Non-linear Chemical Dynamics

I.R. Epstien and J.A. Pojman, An Introduction to Non-linear Chemical Dynamics, Oxford University Press, Oxford, 1998. 

Epstein, IR Poiman, JA. An introduction to non-linear chemical dynamics, Oxford University Press, New York, 1998. 

Self-organization could be considered as a set intersecting self-assembly, ordered self-assembly, that would (1) contain the systems presenting a spontaneous emergence of order in either space or time or both (2) cover spatial (structural) and temporal (dynamic) order of both equilibrium structures and of non-equilibrium, dissipative structures, incorporating non-linear chemical processes, energy flow and the arrow of time (3) concern only the non-covalent, supramolecular level (4) be... 

A. M. Kutepov Chemical Dynamics and Theoretical Bases of Non-Linear Chemical-Technological Processes, Moscow (1998) (in Russian). 

Chadam, J. Ortoleva, P. (1984). Moving interfaces and their stability Applications to chemical waves and solidification. In Dynamics of Non-Linear Systems, ed. V. 

All local concentrations C of particles entering the non-linear functions F in equation (2.1.40) are taken at the same space points, in other words, the chemical reaction is treated as a local one. Taking into account that for extended systems we shouldn t consider distances greater than the distinctive microscopic scale Ao, the choice of equation (2.1.40) means that inside infinitesimal volumes vo particles are well mixed and their reaction could be described by the phenomenological reaction rates earlier used for systems with complete reactant mixing. This means that Ao value must exceed such distinctive scales of the reaction as contact recombination radius, effective radius of a dynamical interaction and the particle hop length, which imposes quite natural limits on the choice of volumes v0 used for averaging. 

Many variables used and phenomena described by fracture mechanics concepts depend on the history of loading (its rate, form and/or duration) and on the (physical and chemical) environment. Especially time-sensitive are the level of stored and dissipated energy, also in the region away from the crack tip (far held), the stress distribution in a cracked visco-elastic body, the development of a sub-critical defect into a stress-concentrating crack and the assessment of the effective size of it, especially in the presence of microyield. The role of time in the execution and analysis of impact and fatigue experiments as well as in dynamic fracture is rather evident. To take care of the specihcities of time-dependent, non-linearly deforming materials and of the evident effects of sample plasticity different criteria for crack instability and/or toughness characterization have been developed and appropriate corrections introduced into Eq. 3, which will be discussed in most contributions of this special Double Volume (Vol. 187 and 188). 

Investigations with the graphs of non-linear mechanisms had been stimulated by an actual problem of chemical kinetics to examine a complex dynamic behaviour. This problem was formulated as follows for what mechanisms or, for a given mechanism, in what region of the parameters can a multiplicity of steady-states and self-oscillations of the reaction rates be observed Neither of the above formalisms (of both enzyme kinetics and the steady-state reaction theory) could answer this question. Hence it was necessary to construct a mainly new formalism using bipartite graphs. It was this formalism that was elaborated in the 1970s. 

We have already mentioned the view of Daniels on the confusion in chemical kinetics. Horiuti emphasized this view by using the word "chaos . The experiment discovered a complex kinetic behaviour which is likely to have supported this point of view. But the situation has changed drastically in the last 10 years. New concepts of mathematical physics connected with the study of non-linear systems make us understand complex dynamics ("chaos ) is the result of a certain law. In kinetic Chaos, we can notice Harmony and Hope to see it more clearly. 

Hudson, J. L., Mankin, J., McCullough, M. and Lamba, P., "Non-Linear Phenomena in Chemical Dynamics", Pacault and Vidal, eds., Springer, 1982. 

In these past 10 years, it has been demonstrated that the TR-QELS method is a versatile technique that can provide much information on interfacial molecular dynamics [1-11]. In this chapter, we intend to show interfacial behaviour of molecules elucidated by the TR-QELS method. In Section 3.2, we present the principle, the historical background and the experimental apparatus for TR-QELS. The dynamic collective behaviour of molecules at liquid/liquid interfaces was first obtained by improving the time resolution of the TR-QELS method. In Section 3.3, we present an application of the TR-QELS method to a phase transfer catalyst system and describe results on the scheme of the catalytic reactions. This is the first application of the TR-QELS method to a practical liquid/liquid interface system. In Section 3.4, we show chemical oscillations of interfacial tension and interfacial electric potential. In this way, the TR-QELS method allows us to analyze non-linear adsorption/desorption behaviour of surfactant molecules in the system. 

Autocatalysis is a distinctive phenomenon while in ordinary catalysis the catalyst re-appears from the reaction apparently untouched, additional amounts of catalyst are actively produced in an autocatalytic cycle. As atoms are not interconverted during chemical reactions, this requires (all) the (elementary or otherwise essential) components of autocatalysts to be extracted from some external reservoir. After all this matter was extracted, some share of it is not introduced in and released as a product but rather retained, thereafter supporting and speeding up the reaction(s) steadily as amounts and possibly also concentrations of autocatalysts increase. At first glance, such a system may appear doomed to undergo runaway dynamics ( explosion ), but, apart from the limited speeds and rates of autocatalyst resupply from the environment there are also other mechanisms which usually limit kinetics even though non-linear behavior (bistability, oscillations) may not be precluded ... 

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