2-DIMENSIONAL AVALANCHES AS STOCHASTIC MARKOV-PROCESSES

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