316 citations · 2.7k across the 94 of their papers we have counts for
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Fractal rain distributions and chaotic advection
Ronald Dickman
Localized rain events have been found to follow power-law distributions over several decades, suggesting parallels between precipitation and seismic activity [O. Peters et al., PRL…
Series expansion for a stochastic sandpile
Jurgen F. Stilck, Ronald Dickman, Ronaldo R. Vidigal
Using operator algebra, we extend the series for the activity density in a one-dimensional stochastic sandpile with fixed particle density p, the first terms of which were obtained…
Variable survival exponents in history-dependent random walks: hard movable reflector
Ronald Dickman, Francisco Fontenele Araujo, Daniel ben-Avraham
We review recent studies demonstrating a nonuniversal (continuously variable) survival exponent for history-dependent random walks, and analyze a new example, the hard movable part…
On singular probability densities generated by extremal dynamics
Guilherme J. M. Garcia, Ronald Dickman
Extremal dynamics is the mechanism that drives the Bak-Sneppen model into a (self-organized) critical state, marked by a singular stationary probability density . With the ai…
Avalanche exponents and corrections to scaling for a stochastic sandpile
Ronald Dickman, J. M. M. Campelo
We study distributions of dissipative and nondissipative avalanches in Manna's stochastic sandpile, in one and two dimensions. Our results lead to the following conclusions: (1) av…