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Title: Features in chemical kinetics. III. Attracting subspaces in a hyper-spherical representation of the reactive system

Abstract

In this work, we deal with general reactive systems involving N species and M elementary reactions under applicability of the mass-action law. Starting from the dynamic variables introduced in two previous works [P. Nicolini and D. Frezzato, J. Chem. Phys. 138(23), 234101 (2013); 138(23), 234102 (2013)], we turn to a new representation in which the system state is specified in a (N × M){sup 2}-dimensional space by a point whose coordinates have physical dimension of inverse-of-time. By adopting hyper-spherical coordinates (a set of dimensionless “angular” variables and a single “radial” one with physical dimension of inverse-of-time) and by examining the properties of their evolution law both formally and numerically on model kinetic schemes, we show that the system evolves towards the equilibrium as being attracted by a sequence of fixed subspaces (one at a time) each associated with a compact domain of the concentration space. Thus, we point out that also for general non-linear kinetics there exist fixed “objects” on the global scale, although they are conceived in such an abstract and extended space. Moreover, we propose a link between the persistence of the belonging of a trajectory to such subspaces and the closeness to the slow manifold which wouldmore » be perceived by looking at the bundling of the trajectories in the concentration space.« less

Authors:
;  [1];  [2]
  1. Dipartimento di Scienze Chimiche, Università degli Studi di Padova, Via Marzolo 1, I-35131 Padova (Italy)
  2. Department of Control Engineering–K335, Faculty of Electrical Engineering, Czech Technical University in Prague, Karlovo náměstí 13, 121 35 Prague 2 (Czech Republic)
Publication Date:
OSTI Identifier:
22493304
Resource Type:
Journal Article
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 143; Journal Issue: 22; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9606
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; ABUNDANCE; CHEMICAL REACTION KINETICS; CHEMICAL REACTIONS; CONCENTRATION RATIO; COORDINATES; EQUILIBRIUM; EVOLUTION; MASS; NONLINEAR PROBLEMS; SPACE; SPHERICAL CONFIGURATION; TWO-DIMENSIONAL SYSTEMS

Citation Formats

Ceccato, Alessandro, Frezzato, Diego, and Nicolini, Paolo. Features in chemical kinetics. III. Attracting subspaces in a hyper-spherical representation of the reactive system. United States: N. p., 2015. Web. doi:10.1063/1.4936833.
Ceccato, Alessandro, Frezzato, Diego, & Nicolini, Paolo. Features in chemical kinetics. III. Attracting subspaces in a hyper-spherical representation of the reactive system. United States. doi:10.1063/1.4936833.
Ceccato, Alessandro, Frezzato, Diego, and Nicolini, Paolo. Mon . "Features in chemical kinetics. III. Attracting subspaces in a hyper-spherical representation of the reactive system". United States. doi:10.1063/1.4936833.
@article{osti_22493304,
title = {Features in chemical kinetics. III. Attracting subspaces in a hyper-spherical representation of the reactive system},
author = {Ceccato, Alessandro and Frezzato, Diego and Nicolini, Paolo},
abstractNote = {In this work, we deal with general reactive systems involving N species and M elementary reactions under applicability of the mass-action law. Starting from the dynamic variables introduced in two previous works [P. Nicolini and D. Frezzato, J. Chem. Phys. 138(23), 234101 (2013); 138(23), 234102 (2013)], we turn to a new representation in which the system state is specified in a (N × M){sup 2}-dimensional space by a point whose coordinates have physical dimension of inverse-of-time. By adopting hyper-spherical coordinates (a set of dimensionless “angular” variables and a single “radial” one with physical dimension of inverse-of-time) and by examining the properties of their evolution law both formally and numerically on model kinetic schemes, we show that the system evolves towards the equilibrium as being attracted by a sequence of fixed subspaces (one at a time) each associated with a compact domain of the concentration space. Thus, we point out that also for general non-linear kinetics there exist fixed “objects” on the global scale, although they are conceived in such an abstract and extended space. Moreover, we propose a link between the persistence of the belonging of a trajectory to such subspaces and the closeness to the slow manifold which would be perceived by looking at the bundling of the trajectories in the concentration space.},
doi = {10.1063/1.4936833},
journal = {Journal of Chemical Physics},
issn = {0021-9606},
number = 22,
volume = 143,
place = {United States},
year = {2015},
month = {12}
}