The Library
Bifurcations of transition states : morse bifurcations
Tools
MacKay, Robert S. and Strub, Dayal C. (2014) Bifurcations of transition states : morse bifurcations. Nonlinearity, Volume 27 (Number 5). pp. 859-895. doi:10.1088/0951-7715/27/5/859 ISSN 0951-7715.
|
PDF
WRAP_MacKay_0951-7715_27_5_859.pdf - Published Version - Requires a PDF viewer. Available under License Creative Commons Attribution. Download (1019Kb) | Preview |
Official URL: http://dx.doi.org/10.1088/0951-7715/27/5/859
Abstract
A transition state for a Hamiltonian system is a closed, invariant, oriented, codimension-2 submanifold of an energy level that can be spanned by two compact codimension-1 surfaces of unidirectional flux whose union, called a dividing surface, locally separates the energy level into two components and has no local recrossings. For this to happen robustly to all smooth perturbations, the transition state must be normally hyperbolic. The dividing surface then has locally minimal geometric flux through it, giving an upper bound on the rate of transport in either direction.
Transition states diffeomorphic to $\mathbb S^{2m-3}$ are known to exist for energies just above any index-1 critical point of a Hamiltonian of m degrees of freedom, with dividing surfaces $\mathbb S^{2m-2}$ . The question addressed here is what qualitative changes in the transition state, and consequently the dividing surface, may occur as the energy or other parameters are varied? We find that there is a class of systems for which the transition state becomes singular and then regains normal hyperbolicity with a change in diffeomorphism class. These are Morse bifurcations.
Various examples are considered. Firstly, some simple examples in which transition states connect or disconnect, and the dividing surface may become a torus or other. Then, we show how sequences of Morse bifurcations producing various interesting forms of transition state and dividing surface are present in reacting systems, by considering a hypothetical class of bimolecular reactions in gas phase.
Item Type: | Journal Article | ||||||||
---|---|---|---|---|---|---|---|---|---|
Subjects: | Q Science > Q Science (General) Q Science > QA Mathematics Q Science > QC Physics |
||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Research Centres > Centre for Complexity Science Faculty of Science, Engineering and Medicine > Science > Mathematics |
||||||||
Library of Congress Subject Headings (LCSH): | Mathematical physics, Nonlinear systems, Bifurcation theory, Transport theory, Hamiltonian systems | ||||||||
Journal or Publication Title: | Nonlinearity | ||||||||
Publisher: | Institute of Physics Publishing Ltd. | ||||||||
ISSN: | 0951-7715 | ||||||||
Official Date: | May 2014 | ||||||||
Dates: |
|
||||||||
Volume: | Volume 27 | ||||||||
Number: | Number 5 | ||||||||
Page Range: | pp. 859-895 | ||||||||
DOI: | 10.1088/0951-7715/27/5/859 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Date of first compliant deposit: | 27 December 2015 | ||||||||
Date of first compliant Open Access: | 27 December 2015 | ||||||||
Funder: | Engineering and Physical Sciences Research Council (EPSRC) | ||||||||
Open Access Version: |
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |
Downloads
Downloads per month over past year