Without scattering

1 Models with one isothermal layer a. Without scattering 

The first model considered consists of a nonscattering gas layer at constant pressure and temperature adjacent to a solid surface of unit emissivity. This model is illustrated in Fig. 4.1.1. We consider the absorbing gas to have only one spectral line. Such a line is not perfectly monochromatic, but, as discussed in Section 3.6, is broadened by various effects. In this section we assume that the gas pressure is sufficiently high and the temperature sufficiently low so that collisional broadening 

According to our postulate, scattering does not occur in the layer. If we assume a surface emissivity of unity, the outgoing monochromatic radiation field is given by Eq. (2.4.4), with n = 1. Thus tq = 0 and 

As ri(v)/ increases, 7v(0, /x) increases if the temperature difference 7a — 7s is positive, or decreases if the difference is negative. Thus spectral lines are seen either in emission or absorption depending on whether 7a 7s or Ta Ts. If 7a = 7s the line disappears only the blackbody continuum Bv(Ta) is seen. 

If the optical path length at the line center, ri(vo)/ti, is sufficiently small, the line is relatively weak and the area under the curve (defined relative to the continuum) 

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FIGURE 3.9 A typical Q8+ ion in water. Secondary electron tracks (without scattering) are shaded the core region is dotted. Figures in parentheses denote ejected electron energy, classical ejection angle, and estimated range (qualitative). Reproduced from Mozumder (1969), by permission of John Wiley Sons, Inc. ... 

In principle, metallic CNTs are ballistic conductors (i.e. electrons move without scattering), which means that the resistance is independent of the nanotube length. In MWCNTs, the conductance is defined by the outermost layer [53]. In general, the ballistic nature of CNTs is affected by the presence of structural defects [54]. Still, experimental values for electric current density are exceptionally high, i.e. up to 4 ... 

Figure 11.28—Effect of light scattering on a spectrum recorded in absorbance and on its derivative spectrum. This figure shows a comparison of the derivative spectra corresponding to the spectrum A of a compound in solution without scattering and to the same spectrum B in the presence of scattering. It can be seen that the effect of scattering is in the order of 10% in absorbance units but only about 1% in the derivative spectrum (modelled spectra).

Each current I may be expressed as a product of probabilities scattering at sltes And traveling without scattering between... 

Under the conditions of scattering the phase velocity of capillary waves will deviate from the value for the medium without scatterers. Therefore, it is natural to introduce an effective wave number K for the former case and to choose the following trial functions for the coefficients C ... 

Fig. 9. Diagrams of the second-order process amplitudes (a) without scattering in the intermediate state with single and double scattering in the intermediate state, respectively.

Figure 9 The distribution function atZo = 3 cm within the one-dimensional photobioreactor shown in Fig. 6 where =p = Q, for collimated normal incidence dj — O). (A) Without scattering. (B) With scattering. The results were obtained with the Monte Carlo method (MCM, see Section 4).

Worth noting that this classical description (sometimes known as Drude s tiieory) predicts that for ballistic trajectories of electrons in resistor, i.e., for movement without scattering with the resistor s matrix, the average time between two successive scatterings becomes infinity, thus predicting infinity conductivity, zero resistivity, and thus no resistance recorded ... 

Baerends et al. were the first to show how to do accurate Xa calculations without scattered waves and... 

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