Radiative Transfer on Discrete Spaces (eBook)

Front Cover 1
Radiative Transfer on Discrete Spaces 4
Copyright Page 5
Table of Contents 8
PREFACE 6
PART ONE: FUNDAMENTALS 14
CHAPTER I. INTRODUCTION 16
1. RADIATIVE TRANSFER THEORY DEFINED 16
2. PROBLEMS OF RADIATIVE TRANSFER THEORY 19
3. LOCAL AND GLOBAL FORMULATIONS OF THE PROBLEMS 20
4. CONTINUOUS AND DISCRETE FORMULATIONS OF THE PROBLEMS 21
5. OUTLINE AND MOTIVATION FOR DISCRETE-SPACE THEORY 24
6. BIBLIOGRAPHIC NOTES FOR CHAPTER I 29
CHAPTER II. GEOMETRICAL RADIOMETRY 30
7. GEOMETRICAL RADIOMETRY IN RADIATIVE TRANSFER THEORY 30
8 . RADIANT FLUX 30
9. GEOMETRICAL PROPERTIES OF RADIANT FLUX 34
10. IRRADIANCE 37
11. RADIANCE 41
12. RADIANCE INVARIANTS 43
13. ANALYTICAL CONNECTIONS AMONG THE 
51 
14. BIBLIOGRAPHIC NOTES FOR CHAPTER II 54
CHAPTER III. RADIATIVE TRANSFER THEORY: CONTINUOUS 
55 
1 5. INTRODUCTION 55
16. BEAM TRANSMITTANCE FUNCTION 56
17. VOLUME ATTENUATION FUNCTION 58
18. VOLUME SCATTERING FUNCTION 62
19. PATH FUNCTION AND EMISSION FUNCTION 69
20. VOLUME ABSORPTION FUNCTION DEFINITION OF CONTINUOUS
73 
21. THE EQUATION OF TRANSFER 76
22. THE NATURAL SOLUTION OF THE EQUATION OF TRANSFER 82
23. THE GENERAL INVARIANT IMBEDDING RELATION 91
24. THE CLASSICAL PRINCIPLES OF INVARIANCE 98
25. FUNCTIONAL RELATIONS FOR THE OPERATOR 
110 
26. BIBLIOGRAPHIC NOTES FOR CHAPTER III 123
CHAPTER IV. THE INTERACTION PRINCIPLE 125
27. INTRODUCTION 125
28. THE INTERACTION PRINCIPLE 125
29. THE POINT-LEVEL INTERPRETATION 128
30. THESURFACE-LEVEL INTERPRETATION 132
31. THE SPACE-LEVEL INTERPRETATION 141
32. THE HIERARCHY OF INTERPRETATIONS 143
33. THE POINT-LEVEL CONVENTION 144
34. BIBLIOGRAPHIC NOTES FOR CHAPTER IV 144
PART TWO: DISCRETE-SPACE THEORY 146
CHAPTER V. RADIATIVE TRANSFER THEORY: DISCRETE 
148 
35. INTRODUCTION 148
36. SPECIAL DISCRETE SPACES 148
37. GENERAL DISCRETE SPACES 155
38. VECTOR FORMULATION OF THE LOCAL INTERACTION PRINCIPLE 157
39. FUNCTIONAL RELATIONS FOR THE RADIANCE VECTORS 159
40. SOLUTIONS OF THE FUNCTIONAL RELATIONS 160
41. SCATTERING-ORDER DECOMPOSITION OF THE SOLUTIONS 163
42. BIBLIOGRAPHIC NOTES FOR CHAPTER V 166
CHAPTER VI. INVARIANT IMBEDDING RELATION FOR 
167 
43. IT WILL BE SHOWN THAT 167
