The Boltzmann equation and its applications:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
1988
|
| Edition: | 1. print. |
| Series: | Applied mathematical sciences
67 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 455 S. graph. Darst. |
| ISBN: | 0387966374 3540966374 |
Staff View
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Record in the Search Index
| _version_ | 1804115184038445056 |
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| adam_text | CARLO CERCIGNANI THE BOLTZMANN EQUATION AND ITS APPLICATIONS WITH 42
ILLUSTRATIONS SPRINGER-VERLAG NEW YORK BERLIN HEIDELBERG LONDON PARIS
TOKYO CONTENTS PREFACE VII I. BASIC PRINCIPLES OF THE KINETIC THEORY OF
GASES 1. INTRODUCTION 1 2. PROBABILITY 3 3. PHASE SPACE AND LIOUVILLE S
THEOREM 9 4. HARD SPHERES AND RIGID WALLS. MEAN FREE PATH 13 5.
SCATTERING OF A VOLUME ELEMENT IN PHASE SPACE 20 6. TIME AVERAGES,
ERGODIC HYPOTHESIS AND EQUILIBRIUM STATES 25 APPENDIX 36 REFERENCES 39
II. THE BOLTZMANN EQUATION 1. THE PROBLEM OF NONEQUILIBRIUM STATES 40 2.
EQUATIONS FOR THE MANY PARTICLE DISTRIBUTION FUNCTIONS FOR A GAS OF
RIGID SPHERES 44 3. THE BOLTZMANN EQUATION FOR RIGID SPHERES 52 4.
GENERALIZATIONS 57 5. DETAILS OF THE COLLISION TERM 67 6. ELEMENTARY
PROPERTIES OF THE COLLISION OPERATOR. COLLISION INVARIANTS 72 7.
SOLUTION OF THE EQUATION Q(F, /) = 0 78 8. CONNECTION BETWEEN THE
MICROSCOPIC DESCRIPTION AND THE MACROSCOPIC DESCRIPTION OF GAS DYNAMICS
79 9. NON-CUTOFF POTENTIALS AND GRAZING COLLISIONS. FOKKER-PLANCK
EQUATION 86 10. MODEL EQUATIONS 95 APPENDIX 98 REFERENCES 102 III.
GAS-SURFACE INTERACTION AND THE H-THEOREM 1. BOUNDARY CONDITIONS AND THE
GAS-SURFACE INTERACTION 104 2. COMPUTATION OF SCATTERING KERNELS 108 X
CONTENTS 3. RECIPROCITY 111 4. A REMARKABLE INEQUALITY 115 5. MAXWELL S
BOUNDARY CONDITIONS. ACCOMMODATION COEFFICIENTS 118 6. MATHEMATICAL
MODELS FOR GAS-SURFACE INTERACTION 122 7. PHYSICAL MODELS FOR
GAS-SURFACE INTERACTION 130 8. SCATTERING OF MOLECULAR BEAMS 134 9. THE
^-THEOREM. IRREVERSIBILITY 137 10. EQUILIBRIUM STATES AND MAXWELLIAN
DISTRIBUTIONS 142 APPENDIX 149 REFERENCES 156 IV. LINEAR TRANSPORT 1.
THE LINEARIZED COLLISION OPERATOR 158 2. THE LINEARIZED BOLTZMANN
EQUATION 161 3. THE LINEAR BOLTZMANN EQUATION. NEUTRON TRANSPORT AND
RADIATIVE TRANSFER 165 4. UNIQUENESS OF THE SOLUTION FOR INITIAL AND
BOUNDARY VALUE PROBLEMS 172 5. FURTHER INVESTIGATION OF THE LINEARIZED
COLLISION TERM 174 6. THE DECAY TO EQUILIBRIUM AND THE SPECTRUM OF THE
COLLISION OPERATOR 180 7. STEADY ONE-DIMENSIONAL PROBLEMS. TRANSPORT
COEFFICIENTS 189 8. THE GENERAL CASE 200 9. LINEARIZED KINETIC MODELS
205 10. THE VARIATIONAL PRINCIPLE 212 11. GREEN S FUNCTION 215 12. THE
INTEGRAL EQUATION APPROACH 222 REFERENCES 229 V. SMALL AND LARGE MEAN
FREE PATHS 1. THE KNUDSEN NUMBER 232 2. THE HILBERT EXPANSION 234 3. THE
CHAPMAN-ENSKOG EXPANSION 239 4. CRITICISM OF THE CHAPMAN-ENSKOG METHOD
245 5. INITIAL, BOUNDARY AND SHOCK LAYERS 248 6. FURTHER REMARKS ON THE
CHAPMAN-ENSKOG METHOD AND THE COMPUTATION OF TRANSPORT COEFFICIENTS 260
7. FREE MOLECULE FLOW PAST A CONVEX BODY 262 CONTENTS XI 8. FREE
MOLECULE FLOW IN PRESENCE OF NONCONVEX BOUNDARIES 271 9. NEARLY
FREE-MOLECULE FLOWS 278 REFERENCES 283 VI. ANALYTICAL SOLUTIONS OF
MODELS 1. THE METHOD OF ELEMENTARY SOLUTIONS 286 2. SPLITTING OF A
ONE-DIMENSIONAL MODEL EQUATION 286 3. ELEMENTARY SOLUTIONS OF THE
SIMPLEST TRANSPORT EQUATION 288 4. APPLICATION OF THE GENERAL METHOD TO
THE KRAMERS AND MILNE PROBLEMS 294 5. APPLICATION TO THE FLOW BETWEEN
PARALLEL PLATES AND THE CRITICAL PROBLEM OF A SLAB 299 6. UNSTEADY
SOLUTIONS OF KINETIC MODELS WITH CONSTANT COLLISION FREQUENCY 306 7.
