AUTHOR=Pradhan Punyabrata TITLE=Time-Dependent Properties of Sandpiles JOURNAL=Frontiers in Physics VOLUME=9 YEAR=2021 URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2021.641233 DOI=10.3389/fphy.2021.641233 ISSN=2296-424X ABSTRACT=

Bak, Tang, and Wiesenfeld (BTW) proposed the theory of self-organized criticality (SOC), and sandpile models, to connect “1/f” noise, observed in systems in a diverse natural setting, to the fractal spatial structure. We review some of the existing works on the problem of characterizing time-dependent properties of sandpiles and try to explore if the BTW's original ambition has really been fulfilled. We discuss the exact hydrodynamic structure in a class of conserved stochastic sandpiles, undergoing a non-equilibrium absorbing phase transition. We illustrate how the hydrodynamic framework can be used to capture long-ranged spatio-temporal correlations in terms of large-scale transport and relaxation properties of the systems. We particularly emphasize certain interesting aspects of sandpiles—the transport instabilities, which emerge through the threshold-activated nature of the dynamics in the systems. We also point out some open issues at the end.