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Fluctuation-induced diffusive instabilities

Author

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  • David A. Kessler

    (Bar-Ilan University)

  • Herbert Levine

    (University of California, San Diego)

Abstract

The formation of complex patterns in many non-equilibrium systems, ranging from solidifying alloys to multiphase flow1, nonlinear chemical reactions2 and the growth of bacterial colonies3,4, involves the propagation of an interface that is unstable to diffusive motion. Most existing theoretical treatments of diffusive instabilities are based on mean-field approaches, such as the use of reaction–diffusion equations, that neglect the role of fluctuations. Here we show that finite fluctuations in particle number can be essential for such an instability to occur. We study, both analytically and with computer simulations, the planar interface separating different species in the simple two-component reaction A+ B → 2A (which can also serve as a simple model of bacterial growth in the presence of a nutrient). The interface displays markedly different dynamics within the reaction–diffusion treatment from that when fluctuations are taken into account. Our findings suggest that fluctuations can provide a new and general pattern-forming mechanism in non-equilibrium growth.

Suggested Citation

  • David A. Kessler & Herbert Levine, 1998. "Fluctuation-induced diffusive instabilities," Nature, Nature, vol. 394(6693), pages 556-558, August.
    • Handle: RePEc:nat:nature:v:394:y:1998:i:6693:d:10.1038_29020
    DOI: 10.1038/29020
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    Cited by:

    1. Golding, Ido & Kozlovsky, Yonathan & Cohen, Inon & Ben-Jacob, Eshel, 1998. "Studies of bacterial branching growth using reaction–diffusion models for colonial development," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 260(3), pages 510-554.
    2. Leyva, J. Francisco & Málaga, Carlos & Plaza, Ramón G., 2013. "The effects of nutrient chemotaxis on bacterial aggregation patterns with non-linear degenerate cross diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(22), pages 5644-5662.
    3. Ron, Ilan G. & Golding, Ido & Lifsitz-Mercer, Beatrice & Ben-Jacob, Eshel, 2003. "Bursts of sectors in expanding bacterial colonies as a possible model for tumor growth and metastases," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 320(C), pages 485-496.
    4. Banitz, Thomas & Fetzer, Ingo & Johst, Karin & Wick, Lukas Y. & Harms, Hauke & Frank, Karin, 2011. "Assessing biodegradation benefits from dispersal networks," Ecological Modelling, Elsevier, vol. 222(14), pages 2552-2560.

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