Oscillation process

The oscillations observed with artificial membranes, such as thick liquid membranes, lipid-doped filter, or bilayer lipid membranes indicate that the oscillation can occur even in the absence of the channel protein. The oscillations at artificial membranes are expected to provide fundamental information useful in elucidating the oscillation processes in living membrane systems. Since the oscillations may be attributed to the coupling occurring among interfacial charge transfer, interfacial adsorption, mass transfer, and chemical reactions, the processes are presumed to be simpler than the oscillation in biomembranes. Even in artificial oscillation systems, elementary reactions for the oscillation which have been verified experimentally are very few. 

The voltammetry for ion transfer at an interface of two immiscible electrolyte solutions, VITIES, which is a powerful method for identifying the transferring ion and for determining the amount of ion transferred, must be helpful for the elucidation of the oscillation process [17 19]. The VITIES was also demonstrated to be useful for ion transport through a membrane, considering that the membrane transport of ions is composed of the ion transfers at two aqueous-membrane interfaces and the mass transfers and/or chemical reactions in three phases [2,20,21]. 

Adaptive self-control of the energy contribution in the oscillating process, exhibited in the sustaining of a value for the system s oscillation amplitude and frequency which is stable over significant variance of the amplitude of external influence, the quality factor of the oscillator (the load) and other external variables. 

The method developed of entering energy in oscillation processes and the excitation of quantized oscillations in dynamic macro-systems finds and will find in the future applications in the solving of important practical problems in the creation of new methods and mechanisms for the excitation and the sustaining of continuous oscillations and different energy transformations which could be grouped in the following way ... 

In later work, Roelofs and co-workers discovered further details of the reaction by investigating the sub-systems, and they suggested a 21 step chemical model (RWJ model) to explain the observed non-linear kinetic patterns (163). According to the experimental observations, the oscillation process can be divided into two distinct alternating stages, the stoichiometries of which can be approximated as follows ... 

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. 

From the viewpoint of experimental workers, slow relaxations are abnormally (i.e. unexpected) slow transition processes. The time of a transition process is determined as that of the transition from the initial state to the limit (t -> oo) regime. The limit regime itself can be a steady state, a limit cycle (a self-oscillation process), a strange attractor (stochastic self-oscillation), etc. 

An important conclusion follows from the time monotonic manner (2.31) of changes in values P and d S/dt. In case the system exists near thermody namic equilibrium, the system s spontaneous evolution cannot generate any periodical auto oscillating processes. In fact, periodical processes are described along the closed evolution trajectories, which would make some thermo dynamic parameters (concentration, temperature, etc.) and, as a result, values Ji and Xj return periodically to the same values. This is inconsistent with the one directional time monotonic changes in the P value and with the con stancy of the latter in the stationary point. In terms of Lyapunov s theory of stability, the stationary state under discussion corresponds to a particular point of stable node type (see Section 3.5.2). 

Because the hydrogen termination process takes a considerable amount of time, it is an important element contributing to the oscillation process. 

A Bromate-Malonic Acid Oscillation Process Catalyzed by Ions... 

The oscillation process, the theoretical principles of which are described in Experiment 96, leads to the periodic formation of free iodine, which is characterised by the blue color of the starch-iodine complex. ... 

The application of oscillator circuits as sensor interface for QCM is the most common method. Since a quartz crystal is a resonant element, stable oscillation can be excited by quite simple circuits. They deliver a frequency analog output signal, which can be easily processed in digital systems. Two oscillation conditions can be formulated assuming approximately linear behavior and not considering the pre-oscillation process ... 

Analysis of the two relations (7.51) and (7.52) allow favourable conditions for a manifestation of the electrostatic retardation effects at oscillating surfaces to be defined. At first, the diffusion layer thickness has to be small and decreases with increasing frequency. Secondly, the deviation from equilibrium during the oscillation process must be small, 8r 1. 

Under the condition a l the electrostatic retardation controls the periodic transport of the surfactant ions. During the period of the oscillation the diffusion layer thickness is even smaller than 8q and, therefore, Eq. (7.54) holds for the whole oscillation process. 

When the above reaction-diffusion system is operated in such a responsive medium, cross-coupling between the volume changes and the reaction occurs, that can give rise to relaxation oscillations in both the radius of the sphere and the chemical composition. The oscillating process can be... 

We see in Figure 12.9 that a relatively great number of planes in molybdenum are involved in the oscillation process in the 0.5-1.0 interval of This confirms the existence of the strengthened interatomic d bonding between molybdenum atoms. 

It will be shown that the catalyst bulk is directfy involved in the catal3dic oscillation process due to the dependence on the composition and the thermal conductivity of the gas phase. We observed oscillations with different behaviour and assume different reaction pathways and hence chemical origins for the dynamic behaviour. 

Up to this stage, the generalization is trivial. When one averages with respect to rapidly oscillating processes, however, one must be very careful, and this point turns out to be crucial to the phase description of synchronization. 

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