Narrowband model

A comparison of the results of the predictions of Table 5-5 with values obtained via the integration of the spectral results calculated from the narrowband model in RADCAL is provided in Fig. 5-22. Here calculations are shown for pcL =pwL = 0.12 atm m and a gas temperature of 1500 K. The RADCAL pr ictions are 20 percent higher than the measurements at low values of pL and are 5 percent higher at the lai e values of pL. An extensive comparison of different sources of emissivity data shows that disparities up to 20 percent are to be expected at the current time [Lallemant, N., Sayre, A., and Weber, R., Prog. Energy Combust. Sci., 22, 543-574, (19 )]. However, smaller errors result for the range of the total emissivity measurements presented in the Hottel emissivity tables. This is demonstrated in Example 11. 

Narrowband Models. Given that detailed spectral calculations with wavelength resolution on the order of 10"3 pm is neither computationally efficient nor justifiable for many engineering applications, it is better to develop more affordable models. A close look at the broadened absorption lines depicts that several of them are positioned very close to each other and may overlap, especially for the vibration-rotation transitions of diatomic and polyatomic molecules. The absorption coefficients of individual lines can be added to find the absorption coefficient of the narrowband ... 

Two of the best-known models used for this purpose are the Elsasser and the statistical Goody models, both of which employ the Lorenz profile for description of individual line shapes. These models give very accurate predictions over a bandwidth of approximately 50 cm"1, which is considered narrow for most practical purposes. (At X = 1 pm, this bandwidth translates to about AX = 0.05 pm.) Because of this, the model is called the narrowband model. Although this technique is significantly simpler than the line-by-line models, it still requires an extensive database about the species considered and significant computational effort. Such a detailed model can be considered useful only if the species concentration distribution is known very accurately, which is usually not the case. 

Detailed discussions of narrowband models were given by Tien [127], Ludwig et al. [128], Edwards [129], and Tiwari [130]. The discussion of these approaches can also be found in standard texts [1,2,3]. 

Wideband Models. The narrowband models introduce significant simplification over the line-by-line calculations however, the accurate predictions depend not only on the rigor of the model but also on the accuracy of input data, such as the local temperature, the temperature profile, the partial pressures of the radiating gases, and so on. In most practical systems, these data are not available with good accuracy. This suggests that even simpler approximations may be more appropriate for calculation of gas properties in practical systems. 

SPIN SUSCEPTIBILITIES OF ORGANIC SYSTEMS ON A NARROWBAND MODEL. 

Marques and Almeida, 1988] Marques, J. and Almeida, L. (1988). Sinusoidal modeling of speech Representation of unvoiced sounds with narrowband basis functions. 

Fig. 5.10 CARS intensity change at 1,583 cm in SWNTs as a function of delay time between the broadband pump and narrowband probe. The solid curve is obtained from a model that assumes instantaneous generation of hot G -phonons, but takes into account the finite instrumental time resolution and the exponential dephasing [32]...

Chambers and coworkers [72-74] also explored the properties of semiconductive sheets of polypyrrole treated paper and cloth, which they characterize as a parallel RC circuit. They too report that the capacitive part of the complex impedance of the sheets depends on the morphology of the poly pyrrole coating. Measured reflectivity plots for Salisbury screen (narrowband) and Jaumann (broadband) absorbers fabricated from sheets of polypyrrole-treated material are also presented in their article. The measured results agree well with their model calculations, indicating the potential utility of conductive polymer-treated fabrics in radar-absorbing structures. 

Since a cometary coma is nearly transparent at radio wavelengths, radar is much more capable of unambiguous detection of a cometary nucleus than are optical and infrared methods, and radar observations of several comets (see Table I) have provided useful constraints on nuclear dimensions. The radar signature of one particular comet (IRAS-Araki-Alcock, which came within 0.03 AU of Earth in May 1983) revolutionized our concepts of the physical nature of these intriguing objects. Echoes obtained at both Arecibo (Fig. 26) and Goldstone have a narrowband component from the nucleus as well as a much weaker broadband component from large particles ejected mostly from the sunlit side of the nucleus. Models of the... 

Figure 2.20 Transmittance curves for narrowband spectral filter, (a) Actual, (b) Model.

---