Dimensionless absorption functions

Dressman et al. [13] developed a dimensionless absorption potential (AP) model based on the concept that the fraction of dose absorbed, assuming negligible luminal instability and first-pass metabolism, is a function of drug lipophilicity (log P0/w), solubility (Sw), and dose (D), as defined in Eq. 2.7. 

Fig. 8. Dimensionless absorption flux as function of reaction rate constant for mass transfer with bimolecular chemical reaction in case all K,j equal 1 x 10 m/s except K g = 1 X 10" m/s). The kinetics are given by eqs (38a)-(38c).

We account for only the torque proportional to the string s expansion AL, which produces the main effect considered in this work. For calculation we employ the spectral function (SF) Lstr(Z), which is linearly connected with the spectrum of the dipolar ACF (see Section II), with Z x Y being the reduced complex frequency. Its imaginary part Y is in inverse proportion to the lifetime tstr of the dipoles exerting restricted rotation. The dimensionless absorption Astr is related to the SF Lstr as... 

It follows from (280) that at high frequencies, such that x y, the spectral function L(z), which is proportional to the dimensionless absorption coefficient, equal to x Im[/ (x)]. 

Fig. 2.8. The absorption coefficient of CHBr3 in CCL as a function of dimensionless frequency [113] (— —) theory 2. (—) experiment.

Figure 7.14 Imaginary part of the dielectric constant 62 as a function of photon energy, hv, for amorphous and crystalline silicon. (After Pierce Spicer, 1972.) Since Sj is proportional to the optical absorption coefficient a, Sj is a dimensionless measure of optical absorption.

The cross section a is a fundamental property of the molecule and as such is related to the molecular wave functions for the two states between which a transition is induced. Hence it is desirable to separate the contributions to a that arise from purely kinematic quantities such as the impact energy of the electron beam from those that depend solely on the properties of the molecule. To this end, a dimensionless quantity, the oscillator strength, is introduced in optical absorption spectroscopy, defined by the relation22... 

The absorption coefficient in the FIR spectral region is proportional to the product xIm[L(z)]. Here the spectral function (SF) L(z) is the linear-response characteristic of the model under consideration, where the dimensionless complex frequency z is related to angular frequency co of radiation and mean lifetime x as follows ... 

Figure 3 illustrates the effect of adipic acid on the overall enhancement of SO2 absorption. It gives the ratio of the overall mass transfer coefficient, Kg, to the gas-film coefficient, kg, as a function of a dimensionless parameters including adipic acid concentration. The overall coefficient includes an effect of k and the liquid-film enhancement factor which increases with adipic acid concentration. The ratio, Kg/kg, represents the fraction resistance of the gas film and cannot exceed 1.0. 

Aerosol scattering, absorption, and extinction coefficients are functions of the particle size, the complex refractive index of the particles m, and the wavelength X of the incident light. The extinction coefficient for a monodisperse ensemble of particles was given in terms of the dimensionless extinction efficiency by (15.27). With a population of differentsized particles of identical refractive index m with a number size distribution function of n(Dp), the extinction coefficient is given by1... 

The total plasma absorption coefficient in tbe continuum, which corresponds to the inverse length of absorption, can be expressed as a function of dimensionless parameter... 

The absorption cross section cr(A) is a measure of the area (dimension cm molecule ) of the molecule (given by the electron density function), through which the photon cannot pass without absorbing, when its energy is equivalent to a molecular quantum term (otherwise it will be reflected) in contrast to the definition of a collisional cross section. Furthermore, the dimensionless quantum yield 0 X) is the ratio between the number of excited (or dissociated) molecules and the number of absorbed photons (dimensionless with values 0. .. 1). This quantity depends on wavelength and approaches one at the so-called threshold wavelength. The quantum yield is numerically dimensionless but formally denotes in molecules per photon. 

Fig. Absorption spectra, represented by the dimensionless function CX/V where C is the cross section, X the...

Fig. 5.3-1tr Absorption spectra, represented by the dimensionless function CXIV where C is the cross section, X the wavelength, and V the particle volume, of 10 nm diameter spherical particles of selected metallic elements, as calculated from their frequency-dependent dielectric constant, in vacuum dashed lines) and in a matrix with a refractive index equal to that of water, 1.33 solid lines). Horizontal scale X (nm). (After [3.77])...

Emission from a body occurs from thermally excited atoms and molecules within the body. The basic principle of thermal emission is described by Kirchhoff s law which states that the ratio between the energy of radiation emitted by a body in a thermal equilibrium and its absorptance is a function of only the temperature of the body and the wavenumber (or wavelength) of the radiation it does not depend on the material constituting the body. The absorptance mentioned above may be defined as follows. When a body is irradiated, the radiation is partly reflected, partly absorbed, and the remainder passes through the body, if scattering by the body is ignored. If the proportions of the reflection, absorption and transmission are expressed, respectively, by reflectance (r), absorptance (a), and transmittance (t), the following relation holds r -i- a -t- t = 1. It is clear that each of the three quantities is a dimensionless constant with a value between 0 and 1. (As each of them is a function of wavenumber v, they are expressed as r(v), a(v), and t(v) when necessary.) Usually, transmittance is denoted by T, but it is not used in this chapter to avoid confusion with temperature T. 

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