Abstract
We study a diffusion-limited reaction, which consists in the annihilation of some species A by another species B. However, the B particles can only destroy A if they are in an activated form, whereas they also have an inert form which leaves B unchanged. Each form has a stochastic lifetime following an exponential law. We compute the reaction probability of a particle B, and deduce the kinetics of the reaction. It is shown that in one or two dimensions these fluctuations do not change the reaction kinetics, which differs from the ordinary, mean-field kinetics, as it is the case when there are no fluctuations. In three dimensions, the effective reaction constant, including the fluctuations, is computed. We prove that it is an increasing function of the relaxation frequency of the fluctuations.
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Bénichou, O., Moreau, M., Oshanin, G. (2004). Diffusion-limited reactions of particles with fluctuating activity. In: Descalzi, O., Martínez, J., Tirapegui, E. (eds) Instabilities and Nonequilibrium Structures VII & VIII. Nonlinear Phenomena and Complex Systems, vol 8. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-2149-7_1
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DOI: https://doi.org/10.1007/978-1-4020-2149-7_1
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