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2014 | OriginalPaper | Chapter

6. Timescale Analysis

Authors : Tamás Turányi, Alison S. Tomlin

Published in: Analysis of Kinetic Reaction Mechanisms

Publisher: Springer Berlin Heidelberg

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Abstract

A very characteristic feature of chemical kinetic models (in common with many other models in science) is that they contain a wide range of different timescales. This may have consequences for model behaviour and also for the selection of appropriate solution methods for the resulting equation systems. Several aspects of timescales of models are therefore discussed within this chapter. The discussion begins with the definition of various simple quantities used to measure timescales, such as species half-life and species lifetime, and explores their relationship to the time-dependent behaviour of the model. Timescales are closely related to the dynamic behaviour of the model following a perturbation within the chemical kinetic system, e.g., by suddenly altered concentrations. Systematic investigation of such perturbations can be achieved for large systems using computational singular perturbation (CSP) theory which is introduced here. Another common feature of chemical kinetic models is that the chemical kinetics relaxes the system to lower and lower-dimensional attractors until either a stationary point or chemical equilibrium (zero-dimensional attractor) or other low-dimensional attractor (e.g. a limit cycle) is reached. This leads to the importance of slow manifolds in the space of variables which will be investigated within this chapter. One practically important consequence of the presence of very different timescales is the stiffness of reaction kinetic models. Methods for dealing with stiffness within numerical models are therefore discussed.

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Title: Timescale Analysis
Authors: Tamás Turányi
Alison S. Tomlin
Publisher: Springer Berlin Heidelberg
Book: Analysis of Kinetic Reaction Mechanisms
Print ISBN: 978-3-662-44561-7

Electronic ISBN: 978-3-662-44562-4

Copyright Year: 2014
DOI: https://doi.org/10.1007/978-3-662-44562-4_6

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