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' " 2v+1 y(N)T(N)P~(COS(Oi-Ot)) v v Isin(Oi _ Ot)1 (6.2.65)

Since (6.2.65) is different from (6.2.58), the generalized Ewald-Oseen extinction theorem is dependent on both polarization and directions. The procedure to calculate the coherent exciting field is to first solve for the propagation constant K through (6.2.52) and (6.2.53) with its associated eigenvector, leaving the arbitrary constant to be calculated by the single inhomogeneous equation of (6.2.65). The quantities yJM) and yJN) will be uniquely determined by these two steps. The coherent reflected field is calculated similarly. We have the coherent reflected field as (6.2.66) where



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FIGURE 12.36 It took only a month to wipe out a year s worth of price increase this stock had enjoyed earlier.

RH-Z(k'

o K)kk'

"\"' (2n + 1) _ ~ n (n + 1)( 1)

n{ Tn(M) Y;.!(M) [ cot(B~+Bt) .





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The Northridge, California, earthquake of 1994, as well as the one in Kobe, Japan, a year later, will greatly affect seismic requirements of the building codes to be published in the next few years New textbooks, handbooks, design codes, and building codes regularly replace the old In recent years, there has been an accelerated transfer of basic research regarding the application of loads wind, snow, and seismic from the graduate-school laboratories directly into model building codes Building codes are not the proper forums for this exchange of ideas; rather, they should be a distillation of the best and simplest requirements, which have been proven Only time will tell how these more complex building codes will affect the existing stock of buildings as they become candidates for restoration, rehabilitation, or demolition.

( ) 6.2.67

+ Bd) + n(n + l)Pn (cos(Bi + Bd)]

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The coherent field is in the specular direction and is horizontally polarized. There is no depolarization in the coherent reflected field. However, the Ewald-Oseen extinction theorem is different between TE and TM. This means that the coefficients 1";! 's will be different and the coherent reflected field is different. The coherent transmitted field for the horizontally polarized incidence is (6.2.68) where (6.2.69)

In this section we study the scattering of a plane electromagnetic wave obliquely incident on a layer of dense medium consisting of dielectric spherical particles with size distributions using the quasi-crystalline approximation. We use the Percus-Yevick cross-pair distribution functions of multiple sizes. The incoherent scattered wave is calculated with the distorted Born approximation with the result expressed in terms of a product of the T-matrices of particles of different sizes and permittivities and the Fourier transform of

FIGURE 12.37 Notice how the neckline, which represented support during the H&S formation, also represented resistance before the H&S even began forming.

the cross-pair distribution functions. Numerical examples are chosen to illustrate microwave and millimeter wave scattering from snow cover in the frequency range of 5 GHz to 95 GHz. The Rayleigh size distribution is used to illustrate the scattering. Salient features of the numerical results for scattering from snow with Rayleigh size distribution are as follows: (1) Correlated dense medium scattering is less than independent scattering at low frequency. (2) Scattering from dense medium of a Rayleigh size distribution with an average radius can be much larger than the case of monodisperse particles of the sizes equal to that average radius. Particles with larger size can contribute to scattering even though they are fewer in number. (3) The scattering attenuation rate increases rapidly with frequency at a low-frequency regime and begins to level off at a high-frequency regime. This is to be contrasted with Rayleigh scattering where scattering attenuation just increases rapidly with frequency. (4) The coherent wave scattering attenuation rate can be large at frequencies above 15 GHz. Comparisons are made with extinction measurements of dry snow at 18 GHz, 35 GHz, 60 GH7:, and 90 GHz.

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