Crossover to Self-Organized Criticality in an Inertial Sandpile Model

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We introduce a one-dimensional sandpile model which incorporates particle inertia. The inertial dynamics are governed by a new parameter which, as it passes through a threshold value, alters the toppling dynamics in such a way that the system no longer evolves to a self-organized critical state. A range of mean-field theories based on a kinetic equation approach is presented which confirm the numerical findings. We conclude by considering the physical applications of this model, particularly with reference to recent experimental results.