We study reaction–diffusion systems which involve processes that occur on different time scales. In particular, we apply a multiscale analysis to obtain a reduced description of the slow dynamics. Under certain assumptions this reduction yields a new set of reaction–diffusion equations with rescaled diffusion coefficients. We analyze the Selkov model [E. E. Selkov, Eur. J. Biochem. 4, 79 (1968)] and the ferrocyanide–iodide–sulfite reaction [E. C. Edblom et al., J. Am. Chem. Soc. 108, 2826 (1986)] to determine whether the rescaling in this case may account for the difference of diffusivities that the formation of certain types of patterns requires.
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See EPAPS document No. E-JCPSA6-111-518948 for a detailed derivation.
This document may be retrieved via the EPAPS homepage (http://www.aip.org/pubservs/epaps.html) or from ftp.aip.org in the directory /epaps/. See the EPAPS homepage for more information.
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See, e.g., R. Kapral, S. Consta, and L. McWhirther, in Classical and Quantum Dynamics in Condensed Phase Systems, edited by B. J. Berne, G. Ciccotti and D. Coker (World Scientific, Singapore, 1998), p. 583;
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In order to simplify the notation we do not write explicitly the dependence of the concentrations on x, but actually the concentrations are functions of both x, T and τ.
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