Extinction curve

For the adiabatic condition in which RHL is suppressed, the flame response exhibits the conventional upper and middle branches of the characteristic ignition-extinction curve, with the upper branch representing the physically realistic solutions. It can be noted that the effective Le of this lean methane/air mixture is sub-unity. It can be seen from Figure 6.3.1 that, with increasing stretch rate, first increases owing to the nonequidiffusion effects (S > 0), and then decreases as the extinction state is approached, owing to incomplete reaction. Furthermore, is also expected to degenerate to the adiabatic flame temperature, when v = 0. 

Figure 6. C-shaped extinction curves illustrating the maximum temperature versus the inverse of the strain rate for the 8.4% and 9.3% (mole fraction) hydrogen-air fiames.

Figure 7. Extinction curve illustrating the maximum temperature versus the equivalence ratio for hydrogen-air flames with a strain rate of a = 1000...

The extinction curve of light which has passed through dust clouds tells us which particles are present in the cosmic dust ... 

Fig. 3.11 Interstellar dust particles cause the extinction of starlight by the selective scattering of certain light wavelengths. Far IR is on the left, far UV on the right. Satellite data suggest that the extinction curve consists of three components ...

In the region where water is weakly absorbing (between about 0.5 and 5 jum-1) the extinction curve for a 1.0 jum droplet has several features (1) a series of regularly spaced broad maxima and minima called the interference structure, which oscillates approximately about the value 2 (2) irregular fine... 

There are some notable differences apparent in Fig. 11.14 between the extinction curves for aluminum spheres and those for water droplets. For example, av is still constant for sufficiently small aluminum particles but the range of sizes is more restricted. The large peak is not an interference maximum aluminum is too absorbing for that. Rather it is the dominance of the magnetic dipole term bx in the series (4.62). Physically, this absorption arises from eddy current losses, which are strong when the particle size is near, but less than, the skin depth. At X = 0.1 jam the skin depth is less than the radius, so the interior of the particle is shielded from the field eddy current losses are confined to the vicinity of the surface and therefore the volume of absorbing material is reduced. 

It seems fairly obvious from inspection of Fig. 11.17 that the extinction curve for a collection of randomly oriented cylinders would be similar to that for a polydispersion of spheres. 

The extinction curves for magnesium oxide particles (Fig. 11.2) and aluminum particles (Fig. 11.4) show the dominance of surface modes. The strong extinction by MgO particles near 0.07 eV( - 17 ju.m) is a surface mode associated with lattice vibrations. Even more striking is the extinction feature in aluminum that dominates the ultraviolet region near 8 eV no corresponding feature exists in the bulk solid. Magnesium oxide and aluminum particles will be treated in more detail, both theoretically and experimentally, in this chapter. 

Comparison of measurements for particles dispersed on and in KBr is quite revealing. The extinction curve for particles on a KBr substrate shows a peak at approximately 400 cm-1, the transverse optical mode frequency for bulk MgO. This feature has been observed a number of times and it is discussed in some of the references already cited. Its explanation now appears to be the tendency of MgO cubes to link together into chains, which more closely... 

Stephens, J. R., 1980. Visible and ultraviolet (800-130 nm) extinction of vapor-condensed silicate, carbon, and silicon carbide smokes and the interstellar extinction curve, Astrophys. J., 23H, 450-461. 

The values of kinetic parameters (pre-exponential factors k0j and activation energies Ej of rate constants k and inhibition constant Kg) can for a particular catalyst be determined by weighted least squares method, Eq. (35), from the light-off or complete ignition-extinction curves measured in experiments with slowly varying one inlet gas variable—temperature or concentration of one component (cf., e.g., Ansell et al., 1996 Dubien et al., 1997 Dvorak et al., 1994 Kryl et al, 2005 Koci et al., 2004c, 2007b Pinkas et al., 1995). 

It is rather usual to express the extinction law as a function of the reddening factor. Following the parameterization proposed by Fitzpatrick and Massa (1986) and Fitzpatrick (1999) it is possible to reproduce the extinction curves in different lines of sight in the range 3-8 eV with the function ... 

In general, the photoabsorption cross section of individual and multishell fullerenes reproduce the behaviour of the interstellar extinction curve in the near UV. The theoretical spectra show a prominent absorption band around 5.7 eV which fits well... 

The comparison of the computed cross sections of fullerenes and buckyonions with observations of the UV bump for Ry = 3.1 allow an estimate of the number of these molecules in the diffuse interstellar medium. Let us describe the extinction curve as a + a2x + a37Tx) where 7Tx) is the theoretical cross section computed for each fullerene or buckyonion. Here we assume that indeed the extinction at the energy of the bump is the result of the fullerene plus silicate contributions. We obtain via a least squared fit the relative contribution of the two components (see Fig. 1.6b). The coefficients of this lineal component do not depend significantly on the particular fullerene under consideration taking typical values of a, 1.6 and a2 = 0.07 with a relative error of 20%. 

Among optical DIBs, the 4,430 A band is the strongest. This band is remarkably broad with a width (FWHM) of order a few tens of A. Krelowski and Walker (1987) assign the two broad DIBs 4,430 and 6,177 A to the same family and Krelowski et al. (1989) and McIntosh and Webster (1993) note that the carrier of this family appears to prefer denser interstellar gas than other carriers. There is also evidence of a positive correlation between the 4,430 A band and the strongest feature in the interstellar extinction curve, the UV bump at 2,175 A (Webster 1992 Nandy and Thompson 1975). It is therefore plausible that these two bands are produced by the same type of molecule. 

The cross section obtained for single fullerenes and buckyonions reproduce the behaviour of the interstellar medium UV extinction curve. A power-law size distribution n(R) R m with in = 3.5 1.0 for these molecules can explain the position and widths observed for the 2,175 A bump and, partly, the rise in the extinction curve at higher energies. We infer ISM densities of 0.2 and 0.1 ppm for small fullerenes and buckyonions (very similar to the densities measured in meteorites). If as expected the cosmic carbon abundance is close to the solar atmosphere value, individual fullerenes may lock up 20-25% of the total carbon in the diffuse interstellar space. 

Fig. 2.3 (a) The visible-band EEL spectra of unexposed (dashed line) and hydrogenated (solid line) Cm films shown in Fig. 2.2, spectra labeled (a) and (d), compared with the extinction curve of the variable component (open circles) detailed in Webster (1997). (b) The far-UV to near-IR EEL spectrum of the hydrogenated Cm film (solid line) in Fig. 2.2 (d) compared to the mean interstellar extinction curve (open circles). The vertical scales of the EEL spectra and extinction curves in Fig. 2a and b are incommensurable, and the EEL spectra are arbitrarily scaled to give reasonable qualitative agreement for comparison... 

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