Scaling behavior in interacting systems: joint effect of anisotropy and compressibility

Michal Hnatič, Georgii Kalagov and Tomáš Lučivjanský ()
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Michal Hnatič: Faculty of Science, Šafárik University
Georgii Kalagov: Faculty of Science, Šafárik University
Tomáš Lučivjanský: Faculty of Science, Šafárik University

The European Physical Journal B: Condensed Matter and Complex Systems, 2018, vol. 91, issue 11, 1-12

Abstract: Abstract Motivated by the ubiquity of turbulent flows in realistic conditions, effects of turbulent advection on two models of classical non-linear systems are investigated. In particular, we analyze model A (according to the Hohenberg–Halperin classification [P.C. Hohenberg, B.I. Halperin, Rev. Mod. Phys. 49, 435 (1977)]) of a non-conserved order parameter and a model of the direct bond percolation process. Having two paradigmatic representatives of distinct stochastic dynamics, our aim is to elucidate to what extent velocity fluctuations affect their scaling behavior. The main emphasis is put on an interplay between anisotropy and compressibility of the velocity flow on their respective scaling regimes. Velocity fluctuations are generated by means of the Kraichnan rapid-change model, in which the anisotropy is due to a distinguished spatial direction n and a correlator of the velocity field obeys the Gaussian distribution law with prescribed statistical properties. As the main theoretical tool, the field-theoretic perturbative renormalization group is adopted. Actual calculations are performed in the leading (one-loop) approximation. Having obtained infrared stable asymptotic regimes, we have found four possible candidates for macroscopically observable behavior for each model. In contrast to the isotropic case, anisotropy brings about enhancement of non-linearities and non-trivial regimes are proved to be more stable.

Keywords: Statistical; and; Nonlinear; Physics (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1140/epjb/e2018-90308-1

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