Oscillatory phenomena

In its applications, science was encountering gradually-increasing difficulties in view of the impossibility of explaining numerous oscillatory phenomena, particularly those connected with the so-called self-sustained oscillations (first, the oscillating arcs and gaseous discharges and still later, the electron tube oscillators). 

Nonanalytic Cycles.—In recent years the concept of limit cycles was enlarged so as to include cycles that have widespread application in connection with the description of oscillatory phenomena whose stationary states are not describable in the phase plane by a trajectory that is analytic. 

Introductory Remarks.—In the following sections we apply some of the preceding theories to the investigation of a few very important types of nonlinear oscillatory phenomena. 

This theory is adequate to explain practically all oscillatory phenomena in relaxation-oscillation schemes (e.g., multivibrators, etc.) and, very often, to predict the cases in which the initial analytical oscillation becomes of a piece-wise analytic type if a certain parameter is changed. In fact, after the differential equations are formed, the critical lines T(xc,ye) = 0 are determined as well as the direction of Mandelstam s jumps. Thus the whole picture of the trajectories becomes manifest and one can form a general view of the whole situation. The reader can find numerous examples of these diagrams in Andronov and Chaikin s book4 as well as in Reference 6 (pp. 618-647). 

These phenomena are being actively studied at the present time, and constitute a new chapter in the theory of oscillations that is known as piecewise linear oscillations. There exists already a considerable literature on this subject in the theory of automatic control systems11-34 but the situation is far from being definitely settled. One can expect that these studies will eventually add another body of knowledge to the theory of oscillations, that will be concerned with nonanalytic oscillatory phenomena. 

The technique of photoemission electron spectroscopy (PEEM) is a particularly attractive and important one for spatially resolved work function measurements, as both the Kelvin probe technique and UPS are integral methods with very poor ( mm) spatial resolution. The PEEM technique, pioneered in the area of catalysis by Ertl,72-74 Block75 76 and Imbihl,28 has been used successfully to study catalytic oscillatory phenomena on noble metal surfaces.74,75... 

Somlyo We can see that a very large fraction of the SR is continuous. I remember that the first oscillations that were reported, in muscle, were published in a paper in Nature by Professor Endo (Endo et al 1970). If we see the same mechanisms here, then the presence of the SR is at least sufficient I am not saying that it is necessary. If this is the case, then in some smooth muscles we see sufficient interconnected SR to indicate that it could play a role. In the case of skeletal muscle the overloaded SR is most likely to exhibit oscillatory phenomena. 

Recently there has been an increasing interest in self-oscillatory phenomena and also in formation of spatio-temporal structure, accompanied by the rapid development of theory concerning dynamics of such systems under nonlinear, nonequilibrium conditions. The discovery of model chemical reactions to produce self-oscillations and spatio-temporal structures has accelerated the studies on nonlinear dynamics in chemistry. The Belousov-Zhabotinskii(B-Z) reaction is the most famous among such types of oscillatory chemical reactions, and has been studied most frequently during the past couple of decades [1,2]. The B-Z reaction has attracted much interest from scientists with various discipline, because in this reaction, the rhythmic change between oxidation and reduction states can be easily observed in a test tube. As the reproducibility of the amplitude, period and some other experimental measures is rather high under a found condition, the mechanism of the B-Z reaction has been almost fully understood until now. The most important step in the induction of oscillations is the existence of auto-catalytic process in the reaction network. 

In other words, rapid increase in the concentration of the intermediate species plays the most significant role in the self-oscillatory phenomena. 

Oscillations have been observed in chemical as well as electrochemical systems [Frl, Fi3, Wol]. Such oscillatory phenomena usually originate from a multivariable system with extremely nonlinear kinetic relationships and complicated coupling mechanisms [Fr4], Current oscillations at silicon electrodes under potentio-static conditions in HF were already reported in one of the first electrochemical studies of silicon electrodes [Tul] and ascribed to the presence of a thin anodic silicon oxide film. In contrast to the case of anodic oxidation in HF-free electrolytes where the oscillations become damped after a few periods, the oscillations in aqueous HF can be stable over hours. Several groups have studied this phenomenon since this early work, and a common understanding of its basic origin has emerged, but details of the oscillation process are still controversial. 

TNC.48. G. Nicolis and I. Prigogine, Thermodynamic aspects and bifurcation analysis of spatio-temporal dissipative structures, in Proceedings, Faraday Symposium Chemical Society, no. 9, Physical Chemistry of Oscillatory Phenomena, 1975, pp. 7—20. 

The study of models indicates the existence of two main routes to complex oscillatory phenomena. The first relies on forcing a system that displays simple... 

The use of equation (3.2) to study the behaviour of catalysts is known as solid electrolyte potentiometry (SEP). Wagner38 was the first to put forward the idea of using SEP to study catalysts under working conditions. Vayenas and Saltsburg were the first to apply the technique to the fundamental study of a catalytic reaction for the case of the oxidation of sulfur dioxide.39 Since then the technique has been widely used, with particular success in the study of periodic and oscillatory phenomena for such reactions as the oxidation of carbon monoxide on platinum, hydrogen on nickel, ethylene on platinum and propylene oxide on silver. 

V. Shashoua, Electrical oscillatory phenomena in protein membranes, Symp. Faraday Soc., 9 (1974), pp. 174-181. 

Faraday Symposia of the Chemical Society (1975). Physical chemistry of oscillatory phenomena. The Royal Society of Chemistry, London. 

