Two-dimensional avalanches as stochastic Markov processes
1993; American Physical Society; Volume: 47; Issue: 4 Linguagem: Inglês
10.1103/physreve.47.r2229
ISSN1538-4519
AutoresE. Morales-Gamboa, J. Lomnitz-Adler, Víctor Romero‐Rochín, R. Chicharro-Serra, R. Peralta–Fabi,
Tópico(s)Hydrology and Sediment Transport Processes
ResumoA 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, \ensuremath{\alpha}(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 \ensuremath{\alpha}(t) is a stochastic Markov process. Consequently, a master equation is constructed for P(\ensuremath{\alpha},t), the conditional probability that the slope is \ensuremath{\alpha}, at time t, given an initial state. Finally, a consistency test is carried out, finding full agreement with the experimental data.
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