Tracer particle transport dynamics in the diffusive sandpile cellular automaton

The confinement properties of the diffusive running sandpile are characterized by tracking the motion of a population of marked grains of sand. It is found that, as the relative strength of the avalanching to the diffusive transport channel is varied, a point is reached at which the particle global confinement time and the probability density functions of the jump-sizes and waiting-times of the tracked grains experience a sudden change, thus revealing a dynamical transition, that is consistent with previous studies (Newman DE et al., Phys Rev Lett 2002;88(20):204304). Across this transition, the sandpile moves from a regime characterized by self-similarity and memory, where avalanches of all possible sizes dominate transport across the system, to another regime where transport is taken over by near system-size, quasi-periodic avalanches. Values for the fractional transport exponents that quantify effective transport across the sandpile prior to the transition are also obtained.This research has been sponsored in part by Ministerio de Economía y Competitividad of Spain under Projects No. ENE2015- 68265-P and No. ENE2015-66444-R. Research also supported in part by DOE-OFES Grant No. DE-FG02-04ER5741 at University of Alaska. Sandpile simulations have been run in Uranus, a supercomputer cluster at Universidad Carlos III de Madrid (Spain) that has been funded by the Spanish Government via the national projects UNC313-4E-2361, ENE2009-12213-C03-03, ENE2012-33219 and ENE2012-31753