Mode-coupling theory and simulation results for the ‘‘running-sandpile’’ model of self-organized criticality

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Abstract
We examine the model of self-organized criticality investigated by Hwa and Kardar [Phys. Rev. Lett. 62, 1813 (1989)] based on a continuum, nonlinear driven diffusion equation with stochastic noise. We point out some problems in the heuristic arguments used in relating the temporal response functions of the model to the exponents calculated exactly by dynamic-renormalization-group analysis. We propose an alternative, direct calculation of the response function and its power spectrum for the total energy dissipated in the system by a mode-coupling theory, making use of the renormalization-group recursion relations for the renormalized parameters of the theory. We find a significant difference from the previous results. Simulation results of the ‘‘running-sandpile’’ model agree with our mode-coupling-theory predictions.