Skip to main content
SpringerLink
Log in

A direct method for numerical analysis of relaxation of the statistical characteristics of brownian motion

  • Published:
Radiophysics and Quantum Electronics Aims and scope

Abstract

We propose a numerical method for analyzing the relaxation of coordinate moments of the Brownian motion of a system described by a stochastic Liouville equation of the 1st or 2nd order with moderate-order polynomial nonlinearity. Using exact or approximate recurrence relations for the stationary values, at a certain step, we break the chain of equations for the moments of the Brownian motion. The evolution of the model probability distribution of coordinates is found from the numerical solution of the differential equations of relaxation of moments.

This method is used for analyzing the nonstationary probability characteristics of a system with nonlinear rigidity described by a third-degree polynomial. The relaxation of moments and of the model probability distribution is plotted and tabulated. The results obtained allow us to draw certain conclusions on the statistical dynamics of the Brownian motion of the systems studied.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. V. Horsthemke and R. Lefeuvre,Noise-Induced Transitions: Theory and Application in Physics, Chemistry, and Biology [Russian translation], Mir, Moscow (1987).

    Google Scholar 

  2. R. L. Stratonovich,Selected Problems of the Theory of Fluctuation in Radio Engineering [in Russian], Sovetskoe Radio, Moscow (1961).

    Google Scholar 

  3. V. I. Klyatskin,Statistical Description of Dynamic Systems with Fluctuating Parameters [in Russian], Nauka, Moscow (1975).

    Google Scholar 

  4. V. I. Klyatskin,Stochastic Equations and Waves in Randomly Inhomogeneous Media [in Russian], Nauka, Moscow (1980).

    MATH  Google Scholar 

  5. A. N. Malakhov and A. L. Pankratov,Physica,A229, No. 1, 109 (1996).

    ADS  Google Scholar 

  6. A. N. Malakhov,Chaos,7, No. 3, 488 (1997).

    Article  MATH  ADS  Google Scholar 

  7. O. V. Muzychuk,Izv. Vyssh. Uchebn. Zaved., Radiofiz.,32, No. 2, 169 (1989).

    Google Scholar 

  8. O. V. Muzychuk,Prikl. Mat. Mekh.,55, No. 4, 620 (1991).

    Google Scholar 

  9. A. N. Malakhov,Cumulant Analysis of non-Gaussian Random Processes and Their Transformations [in Russian], Sovetskoe Radio, Moscow (1978).

    Google Scholar 

Download references

Authors
  1. O. V. Muzychuk
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Nizhny Novgorod Architecture and Civil Engineering University, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 42, No. 9, pp. 922–930, September 1999

Rights and permissions

Reprints and permissions

About this article

Cite this article

Muzychuk, O.V. A direct method for numerical analysis of relaxation of the statistical characteristics of brownian motion. Radiophys Quantum Electron 42, 811–818 (1999). https://doi.org/10.1007/BF02676869

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02676869

Keywords

Search

Navigation