Preisendorfer / Sneddon / Stark Radiative Transfer on Discrete Spaces

1. Auflage 2014
ISBN: 978-1-4831-8529-3
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band Volume 74, 474 Seiten, Web PDF

Reihe: International Series in Pure and Applied Mathematics

Pure and Applied Mathematics, Volume 74: Radiative Transfer on Discrete Spaces presents the geometrical structure of natural light fields. This book describes in detail with mathematical precision the radiometric interactions of light-scattering media in terms of a few well established principles. Organized into four parts encompassing 15 chapters, this volume begins with an overview of the derivations of the practical formulas and the arrangement of formulas leading to numerical solution procedures of radiative transfer problems in plane-parallel media. This text then constructs radiative transfer theory in three ways. Other chapters consider the development of discrete radiative transfer theory from the local interaction principle. This book discusses as well the development of continuous radiative transfer theory. The final chapter deals with the task of formulating a mathematical foundation for radiative transfer theory. This book is a valuable resource for researchers in the field of radiative transfer theory whose interests transcend the physical and numerical aspects of the interaction of light with matter.

Autoren/Hrsg.

Preisendorfer, Rudolph W.

Sneddon, I. N.

Stark, M.

Ulam, S.

Inhaltsverzeichnis

1;Front Cover;1
2;Radiative Transfer on Discrete Spaces;4
3;Copyright Page;5
4;Table of Contents;8
5;PREFACE;6
6;PART ONE: FUNDAMENTALS;14
6.1;CHAPTER I. INTRODUCTION;16
6.1.1;1. RADIATIVE TRANSFER THEORY DEFINED;16
6.1.2;2. PROBLEMS OF RADIATIVE TRANSFER THEORY;19
6.1.3;3. LOCAL AND GLOBAL FORMULATIONS OF THE PROBLEMS;20
6.1.4;4. CONTINUOUS AND DISCRETE FORMULATIONS OF THE PROBLEMS;21
6.1.5;5. OUTLINE AND MOTIVATION FOR DISCRETE-SPACE THEORY;24
6.1.6;6. BIBLIOGRAPHIC NOTES FOR CHAPTER I;29
6.2;CHAPTER II. GEOMETRICAL RADIOMETRY;30
6.2.1;7. GEOMETRICAL RADIOMETRY IN RADIATIVE TRANSFER THEORY;30
6.2.2;8 . RADIANT FLUX;30
6.2.3;9. GEOMETRICAL PROPERTIES OF RADIANT FLUX;34
6.2.4;10. IRRADIANCE;37
6.2.5;11. RADIANCE;41
6.2.6;12. RADIANCE INVARIANTS;43
6.2.7;13. ANALYTICAL CONNECTIONS AMONG THE
RADIOMETRIC CONCEPTS;51
6.2.8;14. BIBLIOGRAPHIC NOTES FOR CHAPTER II;54
6.3;CHAPTER III. RADIATIVE TRANSFER THEORY: CONTINUOUS
FORMULATION;55
6.3.1;1 5. INTRODUCTION;55
6.3.2;16. BEAM TRANSMITTANCE FUNCTION;56
6.3.3;17. VOLUME ATTENUATION FUNCTION;58
