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UFN, 2013, Volume 183, Number 1, Pages 103–112 (Mi ufn4089)  

This article is cited in 6 scientific papers (total in 6 papers)

METHODOLOGICAL NOTES

Critical phenomena far from equilibrium

E. N. Rumanov

Institute of Structural Macrokinetics and Materials Science, Russian Academy of Sciences

Abstract: Stationary regimes of active systems—those in which dissipation is compensated by pumping—are considered. Approaching the bifurcation point of such a regime leads to an increase in susceptibility, with soft modes making the dominant contribution. Weak noise, which is inherent to any real system, increases. Sufficiently close to bifurcation, the amplitude of random pulsations is comparable to the average value of the fluctuating quantity, as in the case of developed turbulence. The spectrum of critical pulsations is independent of the original noise. Numerical simulation of the neighborhood of a bifurcation point is considered unreliable because of the poor reproducibility of results. Due to the high susceptibility, calculation roundings result in ‘chaotic’ jumps of the solution in response to a smooth change in the parameters. It is therefore necessary in the simulation process to introduce a small random function of time, white noise. The solutions of the Langevin equations obtained in this way should be processed statistically. Their properties (except for the intensity of pulsations) are independent of the noise induced. Examples of the statistical description of bifurcations are given.

DOI: https://doi.org/10.3367/UFNr.0183.201301g.0103

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English version:
Physics–Uspekhi, 2013, 56:1, 93–102

Bibliographic databases:

PACS: 02.70.-c, 05.45.-a, 64.60.-i
Received: June 24, 2011
Revised: December 22, 2011
Accepted: January 16, 2012

Citation: E. N. Rumanov, “Critical phenomena far from equilibrium”, UFN, 183:1 (2013), 103–112; Phys. Usp., 56:1 (2013), 93–102

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. E. N. Rumanov, “On the transition from deflagration to detonation”, J. Exp. Theor. Phys, 116:6 (2013), 1057  crossref  adsnasa  isi  elib  scopus
    2. Ledenyov O.P. Neklyudov I.M., “Distributing of Dustborne Particles and Adsorbed Chemical Elements in Granular Air Filter of Aes in the Conditions of the Forced Acoustic Resonance”, Probl. At. Sci. Tech., 2013, no. 2, 94–99  isi
    3. Vaganova N.I., Rumanov E.N., “Frequency Locking of Dynamic Chaos”, Dokl. Phys., 58:10 (2013), 421–423  crossref  zmath  adsnasa  isi  elib  scopus
    4. Shuman V.N., “on Prognostication Ability of Active Geosystems: Metastability and Steady Transitions Instead of Attractors”, Geofiz. Zhurnal, 38:6 (2016), 3–24  crossref  isi
    5. Shuman V.N., “Fractional Dynamics and Emissive Activity of Geosystems”, Geofiz. Zhurnal, 38:3 (2016), 72–83  crossref  isi
    6. Shuman V.N., “Spontaneous Emission Activity of Lithosphere and Seismoelectromagnetic Phenomena”, Geofiz. Zhurnal, 38:2 (2016), 79–87  crossref  isi
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