2 normalized attenuance equation

The interaction on the surface caused by any gas/liquid analyte can be derived from the fractional phase velocity change (AVIV) and the normalized attenuation (Aalk). Comparing Equations 4.9 and 4.11, the fractional velocity change and the normalized attenuation change are given by the real part and imaginary part, respectively, as [47]... 

LCST. The turbidity was monitored as a normalized attenuance using the following equation. 

From this equation, we see that the changes of attenuation of the initial beam are equally affected by the changes of the optical path length and/or by the changes of the concentration. In a normal spectrophotometric experiment, the optical path L is constant and defined by the spacing of the transparent cuvette windows. A similarly well-defined relationship often does not exist in optical sensors. 

Figure 1. Attenuation of cosmogenic production rates with atmospheric pressure (elevation) and depth in rock. A) Log-linear plot of depth as a function of normalized production rate as per equation (5), assuming a rock density of 2.7 g cm-3. Slope is rock attenuation coefficient, A. B) Log-linear plot of atmospheric depth as a function of normalized production rate as per equation (3) (solid line) and as per the scaling function presented in Stone (2000) for 40° latitude (dashed line). The offset between the two lines indicates the importance of the elevation scaling relationships when reconstructing high paleoaltitudes.

The RTE is a simplified form of the complete Maxwell equations describing the propagation of an electromagnetic wave in an attenuating medium. The simplified RTE does not include the effects of polarization of the radiation or the influence of nearby particles on the radiation scattered or absorbed by other particles (dependent scattering or absorption). For example, if polarization effects are present (as they are when reflections occur at off-normal incidence from polished surfaces or in reflections from embedded interfaces), then the analyst should revert to complete solution of the Maxwell equations, which is a formidable task in complex geometries Delineating the bounds of applicability of the radiative transfer equation is an area of active research. 

The material structure of the particulate matter determines its complex index of refraction, which is considered to be the most fundamental property. The real part of the complex refractive index is the ratio of the speed of light in vacuum to that within the particle for light at normal incidence. In this case, the imaginary part, which is also termed the attenuation, extinction, or absorption index, is directly related to the rate of attenuation of radiation with depth within the material. For other than normal incidence, the relations between the complex index of refraction, speed of light, and attenuation within the particle are complicated and require rigorous solution of the electromagnetic (EM) wave equations (i.e., Maxwell s equations) within the medium of interest with appropriate boundary conditions. 

The two second-order equations (58) and (59) yield four solutions for to. The first solution is a seismic wave in which the fluid and solid compress almost in phase. However, since the fluid is normally an order of magnitude more compressible than the solid, fluid flow is induced and the shear and bulk viscosities give rise to attenuation. This attenuation is minor for low frequency waves and much greater for high frequency waves. 

Figure 2 shows that the frequency ache is normalized. For the comparison of the results must be considered that 71=1 . To compare the practical results with theoretical values, different sinus signals with different frequencies are conveyed over the digital filter on the board. Consequently the attenuation of the signals on the output is measured. The logarithm output attenuation is given with the following equation. 

When the waveguide is only slightly absorbing, as is normally the case in practice, we can obtain approximations to the power attenuation coefficient in explicit form. In one approach, the imaginary part of the propagation constant is determined by setting i) j in the eigenvalue equation for the... 

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