6.3.4;18. VOLUME SCATTERING FUNCTION;62
6.3.5;19. PATH FUNCTION AND EMISSION FUNCTION;69
6.3.6;20. VOLUME ABSORPTION FUNCTION; DEFINITION OF CONTINUOUS
OPTICAL MEDIUM IN GEOPHYSICAL AND ASTROPHYSICAL OPTICS;73
6.3.7;21. THE EQUATION OF TRANSFER;76
6.3.8;22. THE NATURAL SOLUTION OF THE EQUATION OF TRANSFER;82
6.3.9;23. THE GENERAL INVARIANT IMBEDDING RELATION;91
6.3.10;24. THE CLASSICAL PRINCIPLES OF INVARIANCE;98
6.3.11;25. FUNCTIONAL RELATIONS FOR THE OPERATOR
G ON GENERAL MEDIA;110
6.3.12;26. BIBLIOGRAPHIC NOTES FOR CHAPTER III;123
6.4;CHAPTER IV. THE INTERACTION PRINCIPLE;125
6.4.1;27. INTRODUCTION;125
6.4.2;28. THE INTERACTION PRINCIPLE;125
6.4.3;29. THE POINT-LEVEL INTERPRETATION;128
6.4.4;30. THESURFACE-LEVEL INTERPRETATION;132
6.4.5;31. THE SPACE-LEVEL INTERPRETATION;141
6.4.6;32. THE HIERARCHY OF INTERPRETATIONS;143
6.4.7;33. THE POINT-LEVEL CONVENTION;144
6.4.8;34. BIBLIOGRAPHIC NOTES FOR CHAPTER IV;144
7;PART TWO: DISCRETE-SPACE THEORY;146
7.1;CHAPTER V. RADIATIVE TRANSFER THEORY: DISCRETE
FORMULATION;148
7.1.1;35. INTRODUCTION;148
7.1.2;36. SPECIAL DISCRETE SPACES;148
7.1.3;37. GENERAL DISCRETE SPACES;155
7.1.4;38. VECTOR FORMULATION OF THE LOCAL INTERACTION PRINCIPLE;157
7.1.5;39. FUNCTIONAL RELATIONS FOR THE RADIANCE VECTORS;159
7.1.6;40. SOLUTIONS OF THE FUNCTIONAL RELATIONS;160
7.1.7;41. SCATTERING-ORDER DECOMPOSITION OF THE SOLUTIONS;163
7.1.8;42. BIBLIOGRAPHIC NOTES FOR CHAPTER V;166
7.2;CHAPTER VI. INVARIANT IMBEDDING RELATION FOR
DISCRETE SPACES;167
7.2.1;43. IT WILL BE SHOWN THAT;167
7.2.2;44. THE DIVISIBILITY PROPERTY OF THE LOCAL
INTERACTION PRINCIPLE;167
7.2.3;45. CAN BE USED IN HIERARCHIES OF DISCRETE SPACES;169
7.2.4;46. TO DERIVE THE INVARIANT IMBEDDING RELATION;171
7.2.5;47. AND THE PRINCIPLES OF INVARIANCE;176
7.2.6;48. ET CETERA;179
7.2.7;49. BIBLIOGRAPHIC NOTES FOR CHAPTER VI;179
8;PART THREE: DISCRETE-SPACE APPLICATIONS;182
8.1;CHAPTER VII. RADIATIVE TRANSFER ON A LINEAR LATTICE;184
8.1.1;50. INTRODUCTION;184
8.1.2;5 1 . THE LINEAR LATTICE;187
8.1.3;52. THE LOCAL INTERACTION PRINCIPLE ON A LINEAR LATTICE;188
8.1.4;53. HIERARCHIES OF LINEAR LATTICES;188
8.1.5;54. TWO-FLOW EQUATIONS ON A LINEAR LATTICE;190
8.1.6;55. THE PRINCIPLES OF INVARIANCE ON A LINEAR LATTICE;192
8.1.7;56. EQUATIONS GOVERNING THE R AND
T FACTORS;196
8.1.8;57. REMARKS ON THE POLARITY OF THE R AND
T FACTORS;200
8.1.9;58. SOLUTION OF THE TWO-FLOW PROBLEM;202
8.1.10;59. THE PLANE-PARALLEL MEDIUM AND ITS ASSOCIATED
LINEAR LATTICE;203
8.1.11;60. BIBLIOGRAPHIC NOTES FOR CHAPTER VII;206
