Multidimensional systems, chemical reaction

CHEMICAL REACTIONS IN MULTIDIMENSIONAL PHASE SPACE The unperturbed Hamiltonian //q of the system... 

At the microscopic level, chemical reactions are dynamical phenomena in which nonlinear vibrational motions are strongly coupled with each other. Therefore, deterministic chaos in dynamical systems plays a crucial role in understanding chemical reactions. In particular, the dynamical origin of statistical behavior and the possibility of controlling reactions require analyses of chaotic behavior in multidimensional phase space. 

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. 

The sections which follow outline the general multidimensional distribution theory. Applications of the theory are discussed to describe droplet size distributions and mixing frequencies in chemically equilibrated systems, the effects of droplet mixing on the extent of reaction, the analysis of mass transfer with and without chemical reaction, hydrocarbon fermentation, and emulsion polymerization. 

The acquisition of a single-wavelength fluorescence spectrum of a complex multicomponent mixture is more tedious for many analytical applications that involve the measurement of some essential intermediate components or transient species. The determinations of such systems become more critical if the spectral information for those species is important to the understanding and elucidation of the properties of the final product. Similarly, this is true for chemical measurements of components whose fluorescence intensity decreases continuously with time. A rapid multidimensional data-processing technique becomes exceedingly important in the analysis of these species in a chemical reaction. 

The simplest system in nanoscale may be chosen as a single particle, like an atom or molecule, in a closed space with rigid boundaries. In the absence of chemical reactions, the only processes in which it can participate are transfers of kinetic or potential energy to or from the particle, from or to the walls. The state for this one-particle system is a set of coordinates in a multidimensional space indicating its position and its momentum in various vector directions. 

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. 

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