Journal of Statistical Physics

, Volume 83, Issue 3–4, pp 359–383 | Cite as

Numerical and analytical studies of nonequilibrium fluctuation-induced transport processes

  • T. C. Elston
  • Charles R. Doering


We present a numerical simulation algorithm that is well suited for the study of noise-induced transport processes. The algorithm has two advantages over standard techniques: (1) it preserves the property of detailed balance for systems in equilibrium and (2) it provides an efficient method for calculating nonequilibrium currents. Numerical results are compared with exact solutions from two different types of correlation ratchets, and are used to verify the results of perturbation calculations done on a three-state ratchet.

Key Words

Algorithm stochastic transport ratchets nonequilibrium detailed balance master equation jump process 


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  1. 1.
    M. Magnasco,Phys. Rev. Lett. 71:1477 (1993).Google Scholar
  2. 2.
    J. Maddox,Nature 365:203 (1993).Google Scholar
  3. 3.
    M. Millonas and M. Dykman,Phys. Lett. A 185:65 (1994).Google Scholar
  4. 4.
    C. Peskin, G. Ermentrout, and G. Oster,Cell Mechanics and Cellular Engineering (Springer-Verlag, Berlin, 1994).Google Scholar
  5. 5.
    R. Astumian and M. Bier,Phys. Rev. Lett. 72:1766 (1994).Google Scholar
  6. 6.
    J. Maddox,Nature 368:287 (1994).Google Scholar
  7. 7.
    J. Prost, J. Chauwin, L. Peliti, and A. Adjari,Phys. Rev. Lett. 72:2652 (1994).Google Scholar
  8. 8.
    C. Doering, W. Horsthemke, and J. Riordan,Phys. Rev. Lett. 72:2984 (1994).Google Scholar
  9. 9.
    J. Maddox,Nature 369:181 (1994).Google Scholar
  10. 10.
    J. Rousselet, L. Salome, A. Adjari, and J. Prost,Nature 370:446 (1994).Google Scholar
  11. 11.
    S. Leibler,Nature 369:412 (1994).Google Scholar
  12. 12.
    R. Bartussek, P. Hanggi, and J. G. Kissner,Europhys. Lett. 28:459 (1994).Google Scholar
  13. 13.
    K. Svoboda and S. Block,Cell 77:773 (1994).Google Scholar
  14. 14.
    K. Svoboda, P. Mitra, and S. Block,Proc. Natl. Acad. Sci. USA 91:11782 (1994).Google Scholar
  15. 15.
    C. Peskin and G. Oster,Biophys. J. 68:202s (1995).Google Scholar
  16. 16.
    C. Gardiner,Handbook of Stochastic Processes (Springer-Verlag, Berlin, 1983).Google Scholar
  17. 17.
    W. Press, B. Flannery, S. Teukolsky, and W. Vetterling,Numerical Recipes (Cambridge University Press, Cambridge 1988).Google Scholar
  18. 18.
    C. Doering, In Proceedings of the Workshop on Fluctuations in Physics and Biology,Nuovo Cimento 17:685 (1995).Google Scholar
  19. 19.
    W. Horsthemke and R. Lefever,Noise Induced Transitions (Springer, New York, 1984).Google Scholar
  20. 20.
    N. Van Kampen,Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam, 1981).Google Scholar
  21. 21.
    M. Bier,Phys. Lett. A 211:12 (1996).Google Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • T. C. Elston
    • 1
  • Charles R. Doering
    • 1
  1. 1.Center for Nonlinear StudiesLos Alamos National LaboratoryLos Alamos

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