Effective core half-width

Fig. 10-4 The lateral shift z, of the path in (a) is equivalent to an effective core half width in (b), for the step-profile planar waveguide.

When V is small, only low-order modes can propagate. The term in s in Eq. (36-29) is retained to account for diffraction effects, as discussed in Section 10-4, and the complete expression for T in Eq. (36-30) is now required. However, we can still give a simple physical interpretation. We recall from Section 10-6 that the effect of the lateral shift is to increase the ray half-period from Zp to Zp.+ s, corresponding to the addition ST to the path in Fig. 36-3(b). If we introduce an effective core half-width, Pefr>... 

Inserting protons at - 0.10 V for 3 min (the position of the first redox peak in Fig. 1) turns the electrode green. The effect of proton insertion is clearly seen in the photoelectron spectrum, a low binding energy shoulder appears in the W 4f core level region (Fig. 2a). The new state, referred to as is shifted - 1.27 eV relative to and has a relative intensity of 0.22 with a full width half maximum (FWHM) of 0.91 eV. We also observe that the state increases in FWHM to 1.27 eV. The intensity of the state in the bandgap region has also increased. 

The time for diffusion (without reaction) to increase the average concentration within a fiber wall to one-half of its ultimate value, with the fiber treated as a fully collapsed slab of thickness equal to two fiber wall widths, gives a 0.19. For a fiber wall thickness of a = 4.0 x 10 m and an effective diffusion coefficient of D = 1.3 X 10 m /s, Xd = 0.0023 s. The ozonation of pulp fibers follows a shrinking core mechanism, limited by the rate of ozone diffusion through the fiber wall. Exposed fibers are completely penetrated and reacted in seconds under typical operating conditions (Bennington et al., 1999). 

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