Homogeneous damping

The homogeneous rate of dissipation of acoustic energy per unit volume by viscosity in the gas is of the order of fi V /(a/coy, since a/cu is the wavelength that determines the velocity gradient associated with the sound field. From this estimate and equation (39) we see that the ratio of the homogeneous rate of viscous dissipation to the rate of viscous dissipation at the walls is roughly Here pUpa) is on the 

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The return to equilibrium of a polarized region is quite different in the Debye and Lorentz models. Suppose that a material composed of Lorentz oscillators is electrically polarized and the static electric field is suddenly removed. The charges equilibrate by executing damped harmonic motion about their equilibrium positions. This can be seen by setting the right side of (9.3) equal to zero and solving the homogeneous differential equation with the initial conditions x = x0 and x = 0 at t = 0 the result is the damped harmonic oscillator equation ... 

It is difficult to specify accuracy in this experiment. One reason is that there may be sampling effects, i.e., wide variability in the samples used. Consequently, the sample should be homogeneous and representative. There is a strong dependence of the modulus and damping behavior on molecular and structural parameters. Entrapped air/gas may affect the results obtained using powder or pellet samples. 

In the cases of both homogeneous (undamped) and inhomogeneous (damped) incident waves, the transmitted nontransverse EMS waves become confined to a narrow layer at the vacuum side of the interface, and no energy is extracted from the reflection process. The inclusion of EMS waves in a dissipation-free case is, of course, unnecessary and questionable. 

To achieve the instability of homogeneous broadened line lasers, a satisfaction of much more difficult conditions is required large gain and the so-called bad-cavity properties. This special regime for damping constants and mode intensity is fulfilled in the far-infrared lasers [36]. In 1985 Weiss et al. [37,38] experimentally found a period doubling route to chaos in the NH3 laser. Further experimental investigation of chaotic dynamics in such lasers was reported later [39]. 

With the aid of the two-color Laser-Doppler-Anemometry (LDA), Bewersdorff was able to measure the axial and the radial turbulence intensities simultaneously and also the Reynolds shear stresses. The injection of polymer results in a damping of both intensities in the region of their maxima. In his Reynolds shear stress measurements he showed that the polymer injection results in a drastic damping, and the stress maximum is shifted towards the center of the pipe. In a homogeneous polymer solution the maximum of the Reynolds shear stress remains in the same position-as for water. Only in the region of the buffer zone are the shear stresses reduced. 

Nucleotidases have been studied in liver from various species and activity has been identified in lysosomes, cytoplasmic supernatants and plasma membrane preparations. Arsenis and Touster (31) have purified a 5 -nucleotidase from rat liver lysosomes to apparent homogeneity. The enzyme is unusual in that it hydrolyzes 2 -, 3 -, and 5 -mononucleotides equally well with preference for 5 -dAMP. It also hydrolyzes FMN, p-nitrophenyl phosphate, and /J-glycerol phosphate, but not inorganic pyrophosphate or bis(p-nitrophenyl) phosphate. Unlike the 5 -nucleotidases described thus far, divalent cations such as Co2+, Mn2+, and Mg2+ have no activating effect, but EDTA is inhibitory. In spite of the broad substrate specificity kinetic experiments indicate that a single enzyme is involved. Because of its broad substrate specificity it has been suggested (SI) that it may play a key role in lysosomal catabolism of nucleic acids. 

Mixtures of chemically homogeneous methyl methacrylate— n-butyl acrylate copolymers appear homogeneous optically (clear) and in torsional oscillation experiments (one damping maximum) for A MM A 10-25 mole %. There is no... 

Since the frequency is large, the distance over which a concentration wave proceeds is small, then exp (- / 3) can be considered as equal to one and the velocity modulation being rapidly damped close to the wall, the convective term can be disregarded in the homogeneous part of Eq. (3-2) which becomes ... 

Ignoring the damping term in Eq. (17), the resonance is described by dM/dt = KMxHeff). For homogeneously magnetized ellipsoids of revolution, the effective field is equal to the applied field H = H ez plus the anisotropy field Ha, and the resonance problem is solved by the diagonalization of a 2x2 matrix. This uniform or ferromagnetic resonance (FMR) yields resonance frequencies determined by [17]... 

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