Two-dimensional avalanches as stochastic Markov processes

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Abstract
A theory is proposed to describe two-dimensional avalanches in granular materials. The theoretical framework is based on a set of experiments in which avalanches are generated intermittently by means of a rotating drum. From measurements of the instantaneous average angle of the free surface, α(t), the relevant quantities that characterize avalanches, such as critical angles and times, are found to be given by distributions. It is then shown that α(t) is a stochastic Markov process. Consequently, a master equation is constructed for P(α,t), the conditional probability that the slope is α, at time t, given an initial state. Finally, a consistency test is carried out, finding full agreement with the experimental data.