Chemical dynamics, nonlinear

Epstein I R and Pojnian J A 1998 An Introduction to Nonlinear Chemical Dynamics Oscillations, Waves, Patterns and Chaos (Oxford Oxford University Press)... 

I. R. Epstein and J. A. Pojman, An Introduction to Nonlinear Chemical Dynamics Oscillations, Waves, Patterns, and Chaos (New York Oxford University Press, 1998) I. R. Epstein, K. Kustin, P. De Kepper, and M. Orban, Scientific American, March 1983, p. 112 and H. Degn, Oscillating Chemical Reactions in Homogeneous Phase, J. Chem. Ed. 1972,49. 302. 

Epstein IR, Pojman JA (1998) An introduction to nonlinear chemical dynamics. Oscillations, waves, patterns, and chaos. Oxford University Press, New York... 

I. R. Epstein, J. A. Pojman, An Introduction to Nonlinear Chemical Dynamics, Oxford Press, New York (1998). 

Oscillating reactions, a common feature of biological systems, are best understood within the context of nonlinear chemical dynamics and chaos theory based models that are used to predict the overall behavior of complex systems. A chaotic system is unpredictable, but not random. A key feature is that such systems are so sensitive to their initial conditions that future behavior is inherently unpredictable beyond some relatively short period of time. Accordingly, one of the goals of scientists studying oscillating reactions is to determine mathematical patterns or repeatable features that establish relationships to observable phenomena related to the oscillating reaction. 

Two dependent mathematical variables are needed for a network to be capable of periodic behavior. A third is required to permit chaos. It has become quite a sport among the apostles of nonlinear chemical dynamics to invent ever new simple, if not exactly realistic networks that can admit chaos. A classical example, and one of the simplest, is the Hudson-Rossler model [45]. The core of the network is... 

Despite the importance of the chlorite-iodide systems in the development of nonlinear chemical dynamics in the 1980s, the Belousov-Zhabotinsky(BZ) reaction remains as the most intensively studied nonlinear chemical system, and one displaying a surprising variety of behavior. Oscillations here were discovered by Belousov (1951) but largely unnoticed until the works of Zhabotinsky (1964). Extensive description of the reaction and its behavior can be found in Tyson (1985), Murray (1993), Scott (1991), or Epstein and Pojman (1998). There are several versions of the reaction, but the most common involves the oxidation of malonic acid by bromate ions BrOj in acid medium and catalyzed by cerium, which during the reaction oscillates between the Ce3+ and the Ce4+ state. Another possibility is to use as catalyst iron (Fe2+ and Fe3+). The essentials of the mechanisms were elucidated by Field et al. (1972), and lead to the three-species model known as the Oregonator (Field and Noyes, 1974). In this... 

Epstein I R and Showalter K 1996 Nonlinear chemical dynamics oscillation, patterns and chaos J. Phys. Chem. 100 13 132-47... 

This chapter provides an overview of nonlinear chemical dynamics and synthetic polymeric systems, the progress that has been made in bringing these areas together, and some issues that merit further study. Some key themes and results of nonlinear chemical dynamics are cited, and an attempt is made to link them to important questions in polymeric systems. 

Nonlinear dynamics is a vast field, originating in mathematics and physics, we shall focus here on its chemical aspects. In this section, we provide a brief overview of the key concepts and phenomena relevant to chemical systems. The next section considers nonlinear dynamics in polymeric systems. Finally, we consider future directions for the field. A more detailed treatment of nonlinear chemical dynamics, including a more detailed discussion of polymer systems, may be foimd in reference (7). 

Some key notions in that arise in nonlinear chemical dynamics may be briefly summarized as follows ... 

We list below some of the most interesting and most thoroughly studied phenomena that arise in nonlinear chemical dynamics. 

The study of nonlinear chemical dynamics begins with chemical oscillators - systems in which the concentrations of one or more species increase and decrease periodically, or nearly periodically. While descriptions of chemical oscillators can be found at least as far back as the nineteenth century (and chemical oscillation is, of course, ubiquitous in living systems), systematic study of chemical periodicity begins with two accidentally discovered systems associated with the names of Bray (2) and of Belousov and Zhabotinsky (BZ) 3,4), These initial discoveries were met with skepticism by chemists who believed that such behavior would violate the Second Law of Thermodynamics, but the development of a general theory of nonequilibrium thermodynamics (5) and of a detailed mechanism 6) for the BZ reaction brought credibility to the field by the mid-1970 s. Oscillations in the prototypical BZ reaction are shown in Figure 1. 

Given the importance of the BZ reaction in nonlinear chemical dynamics, it is not surprising that polymers and polymerizations would be coupled to it. Pojman et al. studied the BZ reaction to which acrylonitrile was added and showed that the polyacrylonitrile was produced periodically in phase with the oscillations (41). Given that radicals are produced periodically from the oxidation of malonic acid by ceric ion, it seemed reasonable to assume the periodic appearance of polymer was caused by periodic initiation. However, Washington et al. showed that periodic termination by bromine dioxide caused the periodic polymerization (42). 

Epstein, L Pojman, J.A. An Introduction to Nonlinear Chemical Dynamics Oxford University Prcs Oxford, UK, 1998 ppl-392. 

Epstein, I. R. Pojman J. A. Art Introduction to Nonlinear Chemical Dynamics -Oscillations, ITaves, Patterns, and Chaos Oxford Univ. Press Oxford, 1998 pp 231-248. 

Approach ev the Solution of Problems OF Nonlinear Chemical Dynamics AND Synergetics... 

We summarize our findings. It is suggested the criterion of critical condition, that is, the extremal behavior of the reaction species concentration, may be applied to reveal the critical conditions of nonlinear chemical dynamic systems. This is with the changeover of different dynamic modes of the reactions, such as the quasi-periodic and chaotic oscillations of the intermediate concentrations, as well as the steady-state mode. At the same time the Hamiltonian formalism makes it possible not only to have a successful numerical identification of the critical reaction conditions, but also to specify the role of individual steps of the reaction mechanism under different conditions. 

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