The reaction routes comparison with respect to slow invariant manifold and equilibrium points

Mathematically, complex chemical reactions can be simplified by “model reduction,” that is, the rigorous way of approximating and representing a complex model in simplified form. Furthermore, to reduce the dimension of the reaction mechanism there are different available model reduction techniques (...

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Bibliographic Details
Published in:AIP advances 2019-01, Vol.9 (1), p.015212-015212-9
Main Authors: Sultan, Faisal, Shahzad, Muhammad, Ali, Mehboob, Khan, Waqar Azeem
Format: Article
Language:English
Subjects:
Chemical reactions
Graph theory
Invariants
Manifolds (mathematics)
Model reduction
Organic chemistry
Reaction mechanisms
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Summary:Mathematically, complex chemical reactions can be simplified by “model reduction,” that is, the rigorous way of approximating and representing a complex model in simplified form. Furthermore, to reduce the dimension of the reaction mechanism there are different available model reduction techniques (MRT). Two MRT Spectral Quasi Equilibrium Manifold (SQEM) and Intrinsic Low Dimensional Manifold (ILDM) are applied here. Both techniques are good approximation techniques but not completely analytical. While for a case study, the complex behavior of the two-route reaction mechanism allied graphically. The characteristic properties of nodes and trees of reaction mechanism are addressed with the graph theory. The invariant solution curves and their comparison for two-route reaction mechanism have never been reported so far. Therefore, the aim of this article is to study such facts. The possible approaches to their solution and key problems are based on the Horiuti’s rules and their slow invariants. Both model-reduction techniques are applied to solve the high dimensional complex problem and comparison between invariant curves of both routes are presented graphically. The efficiency of ILDM with respect to time is compared with the SQEM graphically and in tabulated form by using MATLAB.
ISSN:2158-3226
2158-3226
DOI:10.1063/1.5050265