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Anomalous dynamics in reaction-diffusion systems

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Il Nuovo Cimento D

Summary

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 atx>0 andx<0, respectively. We find that whereas ford≥2 the mean-field exponent characterizes the width of the reaction zone, fluctuations are relevant in the one-dimensional system. We also presented analytical and numerical results for the reaction rate on fractals and percolation systems.

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References

  1. M. V. Smoluchowski:Z. Phys. Chem.,92, 129 (1917).

    Google Scholar 

  2. See,e.g.,S. A. Rice:Diffusion-Limited Reactions (Elsevier, Amsterdam, 1985).

    Google Scholar 

  3. A. A. Ovchinnikov andY. B. Zeldovich:Chem. Phys.,28, 215 (1978).

    Article  Google Scholar 

  4. D. Toussiant andF. Wilzeck:J. Chem. Phys.,78, 2642 (1983).

    Article  ADS  Google Scholar 

  5. P. Meakin andH. E. Stanley:J. Phys. A,17, L173 (1984).

    Article  ADS  Google Scholar 

  6. K. Kang andS. Redner:Phys. Rev. Lett.,52, 955 (1984);Phys. Rev. A,32, 435 (1985).

    Article  MathSciNet  ADS  Google Scholar 

  7. K. Lee andE. J. Weinberg:Nucl. Phys. B,246, 354 (1984).

    Article  ADS  Google Scholar 

  8. G. Zumofen, A. Blumen andJ. Klafter:J. Chem. Phys.,82, 3198 (1985).

    Article  ADS  Google Scholar 

  9. R. Kopelman:Science,241, 1620 (1988).

    ADS  Google Scholar 

  10. M. Bramson andJ. L. Lebowitz:Phys. Rev. Lett.,61, 2397 (1988);J. Stat. Phys. Phys.,65, 941 (1991).

    Article  ADS  Google Scholar 

  11. P. Argyrakis andR. Kopelman:Phys. Rev. A,41, 2121 (1990).

    Article  ADS  Google Scholar 

  12. G. H. Weiss, R. Kopelman andS. Havlin:Phys. Rev. A,38, 466 (1989).

    Article  ADS  Google Scholar 

  13. F. Leyvraz andS. Redner:Phys. Rev. Lett.,66, 2168 (1991);S. Redner andF. Leyvraz:J. Stat. Phys.,65, 1043 (1991).

    Article  ADS  Google Scholar 

  14. L. W. Anacker andR. Kopelman:Phys. Rev. Lett.,58, 289 (1987);J. Chem. Phys.,91, 5555 (1987).

    Article  ADS  Google Scholar 

  15. K. Lindenberg, B. J. West andR. Kopelman:Phys. Rev. Lett.,60, 1777 (1988).

    Article  ADS  Google Scholar 

  16. D. Ben-Avraham andC. R. Doering:Phys. Rev. A,37, 5007 (1988).

    Article  ADS  Google Scholar 

  17. E. Clément, L. M. Sander andR. Kopelman:Phys. Rev. A,39, 6455 (1989).

    Article  ADS  Google Scholar 

  18. L. Gàlfi andZ. Ràcz:Phys. Rev. A,38, 3151 (1988).

    Article  ADS  Google Scholar 

  19. Y. E. Koo, L. Li andR. Kopelman:Mol. Cryst. Liq. Cryst.,183, 187 (1990);Y. E. Koo andR. Kopelman:J. Stat. Phys.,65, 893 (1991).

