Skip to main content
SpringerLink
Log in

Diffusion driven instability to a drift driven one: Turing patterns in the presence of an electric field

  • Original Paper
  • Published:
Journal of Mathematical Chemistry Aims and scope Submit manuscript

Abstract

We report a general formula for the critical electric field required to trigger a pattern formation in a Turing system in the presence of an electric field (drift term). Our result encompasses all situations from pure diffusion to pure drift.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

References

  1. A.M. Turing, Philos. Trans. R. Soc. Lond. 327, 37 (1952)

    Article  Google Scholar 

  2. J.D. Murray, Mathematical Biology (Springer, Berlin, 1993)

    Book  Google Scholar 

  3. S.S. Riaz, S. Kar, D.S. Ray, Physica D 203, 224 (2005)

    Article  Google Scholar 

  4. H. Meinhardt, Models of Biological Pattern Formation (Academic Press, London, 1982)

    Google Scholar 

  5. S. Bhattacharya, J. K. Bhattcharjee Indian Natl. Sci. Acad. 71, A, 1=16 (2005)

  6. R.T. Liu, S.S. Liaw, P.K. Maini, J. Kore, Phys. Soc. 50, 234–238 (2007)

    Google Scholar 

  7. R.T. Liu, S.S. Liaw, P.K. Maini, Phys. Rev. E 74, 011914 (2006)

    Article  CAS  Google Scholar 

  8. S.L. Judd, M. Silber, Physica D 136, 45 (2000)

    Google Scholar 

  9. R.A. Satnoianu, M. Menzinger, P.K. Maini, J. Math. Biol. 41, 493 (2000)

    Article  CAS  Google Scholar 

  10. B. Schmidt, P. De Kepper, S.C. Müller, Phys. Rev. Lett. 90, 118302 (2003)

    Article  CAS  Google Scholar 

  11. A.B. Rovinsky, M. Menzinger, Phys. Rev. Lett. 69, 1193 (1992)

    Article  Google Scholar 

  12. A.B. Rovinsky, M. Menzinger, Phys. Rev. Lett. 70, 778 (1993)

    Article  CAS  Google Scholar 

  13. M. Memzinger, A.B. Rovinsky, in chemical waves and patterns, ed. by R. Karpal, K. Showalter (Kluwer, Dordrecht, 1995), pp. 365–397

  14. L. Ji, Q.S. Li, J. Chem. Phys. 123, 94509 (2005)

    Article  Google Scholar 

  15. B.I. Henry, T.A.M. Langlands, S.L. Wearne, Phys. Rev. E 72, 026101 (2005)

    Google Scholar 

  16. R.A. Satnoianu, P.K. Maini, M. Menzinger, Physica D 160, 79 (2001)

    Google Scholar 

  17. S.S. Riaz, S. Kar, D.S. Ray, J. Chem. Phys. 121, 5395 (2004)

    Article  CAS  Google Scholar 

  18. S.S. Riaz, S. Banerjee, S. Kar, D.S. Ray, Eur. Phys. J. B 53, 509–515 (2006)

    Article  CAS  Google Scholar 

  19. B. Schmidt, P. De Kepper, S.C. Muller, J. Phys. Chem. A 102, 2540 (1998)

    Google Scholar 

  20. A. Giere, H. Meinhardt, Kybernatic 12, 30 (1982)

    Article  Google Scholar 

  21. A.J. Koch, H. Meinhardt, Rev. Mod. Phys. 66, 1481 (1994)

    Article  Google Scholar 

  22. I. Lengyl, I.R. Epstein, Science 251, 650 (1991)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics and Centre for computational Science and Engineering, National University of Singapore, Singapore , 117542, Republic of Singapore

    Bijay K. Agarwalla

  2. Department of Computer Science and Engineering, IIT Delhi, Hauz Khas , 110016, New Delhi, India

    Sainyam Galhotra

  3. Harish Chandra Research Institute, Jhunsi, Allahabad , 211019, India

    J. K. Bhattacharjee

Authors
  1. Bijay K. Agarwalla
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sainyam Galhotra
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. K. Bhattacharjee
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sainyam Galhotra.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Agarwalla, B.K., Galhotra, S. & Bhattacharjee, J.K. Diffusion driven instability to a drift driven one: Turing patterns in the presence of an electric field. J Math Chem 52, 188–197 (2014). https://doi.org/10.1007/s10910-013-0254-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10910-013-0254-4

Keywords

Search

Navigation