Low-frequency oscillation

Ii is seen ihai ihe surge frequency during current chopping may rarely exceed 20 kHz and which, in the context of switching. surges, may be considered as low-frequency oscillations, easy to handle and interrupt. 

This approximation is not valid, say, for the ohmic case, when the bath spectrum contains too many low-frequency oscillators. The nonlocal kernel falls off according to a power law, and kink interacts with antikink even for large time separations. We assume here that the kernel falls off sufficiently fast. This requirement also provides convergence of the Franck-Condon factor, and it is fulfilled in most cases relevant for chemical reactions. 

During the operation of some solid-propellant motors, several investigators have observed oscillations occurring at low frequences (0-500 cps), as shown in Fig. 23. These oscillations cannot be associated with any of the acoustic modes of the combustion chamber. Angelus (All) was one of the first to investigate these low-frequency oscillations later, Yount and Angelus (Yl) observed that the amplitude of the oscillations decreased and the frequency increased with increasing mean chamber pressure. They correlated... 

High-frequency pressure oscillations (10-100 Hz) related to time required for pressure wave propagation in system Low-frequency oscillations (-1 Hz) related to transit time of a mass-continuity wave Occurs close to film boiling... 

Sources of Physiological Noise. Despite the apparent importance of Hb, in the literature, the change in HbO is most widely reported and sometimes is the sole response reported. HbO is sometimes preferred due to its higher sensitivity to NIR based measurements than Hb. However, HbO measurements are not without disadvantages. There have been some studies (see for example [77] [22] [23] [47]) which indicate the presence of low frequency modulation ( 0.1 Hz) of both vascular (Hb, HbO) and metabolic (cytocrhome-c-oxidase) responses to visual stimuli with unknown origin. The cause of these low frequency oscillations are... 

H. Obrig, M. Neufang, R. Wenzel, M. Kohl, J. Steinbrink, K. Einhaupl, and A. Villringer. Spontaneous low frequency oscillations of cerebral hemodynamics and metabolism in human adults. Neuroimage, 12 623-639, 2000. 

Kailasanath, K., J.H. Gardner, J.P. Boris, and E.S. Oran. 1989. Acoustic-vortex interactions and low-frequency oscillations in axisymmetric combustors. J. Propulsion Power 5 165-71. 

Mahasenan, N., R. G. Watts, and H. Dowlatabadi, Low-Frequency Oscillations in Temperature-Proxy Records and Implications for Recent Climate Change, Geophys. Res. Lett, 24, 563-566 (1997). 

Low-frequency oscillation in a rocket motor depends on the pressure exponent of propellant burning rate and the free volume of the chamber. [ -7] when a double-base propellant composed of nc(0 510), ng( - 55), and dep(0.120), with pbsa(0.015) as a platonizing catalyst, bums in a strand burner, the burning rate characteristicsmay be divided into four zones, as shown in Fig. 13.14. The pressure exponent varies between the pressure zones n = 0.44 in zone I above 3.7 MPa, n= 1.1 in zone II between 3.7 MPa and 2.1 MPa, n = 0.77 in zone III between 2.1 MPa and 1.1 MPa, and n = 1.4 in zone IV below 1.1 MPa. 

Other mathematical transformations of the data allow for low-frequency oscillation data to be calculated from step change data, which is desirable since step change tests are generally quicker than low-frequency studies. This technique is outside the scope of these protocols, but interested readers are referred to Ferry (1980). 

Chamberlain and co-workers (17) have noted that no distinct peak occurs in the infrared absorption spectrum of water below 193 cm.-1. The Raman scattering does give rise to a peak near 60 cm."1 while slow neutron scattering give rise to a number of peaks, including a notable one at 56 cm.-1. This discrepancy implies that a significant number of low frequency oscillations may exist in liquid water with little if any infrared activity. 

Value of qeff, Q, and AP similar in terms of tendencies and scale of changes have been confirmed experimentally for polyethylene and polypropylene at low-frequency oscillations of the core (25 Hz) at amplitudes up to 22.3° 29 39 ... 

Dayhoff [50] suggested that one might measure a rest mass of photon by designing a low-frequency oscillator from an inductor-capacitor (LC) network. The expected frequency can be calculated from Maxwell s equations, and this may be used to give an effective wavelength for photons of that frequency. He claimed that one would have a measure of the dispersion relationship at low frequencies. Williams [51] calculated the effective capacitance of a spherical capacitor using Proca equations. This calculation can then be generalized to any capacitor with the result that a capacitor has an additional term that is quadratic in the area of the plates of the capacitor. However, this term is not exactly the one that Dayhoff referred to. But it seems to be a very close description of it. One can add two identical capacitors C in parallel and obtain the result... 

The asymptotic properties are determined by the low-frequency oscillators, with Co, —> 0. However, when we set 8 > 1 we make the weight of these frequencies smaller and smaller as their values become smaller and smaller. The choice 8 < 1, on the contrary, makes the slower oscillators more important than... 

However, these very low-frequency oscillations periodic in jB could be successfully explained by the standard model for field induced spin density waves [75, 76], see also Figs. 2.8 and 2.9 in Sect. 2.2.3. Although this effect is strongly related to the quasi-lD band structure and is by itself highly interesting no direct conclusions concerning the FS topology can be extracted from the measurements. 

Abstract Ionic liquids have shown to be excellent solvents for optical investigation of solutes. Transition metal complexes as well as /-element compounds have been studied in ionic liquids. Not only are neat and clean ionic liquids transparent in the NIR and visible region, but the absence of anions with low frequency oscillators such as C-H, N-H and O-H have been found to be favourable when it comes to photoluminescence and future applications can be envisioned. Of fundamental interest is the study of the absorption spectra of organic dyes dissolved in an ionic liquid as the many physicochemical parameters such as the dipolarity and polarizability of the ionic liquid and its hydrogen bond ability can be determined. 

There is an extra oscillation module, based on direct measurements of the capillary pressure, which operates from 1 to 150 Hz. There is also an additional accessory for the PAT1 for low-frequency oscillations. The range of surface and interfacial tension is 1 to 1000 mN/m with a resolution of 0.1 mN/m. The instrument allows for transient relaxation measurements, using perturbations such as ramp, square pulse, or trapezoidal area changes. 

High frequency oscillations correspond well with vagal tone, and respiratory sinus arrhythmia is a large determinant of the high frequency component (59). Sympathetic and parasympathetic tone contribute to low frequency oscillations the physiology underlying very low frequency and ultra-low frequency is not well understood (59). 

Which brings us to a related point. Modern computer-based data acquisition methods sometimes show a low-frequency oscillation superimposed on the signal. Say that we have a transient signal decaying with a time constant of 0.1 s, and sampled with a 20 ms. Any 60 Hz pick-up will then show as a 10 Hz oscillation, i.e., as the beat frequency between the sampling rate of 50 Hz and the 60 Hz pick-up. Fig. 7.4-9a illustrates this. 

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