Chord length, average

Let us introduce the number-average chord length ( P) hy For one crystal (of convex shape) it is defined by its volume divided by the shade it throws when illuminated in direction (h). Then a series expansion... 

Determination of the Average Chord Length. The average chord length p can be determined even from scattering data that are not calibrated. For this purpose Ap is determined from Porod s law in relative units and k is computed by integration of the scattering curve. Finally ip is found from Eq. (8.43). 

Check. Do the moments reflect the requirement that gsi is normalized to 1 and that the average chord length of a sphere with unit diameter is... 

Fig. 5 Theoretical chord length distribution for single crystal from orientation averaging.

In fig. 1, the mean chord length of pores Ip as obtained by SAXS/TPM is plotted versus the average pore diameter Dave derived from N2-adsorption according to eq. (1). The data points are located close to the ideal line Ip = Dave- Fig. 1 also shows the corre-... 

The ratio V/S has dimension of length and can be regarded as the length scale that characterizes the structure. To elaborate on this, let us consider a line, as in Figure 5.11, that crosses the system in an arbitrary direction and cuts out alternating chords l and l2 from the two phases. The average chord lengths (/i) and (l2) are related to V/S by... 

The second method involves the calculation of the so called average chord length (62),... 

To illustrate this point, one must look at the derivative of drag with respect to chord length. We wish to treat velocity, area, and lift coefficient as constants, so the span must be a function of aspect ratio. Using the definition for aspect ratio and defining the average chord length c =A/b, we obtain... 

The DancofF correction in the rational approximation is thus equivalent to a Active reduction of the surface area of the lumps. This is consistent with the alternative interpretation of the Dancofif correction as the fractional reduction of the flux into an absorber lump due to the shadowing by the adjacent ones. These considerations suggest that a somewhat better approximation than Equation (7.11) will be obtained by simply introducing this surface correction into the average chord length, i.e., by equating... 

The correlation length m in (21.10) is the geometrical average over the chord length, i.e., the mean extensions of the solid s and the void phase... 

This notwithstanding, the variance over the average path traveled by particles on the free surface (some fraction over the chord length, Lc) might be included in the geometric derivations from an operational standpoint (McTait et al., 1995). 

If radiation from infinitely removed sources is allowed to pass through a sphere of radius 72, it may be shown directly that the average chord length of radiation path in the sphere is given by 6 = 472. 

The average chord length s through V may then be defined by... 

The result (7.229) has been used in evaluating the general relation for (7.228). For this case the average chord length is shown from (7.230) to be 5 = 2a. 

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