Oscillating phenomena

Flows through charged membranes. II. Oscillation phenomena, 3. Chem. Phys.,... 

In the homogeneous systems at low temperatures, oscillation phenomena were also observed for this reaction system. Similar observations were made for the CO and 02 system. In order to explain the oscillation mechanism mathematically, a complicated kinetic scheme was devised which is capable of predicting the sustained oscillations [Yang (26, 27)]. Apparently a similar complicated kinetic mechanism governs the undamped oscillations in the heterogeneous system, however, a pertinent analysis has not been performed in the literature so far. 

While the trend of the research activity in the area of multiplicity and periodic activity in the 1960s has been focused on theoretical investigation, the recent development has indicated an increase of experimental information. However, the number of experimental papers in comparison with the theoretical studies is still low and the need for additional laboratory studies is obvious. We have tried in this report to focus only on experimental papers and on behavior of real systems. We hope that a qualitative description of multiplicity and oscillations phenomena presented here will catalyze the research oriented to more detailed investigation of fundamental laws governing transport phenomena in chemically reacting systems. 

This obiously does not exclude the possibility of oscillation phenomena such as ionization waves, etc., which are among the most frequently observed instabilities in d.c. glow discharges49. Any allowance for these phenomena in the theoretical treatment of chemical processes would introduce major complications and, we shall therefore ignore them in the first approximation. Such a simplification is justified, because the relaxation processes related to the ionization waves are usually much faster than chemical processes. Therefore, the oscillations take place on a time scale which is different from that of the chemistry. Moreover, the waves arise in a d.c. discharge rather than in a high frequency discharge, which was used in most experiments on chemical transport. 

Oscillating phenomena and hysteresis behaviour (bi-, multistability) are the most important phenomena in systems far from thermal equilibrium, excluding spatial structures (patterns, travelling waves). Examples of both types of temporal structures can be found in all disciplines where nonlinear dynamics play a significant role. In biophysics it appears that dissipation provides a general mechanism and may also account for the functional... 

Philander, S. G. H., 1983. El Nino southern oscillation phenomena. Nature, 302, 295-301. 

The oscillation phenomena of diols properties is also observed when plotting their fusion points vs. their number of carbon atoms. Uneven diols have lower fusion points than odd ones an observation that is explained by the possibility even diols have, for evident steric reasons, to form dimers , where odd diols may more easily form polymers . Applying these arguments to the grafted chains, we arrive at the situation depicted in Fig. 8. 

In this work the oxidative transformations of methane were studied with a catalyst system that combines an oxide and a metal component. The presence of both components gave rise to complex oscillation phenomena. The influence of pretreatment and reaction conditions over a wide range of parameters (temperature, total pressure, and oxygen concentration) on the oscillatory process was studied. The possible role of mass transfer and the balance of heat in the reactor were analyzed, and a model for the role of the components in the binary catalyst system is suggested. 

The consequences of a filter shape can be visualised most easily by picturing what happens if there is a spike in the signal. The output of the filter than contains a copy of the filter shape on the position of the spike. In other words, we get to see the impulse response of the filter. For a filter shape that is wide and oscillating, phenomena that are purely local in the time domain get spread out and deformed. If we want to have a more reasonable filter shape in the time domain, we have to use a smoother cut-off in the frequency domain. It is the sharpness of the cut that introduces the oscillations, as it disturbs the delicate balance of frequencies required to localise something in... 

Cobbold, P.H. K.S.R. Cuthbertson. 1990. Calcium oscillations Phenomena, mechanisms and significance. Semin. Cell Biol. 1 311-21. 

Prazak, J. Sir, M. Kubik, F. Tywoniak, J. Zaicone, C. Oscillation Phenomena in Gravity-Driven Drainage in Coarse Porous Media. Water ReKour. Res. 1992.25(7), 1849-1855. 

The examples to be presented illustrate the diversity of fields of applications, but they are mentioned in outline form only. Many biological phenomena used to be modelled by real or formal kinetic models. A biochemical control theory that is partially based on non-mass-action-type enzyme kinetics seems to be under elaboration, and certain aspects will be illustrated. A few specific models of fluctuation and oscillation phenomena in neurochemical systems will be presented. The formal structure of population dynamics is quite similar to that of chemical kinetics, and models referring to different hierarchical levels from elementary genetics to ecology are well-known examples. Polymerisation, cluster formation and recombination kinetics from the physical literature will be mentioned briefly. Another question to be discussed is how electric-circuit-like elements can be constructed in terms of chemical kinetics. Finally, kinetic theories of selection will be mentioned. 

In the present oscillation phenomena the CO2 volume fraction oscillates with substantial amplitudes, whereas the formaldehyde shows smaller or no oscillations. Therefore, the overall oscillations are mainly due to a variation of the total oxidation activity (cf. Equation 3 and 4) whereas the changes of the partial oxidation activity are of minor importance which is due to the choice of a lean reaction mixture. 

Oscillating phenomena have also been observed for N2O decomposition by Cu-exchang-ed ZSM-5 zeolites . A dynamic state consisting of monomeric Cu+ and dimeric Cu +OCu + is also proposed here. 

Gabrielli, C., Huet, F. and Nogueira, R.P. (2002) Electrochemical noise measurements of coalescence and gas-oscillator phenomena on gas-evolving electrodes. Journal of the Electrochemical Society, 149, E71-E77. 

Oscillatory behavior of electrochemical systems is not uncommon. The most familiar in this respect are the systems containing surface-active substances. Most surfactants are capable of forming inhibiting adsorption layers, which are responsible for a significant decrease in the cathodic current in a certain range of potentials. For instance, the electroreduction of copper [106] or tin [107] in the presence of inhibitors is accompanied by oscillation phenomena. 

In summary, the dc current absorption is observed in the oxidized polyacrylonitrile based-ER fluids. The conductive behaviors of ER suspensions with or without an oscillatory mechanical field are confined by the microstructure—the fibrillated chain structure induced by an external electric field. The de current oscillates with the mechanical frequency and strain amplitude, implying that ER suspensions could be used as a mechanical sensor transferring a mechanical signal to an electric one. The conductive mechanism of an oxidized polyacrylonitrile-based ER suspension can be well described by a Quasi-Id-VRH model, where the localized charges hop from one localized state to another along the chains. This conduction model can be used to quantitatively describe the dc current oscillation phenomena. 

Potentiometric sertsors are very well srrited to perform measurements in real time. For servo control, low respottse times avoid oscillation phenomena. The intrinsic response time is a function of the kinetics of different interfaces and of the electrical properties of the ionic materials (SIC and internal reference compounds). To simplify, one can model a potentiometric sensor by the eqrrivalent electric circuit drawn in Figure 10.16 (this description is very simplified for more details we refer to the specialized literature). Each interface and each material are equivalent to a parallel RC circuit with its time constant x . The transient response is given by... 

As for attractive minimal sets, it follows from Pugh s theorem that they are structurally unstable. Although the minimal sets composed of recurrent and limit-quasiperiodic orbits are by far not key players in the nonlinear dynamics, quasiperiodic motions have always been of major interest because they model many oscillating phenomena having a discrete spectrum. 

The science of chemical oscillation is a wide field. The oscillations may be oscillations in time, as in our example, or spatial oscillations. The description of real oscillation phenomena also requires to include diffusive or convective flows. A rather detailed discussion of oscillation phenomena in the context of non-equilibrium thermodynamics is given in Nicolis and Progogine (1977). 

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