Effects of Turbulent Environment on Self-Organized Critical Behavior: Isotropy vs. Anisotropy
| Autor: | P. I. Kakin, German E. Kochnev, N. M. Gulitskiy, N. V. Antonov |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
lcsh:QC793-793.5
FOS: Physical sciences General Physics and Astronomy Fixed point Radial distribution function Computer Science::Digital Libraries 01 natural sciences turbulent advection 010305 fluids & plasmas 0103 physical sciences 010306 general physics Anisotropy Condensed Matter - Statistical Mechanics Mathematical physics Physics Statistical Mechanics (cond-mat.stat-mech) lcsh:Elementary particle physics Isotropy Renormalization group Self-organized criticality Universality (dynamical systems) Exponent Computer Science::Programming Languages self-organized criticality renormalization group non-equilibrium critical behavior |
| Zdroj: | Universe, Vol 6, Iss 145, p 145 (2020) Universe Volume 6 Issue 9 |
| ISSN: | 2218-1997 |
| DOI: | 10.3390/universe6090145 |
| Popis: | We study a self-organized critical system under the influence of turbulent motion of the environment. The system is described by the anisotropic continuous stochastic equation proposed by Hwa and Kardar [Phys. Rev. Lett.62: 1813 (1989)]. The motion of the environment is modelled by the isotropic Kazantsev&ndash Kraichnan &ldquo rapid-change&rdquo ensemble for an incompressible fluid: it is Gaussian with vanishing correlation time and the pair correlation function of the form &prop &delta (t&minus t&prime )/kd+&xi where k is the wave number and &xi is an arbitrary exponent with the most realistic values &xi =4/3 (Kolmogorov turbulence) and &xi &rarr 2 (Batchelor&rsquo s limit). Using the field-theoretic renormalization group, we find infrared attractive fixed points of the renormalization group equation associated with universality classes, i.e., with regimes of critical behavior. The most realistic values of the spatial dimension d=2 and the exponent &xi =4/3 correspond to the universality class of pure turbulent advection where the nonlinearity of the Hwa&ndash Kardar (HK) equation is irrelevant. Nevertheless, the universality class where both the (anisotropic) nonlinearity of the HK equation and the (isotropic) advecting velocity field are relevant also exists for some values of the parameters &epsilon =4&minus d and &xi Depending on what terms (anisotropic, isotropic, or both) are relevant in specific universality class, different types of scaling behavior (ordinary one or generalized) are established. |
| Databáze: | OpenAIRE |
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