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Continuum Theory with Memory for Avalanches in Self-Organized Criticality | | Maya Paczuski
; Stefan Boettcher
; | | Date: |
13 Mar 1996 | | Subject: | Condensed Matter; Adaptation and Self-Organizing Systems | cond-mat adap-org nlin.AO | | Affiliation: | Brookhaven National Laboratory, University of Oklahoma | | Abstract: | The propagator for the activity in a broad class of self-organized critical models obeys an imaginary-time Schrödinger equation with a nonlocal, history-dependent potential representing memory. Consequently, the probability for an avalanche to spread beyond a distance $r$ in time $t$ has an anomalous tail $exp{[-C,x^{1/(D-1)}]}$ for $x=r^D/t gg 1$ and $D>2$, indicative of glassy dynamics. The theory is verified for an exactly solvable model, where $D=4$ and $C=3/4$, and for the Bak-Sneppen model where it is tested numerically. | | Source: | arXiv, cond-mat/9603085 | | Services: | Forum | Review | PDF | Favorites | |
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