Home > Research > Publications & Outputs > Singularities in far-from-equilibrium distribu...

Research

Associated organisational unit

Electronic data

  • UPoN2003Singularities

    2.67 MB, PDF document

Links

Text available via DOI:

View graph of relations

Singularities in far-from-equilibrium distributions at finite noise intensities

Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSN › Chapter

Published

Standard

Singularities in far-from-equilibrium distributions at finite noise intensities. / Bandrivskyy, Andriy; Beri, S.; Luchinsky, Dmitry G et al.
Unsolved Problems of Noise and Fluctuations: UPoN 2002: Third International Conference. Vol. 665 American Institute of Physics, 2003. p. 451-457.

Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSN › Chapter

Harvard

Bandrivskyy, A, Beri, S, Luchinsky, DG & McClintock, PVE 2003, Singularities in far-from-equilibrium distributions at finite noise intensities. in Unsolved Problems of Noise and Fluctuations: UPoN 2002: Third International Conference. vol. 665, American Institute of Physics, pp. 451-457. https://doi.org/10.1063/1.1584920

APA

Bandrivskyy, A., Beri, S., Luchinsky, D. G., & McClintock, P. V. E. (2003). Singularities in far-from-equilibrium distributions at finite noise intensities. In Unsolved Problems of Noise and Fluctuations: UPoN 2002: Third International Conference (Vol. 665, pp. 451-457). American Institute of Physics. https://doi.org/10.1063/1.1584920

Vancouver

Bandrivskyy A, Beri S, Luchinsky DG, McClintock PVE. Singularities in far-from-equilibrium distributions at finite noise intensities. In Unsolved Problems of Noise and Fluctuations: UPoN 2002: Third International Conference. Vol. 665. American Institute of Physics. 2003. p. 451-457 doi: 10.1063/1.1584920

Author

Bandrivskyy, Andriy ; Beri, S. ; Luchinsky, Dmitry G et al. / Singularities in far-from-equilibrium distributions at finite noise intensities. Unsolved Problems of Noise and Fluctuations: UPoN 2002: Third International Conference. Vol. 665 American Institute of Physics, 2003. pp. 451-457

Bibtex

@inbook{3e094a1a127e4c5a816e6437e00748c1,
title = "Singularities in far-from-equilibrium distributions at finite noise intensities",
abstract = "How to find the (strongly non-Boltzmann) distribution in a far-from-equilibrium system is a problem of long standing. It appears in many different contexts, with topical examples including stochastic resonance and Brownian ratchets. One of the most promising approaches to the problem is through asymptotic analysis of the Fokker-Planck equation in the limit of small noise intensity. In simulations and experiments on real systems, however, the noise intensity is necessarily finite. Corrections to allow for finite noise intensity have recently been introduced for the particular case of escape. We are currently investigating the non-equilibrium distribution over the whole of phase space, for two model systems: the periodically driven, overdamped, Duffing oscillator and the inverted van der Pol oscillator. A modified Monte Carlo technique is being applied to investigate the limit of very small noise intensities. The next-to-leading order of approximation of the solution of the Fokker-Planck equation is used to compare the numerical results with the theory. We show, in particular, how changes in the non-equilibrium probability distribution induced by finite noise intensity are linked to an observable modification in the pattern of optimal paths. The numerical observations are in good agreement with theory. ",
author = "Andriy Bandrivskyy and S. Beri and Luchinsky, {Dmitry G} and McClintock, {Peter V E}",
year = "2003",
doi = "10.1063/1.1584920",
language = "English",
isbn = "0735401276",
volume = "665",
pages = "451--457",
booktitle = "Unsolved Problems of Noise and Fluctuations",
publisher = "American Institute of Physics",

}

RIS

TY - CHAP

T1 - Singularities in far-from-equilibrium distributions at finite noise intensities

AU - Bandrivskyy, Andriy

AU - Beri, S.

AU - Luchinsky, Dmitry G

AU - McClintock, Peter V E

PY - 2003

Y1 - 2003

N2 - How to find the (strongly non-Boltzmann) distribution in a far-from-equilibrium system is a problem of long standing. It appears in many different contexts, with topical examples including stochastic resonance and Brownian ratchets. One of the most promising approaches to the problem is through asymptotic analysis of the Fokker-Planck equation in the limit of small noise intensity. In simulations and experiments on real systems, however, the noise intensity is necessarily finite. Corrections to allow for finite noise intensity have recently been introduced for the particular case of escape. We are currently investigating the non-equilibrium distribution over the whole of phase space, for two model systems: the periodically driven, overdamped, Duffing oscillator and the inverted van der Pol oscillator. A modified Monte Carlo technique is being applied to investigate the limit of very small noise intensities. The next-to-leading order of approximation of the solution of the Fokker-Planck equation is used to compare the numerical results with the theory. We show, in particular, how changes in the non-equilibrium probability distribution induced by finite noise intensity are linked to an observable modification in the pattern of optimal paths. The numerical observations are in good agreement with theory.

AB - How to find the (strongly non-Boltzmann) distribution in a far-from-equilibrium system is a problem of long standing. It appears in many different contexts, with topical examples including stochastic resonance and Brownian ratchets. One of the most promising approaches to the problem is through asymptotic analysis of the Fokker-Planck equation in the limit of small noise intensity. In simulations and experiments on real systems, however, the noise intensity is necessarily finite. Corrections to allow for finite noise intensity have recently been introduced for the particular case of escape. We are currently investigating the non-equilibrium distribution over the whole of phase space, for two model systems: the periodically driven, overdamped, Duffing oscillator and the inverted van der Pol oscillator. A modified Monte Carlo technique is being applied to investigate the limit of very small noise intensities. The next-to-leading order of approximation of the solution of the Fokker-Planck equation is used to compare the numerical results with the theory. We show, in particular, how changes in the non-equilibrium probability distribution induced by finite noise intensity are linked to an observable modification in the pattern of optimal paths. The numerical observations are in good agreement with theory.

U2 - 10.1063/1.1584920

DO - 10.1063/1.1584920

M3 - Chapter

SN - 0735401276

VL - 665

SP - 451

EP - 457

BT - Unsolved Problems of Noise and Fluctuations

PB - American Institute of Physics

ER -