A general analysis of exact nonlinear lumping in chemical kinetics

Li, Genyuan; Rabitz, Herschel; Tóth, János

doi:10.1016/0009-2509(94)87006-3

Cited by 64 publications

(38 citation statements)

References 11 publications

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“…The transformation can be operated with rigorous mathematical approaches, such as exact lumping methods Li and Rabitz, 1989;Li et al, 1994a), and approximate lumping Li and Rabitz, 1990;Li et al, 1994b;Tomlin et al, 1994;Wang et al, 1998). For example, during the development of RADM2 (Stockwell et al, 1990), the primary VOCs were lumped based on aggregation factors of their reactivity with OH radicals.…”

Section: Methods To Eliminate Speciesmentioning

confidence: 99%

Mechanism reduction for the formation of secondary organic aerosol for integration into a 3-dimensional regional air quality model: <i>α</i>-pinene oxidation system

2009

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Section: Methods To Eliminate Speciesmentioning

confidence: 99%

Mechanism reduction for the formation of secondary organic aerosol for integration into a 3-dimensional regional air quality model: <i>α</i>-pinene oxidation system

2009

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“…Farkas [15] has analysed kinetic lumping schemes consisting of linear projective transformation of the original concentrations, and gave conditions for the transformation and its pseudo-inverse that preserve the reaction kinetic form of the reduced model. The general nonlinear exact and approximate lumping of reaction kinetic models has been analysed by Li and co-workers [16], who also treated the model reduction as a nonlinear projective model transformation.…”

Section: Model Reduction Using Variable Lumpingmentioning

confidence: 99%

“…Linear kinetic lumping schemes were defined and analysed by Farkas [15], while general nonlinear lumping in chemical kinetics was investigated by Lee et al [16]. Although both of the above model reduction methods are quite widespread, none of them has been analysed from a thermodynamic or from a system theoretical viewpoint yet.…”

Section: Introductionmentioning

confidence: 99%

Engineering Model Reduction and Entropy-based Lyapunov Functions in Chemical Reaction Kinetics

Hangos

2010

Entropy

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In this paper, the structural properties of chemical reaction systems obeying the mass action law are investigated and related to the physical and chemical properties of the system. An entropy-based Lyapunov function candidate serves as a tool for proving structural stability, the existence of which is guaranteed by the second law of thermodynamics. The commonly used engineering model reduction methods, the so-called quasi equilibrium and quasi steady state assumption based reductions, together with the variable lumping are formally defined as model transformations acting on the reaction graph. These model reduction transformations are analysed to find conditions when (a) the reduced model remains in the same reaction kinetic system class, (b) the reduced model retains the most important properties of the original one including structural stability. It is shown that both variable lumping and quasi equilibrium based reduction preserve both the reaction kinetic form and the structural stability of reaction kinetic models of closed systems with mass action law kinetics, but this is not always the case for the reduction based on quasi steady state assumption.

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“…• reduce the number of variables either by constructing an appropriate lumping scheme [17] or by simply eliminating some variables;…”

Section: Introductionmentioning

confidence: 99%

Quadratic first integrals of kinetic differential equations

Nagy

Tóth

2013

J Math Chem

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Classes of kinetic differential equations are delineated which do have a quadratic first integral, and classes which can not have one. Example reactions corresponding to the obtained kinetic differential equations are shown, and a few figures showing the trajectories of the corresponding systems are also included. Connections to other areas are mentioned and unsolved problems collected. The new results are theoretical, although computational tools are heavily used. Applications from biology and combustion theory will come later.

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A general analysis of exact nonlinear lumping in chemical kinetics

Cited by 64 publications

References 11 publications

Mechanism reduction for the formation of secondary organic aerosol for integration into a 3-dimensional regional air quality model: <i>α</i>-pinene oxidation system

Mechanism reduction for the formation of secondary organic aerosol for integration into a 3-dimensional regional air quality model: <i>α</i>-pinene oxidation system

Engineering Model Reduction and Entropy-based Lyapunov Functions in Chemical Reaction Kinetics

Quadratic first integrals of kinetic differential equations

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A general analysis of exact nonlinear lumping in chemical kinetics

Cited by 64 publications

References 11 publications

Mechanism reduction for the formation of secondary organic aerosol for integration into a 3-dimensional regional air quality model: &lt;i&gt;α&lt;/i&gt;-pinene oxidation system

Mechanism reduction for the formation of secondary organic aerosol for integration into a 3-dimensional regional air quality model: &lt;i&gt;α&lt;/i&gt;-pinene oxidation system

Engineering Model Reduction and Entropy-based Lyapunov Functions in Chemical Reaction Kinetics

Quadratic first integrals of kinetic differential equations

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Product

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Mechanism reduction for the formation of secondary organic aerosol for integration into a 3-dimensional regional air quality model: <i>α</i>-pinene oxidation system

Mechanism reduction for the formation of secondary organic aerosol for integration into a 3-dimensional regional air quality model: <i>α</i>-pinene oxidation system