Damping phenomenon

Gutowski, M., Verbeek, J., van Lenthe, J. H., and Chalasinski, G., The impact of higher polarization functions on second-order dispersion energy. Partial wave expansion and damping phenomenon for He2, Chem. Phys. 111, 271-283 (1987). 

One observation of interest has been made and is illustrated in Figure 22. The question is what happens if we synchronize repetitively, using four shocks spaced 150 minutes apart, and then shift to the multiple heat shock procedure. We know by now that the first four shocks can start a train of synchronous, free-running cell divisions, each closely followed by synchronous DNA replication. However, when the shift is made as described to the multiple shock procedure, divisions are suppressed but DNA replication continues as a cyclic, though damped, phenomenon occurring with a period of nearly four hours (lower curve, main culture). Samples were removed at the end of each new heat shock. They displayed synchronous division after 1.5 hours at 28 C. The quality of this synchrony (upper curves) bears a distinct relationship to the phase in the DNA replication cycle at the time the sample was removed from the main culture. 

M. Gutowski, J. Verbeek, J. H. van Lenthe and G. Chalasinski, Chem. Phys., Ill, 271 (1987). The Impact of Higher Polarization Functions on Second-Order Dispersion Energy. Partial Wave Expansion and Damping Phenomenon for He2. 

A phenomenon known as silver migration has limited the use of silver plating in miniature circuit boards under a positive d-c potential within a damp environment silver can migrate across insulation. On drying, silver is found in the insulation or media creating a leakage path. Silver plating is forbidden in many military specifications for circuit boards. 

This speed becomes critical when the frequency of excitation is equal to one of the natural frequencies of the system. In forced vibration, the system is a function of the frequencies. These frequencies can also be multiples of rotor speed excited by frequencies other than the speed frequency such as blade passing frequencies, gear mesh frequencies, and other component frequencies. Figure 5-20 shows that for forced vibration, the critical frequency remains constant at any shaft speed. The critical speeds occur at one-half, one, and two times the rotor speed. The effect of damping in forced vibration reduces the amplitude, but it does not affect the frequency at which this phenomenon occurs. 

We shall give here a brief summary of our previous work [71,72] that was concerned with the introduction of the relaxation phenomenon within the adiabatic treatment of the Hamiltonian (77), as was done in the undamped case by Witkowski and Wojcik [74]. Following these authors, we applied the adiabatic approximation and then we restricted the representation of the Hamiltonian to the reduced base (89). Within this base, the Hamiltonian that describes a damped H bond involving a Fermi resonance may be split into effective Hamiltonians whose structure is related to the state of the fast and bending modes ... 

In situations where absorption of the incident radiation by the transducing gas is troublesome a piezoelectric transducer (made from barium titanate, for example) can be attached to the sample (or sample cuvette in the case of liquids) to detect the thermal wave generated in the sample by the modulated light (8,9). The low frequency, critically damped thermal wave bends the sample and transducer thus producing the piezoelectric response. The piezoelectric transducer will also respond to a sound wave in the solid or liquid but only efficiently at a resonant frequency of the transducer typically of the order of 10 to 100 KHz (see Figure 4). Thus neither in the case of microphonic nor piezoelectric detection is the PA effect strictly an acoustic phenomenon but rather a thermal diffusion phenomenon, and the term "photoacoustic" is a now well established misnomer. 

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. 

In parallel with the studies described above, which concern perfectly deterministic equations of evolution, it appeared necessary to complete the theory by studying the spontaneous fluctuations. Near equilibrium, any deviation is rapidly damped but near a bifurcation point, a fluctuation may may lead the system across the barrier. The fluctuation is then stabilized, or even amplified this is the origin of the phenomenon which Prigogine liked calling creation of order through fluctuations. More specifically, one witnesses in this way a step toward self-organization. 

Spinning detonation would, therefore, be most likely to occur whenever the induction zone is so thick that the transverse vibrations responsible for the phenomenon are not damped out by the mass flow. This would explain why spin is associated with mixtures near the detonation limits, and disappears in highly detonable mixtures in which induction times are very short and induction zones are very thin... 

If absorption is measured not too close to the damping peak (tan 8) both longitudinal and shear absorption often increase linearly with frequency. This is demonstrated in Fig. 14.5 for polyethylene (Hartmann and Jarynski, 1972). This phenomenon is called hysteresis behaviour in acoustics (it does not refer to absorption as is common among polymer scientists (Hartmann, 1990). At any frequency shear absorption is much higher than longitudinal absorption. 

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