Elimination of fast variables in stochastic nonlinear kinetics

Morgado, Gabriel; Nowakowski, B.; Lemarchand, A.

doi:10.1039/d0cp02785e

Cited by 2 publications

(5 citation statements)

References 30 publications

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“…The conditions given in Eqs. (16,17) involve the rate constants. They are necessary but not sufficient to ensure the validity of the elimination of the variable C i in the entire space of the concentrations since they result from a linearization of dynamics around the steady state.…”

Section: Evolution Of the Extents Of The Reaction Stepsmentioning

confidence: 99%

“…The conditions given in Eqs. (16,17) applied to the elimination of the extent ξ 1 are written as According to Eqs. (48,56,58), the slow manifold is defined by…”

Section: Partial-equilibrium Approximation (Pea)mentioning

confidence: 99%

“…[13][14][15] Nevertheless QSSA and PEA do not simply consist in eliminating a fast variable from a system of rate equations. The eliminated variable must be either a concentration for QSSA 16 or an extent for PEA. 5 Both methods are singular perturbation methods introducing a small parameter in the rate equations.…”

Section: Introductionmentioning

confidence: 99%

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Quasi-Steady-State and Partial-Equilibrium Approximations in Chemical Kinetics: One Stage Beyond the Elimination of a Fast Variable

Pellissier-Tanon¹,

Morgado²,

Jullien³

et al. 2021

Preprint

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<pre>Classical approximations in chemical kinetics, the quasi-steady-state approximation (QSSA) and the partial-equilibrium approximation (PEA), are used to reduce rate equations for the concentrations and the extents of the reaction steps, respectively. We make precise two conditions on the rate constants necessary and sufficient to eliminate a well-chosen variable in the vicinity of a steady state. The first condition expresses that dynamics admits a small characteristic time associated with a fast variable. The second condition ensures that the fast variable is a concentration for QSSA and an extent for PEA. Both approximations exploit the zeroth order of a singular perturbation method. Eliminating a fast variable does not mean that it has reached a steady state. The fast evolution is considered over and the slow evolution of the eliminated variable is governed by the slow variables. The evolution of the slow variables occurs on a slow manifold in the space of the concentrations or the extents. In some cases the dynamics of the slow variables can be associated with a reduced chemical scheme. QSSA and PEA are applied to three chemical schemes associated with linear and nonlinear dynamics. We find that QSSA cannot be identified with the elimination of a reactive intermediate. The nonlinearities of the rate equations induce a more complex behavior.</pre>

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Section: Evolution Of the Extents Of The Reaction Stepsmentioning

confidence: 99%

“…The conditions given in Eqs. (16,17) applied to the elimination of the extent ξ 1 are written as According to Eqs. (48,56,58), the slow manifold is defined by…”

Section: Partial-equilibrium Approximation (Pea)mentioning

confidence: 99%

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Quasi-Steady-State and Partial-Equilibrium Approximations in Chemical Kinetics: One Stage Beyond the Elimination of a Fast Variable

Pellissier-Tanon¹,

Morgado²,

Jullien³

et al. 2021

Preprint

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“…15,[18][19][20][21][22] These approximations are zeroth-order perturbation methods consisting in writing dv i dt = 0 for a fast variable v i in a system of differential equations involving n variables. 4,5,[23][24][25][26][27] After linearization of the system of differential equations around a stable steady state, standard linear algebra calculations give the expression of each variable in the form of a weighted sum of exponential decays. The weights depend on the rate constants and the initial conditions.…”

Section: Elimination Of a Fast Variablementioning

confidence: 99%

“…

Two approximations exploiting evolutions at different time scales are usually used to simplify rate laws in chemical kinetics. [1][2][3][4][5] The quasi-steady-state approximation (QSSA) is used to eliminate a chemical species which evolves faster than the others. 6 The partialequilibrium approximation (PEA) is employed to remove a reaction step associated with an extent evolving faster than the other extents.

…”

mentioning

confidence: 99%

Teaching and Learning Materials on the Quasi-Steady-State Approximation and the Partial-Equilibrium Approximation

Pellissier-Tanon

Morgado²,

Jullien³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

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Elimination of fast variables in stochastic nonlinear kinetics

Abstract: A reduced chemical scheme involving a small number of variables is often sufficient to account for the deterministic evolution of the concentrations of the main species contributing to a reaction....

Cited by 2 publications

References 30 publications

Quasi-Steady-State and Partial-Equilibrium Approximations in Chemical Kinetics: One Stage Beyond the Elimination of a Fast Variable

Quasi-Steady-State and Partial-Equilibrium Approximations in Chemical Kinetics: One Stage Beyond the Elimination of a Fast Variable

Teaching and Learning Materials on the Quasi-Steady-State Approximation and the Partial-Equilibrium Approximation

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