High Frequency Case

The most common digital microfluidic fluid actuation techniques utilize a combination of strategically placed electrodes and changes in contact angle induced by one of two principles electrowetting on dielectric (EWOD) or dielectrophoresis (DEP). EWOD and DEP can be considered as the low- and high-frequency cases, respectively, of the application of a sufficient electric field to polarizable liquids along the correct axes.7... 

To make connection between the spectra and tire ET process clearer, we note a simple model for tire lineshape that includes a classical and a high-frequency degree of freedom. In tliis case tire overall lineshape is... 

In this paper, we discuss semi-implicit/implicit integration methods for highly oscillatory Hamiltonian systems. Such systems arise, for example, in molecular dynamics [1] and in the finite dimensional truncation of Hamiltonian partial differential equations. Classical discretization methods, such as the Verlet method [19], require step-sizes k smaller than the period e of the fast oscillations. Then these methods find pointwise accurate approximate solutions. But the time-step restriction implies an enormous computational burden. Furthermore, in many cases the high-frequency responses are of little or no interest. Consequently, various researchers have considered the use of scini-implicit/implicit methods, e.g. [6, 11, 9, 16, 18, 12, 13, 8, 17, 3]. 

It is advisable in most of these cases to use accelerometers. Displacement probes will not give the high-frequency signals and velocity probes because their mechanical design is very directional and prone to deterioration. Figure 10-64 shows me signal from the various types of probes. 

Commercial dryers differ fundamentally by the methods of heat transfer employed (see classification of diyers, Fig. 12-45). These industrial-diyer operations may utihze heat transfer by convection, conduction, radiation, or a combination of these. In each case, however, heat must flow to the outer surface and then into the interior of the solid. The single exception is dielectric and microwave diying, in which high-frequency electricity generates heat internally and produces a high temperature within the material and on its surface. 

Note that localized corrosion having the appearance illustrated in Figs. 12.18 through 12.20 could be associated with brief exposure to a strong acid. In this case, however, all available information indicated that the tubes had never been exposed to an acid of any type. Cavitation was caused by high-frequency vibration of the tubes. The vibration apparently induced a threshold cavitation intensity such that rough or irregular surfaces produced cavitation bubbles, and smooth internal surfaces did not. 

While being very similar in the general description, the RLT and electron-transfer processes differ in the vibration types they involve. In the first case, those are the high-frequency intramolecular modes, while in the second case the major role is played by the continuous spectrum of polarization phonons in condensed 3D media [Dogonadze and Kuznetsov 1975]. The localization effects mentioned in the previous section, connected with the low-frequency part of the phonon spectrum, still do not show up in electron-transfer reactions because of the asymmetry of the potential. 

As a simple illustration of this technique consider the case of high frequency co, viz. co, 5co,/5t 1 for the instanton trajectory (but co, is still small compared to the total barrier... 

The adiabatic approximation in the form (5.17) or (5.19) allows one to eliminate the high-frequency modes and to concentrate only on the low-frequency motion. The most frequent particular case of adiabatic approximation is the vibrationally adiabatic potential... 

When both vibrations have high frequencies, Wa, coq, the transition proceeds along the MEP (curve 1). In the opposite case of low frequencies, rUa.s the tunneling occurs in the barrier, lowered and reduced by the symmetrically coupled vibration q, so that the position of the antisymmetrically coupled oscillator shifts through a shorter distance, than that in the absence of coupling to qs (curve 2). The cases (0 (Oq, < (Oo, and Ws Wo, (Oq, characterized by combined trajectories (sudden limit for one vibration and adiabatic for the other) are also presented in this picture. 

Charts are available to convert from one type of measurement to another as shown in Figure 19-13. Many of these charts also show approximate vibration limits. The charts demonstrate the independence of velocity measurements relative to frequency, except at very low and very high frequencies where the amplitude limits are constant throughout the operating speed range. These limits are approximate—the type of machinery, casing, foundation, and bearings must be considered to determine final vibration limits. 

The purpose of an input conducted EMI filter is to keep the high-frequency conducted noise inside the case. The main noise source is the switching power supply. Filtering on any of the input/output (I/O) lines is also important to keep noise from any internal circuit, like microprocessors, inside the case. 

Characterized by high frequency response, accelerometers are compact and rugged, ideal for mounting on machinery cases, foundations, piping, etc. Applications to gear trains and rolling element bearings are typical. 

Whether or not a polymer is rubbery or glass-like depends on the relative values of t and v. If t is much less than v, the orientation time, then in the time available little deformation occurs and the rubber behaves like a solid. This is the case in tests normally carried out with a material such as polystyrene at room temperature where the orientation time has a large value, much greater than the usual time scale of an experiment. On the other hand if t is much greater than there will be time for deformation and the material will be rubbery, as is normally the case with tests carried out on natural rubber at room temperature. It is, however, vital to note the dependence on the time scale of the experiment. Thus a material which shows rubbery behaviour in normal tensile tests could appear to be quite stiff if it were subjected to very high frequency vibrational stresses. 

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