Fractal Character of Chemical Reactions in Disordered Media

Argyrakis, Panos

doi:10.1007/978-94-009-3005-6_3

Cited by 2 publications

(1 citation statement)

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“…In principle, the rate laws v j ( X , k ) can have any form, but in (1) and (2) we effectively assume that in practice rate laws can be approximated locally, around the steady state, by the traditional power law, in which the reaction orders κ ij are not restricted to the integer values given by the law of mass action. These noninteger values have already been found in situations where the mean-field approximation does not hold, as it happens in diffusion-limited kinetics, either in disordered media with fractal structures or on regular lattices of dimensionality smaller than the critical value d = 2 . Here, the single elementary reaction displays a noninteger order of reaction, which may be even greater than 3 when occurring on fractal “dust”, with spectral dimension 0 ≤ d s ≤ 1.…”

Section: Introductionmentioning

confidence: 75%

Mass Action Law Conjugate Representation for General Chemical Mechanisms

Fairén

Hernández‐Bermejo

1996

J. Phys. Chem.

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Power-law rates constitute a common approximation to the general analysis of the stability properties of complex reaction networks. We point out in this paper that this form for the rates does not need to be assumed as an approximation for general rate laws. On the contrary, any functional form for a rate law can be represented exactly in terms of power laws. Moreover, we can uniquely associate to any set of kinetic equations an equivalent "conjugate" representation in terms of the well-known generalized Lotka-Volterra equations, standing for what we call per capita rates, which amounts to a great simplification in terms of the structural form of the mathematical representation of a reaction network.

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