IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v227y1996i1p1-33.html
   My bibliography  Save this article

Transient survival probability of a particle diffusing in a disordered system of perfectly absorbing spherical sinks

Author

Listed:
  • Kauerauf, A.
  • Felderhof, B.U.

Abstract

The transient survival probability of a particle diffusing in a disordered system of perfectly absorbing non-overlapping spherical sinks is studied by use of a self-consistent cluster expansion for its Laplace transform. The self-consistent cluster expansion, which in principle is exact, is formulated in two alternative versions, corresponding to different ways of handling the instantaneous absorption of particles created initially inside a sink. In each version of the theory the cluster expansion is truncated at either the singlet or the pair level, so that four different approximations to the exact result are obtained. An approximation on the pair level constitutes an improvement to the corresponding singlet approximation. It is shown that at moderate volume fraction of the sink system the two pair approximations yield almost identical results for the survival probability. All four approximations lead to a band gap in the spectrum of relaxation rates, followed by a continuum extending to infinity.

Suggested Citation

  • Kauerauf, A. & Felderhof, B.U., 1996. "Transient survival probability of a particle diffusing in a disordered system of perfectly absorbing spherical sinks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 227(1), pages 1-33.
    • Handle: RePEc:eee:phsmap:v:227:y:1996:i:1:p:1-33
    DOI: 10.1016/0378-4371(96)00008-8
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0378437196000088
    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(96)00008-8?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. Burschka, M.A. & Titulaer, U.M., 1982. "The kinetic boundary layer for the Fokker-Planck equation: A Brownian particle in a uniform field," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 112(1), pages 315-330.
    2. Hills, B.P. & Deutch, J.M., 1976. "Renormalization of the rotational diffusion coefficient in a fluctuating fluid," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 83(2), pages 401-410.
    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. Mattern, K. & Felderhof, B.U., 1986. "Rate of diffusion-controlled reactions in a random array of monopole sinks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 135(2), pages 505-518.
    2. Borodin, V.A., 1994. "Generalized rate theory for spatially inhomogeneous systems of point defect sinks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 211(2), pages 279-316.
    3. Høye, J.S. & Bedeaux, D., 1977. "On the dielectric constant for a non-polar fluid, a comparison," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 87(2), pages 288-301.
    4. Kapral, R. & Bedeaux, D., 1978. "The effective shear viscosity of a regular array of suspended spheres," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 91(3), pages 590-602.
    5. Jones, R.B. & Burfield, G.S., 1982. "Memory effects in the diffusion of an interacting polydisperse suspension," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 111(3), pages 577-590.
    6. Felderhof, B.U & Kauerauf, A, 1995. "Electron spectral density in a disordered system of hard sphere scatterers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 220(3), pages 376-389.
    7. Krüger, Jens, 1992. "Effective-medium theory of diffusion and chemical reactions in the presence of stationary overlapping sinks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 182(1), pages 9-22.
    8. Felderhof, B.U., 1985. "Wigner solids and diffusion controlled reactions in a regular array of spheres," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 130(1), pages 34-56.
    9. Felderhof, B.U. & Jones, R.B., 1978. "Faxén theorems for spherically symmetric polymers in solution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 93(3), pages 457-464.
    10. Felderhof, B.U. & Mattern, K., 1984. "Optical potential of a disordered array of scatterers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 128(3), pages 404-426.
    11. Krüger, Jens, 1990. "Effective medium theory of diffusion-controlled reactions among stationary perfect sinks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 166(2), pages 206-219.

    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:227:y:1996:i:1:p:1-33. 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.