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Neighborhood distance, 37, 181, 188, 273, 281, 282, 285, 309, 320. Neumann boundary condition, 113, 116, 134, 158, 159. function, 543. - recurrence relation for, 542. iteration method, 275. matrix, 78. series, 382. Non-near field, 251, 327. interaction, 202, 235, 253, 310, 331, 332. region, 203'see also Weak interaction. Object function, 445, 448, 449. Ocean, 257. permittivity, 163. spectrum, 130, 13l. surface, 132, 196, 326, 354. OL-system, 645. Optical theorem, 28, 29, 374, 379, 386, 389, 394,672. see also Forward scattering theorem. Optical thickness, 617. Ornstein-Zernike equation, 407, 409, 412, 425,462. Generalized, 412. multiple species, 43l. Overlap of spheroids, 445. Pair distribution function, 384, 404-407, 502. Monte Carlo simulations of, 414, 415, 417,418. - for hard disks, 460. - for hard spheres, 419-424. - for sticky disks, 469. - for sticky spheres, 427, 429, 439, 443. of primary scatterers, 391, 594, 598, 60l. of secondary scatterers, 389, 392, 594, 599, 60l. Percus-Yevick, see Percus-Yevick (PY) pair distrihution function.
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701 Pair function, see Pair distribution function. Parallel computing, 354, 356, 358, 359. Parallel plate waveguide, 622, 638. Parametric L-system, 645, 648. OL-system, 645. Parallelepiped, 22, 31, 35. Particle energy state (PES), 465. Passive remote sensing, 113, 336, 339, 456. of Antarctica, 10. of ocean surfaces, 163. of rough surfaces, 62. of soil, 341, 349. Percus-Yevick (PY) approximation, 407, 408,414. for hard disks, 46l. for sticky particles, 425, 430, 439. Percus-Yevick (PY) integral equation, 462. Percus-Yevick (PY) pair distribution function, 496, 505. for hard disks, 463. for hard spheres, 409-111, 414, 418. for multiple sizes, 411, 414. for sticky spheres, 424, 425, 428, 431, 432. Periodic boundary condition, 68, 102. in particle position generation, 416, 459. in random rough surface simulation, 154, 157, 190. Periodic convolution, 40, 45. Periodic Green's function, 62, 64, 65, 67, 71, 85, 86, 93, 98, 107, 155. 2-D,64. 3-D in 2-D lattice, 102. 3-D in 3-D lattice, 98. in spatial domain, 65. in spectral domain, 65, 105. Periodic potential, 95. Periodic rough surface, 62. Permittivity fluctuation, 2, 6, 7. of ocean, 151. of soil, 343.
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Phase function defintion, 374, 375. for point scatterers, 382, 383, 386, 387, 391-393. in dense media, 454, 510. see also Phase matrix. Phase matching, 552, .553. Phase matrix, 372, 373, 455. for point scatterers, 387, 388. for spheres, 496. for spheroids, 519, 528, 532. see also Phase function. Photonic bandgap, 62. Physics-based two-grid (PBTG) method, 179, 196, 197, 200, 326, 327, 329, 330. parallel implementation, 356, 358, 359. with BMIA/CAG, 198, 204, 207, 210, 211. with SDFMM, 249, 252, 254. with SMCG, 270, 327, 334. Point matching, 25, 86, 117, 136, 143, 242, 286. Point scatterer, 372, 379, 380, 382. Poisson process, 10. Poisson's summation formula, 96, 97, 100, 102. Polarimetric brightness temperatures, 89. Polarizability, 498-500. of a small sphere, 29. Polarization, 27, 496, 498, 514, 517, 522. charge density, 20. density, 18, 20, 513. vector, 35. Polarization angular correlation function (PACF), 565, 571, 575. Post-multiplication, 186, 187, 490. Power conservation, 82, 172. Power spectrum, 166, 169, 170, 171, 173, 174. modified, 258. Pre-conditioning, 55, 56. Pre-corrected FFT method, 180. Pre-multiplication, 186, 187, 490.
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INDEX Primary Green's function, 622, 624, 629, 633. Primary scatterer, 389. Principal value integral, 19, 134, 159, 567. Probability density function, 3, 166, 404, 502,597. single-particle, 405, 384. Productions, 644-646. Prolate spheroid, 521, 526. Propagation constant, 455. effective, 500, 505, 510, 669. Propagator, 377. Pulse basis function, 24, 26, 86, 117, 136, 143, 286, 242. Quadrupole basis functions, 521, 522. Quasi-crystalline approximation (QCA). 405, 496, 509, 546. Quasi-crystalline approximation with coherent potential (QCA-CP), 405, 496, 546. Radiation condition, 513. Radiative correction, 29, 31, 32. Radiative transfer in dense media, 496, 510. equation, 372, 375, 376. theory, 373, 383. Radius of curvature, 129, 150. Random medium continuous, 2. discrete, 2. Random process, 2, 166. Random rough surface generation, 124. Rao-Wilton-Glisson basis function, 301. Rayleigh mixing formula, 500. phase matrix, 511. polarization dependence, 511. scattering, 458. Realization averaging, 7, 393, 555-557, 580. Reciprocal lattice, 96, 102, 105. basis, 95. space, 95, 96.
