Davies approximation

One of the equations commonly used to estimate values of y is the Davies approximation (Stumm and Morgan, 1996) ... 

Many optical particle sizing instruments and particle characterization methods are based on scattering by particles illuminated with laser beams. A laser beam has a Gaussian intensity distribution and the often used appellation Gaussian beam appears justified. A mathematical description of a Gaussian beam relies on Davis approximations [45]. An nth Davis beam corresponds to the first n terms in the series expansion of the exact solution to the Maxwell equations in power of the beam parameter s,... 

Ankyrin deficiency, amounting to a reduction of approximately 50%, has been found in some patients with the dominant type of HS. A primary defect in ankyrin almost certainly reduces the assembly of spectrin into the membrane skeleton of the red blood cell (Davies and Lux, 1989). 

In Figure 10, we present flow velocity predictions of the high density approximation, Equations 32 - 33, 38 and 39, of Davis extension of Enskog s theory to flow In strongly Inhomogeneous fluids (1 L). The velocity profile predicted In this way Is also plotted In Figure 10. The predicted profile, the simulated profile, and the profile predicted from the LADM are quite similar. 

Blaha, M. Davis, J. Electron Ionization Cross Sections in the Distorted Wave Approximation. N.R.L. Memorandum Report 4245, Naval Research Laboratory, Washington, DC, 1980. 

In this formulation, the resolution is assumed to be independent of angle between zones. This assumption was checked by Schure (1997) as the equation for resolution as a function of angle between the two zones was previously available (Shi and Davis, 1993). This analysis shows that for a number of cases, the error is approximately less than 10% when using the Euclidean norm of resolutions, as shown in Fig. 2.3. 

The more incisive calculation of Springett, et al., (1968) allows the trapped electron wave function to penetrate into the liquid a little, which results in a somewhat modified criterion often quoted as 47r/)y/V02< 0.047 for the stability of the trapped electron. It should be noted that this criterion is also approximate. It predicts correctly the stability of quasi-free electrons in LRGs and the stability of trapped electrons in liquid 3He, 4He, H2, and D2, but not so correctly the stability of delocalized electrons in liquid hydrocarbons (Jortner, 1970). The computed cavity radii are 1.7 nm in 4He at 3 K, 1.1 nm in H2 at 19 K, and 0.75 nm in Ne at 25 K (Davis and Brown, 1975). The calculated cavity radius in liquid He agrees well with the experimental value obtained from mobility measurements using the Stokes equation p = eMriRr], with perfect slip condition, where TJ is liquid viscosity (see Jortner, 1970). Stokes equation is based on fluid dynamics. It predicts the constancy of the product Jit rj, which apparently holds for liquid He but is not expected to be true in general. 

Activity coefficients in the aqueous phase, yiw, of neutral molecules are set equal to one because of the zero charge, and under the assumption that the activity coefficient of the infinitely diluted solution equals the actual activity coefficient. The activity coefficients of the charged species can be approximated with the Davies equation ... 

In a laboratory scale dehydrocyclization reaction using a dual-function catalyst, Davis (8) reported that the aromatic products were o-xylene, /w-xylene and ethylbenzene in approximately equal amounts (ca. 20-30% each) and p-xylene (ca, 15%). The formation of these was assumed to be from a direct 1,6-ring closure, as sketched in the following two diagrams ... 

In our calculations we will first discuss our results starting with both the 2-and 3- octyl cations (the 4- octyl cation cannot form a 1,6-p-H-structure). The n-octane conversion to aromatics, as described by Davis (8), is a good test of our proposed mechanisms, for several reasons (1) his experimental observation would require the formation of approximately equal amounts of 1,2-dimethylcyclohexane (o-xylene) and ethylcyclohexane (ethylbenzene), even though in our mechanism the structure of the needed 1,6-p-H cation intermediates are quite different, and (2) the formation of to- and p-xylene requires a prior isomerization of n-octane to 2- and 3- methylheptane, and this must be a faster reaction than the dehydrocyclization (or at least competitive with it). If our mechanisms are valid, we should be able to reproduce some aspects of the above results. 

In Canada, where endrin was registered for use from 1954 to 1990, a dietary intake study estimated the adult annual intake of endrin at approximately 32 pg (0.001 pg/kg [ppb] body weight/day) (Davies 1988). 

Another approximation we will make is that 1 — S2 1, since S is usually considered to be small for oxide surfaces. According to the table of values obtained by Davis et al. (5), S is at most equal to 3 x 10 3. Other authors tend to find somewhat higher values,... 

Descriptions of field studies of power-plant stack plumes were given by Davis et al. The ozone concentration appears to be lower in regions of high sulfur dioxide content. At 32 km downwind from the stacks, it was claimed that the ozone concentration in the plume (now 11 km wide) is higher than the ambient concentration ( 0.08 ppm) by approximately 0.02 ppm. Simultaneous measurements of nitric oxide and nitrogen dioxide were integrated across the plume. Values of the ratio of nitric... 

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