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TMF, 2011, Volume 167, Number 1, Pages 50–77 (Mi tmf6625)  

This article is cited in 3 scientific papers (total in 3 papers)

The effect of strongly anisotropic turbulent mixing on critical behavior: Renormalization group analysis of two nonstandard systems

N. V. Antonov, A. V. Malyshev

Fock Institute of Physics, St.~Petersburg State University, St.~Petersburg, Russia

Abstract: 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

DOI: https://doi.org/10.4213/tmf6625

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English version:
Theoretical and Mathematical Physics, 2011, 167:1, 444–467

Bibliographic databases:

Received: 16.06.2010
Revised: 15.10.2010

Citation: N. V. Antonov, A. V. Malyshev, “The effect of strongly anisotropic turbulent mixing on critical behavior: Renormalization group analysis of two nonstandard systems”, TMF, 167:1 (2011), 50–77; Theoret. and Math. Phys., 167:1 (2011), 444–467

Citation in format AMSBIB
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\by N.~V.~Antonov, A.~V.~Malyshev
\paper The~effect of strongly anisotropic turbulent mixing on critical behavior: Renormalization group analysis of two nonstandard systems
\jour TMF
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\vol 167
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\pages 50--77
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\issue 1
\pages 444--467
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  • https://doi.org/10.4213/tmf6625
  • http://mi.mathnet.ru/eng/tmf/v167/i1/p50

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. N. V. Antonov, A. S. Kapustin, A. V. Malyshev, “Effects of turbulent transfer on critical behavior”, Theoret. and Math. Phys., 169:1 (2011), 1470–1480  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    2. Antonov N.V. Malyshev A.V., “Effects of turbulent mixing on critical behaviour: renormalization-group analysis of the Potts model”, J. Phys. A, 45:25 (2012), 255004, 21 pp.  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    3. Antonov N.V. Gulitskiy N.M., “Passive Advection of a Vector Field: Anisotropy, Finite Correlation Time, Exact Solution, and Logarithmic Corrections To Ordinary Scaling”, Phys. Rev. E, 92:4 (2015), 043018  crossref  adsnasa  isi  elib  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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