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Effects of random environment on a self-organized critical system: Renormalization group analysis of a continuous model | N. V. Antonov
; P. I. Kakin
; | Date: |
2 Aug 2015 | Abstract: | 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 [{it Phys. Rev. Lett.} {f 62}: 1813 (1989)]. The
advecting velocity field is Gaussian, not correlated in time, with the pair
correlation function of the form $propto delta(t-t’) / k_{ot}^{d-1+xi}$,
where $k_{ot}=|{f k}_{ot}|$ and ${f k}_{ot}$ 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 [{it Commun. Math. Phys.} {f 131}: 381 (1990)]. Using the field
theoretic renormalization group we show that, depending on the relation between
the exponent $xi$ 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 to the "pure" Hwa--Kardar model (the
advection is irrelevant). For the special choice $xi=2(4-d)/3$ both the
nonlinearity and the advection are important. The corresponding critical
exponents are found exactly for all these cases. | Source: | arXiv, 1508.0236 | Services: | Forum | Review | PDF | Favorites |
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