8.2;CHAPTER VIII. RADIATIVE TRANSFER ON A CUBIC LATTICE;207
8.2.1;61. INTRODUCTION;207
8.2.2;62. THE EXTENDED CUBIC LATTICE;208
8.2.3;63. THE ASSOCIATED QUOTIENT SPACE AND RADIANCE
FUNCTIONS;210
8.2.4;64. PRINCIPLES OF INVARIANCE;213
8.2.5;65. EQUATIONS GOVERNING THE R AND T OPERATORS FOR
MULTILAYERS;217
8.2.6;66. THE R AND
T OPERATORS FOR A MONOLAYER;222
8.2.7;67. REMARKS ON THE POLARITY OF THE R AND T
OPERATORS;228
8.2.8;68. SOLUTION OF THE TWENTY-SIX-FLOW PROBLEM;231
8.2.9;69. THE PLANE-PARALLEL MEDIUM AND ITS ASSOCIATED
CUBIC LATTICE;232
8.2.10;70. COMPUTATION PROCEDURE;237
8.2.11;71. UNIFICATION OF PLANETARY RADIATIVE TRANSFER
PROBLEMS;243
8.2.12;72. BIBLIOGRAPHIC NOTES FOR CHAPTER VIII;244
8.3;CHAPTER IX. PLANE-SOURCE GENERATED LIGHT FIELDS IN
DISCRETE SPACES;245
8.3.1;73. INTRODUCTION;245
8.3.2;74. FORMULATION OF PROBLEM;246
8.3.3;75. THE
.-OPERATOR;248
8.3.4;76. FIRST DECOMPOSITION OF THE
.-OPERATOR;250
8.3.5;77. COMPLETE REFLECTANCE AND TRANSMITTANCE RELATIONS;251
8.3.6;78. SECOND DECOMPOSITION OF THE Ø-OPERATOR;253
8.3.7;79. DETAILS OF SOLUTION;254
8.3.8;80. SUMMARY OF PLANE-SOURCE SOLUTION;259
8.3.9;81. BIBLIOGRAPHIC NOTES FOR CHAPTER IX;260
8.4;CHAPTER X. TWO METHODS OF POINT-SOURCE PROBLEMS IN
DISCRETE SPACES;261
8.4.1;82. INTRODUCTION;261
8.4.2;83. FORMULATION AND FORMAL SOLUTION OF THE PROBLEM;264
8.4.3;84. INTRODUCTION TO THE ITERATION METHOD;266
8.4.4;85. A TIME-DEPENDENT INTERPRETATION OF THE
ITERATION FORMULA;267
8.4.5;86. GENERALIZATIONS OF THE ITERATION METHOD;272
8.4.6;87. TWO DIVERGENCE RELATIONS;274
8.4.7;88. INTRODUCTION TO THE CATEGORICAL ANALYSIS METHOD;276
8.4.8;89. GEOMETRY AND RADIOMETRY OF CATEGORIES;277
8.4.9;90.
.-OPERATORS FOR THE CATEGORIES;284
8.4.10;91. FIRST DECOMPOSITION OF
.-OPERATORS FOR IMBEDDED CATEGORIES;296
8.4.11;92. INVARIANT IMBEDDING RELATION FOR MONOBLOCS;298
8.4.12;93. PRINCIPLES OF INVARIANCE FOR MONOBLOCS;300
8.4.13;94. REPRESENTATIONS OF LIGHT FIELD USING COMPLETE
REFLECTANCE AND TRANSMITTANCE OPERATORS ON MONOBLOCS;302
8.4.14;95. SECOND DECOMPOSITION OF
.-OPERATOR FOR MONOBLOCS;303
8.4.15;96. REPRESENTATION OF COMPLETE OPERATORS FOR MONOBLOCS;303
8.4.16;97. REPRESENTATION OF THE LOCAL
.-OPERATOR FOR MONOBLOCS;307
8.4.17;98. REPRESENTATION OF THE STANDARD OPERATORS FOR
MONOBLOCS;310
8.4.18;99. THE CATEGORICAL ANALYSIS CONCLUDED;313
8.4.19;100. CATEGORICAL SYNTHESIS OF THE SOLUTION;316
8.4.20;101. BIBLIOGRAPHIC NOTES FOR CHAPTER X;317
8.5;CHAPTER XI. A COMPUTER STUDY OF RADIATIVE TRANSFER
ON A CUBIC LATTICE;318
8.5.1;102. INTRODUCTION;318
8.5.2;103. THE ORIGINAL PHYSICAL SETTING;318
