Abstract
Self-organized critical system in turbulent fluid environment is studied with the renormalization group analysis. The system is modelled by the anisotropic stochastic differential equation for a coarse-grained field proposed by Hwa and Kardar [Phys. Rev. Lett. 62, 1813 (1989)]. The turbulent motion of the environment is described by the anisotropic d-dimensional velocity ensemble based on the one introduced by Avellaneda and Majda [Commun. Math. Phys. 131, 381 (1990)] and modified to include dependence on time (finite correlation time). Renormalization group analysis reveals three universality classes (types of critical behavior) differentiated by the parameters of the system.
Highlights
The phenomenon of self-organized criticality (SOC) is observed in numerous open nonequilibrium biological, ecological and social systems with dissipative transport [1, 2]
While SOC is usually described by discrete models, the authors of [3] proposed a continuous anisotropic model, i.e., a differential stochastic equation for a smoothed field of the deviation from the average height of the sand profile
The paper is organized as follows: the field theoretic formulation of the model is given in Sec. 2; Sec. 3 is devoted to the remormalization of the model while the fixed points of the renormalization group (RG) equation and corresponding universality classes are discussed in Sec. 4; Sec. 5 is reserved to a brief conclusion
Summary
The phenomenon of self-organized criticality (SOC) is observed in numerous open nonequilibrium biological, ecological and social systems with dissipative transport [1, 2]. The model describes a running sandpile with a constant preferred transport direction. This is the reason why we want to consider the critical behavior under the influence of the turbulent flow. The replacement ∂t → ∇t = ∂t + vk∂k introduces a coupling with the velocity field u(x) The latter is chosen in the form u(x) = v(t, x⊥) n. The model (1) – (2) with Gaussian δ-correlated in time (rapid-changing) velocity ensemble has been studied in [12]. The paper is organized as follows: the field theoretic formulation of the model is given in Sec. 2; Sec. 3 is devoted to the remormalization of the model while the fixed points of the renormalization group (RG) equation and corresponding universality classes are discussed in Sec. 4; Sec. 5 is reserved to a brief conclusion
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