Density relaxation in conserved Manna sandpiles

Tapader, Dhiraj; Pradhan, Punyabrata; Dhar, Deepak

doi:10.1103/physreve.103.032122

Cited by 6 publications

(2 citation statements)

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“…Moreover we should now emphasize more on the problem of characterizing one of the most interesting aspects-the transport instabilities in sandpiles, which are present in the system near criticality. As demonstrated in the past through the studies of simple model systems, the bulk-diffusion coefficient, which governs the long wavelength density relaxation in the system, diverges near criticality [67,92]. This particular feature, as opposed to that near an equilibrium critical point, where the bulk diffusivity vanishes (known as "critical slowdown"; [93]), is presumably associated with the unique nature of the thresholdactivated dynamics in sandpiles.…”

Section: Discussionmentioning

confidence: 93%

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Time-Dependent Properties of Sandpiles

Pradhan

2021

Front. Phys.

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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.

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Section: Discussionmentioning

confidence: 93%

“…(ρ − ρ c ) β near criticality, where critical exponent β < 1. Using Equation (28), we indeed get a diverging bulk-diffusion coefficient D(ρ) ∼ 1/(ρ − ρ c ) 1−β → ∞ as ρ → ρ + c [78,92]. On the other hand, the conductivity in the system vanishes as one approaches criticality.…”

Section: The Conserved Manna Sandpilementioning

confidence: 86%