Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Anomalous diffusion in run-and-tumble motion

Felix Thiel, Lutz Schimansky-Geier, and Igor M. Sokolov

  • Institute of Physics, Humboldt University Berlin, Newtonstr. 15, 12489 Berlin, Germany

Phys. Rev. E 86, 021117 – Published 16 August, 2012

DOI: https://doi.org/10.1103/PhysRevE.86.021117

Abstract

A random walk scheme, consisting of alternating phases of regular Brownian motion and Lévy walks, is proposed as a model for run-and-tumble bacterial motion. Within the continuous-time random walk approach we obtain the long-time and short-time behavior of the mean squared displacement of the walker as depending on the properties of the dwelling time distribution in each phase. Depending on these distributions, normal diffusion, superdiffusion, and ballistic spreading may arise.

Article Text

References (26)

  1. D. L. Kramer and R. L. McLaughlin, Amer. Zool. 41, 137 (2001).
  2. T. H. Harris, E. J. Banigan, D. A. Christian, C. Konradt, E. D. T. Wojno, K. Norose, E. H. Wilson, B. John, W. Weninger, A. D. Luster, A. J. Liu, and C. A. Hunter, Nature (London) 486, 545 (2012).
  3. M. de Jager, F. J. Weissing, P. M. J. Herman, B. A. Nolet, and J. van de Koppel, Science 332, 1551 (2011).
  4. M. C. Santos, D. Boyer, O.Miramontes, G. M. Viswanathan, E. P. Raposo, J. L. Mateos, and M. G. E. da Luz, Phys. Rev. E 75, 061114 (2007).
  5. T. D. Yang, J.-S. Park, Y. Choi, W. Choi, T.-W. Ko, and K. J. Lee, PLoS One 6, e20255 (2011).
  6. M. C. González, C. A. Hidalgo, and A. Barabási, Nature (London) 453, 779 (2008).
  7. A. M. Reynolds, Behav. Ecol. Sociobiol. 64, 19 (2009).
  8. A. M. Edwards, R. A. Phillips, N. W. Watkins, M. P. Freeman, E. J. Murphy, V. Afanasyev, S. V. Buldyrev, M. G. E. da Luz, E. P. Raposo, H. E. Stanley, and G. M. Viswanathan, Nature (London) 449, 1044 (2007).
  9. F. Lenz, T. C. Ings, L. Chittka, A. V. Chechkin, and R. Klages, Phys. Rev. Lett. 108, 098103 (2012).
  10. N. E. Huphries, N. Queiroz, J. R. M. Dyer, N. G. Payde, M. K. Musyl, K. M. Schaefer, D. W. Fuller, J. M. Brunnschweiler, T. K. Doyle, J. D. R. Houghton, G. C. Hays, C. S. Jones, L. R. Noble, V. J. Wearmouth, E. J. Southall, and D. W. Sims, Nature (London) 465, 1066 (2010).
  11. H. C. Berg, E. Coli in Motion (Springer, Heidelberg, 2004).
  12. H. G. Othmer, S. R. Dunbar, and W. Alt, J. Math. Biol. 26, 263 (1988).
  13. A. W. Visser and U. H. Thygesen, J. Plankton Res. 25, 1157 (2003).
  14. D. V. Nicolau, Jr., J. P. Armitage, and P. K. Maini, Comput. Biol. Chem. 33, 269 (2009).
  15. J. Martin, Behav. Proc. 67, 207 (2004).
  16. M. A. Lomholt, T. Koren, R. Metzler, and J. Klafter, Proc. Natl. Acad. Sci. USA 105, 11055 (2011).
  17. O. Bénichou, M. Coppey, M. Moreau, P.-H. Suet, and R. Voituriez, Phys. Rev. Lett. 94, 198101 (2005).
  18. E. W. Montroll and G. H. Weiss, J. Math. Phys. 6, 167 (1965).
  19. M. F. Shlesinger, B. J. West, and J. Klafter, Phys. Rev. Lett. 58, 1100 (1987).
  20. F. Matthäus, M. Jagodič, and J. Dobnikar, Biophys. J. 97, 946 (2009).
  21. I. Gomez Portillo, D. Campos, and V. Méndez, J. Stat. Mech. (2011) P02033.
  22. G. Zumofen and J. Klafter, Phys. Rev. E 51, 1818 (1995).
  23. F. Bartumeus and S. A. Levin, Proc. Natl. Acad. Sci. USA 105, 19072 (2008).
  24. J. Klafter and I. M. Sokolov, First Steps in Random Walks (Oxford University Press, New York, 2011).
  25. D. Campos and V. Méndez, J. Chem. Phys. 130, 134711 (2009).
  26. R. Golestanian, Phys. Rev. Lett. 102, 188305 (2009).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation