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Fluctuation-dominated kinetics in the a+b→0 reaction between immobile particles

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Abstract

We consider the accumulation of immobile particles landing on a one-dimensional lattice and annihilating via the A + B → 0 bimolecular reaction. Here we focus on short-range interactions with cutoff. We investigate through computer simulations both the kinetics of the particles' accumulation and also their spatial distribution. The relation between the exponents describing the growth of the particles' concentration and the correlation length of their distribution shows that the kinetics of accumulation is fluctuation-dominated.

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References

  1. A. A. Ovchinnikov and Ya. B. Zeldovich,Chem. Phys. 28:215 (1978).

    Google Scholar 

  2. D. Toussaint and F. Wilczek,J. Chem. Phys. 78:2642 (1983).

    Google Scholar 

  3. K. Kang and S. Redner,Phys. Rev. Lett. 52:955 (1984);Phys. Rev. A 32:435 (1985).

    Google Scholar 

  4. G. Zumofen, A. Blumen, and J. Klafter,J. Chem. Phys. 82:3198 (1985); A. Blumen, J. Klafter, and G. Zumofen, inOptical Spectroscopy of Glasses, I. Zschokke, ed. (Reidel, Dordrecht, 1986), pp. 199–265.

    Google Scholar 

  5. G. H. Weiss,J. Stat. Phys. 42:3 (1986); H. Taitelbaum, S. Havlin, J. E. Kiefer, B. Trus, and G. H. Weiss, to be published.

    Google Scholar 

  6. I. M. Sokolov,Zh. Eksp. Teor. Fiz. Pis'ma 44:53 (1986) [Sov. Phys. JETP Lett. 44:67 (1986)].

    Google Scholar 

  7. S. F. Burlatskii, A. A. Ovchinnikov, and K. A. Pronin,Zh. Eksp. Teor. Phys. 92:625 (1986) [Sov. Phys. JETP 65:353 (1987)].

    Google Scholar 

  8. A. G. Vitukhnovskii, B. L. Pyttel, and I. M. Sokolov,Phys. Lett. A 128:161 (1988).

    Google Scholar 

  9. I. M. Sokolov,Zh. Eksp. Teor. Fiz. 94:199 (1988) [Sov. Phys. JETP 67:1846 (1988)].

    Google Scholar 

  10. K. Lindenberg, B. J. West, and R. Kopelman,Phys. Rev. Lett. 60:1777 (1988).

    Google Scholar 

  11. M. Bramson and J. L. Lebowitz,Phys. Rev. Lett. 61:2397 (1988).

    Google Scholar 

  12. V. Kuzovkov and E. Kotomin,Rep. Prog. Phys. 51:1479 (1988).

    Google Scholar 

  13. A. Szabo, R. Zwanzig, and N. Agmon,Phys. Rev. Lett. 61:2496 (1988).

    Google Scholar 

  14. D. Ben-Avraham and C. R. Doering,Phys. Rev. A 37:5007 (1988).

    Google Scholar 

  15. E. Clément, L. M. Sander, and R. Kopelman,Phys. Rev. A 39:6455, 6466 (1989).

    Google Scholar 

  16. G. S. Oshanin, S. F. Burlatskii, and A. A. Ovchinnikov,Phys. Lett. A 139:245 (1989).

    Google Scholar 

  17. B. J. West, R. Kopelman, and K. Lindenberg,J. Stat. Phys. 54:1429 (1989).

    Google Scholar 

  18. P. Argyrakis and R. Kopelman,J. Phys. Chem. 91:2699 (1987);93:225 (1989).

    Google Scholar 

  19. K. Lindenberg, B. J. West, and R. Kopelman,Phys. Rev. A 42:890 (1990).

    Google Scholar 

  20. W.-S. Sheu, K. Lindenberg, and R. Kopelman,Phys. Rev. A 42:2279 (1990).

    Google Scholar 

  21. H. Schnörer, I. M. Sokolov, and A. Blumen,Phys. Rev. A 42:7075 (1990).

    Google Scholar 

  22. I. M. Sokolov and A. Blumen,Phys. Rev. A 43:2714 (1991).

    Google Scholar 

  23. I. M. Sokolov and A. Blumen,Phys. Rev. Lett. 66:1942 (1991).

    Google Scholar 

  24. H. Schnörer, V. Kuzovkov, and A. Blumen,Phys. Rev. Lett. 63:805 (1989).

    Google Scholar 

  25. H. Schnörer, V. Kuzovkov, and A. Blumen,J. Chem. Phys. 92:2310 (1990).

    Google Scholar 

  26. H. Schnörer, S. Luding, and A. Blumen, inFractals in the Fundamental and Applied Sciences, J. Henriques, ed. (Fundacao Calouste Gulbenkian, Lisbon, 1990).

    Google Scholar 

  27. E. Kotomin, I. Tāle, V. Tāle, and P. Kūlis,J. Phys.: Condensed Matter 1:6777 (1989).

    Google Scholar 

  28. S. F. Burlatsky and A. I. Chernoutsan,Phys. Lett. A 145:56 (1990).

    Google Scholar 

  29. K. Dettmann,Phys. Stat. Sol. 10:269 (1965).

    Google Scholar 

  30. V. N. Kuzovkov and E. A. Kotomin,J. Phys. C: Solid State Phys. 17:2283 (1984).

    Google Scholar 

  31. V. V. Antonov-Romanovskii,Phys. Stat. Sol. (b) 121:133 (1984).

    Google Scholar 

  32. V. V. Antonov-Romanovskii,Fiz. Tverd. Tela 27:1116 (1985) [Sov. Phys.-Solid State 27:674 (1985)].

    Google Scholar 

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Author notes

  1. A. Blumen, S. Luding & I. M. Sokolov

    Present address: Theoretical Polymer Physics, University of Freiburg, W-7800, Freiburg, Germany

Authors and Affiliations

  1. Physical Institute and BIMF, University of Bayreuth, W-8580, Bayreuth, Germany

    A. Blumen, S. Luding & I. M. Sokolov

  2. P. N. Lebedev Physical Institute of the Academy of Sciences of the USSR, 117924, Moscow, USSR

    I. M. Sokolov

Authors
  1. A. Blumen
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  2. S. Luding
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  3. I. M. Sokolov
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This work is dedicated to Prof. George H. Weiss.

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Blumen, A., Luding, S. & Sokolov, I.M. Fluctuation-dominated kinetics in the a+b→0 reaction between immobile particles. J Stat Phys 65, 849–857 (1991). https://doi.org/10.1007/BF01049585

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