Modeling transport across the running-sandpile cellular automaton by means of fractional transport equations

R. Sánchez, D. E. Newman, J. A. Mier
2018 Physical review. E  
Fractional transport equations are used to build an effective model for transport across the running sandpile cellular automaton [T. Hwa and M. Kardar, Phys. Rev. A 45, 7002 (1992).]. It is shown that both temporal and spatial fractional derivatives must be considered to properly reproduce the sandpile transport features, that are governed by self-organized criticality, at least over sufficiently long/large scales. In contrast to previous applications of fractional transport equations to other
more » ... ystems, the specifics of sand motion require in this case that the spatial fractional derivatives used for the running sandpile must be of the completely asymmetrical Riesz-Feller type. Appropriate values for the fractional exponents that define these derivatives in the case of the running sandpile are obtained numerically.
doi:10.1103/physreve.97.052123 pmid:29906898 fatcat:bbetq6twpjhhlfwmprdl45gfyu