D. E. Juanico | Searcharxiv

arXiv2008

Avalanche Statistics of Driven Granular Slides in a Miniature Mound

We examine avalanche statistics of rain- and vibration-driven granular slides in miniature sand mounds. A crossover from power-law to non power-law avalanche-size statistics is demonstrated as a generic driving rate $ν$ is increased. For slowly-driven mounds, the tail of the avalanche-size distribution is a power-law with exponent $-1.97\pm 0.31$, reasonably close to the value previously reported for landslide volumes. The interevent occurrence times are also analyzed for slowly-driven mounds; its distribution exhibits a power-law with exponent $-2.670\pm 0.001$.

nlin.AO↗

arXiv2006

Criticality of a dissipative self-organizing process in a dynamic population

We derive a general formulation of the self-organized branching process by considering sandpile dynamics in an evolving population characterized by "birth" (excitation) and "death" (de-excitation) of active sites ($z=1$). New active sites are born in empty sites ($z=0$) with a probability of $η$, whereas active sites die, thus becoming empty, with a probability $λ$. Subsequently, when an active site becomes unstable ($z=2$), it topples by transferring two grains to two randomly chosen sites with probability $α$ or, by transferring only one grain to a randomly selected site (while retaining the other) with probability $β=1+\fracλη-2α$, thus remaining active after toppling. We show that when sandpile dynamics occurs in an evolving population, self-organized criticality, characterized by a power-law avalanche size distribution with exponent $τ_s=3/2$ and power-law avalanche duration distribution with exponent $τ_T=2$ at very high dimension $n >> 1$, is achieved even in the presence of dissipation ($ε= 1-α- β> 0$), contrary to previous claims.

nlin.AO↗