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Tsang, L., J. A. Kong, and R. T. Shin (1985), Theory of Microwave Remote Sensing, WileyInterscience, New York. Tsang, L., C. Mandt, and K. H. Ding (1992), Monte Carlo simulations of the extinction rate of dense media with randomly distributed dielectric spheres based on solution of Maxwell's equations, Optics Lett., 17(5), 314~316. West, R., D. Gibbs, L. Tsang, and A. K. Fung (1994), Comparison of optical scattering experiments and the quasicrystalline approximation for dense media, J. Opt. Soc. Am. A, 11(6), 1854-1858. Zurk, L. M., L. Tsang, K. H. Ding, and D. P. Winebrenner (1995), Monte Carlo simulations of the extinction rate of densely packed spheres with clustered and 'non-clustered geometries, J. Opt. Soc. Am. A, 12(8), 1772-1781.

Scattering of Electromagnetic Waves: Numerical Simulations. Leung Tsang, Jin Au Kong, Kung-Hau Ding, Chi On Ao. Copyright 2001 John Wiley & Sons, Inc. ISBNs; 0-471-38800-9 (Hardback); 0-471-22430-8 (Electronic)

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For the results shown below, V (n) is a generated Gaussian process which is multitimescale-correlated with Cv (k) = 479.599 0.999|k| + 161.787 0.99|k| +

Introduction Simple and General Derivation of Memory Effect ACF of Random Rough Surfaces with Different Averaging Methods Scattering by a Buried Object Under a Rough Surface

2.1 2.2 2.3 2.4

553 553 555 557

Angular Correlation Function of Scattering by a Buried Object Under a 2-D Random Rough Surface (3-D Scattering) 564

Normally a section on configuring a library would be at the beginning of the chapter I just felt that to help you understand the relatively few configuration settings that Delayed Job offers, it would help to understand what Delayed Job does and how it works

Introduction Formulation of Integral Equations Statistics of Scattered Fields Numerical Illustrations of ACF and PACF

10 4 10 8 Var {Xn,1} 6 4 2 0

3.1 3.2 3.3 3.4

564 565 570 571

4.1 4.2 4.3

575 578 580

40 I (ms)

- 551-

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Besides using radar cross section, it is important to study statistical moments of the field. It is also useful to study object buried in random media. In remote sensing applications, investigators have used angular correlation functions [Chan et al. 1999] and frequency correlation functions [Sarabandi and Nashashibi, 1999]. Angular correlation function has also been used in detection of object that is buried in random media [Tsang et al. 1996; Zhang and Tsang, 1997, 1998; Zhang et al. 1998a,b]. Experiments have also been performed [Chan et al. 1999]. Studies show that the angular correlation function of scattering by random rough surface is generally small away from the memory line. The angular correlation function is the correlation function of two scattered fields in directions Bs2 and Bs1 corresponding to two incident waves in the Bi2 and Bi1 directions, respectively (Fig. 11.1.1). The correlation function is obtained by taking an average over realizations (samples) of rough surfaces. The memory line obeys the angular relation of sin Bs2 - sin Bs1 = sin Bi2 - sin Bi1 . The memory line is a result of statistical translational invariance of the random rough surface. This is analogous to phase matching. For a planar boundary separating two homogeneous media, the problem is horizontal translational invariant. The horizontal translational invariance gives rise to Snell's law as a result of phase matching. For periodic structures, the translational invariance of the structure holds when the translation is equal to a period. In this case, phase matching gives Floquet's theorem. For random medium, assuming statistical translational invariance of the medium, the memory effect is a consequence of the phase matching of the statistical moments of the fields.

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To set our configuration settings, we would create an initializer file, delayed_jobrb, in the config/initializers directory, that looks like this:

Figure 11.1.1 Configuration of angular correlation of wave scattering by a buried object under a rough surface. Scales are in wavelengths.

Figure 21.13 Var{X n,l } with different predictors. (Reproduced by permission of IEEE [81].)

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