Rayleigh coefficient

Day and France found that the addition of lead fluoride to ZBLAN fibers caused, however, a marked increase of the Rayleigh coefficient (A = 1.12 dB km-1 nm4) [20], [21], Very likely, this is due to an increase of the concentration of submicron crystallites related to the lower stability of ZBLAN-Pb glass, as compared to pure ZBLAN. 

An accurate representation of wave drag is essential for chemical modeling because chemical species are advected by the mean meridional circulation and are also transported by the irreversible mixing which accompanies wave drag. Modeling studies (e.g., Schoeberl and Strobel, 1978 Holton and Wehrbein, 1980) sometimes use a Rayleigh coefficient to crudely parameterize the effects of wave dissipation. In this case, a deceleration is assumed to act linearly on u, and is substituted for the wave drag term Gu as follows ... 

Independent prior distributions for the parameters are taken as follows a Gaussian distribution for the natural frequencies with mean 0.5(2m - 1) Hz and a coefficient of variation 10% for the mth mode. Furthermore, the Rayleigh coefficients, the modal participation factor and the spectral intensity of the prediction error are assumed to be uniformly distributed over a sufficiently wide range to let the likelihood function determine their values. Note that the ranges of these distributions do not affect the model class selection results since they influence all modal models in the same way. Therefore, the computation of the Ockham factor and plausibility will exclude the prior PDF of these parameters but the one for the modal frequencies will still be included. 

The traditionally adopted procedures for the calibration of the Rayleigh coefficients (e.g., Hudson et al. 1994) can lead to large... 

The Rayleigh scattering extinction coefficient for particle-free air is 0.012 km for "green" light (y = 0.05 /rm) at sea level (4). This permits a visual range of —320 km. The particle-free, or Rayleigh scattering, case represents the best visibility possible with the current atmosphere on earth. 

The same information may be obtained from purely rotational far infrared spectroscopy (FIR) and depolarized Rayleigh spectra. Dielectric relaxation measurements are also used for the same goal, most successfully in combination with far-infrared data. The absorption coefficient of a periodic electric field... 

Lord Rayleigh [310] modeled transport in a homogeneous suspension of spheres placed in a square lattice. In terms of diffusion coefficients, his solution was... 

Van der Waals further finds a relation between the temperature coefficient of surface tension and the molecular surface energy which is in substantial agreement with the Eotvos-Ramsay-Shields formula (see Chapter V.). He also arrives at a value for the thickness of the transition layer which is of the order of magnitude of the molecular radius, as deduced from the kinetic theory, and accounts qualitatively for the optical effects described on p. 33. Finally, it should be mentioned that Van der Waals theory leads directly to the conclusion that the existence of a transition layer at the boundary of two media reduces the surface tension, i.e., makes it smaller than it would be if the transition were abrupt—a result obtained independently by Lord Rayleigh. 

Such columns can be used for the CEC separation of small neutral compounds. The problem with this type of open-tubular column, however, is the low efficiency obtained due to the small diffusion coefficients of the analytes in the polymeric stationary phase, and the heterogeneous film structure caused by Rayleigh instability. 

Dunham [5] derived these expressions Y ((t)e,Be,a0, necessarily manually, through a JBKW procedure, which he claimed to make more general [4] than what had appeared in previous literature. Dunham reported expressions F containing coefficients aj up to a, and Sandeman [19] and Woolley [20] extended manually these results according to a roughly analogous procedure. Kilpatrick [21] applied perturbation theory in successive orders to derive expressions for 1, and Bouanich [22] applied Rayleigh-Ritz perturbation theory for solution of... 

Stimulated Rayleigh scattering from localised thermal fluctuations in gases 258) and liquids 259) has been reported with measurements of the line shifts, thresholds and critical absorption coefficients. 

The compositional relations discussed above are explained by Rayleigh s distillation process (Rayleigh, 1896), choosing a suitable partition coefficient for the component of interest—i.e., for component An, we can write... 

During Rayleigh s crystallization process (formation of crystals with equilibrium limited to the solid/liquid interface), the relative concentration of a trace element in liquid Q with respect to the initial concentration in system Cq is described by the Doerner-Hoskins equation (Doerner and Hoskins, 1925 we will omit hereafter subscripts in the indicization of coefficients, for the sake of simplicity) ... 

Equation 10.93 clearly shows that, if apparent partition coefficient is adopted instead of conventional partition coefficient K actually valid at the solid/liquid interface to model Rayleigh s crystallization, errors arise whose magnitudes increase the more K differs from 1 and the longer the process advances. This is clearly shown in figure 10.15, in which fractional differences — K )IK are plotted as functions of T for various values of K . 

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