problems like Invasion Percolation and Bak and Sneppen.