| Issue |
Europhys. Lett.
Volume 38, Number 7, June I 1997
|
|
|---|---|---|
| Page(s) | 491 - 496 | |
| Section | General | |
| DOI | https://doi.org/10.1209/epl/i1997-00273-1 | |
| Published online | 01 September 2002 | |
Theory of self-organized criticality for problems with extremal dynamics
1
Dipartimento di Fisica, Universitá di Roma “Tor Vergata”, Via della Ricerca Scientifica 1, I-00133 Roma, Italy
2
Dipartimento di Fisica, Universitá di Roma “La Sapienza”, P.le Aldo Moro 2, I-00185 Roma, Italy; and INFM, unitá di Roma I
3
Institut de Physique Theorique Universitè de Fribourg, Pérolles CH-1700 Fribourg, Suisse
Received:
12
September
1996
Accepted:
3
May
1997
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.
PACS: 02.50.-r – Probability theory, stochastic processes, and statistics / 05.40.+j – Fluctuation phenomena, random processes, and Brownian motion / 05.90.+m – Other topics in statistical physics and thermodynamics
© EDP Sciences, 1997
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