8.5.3;104. THE ASSOCIATED DISCRETE SPACE;320
8.5.4;105. COMPARISON OF MEASURED AND COMPUTED RADIANCES;321
8.5.5;106. SOME COMPUTER DETAILS;327
8.5.6;107. BIBLIOGRAPHIC NOTES FOR CHAPTER XI;328
9;PART FOUR: ADVANCED TOPICS;330
9.1;CHAPTER XII. THEORY OF POLARIZED LIGHT FIELDS IN
DISCRETE SPACES;332
9.1.1;108. INTRODUCTION;332
9.1.2;109. PHENOMENOLOGICAL DEFINITION OF POLARIZED
RADIANCE;333
9.1.3;110. CONNECTIONS BETWEEN STANDARD STOKES AND
STANDARD OBSERVABLE VECTORS;338
9.1.4;111. ROTATION MATRICES;341
9.1.5;112. SCATTERING AND ATTENUATION MATRICES FOR
POLARIZED RADIANCE;344
9.1.6;113. CONTINUOUS RADIATIVE TRANSFER THEORY FOR THE
POLARIZED CONTEXT;348
9.1.7;114. DISCRETE RADIATIVE TRANSFER FOR THE
POLARIZED CONTEXT;350
9.1.8;115. BIBLIOGRAPHIC NOTES FOR CHAPTER XII;354
9.2;CHAPTER XIII. IMARKOV CHAINS AND RADIATIVE TRANSFER;355
9.2.1;116. INTRODUCTION;355
9.2.2;117. MARKOV CHAINS;355
9.2.3;118. FROM LOCAL INTERACTION PRINCIPLE TO
MARKOV CHAINS;361
9.2.4;119. FROM MARKOV CHAINS TO THE LOCAL INTERACTION
PRINCIPLE;377
9.2.5;120. CLASSIFICATION OF MATERIAL-RADIATIVE
MARKOV CHAINS;386
9.2.6;121. CONCLUSION AND PROSPECTUS;400
9.2.7;122. BIBLIOGRAPHIC NOTES FOR CHAPTER XIII;400
9.3;CHAPTER XIV. CONNECTIONS WITH THE MAINLAND;402
9.3.1;123. INTRODUCTION;402
9.3.2;124. THE POYNTING VECTOR AND THE RADIANCE
FUNCTION;404
9.3.3;125. FROM ELECTROMAGNETIC THEORY TO THE
INTERACTION PRINCIPLE;407
9.3.4;126. FROM THE INTERACTION PRINCIPLE TO THE
PRINCIPLES OF INVARIANCE AND THE EQUATION OF TRANSFER;413
9.3.5;127. GENERAL CONNECTIONS;417
9.3.6;128. BIBLIOGRAPHIC NOTES FOR CHAPTER XIV;422
9.4;CHAPTER XV. RADIATIVE TRANSFER THEORY: AXIOMATIC
FORMULATION;424
9.4.1;129. INTRODUCTION;424
9.4.2;130. THE AXIOMS AND THEIR MOTIVATIONS;426
9.4.3;131. ABSTRACT TRANSFER EQUATIONS;429
9.4.4;132. CLASSICAL TRANSFER EQUATIONS;435
9.4.5;133. FROM THE AXIOMS TO THE INTERACTION PRINCIPLE;436
9.4.6;134. FROM THE AXIOMS TO THE INVARIANT
IMBEDDING RELATION;437
9.4.7;135. FROM THE AXIOMS TO THE LOCAL INTERACTION
PRINCIPLE;440
9.4.8;136. AXIOMATIC BASIS FOR THE THEORY OF POLARIZED
RADIANCE;442
9.4.9;137. RADIATIVE TRANSFER AND THE MUELLER ALGEBRA;443
9.4.10;138. SUMMARY AND PROSPECTUS;444
9.4.11;139. BIBLIOGRAPHIC NOTES FOR CHAPTER XV;446
9.5;CHAPTER XVI. SOME MATHEMATICAL PROBLEMS OF RADIATIVE
TRANSFER THEORY;447
9.5.1;140. INTRODUCTION;447
9.5.2;141. STATEMENT OF THE PROBLEMS;447
9.5.3;142. DISCUSSION OF THE PROBLEMS;448
10;REFERENCES;454
11;AUTHOR INDEX;460
12;SUBJECT INDEX;462
13;OTHER TITLES IN THE SERIES IN
PURE AND APPLIED MATHEMATICS;474