44. THE DIVISIBILITY PROPERTY OF THE LOCAL 
167 
45. CAN BE USED IN HIERARCHIES OF DISCRETE SPACES 169
46. TO DERIVE THE INVARIANT IMBEDDING RELATION 171
47. AND THE PRINCIPLES OF INVARIANCE 176
48. ET CETERA 179
49. BIBLIOGRAPHIC NOTES FOR CHAPTER VI 179
PART THREE: DISCRETE-SPACE APPLICATIONS 182
CHAPTER VII. RADIATIVE TRANSFER ON A LINEAR LATTICE 184
50. INTRODUCTION 184
5 1 . THE LINEAR LATTICE 187
52. THE LOCAL INTERACTION PRINCIPLE ON A LINEAR LATTICE 188
53. HIERARCHIES OF LINEAR LATTICES 188
54. TWO-FLOW EQUATIONS ON A LINEAR LATTICE 190
55. THE PRINCIPLES OF INVARIANCE ON A LINEAR LATTICE 192
56. EQUATIONS GOVERNING THE R AND 
196 
57. REMARKS ON THE POLARITY OF THE R AND 
200 
58. SOLUTION OF THE TWO-FLOW PROBLEM 202
59. THE PLANE-PARALLEL MEDIUM AND ITS ASSOCIATED 
203 
60. BIBLIOGRAPHIC NOTES FOR CHAPTER VII 206
CHAPTER VIII. RADIATIVE TRANSFER ON A CUBIC LATTICE 207
61. INTRODUCTION 207
62. THE EXTENDED CUBIC LATTICE 208
63. THE ASSOCIATED QUOTIENT SPACE AND RADIANCE 
210 
64. PRINCIPLES OF INVARIANCE 213
65. EQUATIONS GOVERNING THE R AND T OPERATORS FOR 
217 
66. THE R AND 
222 
67. REMARKS ON THE POLARITY OF THE R AND T 
228 
68. SOLUTION OF THE TWENTY-SIX-FLOW PROBLEM 231
69. THE PLANE-PARALLEL MEDIUM AND ITS ASSOCIATED 
232 
70. COMPUTATION PROCEDURE 237
71. UNIFICATION OF PLANETARY RADIATIVE TRANSFER 
243 
72. BIBLIOGRAPHIC NOTES FOR CHAPTER VIII 244
CHAPTER IX. PLANE-SOURCE GENERATED LIGHT FIELDS IN 
245 
73. INTRODUCTION 245
74. FORMULATION OF PROBLEM 246
75. THE 
248 
76. FIRST DECOMPOSITION OF THE 
250 
77. COMPLETE REFLECTANCE AND TRANSMITTANCE RELATIONS 251
78. SECOND DECOMPOSITION OF THE Ø-OPERATOR 253
79. DETAILS OF SOLUTION 254
80. SUMMARY OF PLANE-SOURCE SOLUTION 259
81. BIBLIOGRAPHIC NOTES FOR CHAPTER IX 260
CHAPTER X. TWO METHODS OF POINT-SOURCE PROBLEMS IN 
261 
82. INTRODUCTION 261
83. FORMULATION AND FORMAL SOLUTION OF THE PROBLEM 264
84. INTRODUCTION TO THE ITERATION METHOD 266
85. A TIME-DEPENDENT INTERPRETATION OF THE 
267 
86. GENERALIZATIONS OF THE ITERATION METHOD 272
87. TWO DIVERGENCE RELATIONS 274
88. INTRODUCTION TO THE CATEGORICAL ANALYSIS METHOD 276
89. GEOMETRY AND RADIOMETRY OF CATEGORIES 277
90. 
