1982
DOI: 10.1002/9780470142691.ch5
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Nonequilibrium Phase Transitions and Chemical Instabilities

Abstract: The cffcct of inlioimigcncous fluclualions on inslabililies in various nonlincar Chemical mmicis is stiidied in lerms of concep ts develop ed in Ihe lhcot7 of equilibrium p hase transitions.

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Cited by 112 publications
(8 citation statements)
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“…where X , and b are, respectively, the slowly and rapidly varying parts of X . Inserting (22) into equation ( 7) one obtains, for various orders of perturbation theory, a set of linear inhomogeneous equations, similar to those arising in the Chapman-Enskog solution of the Boltzmann equation. The solvability condition for these equations leads then to a closed-form equation for the phase:…”
Section: Az/atmentioning
confidence: 99%
“…where X , and b are, respectively, the slowly and rapidly varying parts of X . Inserting (22) into equation ( 7) one obtains, for various orders of perturbation theory, a set of linear inhomogeneous equations, similar to those arising in the Chapman-Enskog solution of the Boltzmann equation. The solvability condition for these equations leads then to a closed-form equation for the phase:…”
Section: Az/atmentioning
confidence: 99%
“…This function measures how strongly correlated two measurements performed at a temporal distance t − t′ are during the oscillations. It has been predicted that C(t − t′) presents damped oscillations in the case of a noisy limit cycle, first for specific examples of simple reactions 32,39 and then in a more general fashion. 36,37 More precisely, it has been shown that the envelope of this function decreases exponentially as e −t/τ with a decay rate given by…”
mentioning
confidence: 99%
“…For smaller systems where noise manifests itself, a phenomenon called phase diffusion has been reported. The spontaneously occurring fluctuations induce a diffusion of the trajectories along (i.e., tangentially to) the limit cycle. As a consequence, the first return time is a statistically distributed quantity.…”
mentioning
confidence: 99%
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“…Only those D-R systems have been chosen in the past for AE derivation, for which the kinetic steady state is analytically solvable as well as simplelooking in algebraic form. As for example, AE 2,3 for Turing pattern selection [4][5][6] has been derived in the past for a few D-R systems -examples include the Brusselator 7,8 and other models. [9][10][11][12][13] AE derivation for the Swift-Hohenberg model 14 has been widely used for a qualitative description of the convective structures originated from Benard-Marangoni instability or non-Boussinesq Benard convection.…”
Section: Introductionmentioning
confidence: 99%