Skip to main content
Log in

Brownian dynamics simulation of polydisperse hard spheres

  • Regular Article
  • Published:
The European Physical Journal Special Topics Aims and scope Submit manuscript

Abstract

Standard algorithms used for the numerical integration of the Langevin equation require that interactions should slowly vary during the integration time-step. This in not the case for hard-body systems, where there is no clear-cut between the correlation time of the noise and the time-scale of the interactions. Starting with a short time approximation of the Smoluchowski equation, we introduce an algorithm for the simulation of the over-damped Brownian dynamics of polydisperse hard-spheres in absence of hydrodynamic interactions and briefly discuss the extension to the case of external drifts.

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

Access this article

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. P.N. Pusey, W. van Megen, Nature 320, 340 (1986)

    Article  ADS  Google Scholar 

  2. A. Yethiraj, A. van Blaaderen, Nature 421, 513 (2003)

    Article  ADS  Google Scholar 

  3. M.P. Allen, D.J. Tildesley, Computer Simulation of Liquids, 2nd edn. (Clarendon Press, Oxford, 1987)

  4. H.A. Kramers, Physica 7, 284 (1940)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  5. A. Scala, Phys. Rev. E 86, 026709 (2012)

    Article  ADS  Google Scholar 

  6. H. Trotter, Proc. Amer. Mat. Soc. 10, 545 (1959)

    Article  MATH  MathSciNet  Google Scholar 

  7. G. De Fabritiis, M. Serrano, P. Espanol, P.V. Coveney, Physica A: Stat. Mech. Appl. 361, 429 (2006)

    Article  ADS  Google Scholar 

  8. A. Scala, C. De Michele, Th. Voigtmann, J. Chem. Phys. 126, 134109 (2007)

    Article  ADS  Google Scholar 

  9. P.E. Kloeden, E. Platen, Applications of Mathematics, vol. 23, 3rd edn. (Springer, 1999)

  10. D. Kannan, V. Lakshmikantham, Handbook of stochastic analysis and applications (Marcel Dekker, 2002)

  11. M.H. Ernst, J.R. Dorfman, W.R. Hoegy, J.M.J. Van Leeuwen, Physica 45, 127 (1969)

    Article  ADS  Google Scholar 

  12. T.P.C. van Noije, M.H. Ernst, R. Brito, Physica A: Stat. Theor. Phys. 251, 266 (1998)

    Article  ADS  Google Scholar 

  13. M.V. Smoluchowski, Z. Phys. 17, 585 (1916)

    Google Scholar 

  14. B. Cichocki, Z. Phys. B Cond. Matter 66, 537 (1987)

    Article  Google Scholar 

  15. B. Cichocki, K. Hinsen, Physica A 166, 473 (1990)

    Article  ADS  Google Scholar 

  16. W. Schaertl, H. Sillescu, J. Stat. Phys. 74, 687 (1994)

    Article  ADS  Google Scholar 

  17. P. Strating, Phys. Rev. E 59, 2175 (1999)

    Article  ADS  Google Scholar 

  18. T.M.A.O.M. Barenbrug, E.A.J.F.F. Peters, J.D. Schieber, J. Chem. Phys. 117, 9202 (2002)

    Article  ADS  Google Scholar 

  19. M. Terada, Y. Tokuyama, J. Korean Phys. Soc. 38, 512 (2001)

    Google Scholar 

  20. G. Foffi, C.D. De Michele, F. Sciortino, P. Tartaglia, Phys. Rev. Lett. 94, 078301 (2005)

    Article  ADS  Google Scholar 

  21. D.C. Rapaport, The Art of Molecular Dynamics Simulation (Cambridge University Press, 2004)

  22. S. Hanna, W. Hess, R. Klein, Physica A 111, 181 (1982)

    Article  ADS  MathSciNet  Google Scholar 

  23. B.J. Ackerson, L. Fleishman, J. Chem. Phys. 76, 2675 (1982)

    Article  ADS  Google Scholar 

  24. S. Redner, A Guide to First-Passage Processes (Cambridge University Press, 2001)

  25. G. Lamm, K. Schulten, J. Chem. Phys. 78, 2713 (1983)

    Article  ADS  Google Scholar 

  26. O. Henrich, F. Weysser, M.E. Cates, M. Fuchs, Phil. Trans. R. Soc. A 367, 5033 (2009)

    Article  MATH  ADS  Google Scholar 

  27. M. Krüger, F. Weysser, T. Voigtmann, Phys. Rev. E 81, 061506 (2010)

    Article  ADS  Google Scholar 

  28. M. Krüger, F. Weysser, M. Fuchs, Eur. Phys. J. E: Soft Matter Biol. Phys. 34, 1 (2011)

    Article  Google Scholar 

  29. M. Marechal, M. Hermes, M. Dijkstra, J. Chem. Phys. 135, 034510 (2011)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. Scala.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Scala, A. Brownian dynamics simulation of polydisperse hard spheres. Eur. Phys. J. Spec. Top. 216, 21–29 (2013). https://doi.org/10.1140/epjst/e2013-01725-3

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjst/e2013-01725-3

Keywords

Navigation