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A necessary condition for the emergence of diffusion instability in media with nonclassical diffusion

  • Statistical, Nonlinear, and Soft Matter Physics
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Abstract

A necessary condition is derived for the emergence of diffusion instability in media in which diffusion does not obey classical Fick laws. The equations derived by Yadav and Horsthemke [Phys. Rev. E 74, 066118 (2006)] using the continuous-time random walk model are employed as equations simulating reaction—diffusion processes. The waiting-time distribution function is represented by the sum of a finite number of exponents. It is shown that passage to the diffusion limit in the time variable is an incorrect operation if it is used to analyze diffusion instability in media with a distribution function that differs from the Poisson distribution function.

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References

  1. A. M. Turing, Philos. Trans. R. Soc. London, Ser. B 237, 37(1952).

    Article  ADS  Google Scholar 

  2. D. Walgraef, Spatio-Temporal Pattern Formation (Springer, New York, 1996).

    MATH  Google Scholar 

  3. V. Castets, E. Dulos, J. Boissonade, and P. De Kepper, Phys. Rev. Lett. 64, 2953 (1990).

    Article  ADS  Google Scholar 

  4. P. K. Maini, K. J. Painter, and H. N. P. Chau, J. Chem. Soc., Faraday Trans. 93, 3601 (1997).

    Article  Google Scholar 

  5. T. A. M. Langlands, B. I. Henry, and S. I. Wearne, J. Phys.: Condens. Matter 19, 065 115 (2007).

    Article  Google Scholar 

  6. V. V. Gafiychuk and B. Y. Datsko, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys. 77, 066210 (2008).

    MathSciNet  Google Scholar 

  7. Y. Nec and A. A. Nepomnyashchy, Eur. J. Appl. Math. 19, 329 (2008).

    Article  MATH  MathSciNet  Google Scholar 

  8. A. Yadav and W. Horsthemke, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys. 74, 066118 (2006).

    MathSciNet  Google Scholar 

  9. A. Yadav, S. M. Milu, and W. Horsthemke, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys. 78, 026116 (2008).

    MathSciNet  ADS  Google Scholar 

  10. D. Hernandez, C. Varea, and R. A. Barrio, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys. 79, 026109 (2009).

    MathSciNet  ADS  Google Scholar 

  11. M. O. Vlad and J. Ross, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys. 66, 061908 (2002).

    MathSciNet  Google Scholar 

  12. V. P. Shkilev, Zh. Éksp. Teor. Fiz. 135(2), 403 (2009) [JETP 108(2),356(2009)].

    Google Scholar 

  13. G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers (McGraw-Hill, New York, 1967; Nauka, Moscow, 1984).

    Google Scholar 

  14. V. P. Shkilev, Zh. Éksp. Teor. Fiz. 128(3), 655 (2005) [JETP 101 (3), 562 (2005)].

    Google Scholar 

  15. D. Froemberg and I. M. Sokolov, Acta Phys. Pol., B 12, 1199 (2008).

    ADS  Google Scholar 

  16. V. M. Kenkre, Z. Kalay, and P. E. Parris, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys. 79, 011114 (2009). Translated by N. Wadhwa

    ADS  Google Scholar 

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Authors and Affiliations

  1. Institute of Surface Chemistry, National Academy of Sciences of Ukraine, Kiev, 03164, Ukraine

    V. P. Shkilev

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  1. V. P. Shkilev
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Correspondence to V. P. Shkilev.

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Original Russian Text © V.P. Shkilev, 2010, published in Zhurnal Éksperimental’noĭ i Teoreticheskoĭ-Fiziki, 2010, Vol. 137, No. 1, pp. 183–190.

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Shkilev, V.P. A necessary condition for the emergence of diffusion instability in media with nonclassical diffusion. J. Exp. Theor. Phys. 110, 162–169 (2010). https://doi.org/10.1134/S106377611001019X

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  • DOI: https://doi.org/10.1134/S106377611001019X

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