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Scientific article
English

A renormalization group study of a class of reaction-diffusion models, with particles input

Published inJournal of Physics A: Mathematical and General, vol. 30, no. 4, p. 1101-1114
Publication date1997
Abstract

We study a class of reaction-diffusion models extrapolating continuously between the pure coagulation-diffusion case and the pure annihilation-diffusion one with particles input at a rate J. For dimension d ≤ 2, the dynamics strongly depends on the fluctuations while, for d > 2, the behaviour is mean-field like. The models are mapped onto a field theory whose properties are studied in a renormalization group approach. Simple relations are found between the time-dependent correlation functions of the different models of the class. For the pure coagulation-diffusion model the time-dependent density is found to be of the form c(t,J,D)=(J/D)1/δ F[(J/D)ΔDt], where D is the diffusion constant. The critical exponent δ and Δ are computed to all orders in ε = 2-d, where d is the dimension of the system, while the scaling function F is computed to second order in ε. For the one-dimensional case an exact analytical solution is provided whose predictions are compared with the results of the renormalization group approach for ε = 1.

Citation (ISO format)
REY, Pierre-Antoine, DROZ, Michel. A renormalization group study of a class of reaction-diffusion models, with particles input. In: Journal of Physics A: Mathematical and General, 1997, vol. 30, n° 4, p. 1101–1114. doi: 10.1088/0305-4470/30/4/013
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ISSN of the journal1361-6447
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