Abstract
We study the fluctuations arising from the discrete particle nature of the reactants in chemical processes, which we termdiscrete fluctuations. It is shown how the magnitude of discrete fluctuations is formally obtained from the Van KampenΩ-expansion of the master equation for the process in question. It is claimed that discrete fluctuations are, at times, an important factor in determining the anomalous kinetics of reaction systems. We specialize to diffusionlimited reactions in systems below their upper critical dimensionality. Some variations of the two-species annihilation process A + B → inert, as well as some other examples, are presented and analyzed. Many of these examples prove our point about the dramatic influence of discrete fluctuations on the reaction kinetics. Our theoretical scaling predictions are backed by extensive Monte Carlo simulations.
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References
K. J. Laidler,Chemical Kinetics (McGraw-Hill, New York, 1965).
S. W. Benson,The Foundations of Chemical Kinetics (McGraw-Hill, New York, 1960).
N. G. Van Kampen,Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam, 1981).
P. Grassberger,Z. Phys. B 47:365 (1982).
D. Toussaint and F. Wilczek,J. Chem. Phys. 78:2642 (1983).
K. Kang and S. Redner,Phys. Rev. Lett. 52:955 (1984).
P. Meakin and H. E. Stanley,J. Phys. A 17:L173 (1984).
K. Lee and E. J. Weinberg,Nucl. Phys. B 246:354 (1984).
G. Zumofen, A. Blumen, and J. Klafter,J. Chem. Phys. 82:3198 (1985).
D. C. Torney and H. M. McConnell,Proc. R. Soc. Lond. A 387:147 (1983).
K. Kang and S. Redner,Phys. Rev. A 32:435 (1985).
D. Ben-Avraham and S. Redner,Phys. Rev. A 34:501 (1986).
S. Chandrasekhar, inSelected Papers on Noise and Stochastic Processes, N. Wax, ed. (Dover, New York, 1954).
G. H. Weiss, ed.,J. Stat. Phys. 42:1–246 (1986), and references therein.
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Ben-Avraham, D. Discrete fluctuations and their influence on kinetics of reactions. J Stat Phys 48, 315–328 (1987). https://doi.org/10.1007/BF01010411
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DOI: https://doi.org/10.1007/BF01010411