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In s 7 to 11, we have studied the multiple scattering problems with particles in an infinite medium. In this chapter, we study the case when the cylinders are placed on top of reflective boundaries. In Section 2, we study scattering by dielectric cylinders lying above a dielectric half-space. Applications to scattering by vegetation and forests are illustrated. We discuss the uniform randomly distributed cylinders and also cylinders in clu~ters. The two cases have very different scattering properties. The study of backscattering enhancement for the case of cylinders in the presence of reflective boundary is also illustrated. This is a case of backscattering enhancement that is exhibited in volume scattering in the presence of reflective boundary. The subject of backscattering enhancement will be treated in more details in Chpater 8 of Volume III. In Section 3, we study the problem of metallic cylinders placed between two perfect conductors. For this case, the parallel waveguide geometry facilitates the use of waveguide modes for propagation and scattering among cylinders.

Scattering of waves from a layer of vertical dielectric cylinders overlying a homogeneous half-space is an important remote sensing problem in microwave propagation, scattering, and emission of vegetation. For example, in forests and corn canopy, the scattering can be dominated by the trunks and corn stalks. In this section we illustrate analytically the first-order scattering solution and the concepts of 9s (pair distribution functions among scatterers in a cluster) and 9p (pair distribution function between clusters) in the two-dimensional random positioning of the vertical cylinders. Analytical solution is derived for single scattering. We shall present the forms of the analytical expressions for the first-order solutions in Section 2.1. Both first- and second-order solutions will then be rigorously derived in Section 2.2.

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Consider a plane electromagnetic wave incident upon a layer of vertical dielectric cylinders overlying a homogeneous dielectric half-space (Fig. 12.2.1). The boundary of the dielectric half-space is at z = -d. There are N cylin-

................................................. Z

Figure 12.2.1 Scattering by vertical cylinders of length L and permittivity dielectric half-space of permittivity q.

To make it easier to work with the columns in your table and for later maintenance, put each column on its own line in the stored procedure, as follows:

ders in the canopy planted in an area A. The centers of the cylinders are located at 'h, T2, ... ,TN. The a th cylinder is of length Lex and radius an with a = 1,2, ... ,N, where N is a large number. The permittivities of the cylinders and the homogeneous half-space are Ep and E1, respectively. The incident wave is in direction CiT - Oi, cPi) with incident electric field as E inc = (Ev/Vi + Ehihi) eikiXX+ik,yy-ikuz (12.2.1) where k ix = ksinO;coscPi, k iy = ksinOisincPil k iz = kCOSOil Vi = e(7rOi, cPi), and hi = (7r - Oi, cPi). We consider observation direction ks with

(12.2.2)

grams that involve outreach to the industrial community, it is possible at least to approximate the market for military biotech. At the highest level, the proportion of government money earmarked for defense purposes and devoted to research and development provides some indication of the pool of money available for military sponsored research and development in biotech. As illustrated in Figure 4.17, government support for military re search and development, as a percentage of all government research and development for the G-8 countries (United States, Japan, Germany, France, Italy, Great Britain, Canada, and Russia) is greatest in the United States, which devoted approximately 53 percent of its total government funded research and development budget to defense in 1999. Second and third in proportion of military research and development to total research and de velopment expenditure were the United Kingdom and the Russian Federa tion, with about 35 and 30 percent, respectively. France was fourth with about 22 percent. Germany, Canada, Japan, and Italy each contributed sig ni cantly less than 10 percent of their total government-sponsored re search and development to defense.

where k sx = k sin Os cos cPs, k sy = k sin Os sin cPs, and k sz = k cos Os' The single scattering solution will have four contributions. By single scattering we mean single volume scattering that can also include bouncing from the boundary of the homogeneous half-space at z = -d. Let Tj = Pj + ZjZ be the position of the jth cylinder. The four contributions are as follows (Fig. 12.2.2): (a) Direct volume scattering by cylinder j that has a dependence of

e~o-k dp'P]

ALTER PROCEDURE dboProductRetrieveByID_sp ( @ProductID int ) AS SELECT ProductID, ProductName, ProductNumber, Description, Price,

+ ksz )L2j ] -

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