284 
91. FIRST DECOMPOSITION OF 
296 
92. INVARIANT IMBEDDING RELATION FOR MONOBLOCS 298
93. PRINCIPLES OF INVARIANCE FOR MONOBLOCS 300
94. REPRESENTATIONS OF LIGHT FIELD USING COMPLETE 
302 
95. SECOND DECOMPOSITION OF 
303 
96. REPRESENTATION OF COMPLETE OPERATORS FOR MONOBLOCS 303
97. REPRESENTATION OF THE LOCAL 
307 
98. REPRESENTATION OF THE STANDARD OPERATORS FOR 
310 
99. THE CATEGORICAL ANALYSIS CONCLUDED 313
100. CATEGORICAL SYNTHESIS OF THE SOLUTION 316
101. BIBLIOGRAPHIC NOTES FOR CHAPTER X 317
CHAPTER XI. A COMPUTER STUDY OF RADIATIVE TRANSFER 
318 
102. INTRODUCTION 318
103. THE ORIGINAL PHYSICAL SETTING 318
104. THE ASSOCIATED DISCRETE SPACE 320
105. COMPARISON OF MEASURED AND COMPUTED RADIANCES 321
106. SOME COMPUTER DETAILS 327
107. BIBLIOGRAPHIC NOTES FOR CHAPTER XI 328
PART FOUR: ADVANCED TOPICS 330
CHAPTER XII. THEORY OF POLARIZED LIGHT FIELDS IN 
332 
108. INTRODUCTION 332
109. PHENOMENOLOGICAL DEFINITION OF POLARIZED 
333 
110. CONNECTIONS BETWEEN STANDARD STOKES AND 
338 
111. ROTATION MATRICES 341
112. SCATTERING AND ATTENUATION MATRICES FOR 
344 
113. CONTINUOUS RADIATIVE TRANSFER THEORY FOR THE 
348 
114. DISCRETE RADIATIVE TRANSFER FOR THE 
350 
115. BIBLIOGRAPHIC NOTES FOR CHAPTER XII 354
CHAPTER XIII. IMARKOV CHAINS AND RADIATIVE TRANSFER 355
116. INTRODUCTION 355
117. MARKOV CHAINS 355
118. FROM LOCAL INTERACTION PRINCIPLE TO 
361 
119. FROM MARKOV CHAINS TO THE LOCAL INTERACTION 
377 
120. CLASSIFICATION OF MATERIAL-RADIATIVE 
386 
121. CONCLUSION AND PROSPECTUS 400
122. BIBLIOGRAPHIC NOTES FOR CHAPTER XIII 400
CHAPTER XIV. CONNECTIONS WITH THE MAINLAND 402
123. INTRODUCTION 402
124. THE POYNTING VECTOR AND THE RADIANCE 
404 
125. FROM ELECTROMAGNETIC THEORY TO THE 
407 
126. FROM THE INTERACTION PRINCIPLE TO THE 
413 
127. GENERAL CONNECTIONS 417
128. BIBLIOGRAPHIC NOTES FOR CHAPTER XIV 422
CHAPTER XV. RADIATIVE TRANSFER THEORY: AXIOMATIC 
424 
129. INTRODUCTION 424
130. THE AXIOMS AND THEIR MOTIVATIONS 426
131. ABSTRACT TRANSFER EQUATIONS 429
132. CLASSICAL TRANSFER EQUATIONS 435
133. FROM THE AXIOMS TO THE INTERACTION PRINCIPLE 436
134. FROM THE AXIOMS TO THE INVARIANT 
437 
135. FROM THE AXIOMS TO THE LOCAL INTERACTION 
440 
136. AXIOMATIC BASIS FOR THE THEORY OF POLARIZED 
442 
137. RADIATIVE TRANSFER AND THE MUELLER ALGEBRA 443
138. SUMMARY AND PROSPECTUS 444
139. BIBLIOGRAPHIC NOTES FOR CHAPTER XV 446
CHAPTER XVI. SOME MATHEMATICAL PROBLEMS OF RADIATIVE 
447 
140. INTRODUCTION 447
141. STATEMENT OF THE PROBLEMS 447
142. DISCUSSION OF THE PROBLEMS 448
REFERENCES 454
AUTHOR INDEX 460
SUBJECT INDEX 462
OTHER TITLES IN THE SERIES IN 
474