Optical exponent

Clouds of Nonblack Particles The correction for nonblackness of the particles is complicated by multiple scatter of the radiation reflected by each particle. The emissivity . of a cloud of gray particles of individual surface emissivity 1 can be estimated by the use of Eq. (5-151), with its exponent multiplied by 1, if the optical thickness alv)L does not exceed about 2. Modified Eq. (5-151) would predict an approach of . to 1 as L 0°, an impossibihty in a scattering system the asymptotic value of . can be read from Fig. 5-14 as /, with albedo (0 given by particle-surface refleclance 1 — 1. Particles with a perimeter lying between 0.5 and 5 times the wavelength of interest can be handledwith difficulty by use of the Mie equations (see Hottel and Sarofim, op. cit., chaps. 12 and 13). 

To confirm the shape of the spherulites described by the Avrami exponent, polarized optical micrographs of the isothermal crystallized melt blends were taken, and are shown in Figure 20.26 [44],... 

It should be noted that scattering of light by particles can be measured using remote sensing techniques on satellites, from which such parameters as total aerosol optical thickness i.e., the exponent (bcxlL) in... 

The size distributions of the particles in cloud samples from three coral surface bursts and one silicate surface burst were determined by optical and electron microscopy. These distributions were approximately lognormal below about 3/x, but followed an inverse power law between 3 and ca. 60 or 70p. The exponent was not determined unequivocally, but it has a value between 3 and 4.5. Above 70fi the size frequency curve drops off rather sharply as a result of particles having been lost from the cloud by sedimentation. The effect of sedimentation was investigated theoretically. Correction factors to the size distribution were calculated as a function of particle size, and theoretical cutoff sizes were determined. The correction to the size frequency curve is less than 5% below about 70but it rises rather rapidly above this size. The corrections allow the correlation of the experimentally determined size distributions of the samples with those of the clouds, assuming cloud homogeneity. 

Thus, for most of the reactions of etr in water-alkaline matrices at reasonable values of the parameters v0, ae, and a, eqn. (7) of Chap. 5 describes with good accuracy the kinetics of the process over a broad interval of observation time. At the same time, for a small number of acceptors [Os02(OH)4 and Br03 ] in water-alkaline matrices the experimentally observed kinetic curves were found to deviate markedly from eqn. (7) of Chap. 5 or values of IV, were obtained that are unreasonable from the viewpoint of the theory of an elementary act of electron tunneling. The reasons for these deviations have not yet been finally made clear. It will only be noted here that they may be connected, for example, with possible errors in measuring the concentration of et r by the optical method in the presence of reaction products that can perhaps have absorption bands in the same spectral region as etr, with the simultaneous presence of several forms of an acceptor in vitreous solutions [104], as well as with deviations of the dependence of the probability VT(R) of tunneling on the distance, R, from a simple exponent of the form of eqn. (3) of Chap. 5 for the reasons discussed in Chap. 3. 

A similar expression may be written for optical absorption when the exponent in (II. 1) is sufficiently small. Substituting equation (11.15) in (11.16), we may obtain the generalized oscillator strength over some region AE by simple integration. 

The kinetics of transition from the liquid crystal to the fully ordered crystal of flexible, linear macromolecules was studied by Warner and Jaffe 38) on copolyesters of hydroxybenzoic acid, naphthalene dicarboxylic acid, isophthalic acid, and hydro-quinone. The analytical techniques were optical microscopy, calorimetry and wide angle X-ray diffraction. Despite the fact that massive structural rearrangements did not occur on crystallization, nucleation and growth followed the Avrami expression with an exponent of 2. The authors suggested a rod-like crystal growth. 

Figure 48. Optical Kerr effect data for salol (top). Dashed line t l decay (bottom). Interpolation of the data by the universal p-correlator of MCT fixed by the exponent parameter X — 0.73. Inset Corresponding rectification plot yielding a crossover temperature 252 K (compiled from Ref. 70.)...

In the macroscopic theory of electromagnetic waves [3], the evanescent wave (EW) arises from the requirement that the boundary conditions be satisfied at all points on the flat (ideal) interface between two materials of different optical properties that are uniform throughout the materials. The spatial functions in the exponents describing propagation of plane waves in each material are set equal... 

Another important aerosol optical property is column aerosol extinction, the vertical integral of the aerosol extinction coefficient, again a function of wavelength. This quantity is often also denoted aerosol optical thickness (AOT) or aerosol optical depth. The wavelength dependence of AOT is also often expressed as an Angstrom exponent. 

Figure 17 also shows the Angstrom exponent (cf. Section 4.04.2) evaluated from the dependence of aerosol optical thickness, r p, on wavelength A SiS a = — d log Tgp/d log A. A greater Angstrom... 

Here T is the temperature of acoustic phonons (thermostat), T is the temperature of optical phonons (284), the anharmonicity constant k is much less than 1, and flq is the frequency of acoustic phonons it is possible to assume ilq = (10 2 to 10 1)flDebye. The coupling between the optical and acoustic phonons is strongest near f>Debye 1 and because of this, for sufficiently large anharmonicity, k > 10 2 even at T = T", the last exponential multiplier can be approximated by the exponent below, with the dispersion being neglected ... 

Values between 0.8 and 1.8 are used for the exponent a / varies from /3 = 0 (pure atmosphere) via 0.1 (clear) and 0.2 (cloudy) to 0.3 (very murky atmosphere), see for this [5.34]. The relative optical aerosol mass mfia is generally unknown because of the large fluctuations in the size, distribution and composition of aerosol particles. This is why mrjL from (5.114) is often... 

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