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Slow manifold structure in explosive kinetics. 2. Extension to higher dimensional systems.

M Giona¹, A Adrover, F Creta

¹Dipartimento di Meccanica e Aeronautica and Dipartimento di Ingegneria Chimica, Facoltà di Ingegneria, Università di Roma La Sapienza via Eudossiana 18, 00184 Roma, Italy. max@giona.uniromal.it

The Journal of Physical Chemistry. A

|December 15, 2006

Summary

This study expands the geometric analysis of slow invariant manifolds in explosive kinetics to higher dimensions. It reveals how bifurcations modify manifold structures in exothermic reactions.

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Area of Science:

Chemical Kinetics
Geometric Analysis
Dynamical Systems

Background:

Slow invariant manifolds are crucial for understanding complex reaction dynamics.
Previous work by Creta et al. focused on lower-dimensional systems.
Characterizing these manifolds involves Lyapunov-type numbers and volume element deformations.

Purpose of the Study:

To extend the geometric analysis of slow invariant manifolds to 3D and higher systems.
To investigate the role of bifurcations in altering manifold structures.
To provide a simplified analysis using exterior algebra and Jacobian matrices.

Main Methods:

Geometric analysis of slow invariant manifolds.
Application of Lyapunov-type numbers based on perturbation growth.
Utilizing exterior algebra for volume element deformation analysis.
Local analysis derived from the Jacobian matrix of the vector field.

Main Results:

The geometric analysis framework is successfully extended to higher-dimensional systems.
The deformation of volume elements offers a simplified approach to manifold analysis.
Bifurcations of points-at-infinity were identified as key factors modifying manifold structure.
Analysis was demonstrated on 3D models of exothermic reactions.

Conclusions:

The study provides a robust geometric framework for analyzing slow invariant manifolds in complex kinetic systems.
The methods facilitate a deeper understanding of how system dimensionality and bifurcations impact reaction dynamics.
This work lays the groundwork for analyzing more intricate explosive kinetics models.