IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v219y1995i3p351-360.html
   My bibliography  Save this article

Kinetic equations of interacting Brownian particles

Author

Listed:
  • Rudyak, Valeri
  • Ershov, Igor

Abstract

The dynamics of a single Brownian particle and an ensemble of such particles in an equilibrium bath is considered. Starting from the Liouville equation of the system, the corresponding kinetic equations are derived. To that end the simple perturbation method on a small parameter λ = √m/M is worked out (here m and M are the mass of the carrier medium molecule and Brownian particle, respectively). The kinetic equation of a single Brownian particle is obtained in second order of perturbation. It is shown that the kinetic equation of an ensemble of Brownian particles is in principle a nonlocal equation. It does not reduce to the Fokker-Plank equation even if direct particle-particle interactions are absent.

Suggested Citation

  • Rudyak, Valeri & Ershov, Igor, 1995. "Kinetic equations of interacting Brownian particles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 219(3), pages 351-360.
    • Handle: RePEc:eee:phsmap:v:219:y:1995:i:3:p:351-360
    DOI: 10.1016/0378-4371(95)00091-K
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/037843719500091K
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/0378-4371(95)00091-K?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Fedyanin, V.K. & Gavrilenko, G.M., 1979. "On a derivation of the Fokker-Planck equation for a system weakly interacting with the heat bath," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 99(1), pages 34-46.
    2. Oppenheim, Felix E., 1971. "Comment: Defense of Noncognitivism Defended," American Political Science Review, Cambridge University Press, vol. 65(4), pages 1115-1116, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Fedyanin, V.K. & Gavrilenko, G.M. & Mihalache, D., 1981. "Fokker-Planck equation for the description of the thermalization of beams of energetic charged particles channeled through crystal," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 109(1), pages 305-316.
    2. Titulaer, U.M., 1980. "Corrections to the Smoluchowski equation in the presence of hydrodynamic interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 100(2), pages 251-265.
    3. Braun, E., 1980. "A model of Brownian dynamics for colloidal suspensions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 103(1), pages 325-342.
    4. Lindenberg, Katja & Mohanty, Udayan & Seshadri, V., 1983. "Hamiltonian model for the Brownian motion of a rigid rotor," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 119(1), pages 1-16.
    5. Felderhof, B.U., 1987. "Brownian motion and creeping flow on the Smoluchowski time scale," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 147(1), pages 203-218.
    6. Aizenbud, Boris M. & Gershon, Nahum D., 1981. "Hydrodynamic equations and VH light scattering from viscoelastic (solid-like and fluid-like) systems. Phenomenological approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 107(1), pages 126-142.
    7. Mohanty, U. & Shuler, K.E. & Oppenheim, I., 1982. "On the exact and phenomenological Langevin equations for a harmonic oscillator in a fluid," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 115(1), pages 1-20.
    8. Posch, H.A. & Balucani, U. & Vallauri, R., 1984. "On the relative dynamics of pairs of atoms in simple liquids," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 123(2), pages 516-534.
    9. Mazur, P. & van Saarloos, W., 1982. "Many-sphere hydrodynamic interactions and mobilities in a suspension," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 115(1), pages 21-57.
    10. Balucani, U. & Vallauri, R., 1980. "Relative motions in atomic fluids: A molecular dynamics investigation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 102(1), pages 70-86.
    11. Brey, J.J. & Casado, J.M. & Morillo, M., 1983. "On the derivation of an N-particle analogue of the Fokker-Planck equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 121(1), pages 122-134.
    12. Aizenbud, Boris M., 1981. "Light scattering from fluids. A semi-phenomenological calculation of the coupling constants between the orientational and translational motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 107(2), pages 404-422.
    13. Van Kampen, N.G. & Oppenheim, I., 1986. "Brownian motion as a problem of eliminating fast variables," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 138(1), pages 231-248.
    14. Hynes, James T. & Kapral, Raymond & Weinberg, Michael, 1975. "Microscopic theory of brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 81(4), pages 509-521.
    15. Aizenbud, Boris M. & Gershon, Nahum D., 1981. "Hydrodynamic equations and VH light scattering from viscoelastic (solid like) systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 108(2), pages 583-588.
    16. Hess, W. & Klein, R., 1978. "Dynamical properties of colloidal systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 94(1), pages 71-90.
    17. Aizenbud, B.M. & Gershon, N.D., 1977. "Hydrodynamic equations and VH light scattering from binary mixtures of fluids of nonspherical molecules," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 89(3), pages 461-480.
    18. Gavrilenko, G.M. & Fedyanin, V.K., 1981. "Stochastic processes in channelling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 105(1), pages 229-244.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:219:y:1995:i:3:p:351-360. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.