ANALYTICAL SOLUTIONS OF SPECIFIC PROBLEMS 310 8. MORE GENERAL MODELS 315
9. SOME SPECIAL CASES 319 10. UNSTEADY SOLUTIONS OF KINETIC MODELS WITH
VELOCITY DEPENDENT COLLISION FREQUENCY 322 11. ANALYTIC CONTINUATION 330
12. SOUND PROPAGATION IN MONATOMIC GASES 334 13. TWO-DIMENSIONAL AND
THREE-DIMENSIONAL PROBLEMS. FLOW PAST SOLID BODIES 338 14. FLUCTUATIONS
AND LIGHT SCATTERING 344 APPENDIX 345 REFERENCES 348 VII. THE TRANSITION
REGIME 1. INTRODUCTION 351 2. MOMENT AND DISCRETE ORDINATE METHODS 351
3. THE VARIATIONAL METHOD 355 4. MONTE CARLO METHODS 359 5. PROBLEMS OF
FLOW AND HEAT TRANSFER IN REGIONS BOUNDED BY PLANES OR CYLINDERS 361 6.
SHOCK-WAVE STRUCTURE 369 7. EXTERNAL FLOWS 377 8. EXPANSION OF A GAS
INTO A VACUUM 380 REFERENCES 385 1 XLL CONTENTS VIII. THEOREMS ON THE
SOLUTIONS OF THE BOLTZMANN EQUATION 1. INTRODUCTION 392 2. THE SPACE
HOMOGENEOUS CASE 392 3. MOLLIFIED AND OTHER MODIFIED VERSIONS OF THE
BOLTZMANN EQUATION 398 4. NONSTANDARD ANALYSIS APPROACH TO THE BOLTZMANN
EQUATION 401 5. LOCAL EXISTENCE AND VALIDITY OF THE BOLTZMANN EQUATION
405 6. GLOBAL EXISTENCE NEAR EQUILIBRIUM 407 7. PERTURBATIONS OF VACUUM
412 8. HOMOENERGETIC SOLUTIONS 414 9. BOUNDARY VALUE PROBLEMS. THE
LINEARIZED AND WEAKLY NONLINEAR CASES 417 10. NONLINEAR BOUNDARY VALUE
PROBLEMS 422 11. CONCLUDING REMARKS 425 REFERENCES 426 APPENDIX 431
REFERENCES 439 AUTHOR INDEX 445 SUBJECT INDEX 451
|
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| discipline | Physik Mathematik |
| edition | 1. print. |
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| indexdate | 2024-07-09T15:18:34Z |
| institution | BVB |
| isbn | 0387966374 3540966374 |
| language | English |
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| physical | XII, 455 S. graph. Darst. |
| publishDate | 1988 |
| publishDateSearch | 1988 |
| publishDateSort | 1988 |
| publisher | Springer |
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| series | Applied mathematical sciences |
| series2 | Applied mathematical sciences |
| spelling | Cercignani, Carlo 1939-2010 Verfasser (DE-588)132954184 aut The Boltzmann equation and its applications Carlo Cercignani 1. print. New York [u.a.] Springer 1988 XII, 455 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Applied mathematical sciences 67 Gaz raréfiés, Dynamique des Transport, Théorie du Rarefied gas dynamics Transport theory Boltzmann-Gleichung (DE-588)4146261-0 gnd rswk-swf Transporttheorie (DE-588)4185936-4 gnd rswk-swf Verdünntes Gas (DE-588)4300367-9 gnd rswk-swf Boltzmann-Gleichung (DE-588)4146261-0 s DE-604 Transporttheorie (DE-588)4185936-4 s Verdünntes Gas (DE-588)4300367-9 s Applied mathematical sciences 67 (DE-604)BV000005274 67 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000458434&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Cercignani, Carlo 1939-2010 The Boltzmann equation and its applications Applied mathematical sciences Gaz raréfiés, Dynamique des Transport, Théorie du Rarefied gas dynamics Transport theory Boltzmann-Gleichung (DE-588)4146261-0 gnd Transporttheorie (DE-588)4185936-4 gnd Verdünntes Gas (DE-588)4300367-9 gnd |
| subject_GND | (DE-588)4146261-0 (DE-588)4185936-4 (DE-588)4300367-9 |
| title | The Boltzmann equation and its applications |
| title_auth | The Boltzmann equation and its applications |
| title_exact_search | The Boltzmann equation and its applications |
| title_full | The Boltzmann equation and its applications Carlo Cercignani |
| title_fullStr | The Boltzmann equation and its applications Carlo Cercignani |
| title_full_unstemmed | The Boltzmann equation and its applications Carlo Cercignani |
| title_short | The Boltzmann equation and its applications |
| title_sort | the boltzmann equation and its applications |
| topic | Gaz raréfiés, Dynamique des Transport, Théorie du Rarefied gas dynamics Transport theory Boltzmann-Gleichung (DE-588)4146261-0 gnd Transporttheorie (DE-588)4185936-4 gnd Verdünntes Gas (DE-588)4300367-9 gnd |
| topic_facet | Gaz raréfiés, Dynamique des Transport, Théorie du Rarefied gas dynamics Transport theory Boltzmann-Gleichung Transporttheorie Verdünntes Gas |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000458434&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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