    Google Scholar 

  20. H. Taitelbaum, Y. E. Koo, S. Havlin, R. Kopelman andG. H. Weiss:Phys. Rev. A,46, 2151 (1992).

    Article  ADS  Google Scholar 

  21. Z. Jiang andC. Ebner:Phys. Rev. A,42, 7483 (1990).

    Article  ADS  Google Scholar 

  22. H. Taitelbaum, S. Havlin, J. Kiefer, B. L. Trus andG. H. Weiss:J. Stat. Phys.,65, 873 (1991).

    Article  Google Scholar 

  23. S. Cornell, M. Droz andB. Chopard:Phys. Rev. A,44, 4826 (1991).

    Article  ADS  Google Scholar 

  24. M. Araujo, S. Havlin, H. Larralde andH. E. Stanley:Phys. Rev. Lett.,68, 1791 (1992).

    Article  ADS  Google Scholar 

  25. M. Araujo, H. Larralde, S. Havlin andH. E. Stanley:Phys. Rev. Lett.,71, 3592 (1993).

    Article  ADS  Google Scholar 

  26. E. Ben-Naim andS. Redner:J. Phys. A,25, L575 (1992).

    Article  ADS  Google Scholar 

  27. H. Larralde, M. Araujo, S. Havlin andH. E. Stanley:Phys. Rev. A,46, 855 (1992).

    Article  ADS  Google Scholar 

  28. D. Avnir andM. Kagan:Nature,307, 717 (1984).

    Article  Google Scholar 

  29. G. T. Dee:Phys. Rev. Lett.,57, 275 (1986).

    Article  ADS  Google Scholar 

  30. B. Heidel, C. M. Knobler, R. Hilfer andR. Bruinsma:Phys. Rev. Lett.,60, 2492 (1986).

    Article  ADS  Google Scholar 

  31. R. E. Liesegang:Naturwiss. Wochensch.,11, 353 (1896).

    Google Scholar 

  32. T. Witten andL. M. Sander:Phys. Rev. Lett.,47, 1400 (1981).

    Article  ADS  Google Scholar 

  33. R. A. Ball:Ausr. Gemmol.,12, 89 (1984).

    Google Scholar 

  34. K. F. Mueller:Science,255, 1021 (1984).

    ADS  Google Scholar 

  35. S. Cornell:Phys. Rev. Lett. (submitted).

  36. M. Araujo, H. Larralde, S. Havlin andH. E. Stanley:Phys. Rev. Lett. (submitted).

  37. A. Rodriguez andH. S. Wio: preprint.

  38. M. Howard andJ. Cardy:J. Phys. A (submitted).

  39. B. P. Lee andJ. Cardy:Phys. Rev. E,50, R3287 (1994).

    Article  ADS  Google Scholar 

  40. B. Vilensky, S. Havlin, H. Taitelbaum andG. H. Weiss:J. Phys. Chem.,98, 7325 (1994).

    Article  Google Scholar 

  41. H. Larralde, M. Araujo, S. Havlin andH. E. Stanley:Phys. Rev. A,46, R6121 (1992).

    Article  ADS  Google Scholar 

  42. A. Bunde andS. Havlin (Editors):Fractals and Disordered Systems (Springer, Heidelberg, 1991);Fractals in Science (Springer, Heidelberg, 1994).

    Google Scholar 

  43. S. Havlin andD. Ben-Avraham:Adv. Phys.,36, 695 (1987).

    Article  ADS  Google Scholar 

  44. H. Larralde, Y. Lereah, P. Trunfio, J. Dror, S. Havlin, R. Rosenbaum andH. E. Stanley:Phys. Rev. Lett.,70, 1461 (1993).

    Article  ADS  Google Scholar 

  45. J. Crank:Free and Moving Boundary Problems (Clarendon Press, Oxford, 1984).

    Google Scholar 

  46. H. Larralde, P. Trunfio, S. Havlin andH. E. Stanley: to be published.

  47. S. Alexander andR. Orbach:J. Phys. (Paris) Lett.,43, L625 (1987).

    Google Scholar 

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Authors and Affiliations

  1. Center for Polymer Studies and Department of Physics, Boston University, 02215, Boston, MA, USA

    S. Havlin, M. Araujo, H. Larralde, H. E. Stanley & P. Trunfio

  2. Department of Physics, Bar-Ilan University, Ramat-Gan, Israel

    S. Havlin & A. Shehter

Authors
  1. S. Havlin
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  2. M. Araujo
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  3. H. Larralde
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  4. A. Shehter
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  5. H. E. Stanley
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  6. P. Trunfio
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Havlin, S., Araujo, M., Larralde, H. et al. Anomalous dynamics in reaction-diffusion systems. Il Nuovo Cimento D 16, 1039–1051 (1994). https://doi.org/10.1007/BF02458786

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  • DOI: https://doi.org/10.1007/BF02458786

PACS 64.60.Ak

PACS 05.40

PACS 01.30.Cc

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