- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review E

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Galerkin analysis of light-induced patterns in the chlorine dioxide–iodine–malonic acid reaction-diffusion system

Pushpita Ghosh1, Shrabani Sen1, Syed Shahed Riaz2, and Deb Shankar Ray1,*

  • 1Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700 032, India
  • 2Department of Chemistry, Ramakrishna Mission Vidyamandira, Belur, Howrah 711202, India

  • *pcdsr@iacs.res.in
PDF

Phys. Rev. E 79, 056216 – Published 14 May, 2009

DOI: https://doi.org/10.1103/PhysRevE.79.056216

Abstract

The photosensitive chlorine dioxide–iodine–malonic acid reaction-diffusion system has been an experimental paradigm for the study of Turing pattern over the last several years. When subjected to illumination of varied intensity by visible light the patterns undergo changes from spots to stripes, vice versa, and their mixture. We carry out a nonlinear analysis of the underlying model in terms of a Galerkin scheme with finite number of modes to explore the nature of the stability and existence of various modes responsible for the type and crossover of the light-induced patterns.

View figure in article

Article Text

References (40)

  1. M. C. Cross and P. C. Hohenberg, Rev. Mod. Phys. 65, 851 (1993).
  2. J. Garcia-Ojalvo and J. M. Sancho, Noise in Spatially Extended Systems (Springer, New York, 1999).
  3. I. R. Epstein and J. A. Pojman, An Introduction to Nonlinear Chemical Dynamics: Oscillations, Waves, Patterns and Chaos (Oxford University Press, New York, 1998).
  4. P. Gray and S. K. Scott, Chemical Oscillations and Instabilities (Claredon, Oxford, 1990).
  5. A. M. Turing, Philos. Trans. R. Soc. London, Ser. B 237, 37 (1952).
  6. H. Meinhardt, Models of Biological Pattern Formation (Academic, London, 1982).
  7. V. Castets et al., Phys. Rev. Lett. 64, 2953 (1990).
  8. Q. Ouyang and H. L. Swinney, Nature (London) 352, 610 (1991).
  9. I. Lengyel and I. R. Epstein, Acc. Chem. Res. 26, 235 (1993).
  10. B. Rudovics et al., J. Phys. Chem. A 103, 1790 (1999).
  11. The chemistry of CIMA and CDIMA is the same at the fundamental level. While the initial input components in the former case are chlorite and iodide, these are ClO2 and I2 along with malonic acid in the later version. It has been experimentally observed that after a brief initial period the CDIMA reaction governs the dynamics of pattern formation since ClO2 and I2 act as the working reactants. One can therefore measure and control the relevant parameters more directly while working with ClO2 and I2 along with malonic acid in CDIMA reaction. See also Ref. [3] for further details.
  12. S Schmidt and P Ortoleva, J. Chem. Phys. 71, 1010 (1979); 74, 4488 (1981).
  13. L. Forstova, H. Sevcikova, M. Marek, and J. H. Merkin, J. Phys. Chem. A 104, 9136 (2000).
  14. L. Forstova, H. Sevcikova, and J. H. Merkin, Phys. Chem. Chem. Phys. 4, 2236 (2002).
  15. H. Sevcikova and M. Marek, Physica D 9, 140 (1983).
  16. S. Dutta and D. S. Ray, Phys. Rev. E 73, 026210 (2006).
  17. S. Dutta and D. S. Ray, Phys. Rev. E 77, 036202 (2008).
  18. S. Dutta and D. S. Ray, Phys. Rev. E 75, 016205 (2007).
  19. S. S. Riaz, S. Banerjee, S. Kar, and D. S. Ray, Eur. Phys. J. B 53, 509 (2006).
  20. A. P. Munuzuri et al., J. Am. Chem. Soc. 121, 8065 (1999).
  21. A. K. Horvath et al., J. Phys. Chem. A 104, 5766 (2000).
  22. A. K. Horvath et al., Phys. Rev. Lett. 83, 2950 (1999).
  23. O. Steinbock, E. Kasper, and S. C. Mueller, Z. Phys. Chem. 216, 687 (2002); See also, S. C. Mueller et al., in Nonlinear Dynamics in Polymeric Systems, ACS Symposium Series No. 869, edited by J. A. Pojman and Q. Tran-Cong-Miyata (American Chemical Society, Washington, DC, 2003).
  24. T. R. Marchant, Proc. R. Soc. London, Ser. A 458, 873 (2002); A. W. Thornton and T. R. Marchant, Chem. Eng. Sci. 63, 495 (2008).
  25. M. Dolnik, A. M. Zhabotinsky, and I. R. Epstein, Phys. Rev. E 63, 026101 (2001).
  26. M. Watzl and A. F. Munster, J. Phys. Chem. 102, 2540 (1998).
  27. F. Fecher et al., Chem. Phys. Lett. 313, 205 (1999).
  28. A. Becker and L. Kramer, Phys. Rev. Lett. 73, 955 (1994).
  29. C. Van den Broeck, J. M. R. Parrondo, J. Armero, and A. Hernandez-Machado, Phys. Rev. E 49, 2639 (1994).
  30. P. S. Landa, A. A. Zaikin, and L. Schimansky-Geier, Chaos, Solitons Fractals 9, 1367 (1998).
  31. S. Dutta, S. S. Riaz, and D. S. Ray, Phys. Rev. E 71, 036216 (2005).
  32. S. S. Riaz, S. Dutta, S. Kar, and D. S. Ray, Eur. Phys. J. B 47, 255 (2005).
  33. S. S. Riaz, R. Sharma, D. S. Ray, and S. P. Bhattacharrya, J. Chem. Phys. 127, 064503 (2007).
  34. F. Sagues, J. M. Sancho, and J. Garcia-Ojalvo, Rev. Mod. Phys. 79, 829 (2007).
  35. V. Petrov, Q. Ouyang, and H. L. Swinney, Nature (London) 388, 655 (1997).
  36. A. L. Lin et al., Phys. Rev. Lett. 84, 4240 (2000).
  37. A. Bhattacharyay and J. K. Bhattacharjee, Eur. Phys. J. B 21, 561 (2001).
  38. L. A. Segel and L. J. Jackson, J. Theor. Biol. 37, 545 (1972).
  39. E. N. Lorenz, J. Atmos. Sci. 20, 448 (1963).
  40. A. C. Newell and J. A. Whitehead, J. Fluid Mech. 38, 279 (1969).

Outline

Information

Phys. Rev. E 79, 056216– Published 14 May, 2009
  • Received 5 February 2009

© 2009 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation