Spheroids calculated

Figure 13.8 Calculated and measured scattering diagrams spheroid calculations from Asano and Sato (1980) microwave measurements from Zerull et al. (1980) quartz measurements from Holland and Gagne (1970) and talc measurements from Holland and Draper (1967).

Figure 4.4 Monomer separation energies, Dj yv (see Eq. (42)), from singly cationic Nayv clusters in the range 5 < N < 39. Open squares Experimental measurements from Ref. [76]. Solid dots (bottom panel) theoretical results derived from the SE-SCM method in the case of triaxial deformations. Solid squares (top panel) theoretical results according to the KS-LDA spheroidal calculations of Ref. [77]...

FIG. 33 The normalized monolayer mass of prolate spheroids calculated from Eqs. (194a) and... 

The most conunon choice for a reference system is one with hard cores (e.g. hard spheres or hard spheroidal particles) whose equilibrium properties are necessarily independent of temperature. Although exact results are lacking in tluee dimensions, excellent approximations for the free energy and pair correlation fiinctions of hard spheres are now available to make the calculations feasible. 

The wetted area of the tank or storage vessel shall be calculated as follows For spheres and spheroids, the wetted area is equal to 55 percent of the total surface area or the surface area to a height of 30 feet (9.14 meters), whichever is greater. For horizontal tanks, the wetted area is equal to 75 percent of the total surface area For vertical tanks, the wetted area is equal to the total surface area of the shell within a maximum height of 30 feet (9,14 meters) above grade. 

In a series of papers, Chhabra (1995), Tripathi et al. (1994), and Tripathi and Chhabra (1995) presented the results of numerical calculations for the drag on spheroidal particles in a power law fluid in terms of CD = fn(tVRe, ). Darby (1996) analyzed these results and showed that this function can be expressed in a form equivalent to the Dallavalle equation, which applies over the entire range of n and tVRe as given by Chhabra. This equation is... 

To prevent failure due to the disengagement of the pane out of the frame, bite or edge engagement depths are required. They are based upon the assumption that the plate will distort as a spheroid surface. At the maximum design center deflection of 15 pane thicknesses, this conservatively approximates the deflection shape function. To be conservative, a 0.5-inch safety margin is added to all calculations. 

Fig. 1. Schematic overview of the tumor spheroid-based migration assay. Tumor spheroids (TS) are transferred from their cuiture vessei or piate into a 96-weii fiat-bottomed migration piate pre-coated with an extraceiiuiar matrix (ECM) protein of choice (in this case, geiatin). Digital images of the spheroids are then captured at t=0 and once every 24 h for a period of up to 72 h, exemplified here by CAL spheroids. Image analysis software is used to calculate the spheroid size and extent of migration. Scale bar=100 p.m.

It would seem that no theoretical calculations have been made for shapes other than spheroids. In addition, no experimental measurements have been reported for shapes other than spheres or circular cylinders in creeping flow. Equation (4-60) is useful for cases in which Pe is small. 

The time variation of concentration at the center and at the foci of prolate spheroids has been calculated for negligible external resistance, Bi oo (H2). These appear to be the only calculations for shapes other than those mentioned above. 

Fig. 6.11 Correlations and numerical calculations for heat transfer to spheroids and disks with Pr = 0.7.

Equations (11-15) to (11-17) correspond to the general results for spheroids given in Table 11.1. The velocity and displacement can be calculated as functions of time, either by direct numerical integration (Kl) of Eq. (11-16) with... 

A few particles, such as spores, seem to be rather well approximated by spheroids, and there are many examples of elongated particles which may fairly well be described as infinite cylinders. Our next step toward understanding extinction by nonspherical particles is to consider calculations for these two shapes. To a limited extent this has already been done spheroids small compared with the wavelength in Chapter 5 and normally illuminated cylinders in Chapter 8. We remove these restrictions in this section measurements are presented in the following section. Because calculations for these shapes are more difficult than for spheres, we shall rely heavily on those of others. 

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