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Complex dynamics in initially separated reaction-diffusion systems

Author

Listed:
  • Havlin, S.
  • Araujo, M.
  • Lereah, Y.
  • Larralde, H.
  • Shehter, A.
  • Stanley, H.E.
  • Trunfio, P.
  • Vilensky, B.

Abstract

We review recent developments in the study of the diffusion reaction systems of the type A + B → C in which the reactants are initially separated. We consider the case where the A and B particles are initially placed uniformly in Euclidean space at x > 0 and x < 0, respectively. We find that whereas for d ⩾ 2 the mean field exponent characterizes the width of the reaction zone, fluctuations are relevant in the one-dimensional system. We present analytical and numerical results for the reaction rate on fractals and percolation systems at criticality.We also study the case where the particles are Lévy flights in d = 1. Finally, we consider experimentally, analytically, and numerically the reaction A + Bstatic → C, where species A diffuses from a localized source.

Suggested Citation

  • Havlin, S. & Araujo, M. & Lereah, Y. & Larralde, H. & Shehter, A. & Stanley, H.E. & Trunfio, P. & Vilensky, B., 1995. "Complex dynamics in initially separated reaction-diffusion systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 221(1), pages 1-14.
    • Handle: RePEc:eee:phsmap:v:221:y:1995:i:1:p:1-14
    DOI: 10.1016/0378-4371(95)00246-4
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    Cited by:

    1. Koza, Zbigniew, 1997. "Asymptotic behaviour of initially separated A + B(static) → 0 reaction-diffusion systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 240(3), pages 622-634.

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