Continuous oscillations

Consider the continuous oscillations of a tuning fork. These oscillations generate successive compressions and rarefactions outward through the air. The human ears, w hen receiving these pressure variations, transfer them to the brain, where they are interpreted as sound. Therefore, the phenomenon of sound is a pressure variation in a fixed point in the air or in another elastic medium, such as water, gas, or solid. 

Experimental studies of molecular motion reveal that nuclei vibrate continuously, oscillating about their optimum separation distance like two balls attached to opposite ends of a spring. Figure 9 3 shows this in schematic fashion for a hydrogen molecule vibrating about its optimum separation distance of 74 pm. 

Thus it is possible for continuous stirred-tank reactor systems to be stable, or unstable, and also to form continuous oscillations in output, depending upon the system, constant and parameter, values. 

Several devices are also available to promote airway clearance. Flutter valve devices employ oscillating positive expiratory pressure (OPEP) to cause vibratory air flow obstruction and an internal percussive effect to mobilize secretions. Intrapulmonary percussive ventilation (IPV) provides continuous oscillating pressures during inhalation and exhalation. Finally the most commonly used technique is high-frequency chest compression (HFCC) with an inflatable vest that provides external oscillation. Vest therapy is often preferred by patients because they can independently perform the therapy even from an early age.5,14... 

The phenomenon of continuous oscillation excitation with an amplitude belonging to a discrete set of stationary amplitudes has been demonstrated on the basis of a common model - an oscillator under wave influence. It is shown that the conditions necessary for the manifestation of this phenomenon are realized in a natural way in an oscillator system interacting with a continuous fall wave. 

Here-with is shown the potential for excitation of relatively low frequency continuous oscillations having a discrete amplitude set under the influence of a wave with incompatibly higher frequency. In the... 

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 ... 

Clearly < I and the step response may be calculated from equation 7.82, Volume 3, where M = 14,000 N/m2. f 0 however and thus the step response will approach a continuous oscillation with constant amplitude as shown in Figure 7.28, Volume 3. 

This view was given further support by the discovery of "tautomerism," that is, that some compounds behave as if they have two different structures simultaneously. Peter Laar suggested in 1886 that this can best be explained as the result of continual oscillation of a hydrogen atom between two positions within a single molecule, 109 a hypothesis influenced by Kekule s suggestion that the peculiarities of benzene are the result of an oscillation of atoms in benzene and that "equivalence" or valence is "the relative number of contacts which occur in a unit of time between atoms." 110... 

For acetoacetic ester, the mystery lay in the two rather different forms the "ester" took the so-called enol (hydroxy) form CH3C(OH) = CH-COOC2H5 and the keto (ketone) form CH3COCH2COOC2H5.37 (See fig. 6.) As mentioned briefly in chapter 5, in 1885, Laar at Bonn coined the word "tautomerism" for the behavior of acetoacetic ester, (tautos, the same meros, part), hypothesizing that the phenomenon of two structures in one is due to a continual oscillation of a hydrogen atom between two positions in the molecule, with an accompanying change in the bonds between the atoms. Of course, this hypothesis appears to have been influenced by Kekule s earlier mechanical hypothesis. 

B. Hess, K. Brand, and K. Pye, Continuous oscillations in a cell-free extract of 5. carlsber-gensis. Biochem. Biophys. Res. Commun. 23, 102-108 (1966). 

A typical chemical system is the oxidative decarboxylation of malonic acid catalyzed by cerium ions and bromine, the so-called Zhabotinsky reaction this reaction in a given domain leads to the evolution of sustained oscillations and chemical waves. Furthermore, these states have been observed in a number of enzyme systems. The simplest case is the reaction catalyzed by the enzyme peroxidase. The reaction kinetics display either steady states, bistability, or oscillations. A more complex system is the ubiquitous process of glycolysis catalyzed by a sequence of coordinated enzyme reactions. In a given domain the process readily exhibits continuous oscillations of chemical concentrations and fluxes, which can be recorded by spectroscopic and electrometric techniques. The source of the periodicity is the enzyme phosphofructokinase, which catalyzes the phosphorylation of fructose-6-phosphate by ATP, resulting in the formation of fructose-1,6 biphosphate and ADP. The overall activity of the octameric enzyme is described by an allosteric model with fructose-6-phosphate, ATP, and AMP as controlling ligands. 

An understanding of the transient hehavior of continuous reactors is important for start-up and reactor control considerations. Continuous oscillations have been observed by a number of workers. Figures 10 and 11 show data for styrene and methyl methacrylate. Gerrens and Ley (1974) reported continuous, undamped oscillations in surf e tension during a styrene emulsion polymerization run which lasted for more than 50 mean residence times. Nearly five complete cycles were observed during this run. Berens (1974) conducted experiments with vinyl chloride in whidi the measured panicle size changed with time. No steady state was achieved with the data shown in Fig. 12. 

At any temperature higher than absolute zero, certain frequencies in a phonon spectrum of the crystal lattice are excited and as a result, atoms are in a continuous oscillating motion about their equilibrium positions, which are determined by coordinate triplets (x, y, z). To account for these vibrations, the so-called temperature factor is introduced into the general equation (Eq. 2.87) of the structure amplitude. 

A fully transient simulation that does not use commercial software, but is based on the shallow water approximation relevant to Hall cells has been reported by Zikanov et al. [89], Because of the speed of this simulation, additional features become available for investigation, such as continuing oscillations of constant amplitude, which can sometimes be detected in operating cells. This behavior, due to nonlinear interactions, is not within the capabilities of the linearized stability analyses that have formed the bulk of the literature to date. 

Continuous pusher Continuous worm discharge Continuous oscillating screen... 

These results were in contrast to the previous experiments described above, where nucleation was always observed. It is thought that as nucleation is a stochastic process, a single oscillation of a laser-induced bubble may not always lead to the nucleation. The probability of nucleation is increased by the continuously oscillating bubble produced by the standing wave system, and it is increased further by the multicavitation events produced by the ultrasonic horn. 

A perturbation analysis of Equations 35 and 36 about this singular point shows that the solutions whose initial conditions are close to P, Z, oscillate sinusoidally about this singular point. Hence, no constant solution is possible. The prey and predator populations continually oscillate and are out of phase with each other. When the predator predominates, the prey is reduced, which in turn causes the predator to die for lack of food, which allows the prey to proliferate for lack of predator, which then causes the predator to grow because of the prey available as a food supply, and so on. The interesting feature is that these oscillations continue indefinitely. 

In the middle row the oscillatory regime is illustrated. The systems exhibits continuous oscillations. Perturbations have at this stage little influence on the dynamics. 

Using proportional control only and with the feedback loop closed, introduce a set point change and vary the proportional gain until the system oscillates continuously. The frequency of continuous oscillation is the crossover frequency, cuC0. LetM be the amplitude ratio of the system s response at the crossover frequency. 

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