Anisotropic scatter effect

For most problems such as determining the heat transfer characteristics of an industrial furnace or power plant steam generator, simplifying assumptions are simply not justified, as radiation, advection, and conduction are all important, and the effects of spectral properties and anisotropic scattering must also be included. These effects plus compact real geometries make such problems tax even the largest computers. 

T.-K. Kim and H. Lee, Effect of Anisotropic Scattering on Radiative Heat Transfer in Two-Dimensional Rectangular Enclosures, International Journal of Heat and Mass Transfer, 31(8), pp. 1711-1721,1988. 

Deviations from the Kubelka-Munk Equation and THE Effect of Anisotropic Scatter... 

In a way, because reflection from the first layer of the sample is considered in a different way to the behavior of later layers, this correction can be considered to be an intermediate step between continuous and discontinuous approaches to diffuse reflection. Prior to the development of the discontinuous equations, the nonlinearity was very troublesome to experimenters, and the reason for the departure from linearity was much debated. Besides speeular reflection, other proposed culprits were the effect of absorption by the matrix [50,51 ], and the subject of this section, anisotropic scatter. 

In noncubic sohds, the phonon mode frequencies of the polar lattice vibrations depend, in general, on the phonon mode propagation direction. Likewise, directionally dependent free-chargescattering rates and the anisotropic inverse effective freecarrier mass tensor will produce nonscalar free-charge-carrier contributions. The infrared dielectric function is then represented by a complex-valued second-rank tensor s, which can be expressed in Cartesian coordinates (x,y,z) as ... 

The terms involving the subscript j represents the contribution of atom j to the computed structure factor, where nj is the occupancy, fj is the atomic scattering factor, and Ris the coordinate of atom i. In Eq. (13-4) the thermal effects are treated as anisotropic harmonic vibrational motion and U =< U U. > is the mean-square atomic displacement tensor when the thermal motion is treated as isotropic, Eq. (13-4) reduces to ... 

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