Physics – Condensed Matter – Statistical Mechanics
Scientific paper
1999-09-20
Phys. Rev. E 57, 4375 (1998)
Physics
Condensed Matter
Statistical Mechanics
Scientific paper
10.1103/PhysRevE.57.4375
We propose and study numerically a stochastic cellular automaton model for the dynamics of granular materials with temporal disorder representing random variation of the diffusion probability $1-\mu (t)$ around threshold value $1-\mu_0$ during the course of an avalanche. Combined with the slope threshold dynamics, the temporal disorder yields a series of secondary instabilities, resembling those in realistic granular slides. When the parameter $\mu_0$ is lower than the critical value $\mu_{0}^\star \approx 0.4$, the dynamics is dominated by occasional huge sandslides. For the range of values $\mu_{0}^\star \le \mu_0 < 1$ the critical steady states occur, which are characterized by multifractal scaling properties of the slide distributions and continuously varying critical exponents $\tau_X(\mu_0)$. The mass distribution exponent for $\mu_0\approx 0.45$ is in agreement with the reported value that characterizes Himalayan sandslides. At $\mu_{0}= \mu_{0}^\star$ the exponents governing distributions of large relaxation events reach numerical values which are close to those of parity-conserving universality class, whereas for small avalanches they are close to the mean-field exponents.
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