Nonlinear Stochastic Differential Equations and Self-Organized Criticality

TL;DR

This paper investigates nonlinear stochastic differential equations related to self-organized criticality, analyzing models with different noise correlations to determine critical exponents using dynamic renormalization group methods.

Contribution

It introduces a systematic approach to study models with multiple relevant nonlinearities in self-organized critical phenomena.

Findings

Critical exponents estimated for different noise correlations

All nonlinearities are equally relevant below the upper critical dimension

Dynamic renormalization group provides asymptotic critical values

Abstract

Several nonlinear stochastic differential equations have been proposed in connection with self-organized critical phenomena. Due to the threshold condition involved in its dynamic evolution an infinite number of nonlinearities arises in a hydrodynamic description. We study two models with different noise correlations which make all the nonlinear contribution to be equally relevant below the upper critical dimension. The asymptotic values of the critical exponents are estimated from a systematic expansion in the number of coupling constants by means of the dynamic renormalization group.