A Stochastic Description for Extremal Dynamics
arXiv:cond-mat/9908212 · doi:10.1209/epl/i2000-00330-9
Abstract
We show that extremal dynamics is very well modelled by the "Linear Fractional Stable Motion" (LFSM), a stochastic process entirely defined by two exponents that take into account spatio-temporal correlations in the distribution of active sites. We demonstrate this numerically and analytically using well-known properties of the LFSM. Further, we use this correspondence to write an exact expressions for an n-point correlation function as well as an equation of fractional order for interface growth in extremal dynamics.
4 pages LaTex, 3 figures .eps
References in corpus (6)
- Dynamics of a ferromagnetic domain wall: avalanches, depinning transition and the Barkhausen effect
- Local fractional Fokker-Planck equation
- From Individual to Collective Pinning: Effect of Long-range Elastic Interactions
- Theory of Self-organized Criticality for Problems with Extremal Dynamics
- Dynamic exponent in Extremal models of Pinning
- Pattern Formation in Interface Depinning and Other Models: Erratically Moving Spatial Structures
Cited by in corpus (6)
- Diffusion of Earthquake Aftershock Epicenters, Omori's Law and Generalized Continuous-Time Random Walk Models
- Endogeneous Versus Exogeneous Shocks in Systems with Memory
- Universal depinning force fluctuations of an elastic line: Application to finite temperature behavior
- On the kinetic equation of linear fractional stable motion and applications to modeling the scaling of intermittent bursts
- Material independent crack arrest statistics
- Separable local fractional differential equations