TY - JOUR

T1 - Effects of random environment on a self-organized critical system: Renormalization group analysis of a continuous model

AU - Antonov, N. V.

AU - Kakin, P. I.

PY - 2016

Y1 - 2016

N2 - We study effects of random fluid motion on a system in a self-organized critical state. The latter is described by the continuous stochastic model, proposed by Hwa and Kardar [Phys. Rev. Lett. 62: 1813 (1989)]. The advecting velocity field is Gaussian, not correlated in time, with the pair correlation function of the form ∝ δ(t − t ′ )/kd−1+ξ ⊥ , where k⊥ = |k⊥| and k⊥ is the component of the wave vector, perpendicular to a certain preferred direction – the d-dimensional generalization of the ensemble introduced by Avellaneda and Majda [Commun. Math. Phys. 131: 381 (1990)]. Using the field theoretic renormalization group we show that, depending on the relation between the exponent ξ and the spatial dimension d, the system reveals different types of large-scale, long-time scaling behaviour, associated with the three possible fixed points of the renormalization group equations. They correspond to ordinary diffusion, to passively advected scalar field (the nonlinearity of the Hwa– Kardar model is irrelevant) and

AB - We study effects of random fluid motion on a system in a self-organized critical state. The latter is described by the continuous stochastic model, proposed by Hwa and Kardar [Phys. Rev. Lett. 62: 1813 (1989)]. The advecting velocity field is Gaussian, not correlated in time, with the pair correlation function of the form ∝ δ(t − t ′ )/kd−1+ξ ⊥ , where k⊥ = |k⊥| and k⊥ is the component of the wave vector, perpendicular to a certain preferred direction – the d-dimensional generalization of the ensemble introduced by Avellaneda and Majda [Commun. Math. Phys. 131: 381 (1990)]. Using the field theoretic renormalization group we show that, depending on the relation between the exponent ξ and the spatial dimension d, the system reveals different types of large-scale, long-time scaling behaviour, associated with the three possible fixed points of the renormalization group equations. They correspond to ordinary diffusion, to passively advected scalar field (the nonlinearity of the Hwa– Kardar model is irrelevant) and

U2 - 10.1051/epjconf/201610802009

DO - 10.1051/epjconf/201610802009

M3 - Article

VL - 108

SP - 02009

JO - EPJ Web of Conferences

JF - EPJ Web of Conferences

SN - 2100-014X

ER -