Theory of self-organized criticality for problems with extremal dynamics
Abstract
We introduce a general theoretical scheme for a class of phenomena characterized by an extremal dynamics and quenched disorder. The approach is based on a transformation of the quenched dynamics into a stochastic one with cognitive memory and on other concepts which permit a mathematical characterization of the self-organized nature of the avalanche type dynamics. In addition it is possible to compute the relevant critical exponents directly from the microscopic model. A specific application to invasion percolation is presented but the approach can be easily extended to various other problems.
- Publication:
-
EPL (Europhysics Letters)
- Pub Date:
- June 1997
- DOI:
- 10.1209/epl/i1997-00273-1
- arXiv:
- arXiv:cond-mat/9702176
- Bibcode:
- 1997EL.....38..491G
- Keywords:
-
- 02.50.-r;
- 05.40.+j;
- 05.90.+m;
- Probability theory stochastic processes and statistics;
- Other topics in statistical physics thermodynamics and nonlinear dynamical systems;
- Condensed Matter - Disordered Systems and Neural Networks;
- Condensed Matter - Statistical Mechanics
- E-Print:
- 11 pages Latex (revtex), 3 postscript figures included. Submitted to Europhys. Lett