Geodesic
The~effect of strongly anisotropic turbulent mixing on critical behavior: Renormalization group analysis of two nonstandard systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 167 (2011) no. 1, pp. 50-77

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We consider the effect of strongly anisotropic turbulent mixing on the critical behavior of two systems: a $\varphi^{3}$ critical dynamics model describing universal properties of metastable states in the vicinity of a first-order phase transition and a reaction–diffusion system near the point of a second-order transition between fluctuation and absorption states (a simple epidemic process or the Gribov process). In both cases, we demonstrate the existence of a new strongly nonequilibrium, anisotropic scaling regime (universality class) for which both the mixing and the nonlinearity in the order parameter are relevant. We evaluate the corresponding critical dimensions in the one-loop approximation of the renormalization group.
Keywords: critical behavior, turbulent mixing, renormalization group. 
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     author = {N. V. Antonov and A. V. Malyshev},
     title = {The~effect of strongly anisotropic turbulent mixing on critical behavior: {Renormalization} group analysis of two nonstandard systems},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {50--77},
     publisher = {mathdoc},
     volume = {167},
     number = {1},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2011_167_1_a2/}
}
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N. V. Antonov; A. V. Malyshev. The~effect of strongly anisotropic turbulent mixing on critical behavior: Renormalization group analysis of two nonstandard systems. Teoretičeskaâ i matematičeskaâ fizika, Tome 167 (2011) no. 1, pp. 50-77. http://geodesic.mathdoc.fr/item/TMF_2011_167_1_a2/