28 citations · 28 across the 1 of their papers we have counts for
5 papers
On the scaling of probability density functions with apparent power-law exponents less than unity
Kim Christensen, Nadia Farid, Gunnar Pruessner +1
We derive general properties of the finite-size scaling of probability density functions and show that when the apparent exponent \tautilde of a probability density is less than 1,…
One-Dimensional Directed Sandpile Models and the Area under a Brownian Curve
M A Stapleton, K Christensen
We derive the steady state properties of a general directed ``sandpile'' model in one dimension. Using a central limit theorem for dependent random variables we find the precise co…
Mean-Field Theory and Sandpile Models
Matthew Stapleton, Kim Christensen
We review and refine the concept of a mean-field theory for the study of sandpile models, which are of central importance in the study of self-organized criticality. By considering…
Universality Class of One-Dimensional Directed Sandpile Models
Matthew Stapleton, Kim Christensen
A general n-state directed `sandpile' model is introduced. The stationary properties of the n-state model are derived for n < infty, and analytical arguments based on a central lim…
Sensitivity to initial conditions in self-organized critical systems
Matthew Stapleton, Martin Dingler, Kim Christensen
We discuss sensitivity to initial conditions in a model for avalanches in granular media displaying self-organized criticality. We show that damage, due to a small perturbation in…