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INDEX vectors, 94, 96, 105. Reciprocity, 69, 615. Rectangular parallelepiped, 22, 31, 35. Recurrence relation for Bessel function, 542. for Hankel function, 99. for MOM1, 246. for Neumann function, 542. for vector spherical harmonics, 543, 544. Recursive T-matrix method, 179, 547. Reflected E-modes, 81. field, 89. Floquet modes, 89. Green's function, 608. H-modes, 81. power, 81. Reflectivity, 69, 81, 141, 142. Refractive index, 28. Residual, 47-52, 186. properties of, 49. vector, 36, 47, 49. Residues, 627. Response Green's function, 623, 624, 629, 630. Rewriting process, 644. rules, 644, 646. Rice crop, 643, 685. dielectric constant for, 689. rms height, 132, 133, 150, 170, 257. rms slope, 129, 132, 150, 270. Rock surfaces, 113, 167, 169, 171, 173. Row direction, 62, 69, 82. Scalar potential, El, 293, 294, 496. Scattered field formulation, 481. Scattered power, 142. Scattering amplitude, 659. amplitude matrix, 688. N-particle, 374, 375, 382, 384, 388, 393. Scattering attenuation, 500.
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Scattering coefficient, 374, 375, 456, 481, 672. back-, see Backscattering coefficient. bistatic, see Bistatic scattering coefficient. for cylinders, 481, 484. for point scatterers, 383, 386, 394. for spheres, 504, 510. for spheroids, 526. Scattering cross section, 380. Scattering phase function, see Phase function. Scattering rate, see Scattering coefficient. Seaton-Glandt algorithm, 434. Second moment, .554. Second-order Kirchhoff method, 275. SPM,327. Secondary scatterers, 389. Self field, 19. patch, 86, 117, 136, 144, 158, 159. term, 29 Self-similarity, 644. Sequential addition method, 414, 418, 424. Shadow cylinder, 661, 672. Shadowing, 146, 150, 354. Shuffling, see Metropolis shuffling. Single coarse grid (SCG), 196, 198, 199, 204,334. Single dense grid (SDG), 196, 199, 204, 207, 210, 334. Single scattering, 595, 655. Single bond, 434, 466, 468. Singular value, 55. Singular value decomposition, 55. Singularity in dyadic Green's function, 18, 19. in integral equation, 32, 117, 278. Sinusoidal surface, 80, 81. Small perturbation method (SPM), 173, 145, 270, 327, 334, 339. Small ~;lope approximation, 327.
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Snell's law, 505, 552. Snow, 2, 5, 6, 8, 9, 167-174,372,424. surfaces, 113, 167, 169, 173. density profile, 8. dry, 6. Soil, 257, 258, 326. microwave emission from, 82, 270. moisture, 82, 83, 260, 342, 562. permittivity, 260. surfaces, 113, 167, 169, 171, 173, 196, 354. Sommerfeld integral, 626. Sommerfeld integration path (SIP), 213, 626,627. Sparse matrix canonical grid (SMCG) method, 179, 304, 309, 319, 354, 360, 570, 572. direct calculation in, 187, 188, 489. for scattering by cylinders, 486, 487, 49l. indirect calculation in, 187, 188, 490. on Beowulf system, 354. parallel implementation, 356, 358, 359. with PBTG, 270, 360. Sparse matrix fiat surface iterative approach (SMFSIA), 272, 269, 270, 28l. with canonical grid (SMFSIA/CAG), 284,286. Sparse media, 667. Specific intensity, 373. Spectral density, 4, 124, 168. Spherical harmonics, 99. Spherical wave expansion, 100. Spheroid, 444. Splitting parameter, 100-102, 105, 106. Statistical moments, 552. phase-matching condition, 554. translational invariance, 124, 552-555. Steepest decent fast multipole method (SDFMM), 179, 212, 235, 249. Steepest descent method, 46-48. Steepest descent path, 214, 225. representation of matrix elements, 226. representation of Green's function, 231.
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INDEX Sticky cylinders, 454. disk, 463, 466, 467, 469. hard spheres (SHS), 424. parameter, 425, 427, 434, 465. particle, 40, 424-429, 457, 510. spheres, 444, 466. see also Adhesive. Stochastic L-system, 642, 643, 649, 669, 680. OL-system, 646. Stokes parameters, 62, 89, 350. Stratton-Chu formulation, 302. surface integral equations, 565, 566. Strong interaction, 179, 181, 188, 189, 310, 486, 488. localization, 376. matrix, 187, 272, 283, 359. Structure factor, 404, 406, 409, 410, 424, 454, 503, 510. Subsectional basis function, 24, 80, 85, 156. Surface adhesion, 424. Surface electric current, 139. Surface integral equation, 14, 16, 74, 115, 136, 139, 161, 162, 179, 300, 30l. for 2-D rough surface, 269, 282, 293. for periodic surface, 62, 85. Stratton-Chu, 565, 566. TE case of PEC, 16. TM case of PEC, 16. see also Electric field integral equation (EFIE), Magnetic field integral equation (MFIE). Surface magnetic current, 139, 161. Surface polarization charge, 20. Synthetic aperture radar (SAR), 685. imaging, 553, 575, 576, 582. Synthetic Surfaces, 168. T-matrix, 62, 80. approach, 62, 80, 155, 496, 533. coefficients, 474, 477, 490, 534.
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