Method of invariant manifold for chemical kinetics

By Alexander N Gorban, I. Karlin. 2002

258 citations recorded by the source corpus.

In this paper, we review the construction of low-dimensional manifolds of reduced description for equations of chemical kinetics from the standpoint of the method of invariant manifold (MIM). The MIM is based on a formulation of the condition of invariance as an equation, and its solution by Newton iterations. A review of existing alternative methods is extended by a thermodynamically consistent version of the method of intrinsic low-dimensional manifolds. A grid-based version of the MIM is developed, and model extensions of low-dimensional dynamics are described. Generalizations to open systems are suggested. The set of methods covered makes it possible to effectively reduce description in chemical kinetics.

Subfields: Computational Mechanics, Control and Systems Engineering, Organic Chemistry

View Paper: https://www.semanticscholar.org/paper/10209a0e2aaef1001cffe84d72a12bd41cf99d66

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. Alexander N Gorban
2. I. Karlin
3. Dieter Bothe
4. Michel Pierre
5. A. Zinovyev

In Control and Systems Engineering

1. Dieter Bothe
2. Michel Pierre
3. I. Karlin
4. Alexander N Gorban
5. Eliodoro Chiavazzo
6. Julian Fischer
7. Klemens Fellner

In Organic Chemistry

1. Dieter Bothe
2. Michel Pierre
3. I. Karlin
4. Alexander N Gorban

Citations in the corpus

• Invariant Manifolds for Physical and Chemical Kinetics (2005, methodology): “The Chapman–Enskog method was generalized many times [76] and gave rise to a host of subsequent works and methods, such as the famous method of the quasi-steady state in chemical kinetics, pioneered by Bodenstein and Semenov and explored in considerable detail by many authors (see, for example, [22,”
• Constructive methods of invariant manifolds for kinetic problems (2003, background): “• Reduced description for the chemical kinetics [10,11,81].”
• Automated refinement and inference of analytical models for metabolic networks (2011, methodology): “For example, evolutionary programming produced the best solution for a three-enzyme problem despite its large computation time [42], while gradient methods performed the worst.”
• Quasi-steady-state approximation for a reaction–diffusion system with fast intermediate (2010, methodology): “For the ODE-case of homogeneous systems, this method is reviewed in [15].”
• Reduced description of reactive flows with tabulation of chemistry (2011, unknown): “In the past decade, significant progress has been made in methodologies and algorithms that rationally reduce the computational burden imposed by the use of detailed chemical kinetics in CFD calculations of reactive flows [1, 3-29].”
• Comparison of Invariant Manifolds for Model Reduction in Chemical Kinetics (2007, background): “Spectral-Quasi-Equilibrium-Manifold (SQEM), 3.”