Indeterminacy in kinetic-model parameters due to non-hamiltonian structure of the multipath linear reaction graph

Evstigneev, Viadimir. A.; Yablonskii, G. S.

doi:10.1007/bf00516963

Cited by 2 publications

(3 citation statements)

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“…Stoichiometric and Kinetic Networks. The idea of reaction networks, consisting of various kinetic and stoichiometric pathways, has frequently been employed to analyze the dynamics, equilibrium, and stability of chemical systems. − The identification with graphs is established in other, related literature. ,− …”

Section: Applications To Transport On Networkmentioning

confidence: 99%

“…[7][8][9][10][11][12] The identification with graphs is established in other, related literature. 7,[13][14][15][16][17] Here, we identify the nodes or vertices as chemical species, with nodal potentials u i given by their partial molar Gibbs free energies µ i . Hence, eq 17 corresponds to various forms of Fick's law for diffusional mass transport, with the source term q representing chemical reaction.…”

Section: Applications To Transport On Networkmentioning

confidence: 99%

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A Graph−Theoretical View of Chemical Transport and Reaction on Networks

Goddard

2001

Ind. Eng. Chem. Res.

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Certain new results are presented for the matrix representation of graphs, as it pertains to the graph-theoretical treatment of physicochemical transport networks. With the incidence matrix of graph theory identified as a derivative on a digraph, it is shown that the stoichiometric matrix plays a similar role on the digraph of chemical-reaction networks. These ideas are then applied to obtain the graph-theoretic representation of facilitated transport, one of several fields to which Professor John Quinn has made significant contributions (AIChE J. 1979, 25, 197−200).

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Section: Applications To Transport On Networkmentioning

confidence: 99%

Section: Applications To Transport On Networkmentioning

confidence: 99%

A Graph−Theoretical View of Chemical Transport and Reaction on Networks

Goddard

2001

Ind. Eng. Chem. Res.

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“…However this technique can involve rather cumbersome calculations, first of all for nonlinear mechanisms. Criteria for the appearance of relations between parameters stemming from the structure of the reaction graph were presented in [41] for linear mechanism. On the basis of kinetic polynomial concept we can suggest a new approach to the determination of relations between parameters of nonlinear kinetic models.…”

Section: The Inverse Chemical Kinetics Problem Does Not Necessarimentioning

confidence: 99%

Kinetic Polynomial: A New Concept of Chemical Kinetics

Lazman

Yablonskii

1991

Patterns and Dynamics in Reactive Media

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Abstract. A system of quasi-steady-state equations for a single pathway mechanism of a catalytic reaction can always be reduced to a polynomial in terms of the steady state reaction rate, a kinetic polynomial. The coefficients of this polynomial are polynomials in the parameters of the elementary reaction rates. The form of the lowest coefficient of the polynomial ensures the thermodynamic validity of this form of representation of quasi-steady-state equations. The properties of the kinetic polynomial are discussed in connection with such concepts of chemical kinetics as "molecularity", "stoichiometric number" .Possible applications of this form are: asymptotic analysis of steady-state kinetic models as well as analysis of steady-state multiplicity; description of the steady-state dependences of the reaction rate, determining relations between kinetic constants when solving the inverse problem.On the basis of kinetic polynomial explicit equations for the steady-state rate in case when one of the steps is rate-limiting, and in the neighbourhood of equilibrium have been derived.Algorithm of computation of the kinetic polynomial and its realisation on the basis of computer algebra are described.

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Indeterminacy in kinetic-model parameters due to non-hamiltonian structure of the multipath linear reaction graph

Cited by 2 publications

References 1 publication

A Graph−Theoretical View of Chemical Transport and Reaction on Networks

A Graph−Theoretical View of Chemical Transport and Reaction on Networks

Kinetic Polynomial: A New Concept of Chemical Kinetics

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