It should be stressed that oscillatory phenomena are well-known in biology. They span a wide range of periods, reaching from fractions of seconds (neuronal and EEG activities) and minutes (biochemical oscillators) to hours and days (circadian rhythm...). Besides these cooperative oscillations on an intra-, inter- and supercellular level, the usual oscillations on a microscopic basis (e.g. electronic transitions, intra- and intermolecular vibrations, rotational relaxation,...) must be taken into account. 

In the mechanism-based approach, a model is validated by its ability to reproduce observed temporal behaviors, i.e. wave forms, phase relationships, parameter dependences, and stability properties under many different conditions. For oscillatory phenomena, prediction of amplitudes and frequencies (using independently determined parameters) play a significant role. Further validation of the model is based on its ability to predict the outcome of new experiments, performed under conditions not previously examined. Among the advantages of this approach are that the model can be gradually expanded without changing already consolidated parts and that the model, in principle at least, allows translation by replacement of, e.g. parameters from animal studies by parameters relevant to man. 

Simple oscillatory phenomena typically arise in feedback systems with delays. Such oscillations may serve as pacemakers or biological clocks to organize different processes that have to follow one another in a specific order. Opening and closing of the various ion channels in a cell, for instance, are typically to occur in a rela-... 

A simple Langmuir-Hinshelwood model explains quantitatively the steady-state behavior (4) but it fails to explain the oscillatory phenomena that were observed. The origin of the limit cycles is not clear. Rate oscillations have not been reported previously for silver catalyzed oxidations. Oxidation of ethylene, propylene and ethylene oxide on the same silver surface and under the same temperature, space velocity and air-fuel ratio conditions did not give rise to oscillations. It thus appears that the oscillations are related specifically to the nature of chemisorbed propylene oxide. This is also supported by the lack of any correlation between the limits of oscillatory behavior and the surface oxygen activity as opposed to the isothermal oscillations of the platinum catalyzed ethylene oxidation where the SEP measurements showed that periodic phenomena occur only between specific values of the surface oxygen activity (6,9). 

Before we leave this topic, it would be wise to note the results of some recent research on heterogeneously catalysed gas reactions. Here finite rates of adsorption and desorption had to be introduced into the reaction scheme in order to explain the occurrence of multiple steady states and oscillatory phenomena. This observed exotic behaviour could be reproduced by solving a set of coupled equations for the rates of adsorption/desorption, the rate of the surface reaction, and the mass balance relations [22, 23], Adsorption steps (ii) and (iv) may therefore need to be invoked for any heterogeneously catalysed solution reactions that are found to exhibit similar dynamic behaviour. 

V. P. Parkhutik and E. Matveeva, Observation of new oscillatory phenomena during the electrochemical anodization of silicon, Electrochem. Solid-State Lett. 2, 371, 1999. 

In general, the interaction of two feedback loops constitutes the basis for complex dynamics. Hence also in HNDR oscillators, slow transport should be taken into account as a possible source of complex oscillatory phenomena. However, this mechanism should operate only in parameter regimes in which, or close to which, both suboscillators possess oscillatory solutions. 

In Physical Chemistry of Oscillatory Phenomena, Symposium of the Faraday Society, No. 9, Faraday Division, Chemical Society, London, 129-136... 

The reactions where oscillations are either observed or predicted have been increasingly attracting researchers into the field. Most of the new studies have been directed toward understanding the mechanism behind the oscillatory phenomena. There are experimental as well as theoretical investigations evaluating the effects of changes in reaction variables and parameters on the oscillatory behavior of the systems. In this section some of the recent contributions to the types of reactions and models outlined in (G G) are briefly discussed, and some newly proposed reactions are also added to the list. Wherever it is possible, these contributions are grouped under subsections. 

R) Klonowski, W. Oscillatory Phenomena of the Dissipative Structure Type in Model 1980 Enzyme Systems. Zagadnienia Biofiz. Wspolczesnej 5, 199-230 (Polish)... 

In a tubular heat exchanger, interactions between fluid and tubes or shell include the coupling of fluid flow-induced forces and an elastic structure of the heat exchanger, thus causing oscillatory phenomena known under the generic name flow-induced vibration [122]. Two major types of flow-induced vibration are of a particular interest to a heat exchanger designer tube vibration and acoustic vibration. 

Tube vibrations in a tube bundle are caused by oscillatory phenomena induced by fluid (gas or liquid) flow. The dominant mechanism involved in tube vibrations is the fluidelastic instability or fluidelastic whirling when the structure elements (i.e., tubes) are shifted elastically from their equilibrium positions due to the interaction with the fluid flow. The less dominant mechanisms are vortex shedding and turbulent buffeting. 

During the oxidation of formic acid and formaldehyde on platinum electrodes, an oscillatory behavior is frequently observed. " The surface poisoning species play a central role in the triggering of the oscillatory phenomena. Recent studies on formic acid and formaldehyde oxidation confirm this view. Inzelt and Kert sz reported that by the use of electrochemical quartz crystal microbalance technique (EQCM), the periodical accumulation and consumption of strongly bound species can be observed in the course of potential oscillation produced by the galvanostatic oxidation of formic acid. 

Building on these results, chapters 3 and 4 present extensions of the two-variable model for glycolytic oscillations. These somewhat abstract extensions, not directly based on experimental observations, permit a detailed analysis of the transition from simple to complex oscillatory phenomena, which forms the subject of part II. 

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