Active oscillator

More pertinent to the present topic is the indirect dissipation mechanism, when the reaction coordinate is coupled to one or several active modes which characterize the reaction complex and, in turn, are damped because of coupling to a continuous bath. The total effect of the active oscillators and bath may be represented by the effective spectral density For instance, in the... 

Another conventional simplification is replacing the whole vibration spectrum by a single harmonic vibration with an effective frequency co. In doing so one has to leave the reversibility problem out of consideration. It is again the model of an active oscillator mentioned in section 2.2 and, in fact, it is friction in the active mode that renders the transition irreversible. Such an approach leads to the well known Kubo-Toyozawa problem [Kubo and Toyozava 1955], in which the Franck-Condon factor FC depends on two parameters, the order of multiphonon process N and the coupling parameter S... 

C.G. Vayenas, C.Georgakis, J. Michaels, and J. Tormo, The role of PtOx in the isothermal rate and oxygen activity oscillations of the Ethylene Oxidation on Pt, J. 

All unite developed up to now are based on use of an active oscillator, as shown schematically in Fig, 6.5. This circuit keeps the crystal actively in resonance so that any type of oscillation duration or frequency measurement can be carried out. In this type of circuit the oscillation is maintained as long as sufficient energy is provided by the amplifier to compensate for losses in the crystal oscillation circuit and the crystal can effect the necessary phase shift. The basic stability of the crystal oscillator is created through the sudden phase change that takes place near the series resonance point even with a small change in crystal frequency, see Fig. 6.6. 

INFICON has developed a new technology for overcoming these constraints on the active oscillator. The new system constantly analyzes Ihe response of the crystal fo an applied frequency not only fo determine the (series) resonance frequency, but also fo ensure that the quartz oscillates in the desired mode. The new system is insensitive te mode hopping and the resultant inaccuracy. It is fast and precise. The crystal frequency is determined 10 times a second w/ith an accuracy to less than 0.0005 Hz. 

If decay is possible only by means of tunneling, then it is most profitable to collect all the quanta on the active oscillator and we have, for r(n)... 

Another conventional simplification is replacing the whole vibrational spectrum by a single harmonic vibration with an effective frequency >. In doing so, one eliminates consideration of the reversibility of the process. It is again the model of an active oscillator mentioned in Section 2.2 and,... 

Fast detection of the electro-acoustic impedance is a condition for successful kinetic studies. Soares [64] introduced a circuit to measure both resonant frequency and damping resistance R, though not as fast as simple active oscillator methods mainly used for resonant frequency measurement. Most active circuits operate in the series frequency a>s although some oscillators are designed to operate in the parallel frequency wp , which is slightly higher and very susceptible to the value of Ca. 

Figure 1.1 Pressure dependence of the unimolecular rate constant for C-C3H6 —> H2=CH—CH3. The open and closed circles are data from Prichard et al. (1953) while the x s are data of Chambers and Kistiakowsky (1934). The lower curves are displaced down by 0.3 log units. The solid lines are the experimental results, the open squares are calculated by Slater (1953) assuming 13 active oscillators (in place of the full 21), and the dashed curve is a Kassel or RRK calculation with 13 oscillators by Prichard et al. (1953). Taken in modified form, and with permission, from Prichard et al. (1953).

Yet, scale-up is inevitable, even in the relatively low throughput environment of bulk drugs. Skillful use of the pilot plant environment, by which the preparative task and the process development scale-up coincide in time and place, is essential to a vigorous bulk development program lest the activity oscillate between the extremes of unskilled scale-up and fear of scale-up. Indeed, lack of sufficient scale-up skills is a major disadvantage in bulk drug process development. 

Active oscillator mode Stable oscillations of a quartz plate only occur at the resonance frequency... 

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