Chemical reaction dynamics space

N. De Leon, M. A. Mehta, and R. Q. Topper, Cylindrical manifolds in phase space as mediators of chemical reaction dynamics and kinetics. I. Theory, J. Chem. Phys. 94, 8310 (1991). 

The classical dynamics of a system can also be analyzed on the so-caUed Poincare surface of section (PSS). Hamiltonian flow in the entire phase space then reduces to a Poincare map on a surface of section. One important property of the Poincare map is that it is area-preserving for time-independent systems with two DOFs. In such systems Poincare showed that all dynamical information can be inferred from the properties of trajectories when they cross a PSS. For example, if a classical trajectory is restricted to a simple two-dimensional toms, then the associated Poincare map will generate closed KAM curves, an evident result considering the intersection between the toms and the surface of section. If a Poincare map generates highly erratic points on a surface of section, the trajectory under study should be chaotic. The Poincare map has been a powerful tool for understanding chemical reaction dynamics in few-dimensional systems. 

The robust existence of a skeleton composed of a NHIM and its spherical invariant cylinders in the phase space should play their essential roles not only to help us understand the physical origin of observed nonstatistical, dynamical behavior but also to provide us with a new scope to control chemical reaction dynamics in terms of geometrical feature of the phase space. Here, let us articulate some of the subjects we have to confront in the immediate future ... 

Keeping these subjects in perspective, we organized a conference entitled Geometrical Structures of Phase Space in Multidimensional Chaos— Applications to Chemical Reaction Dynamics in Complex Systems from 26th October to 1st November, 2003, at the Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto, Japan. A pre-conference was also held at Kobe University from 20th to 25th October. 

EFFECTS OF AN INTRINSIC METRIC OF MOLECULAR INTERNAL SPACE ON CHEMICAL REACTION DYNAMICS... 

M. Toda, T. Komatsuzaki, T. Konishi, R. S. Berry and S. A. Rice, Geometrical Structures of Phase Space in Multidimensional Chaos Applications to Chemical Reaction Dynamics in Complex Systems, Advances in Chemical Physics, John-Wiley Sons, Hoboken, NJ, 2005, vol. 130, parts A and B. T. Komatsuzaki, R. S. Berry and D. M. Leitner, Advancing Theory for Kinetics and Dynamics of Complex, Many-Dimensional Systems Clusters and Proteins, Advances in Chemical Physics, John-Wiley Sons, Hoboken, NJ, 2011, vol. 145. 

Excitable media are some of tire most commonly observed reaction-diffusion systems in nature. An excitable system possesses a stable fixed point which responds to perturbations in a characteristic way small perturbations return quickly to tire fixed point, while larger perturbations tliat exceed a certain tlireshold value make a long excursion in concentration phase space before tire system returns to tire stable state. In many physical systems tliis behaviour is captured by tire dynamics of two concentration fields, a fast activator variable u witli cubic nullcline and a slow inhibitor variable u witli linear nullcline [31]. The FitzHugh-Nagumo equation [34], derived as a simple model for nerve impulse propagation but which can also apply to a chemical reaction scheme [35], is one of tire best known equations witli such activator-inlribitor kinetics ... 

---