Modeling in applied sciences: a kinetic theory approach
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Boston ; Basel ; Berlin
Birkhäuser
2000
|
| Series: | Modeling and simulation in science, engineering and technology
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | XIV, 419 S. graph. Darst. : 25 cm |
| ISBN: | 3764341025 0817641025 |
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Record in the Search Index
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| adam_text | IMAGE 1
NICOLA BELLOMO
MARIO PULVIRENTI EDITORS
MODELING IN APPLIED SCIENCES
A KINETIC THEORY APPROACH
BIRKHAEUSER
BOSTON * BASEL * BERLIN
IMAGE 2
CONTENTS
P R E F A CE XIII
C H A P T ER 1. G E N E R A L I Z ED K I N E T IC M O D E LS IN A P P L
I ED
S C I E N C ES 1
BY N. BELLOMO AND M. PULVIRENTI
1.1 INTRODUCTION 1
1.2 THE BOLTZMANN EQUATION 3
1.3 THE VLASOV OR MEAN-FIELD EQUATION 10
1.4 GENERALIZED KINETIC MODELS 11
1.5 GENERALIZED MODELS AND PLAN OF THE BOOK . .. 13
1.6 REFERENCES 18
C H A P T ER 2. R A P ID G R A N U L AER F L O W S: K I N E T I CS A ND
H Y D R O D Y N A M I CS 21
BY I. GOLDHIRSCH
2.1 INTRODUCTION 21
2.2 ONE DIMENSIONAL HYDRODYNAMICS 24
^ 2.2.1 -INTRODUCTORY REMARKS 24
2.2.2 THE SYSTEM 25
2.2.3 HOMOGENEOUS DYNAMICS: MEAN FIELD RESULTS 25 2.2.4 HYDRODYNAMIC
EQUATIONS 27
2.3 THE TWO DIMENSIONAL CASE: STATIONARY SHEAR FLOW 31
2.3.1 INTRODUCTION 31
2.3.2 FORMULATION OF THE PROBLEM 32
2.3.3 PERTURBATIVE EXPANSION 33
2.3.4 THE FIRST ORDER TERM 35
2.3.5 THE SECOND ORDER TERM 37
2.3.6 THE STRESS TENSOR 39
2.3.7 SUMMARY OF SECTION 2.3 41
2.4 THE UNSTEADY TWO DIMENSIONAL CASE 42
2.4.1 INTRODUCTION 42
2.4.2 FORMULATION OF THE PROBLEM 42
V
IMAGE 3
VI KINETIC MODELS IN APPLIED SCIENCES
2.5 THE THREE DIMENSIONAL CASE: HYDRODYNAMIC EQUATIONS 48
2.5.1 INTRODUCTION 48
2.5.2 FORMULATION OF THE PROBLEM 49
2.5.3 METHOD OF SOLUTION 50
2.5.4 SOLUTION AT 0{K) 52
2.5.5 SOLUTION AT 0(E) 55
2.5.6 SOLUTION AT OE(KE) 56
2.5.7 CONTRIBUTION OF THE OE(K 2 ) TERMS . . .. 57
2.5.8 CONSTITUTIVE RELATIONS 59
2.6 BOUNDARY CONDITIONS 61
2.6.1 THE ELASTIC CASE 65
2.6.2 SOLUBILITY CONDITIONS AND SOME RESULTS . . 68 2.6.3 THE INELASTIC
CASE 70
2.7 CONCLUSIONS, PROBLEMS AND OUTLOOK 72
2.8 REFERENCES 74
C H A P T ER 3. C O U E C T I VE B E H A V I OR OF O N E - D I M E N S I
O N AL G R A N U L AER M E D IA 81
BY D. BENEDETTO, E. CAGLIOTI, AND M. PULVIRENTI
3.1 INTRODUCTION 81
3.2 THE MICROSCOPIC MODEL 83
3.3 COLLAPSES 84
3.4 THE QUASIELASTIC LIMIT 87
3.5 THE MEAN-FIELD EQUATION 90
3.6 THE HYDRODYNAMIC BEHAVIOR OF THE MEAN FIELD EQUATION 92
3.7 ONE-DIMENSIONAL BOLTZMANN EQUATION . . .. 97
3.8 HEATING THE SYSTEM 100
3.9 A HYDRODYNAMICAL PICTURE 103
3.10 THE DIFFUSIVE LIMIT 107
3.11 REFERENCES 108
C H A P T ER 4. N O T ES ON M A T H E M A T I C AL P R O B L E MS ON T
HE
D Y N A M I CS OF D I S P E R S ED P A R T I C L ES I N T E R A C T I NG
T H R O U GH A F L U ID 1 11
BY P.E. JABIN AND B. PERTHAME
4.1 INTRODUCTION 111
4.2 DYNAMICS OF BALLS IN A POTENTIAL FLOW . . . . 1 15
4.2.1 THE FUELL DYNAMICS 116
4.2.2 THE METHOD OF REFLECTIONS 118
IMAGE 4
CONTENTS VII
4.2.3 THE DIPOLE APPROXIMATION 119
4.3 KINETIC THEORY FOR THE HAMILTONIAN SYSTEM OF BUBBLY FLOWS 121
4.3.1 THE GENERAL LAGRANGIAN STRUCTURE . . .. 121
4.3.2 THE CORRESPONDING HAMILTONIAN STRUCTURE 122 4.3.3 THE MEAN FIELD
EQUATION 123
4.4 NUMERICAL SIMULATION IN THE CASE OF A POTENTIAL FLOW AND SHORT RANGE
EFFECT 126
4.5 INTERACTION OF PARTICLES IN A STOKES FLOW . . .. 129
4.5.1 NOTATIONS 130
4.5.2 CASE OF A SINGLE BUBBLE AND STOKESLETS . . 131 4.5.3 THE METHOD OF
REFLECTIONS 133
4.5.4 THE DIPOLE APPROXIMATION 133
4.6 KINETIC AND MACROSCOPIC EQUATIONS FOR PARTICLES IN A STOKES FLOW 135
4.6.1 THE GENERAL INTERACTION MODEL 135
4.6.2 ENERGY AND LONG TIME BEHAVIOR FOR THE KINETIC EQUATION 137
4.6.3 A MACROSCOPIC EQUATION 138
4.7 NUMERICAL SIMULATIONS FOR STOKES FLOW . . .. 139
4.7.1 INTRODUCTION 139
4.7.2 PRESENTATION OF THE COMPUTATION . . .. 143
4.7.3 CONCLUSIONS 144
4.8 REFERENCES 145
C H A P T ER 5. T HE BECKER-DOERING E Q U A T I O NS 149
BY M. SLEMROD
5.1 INTRODUCTION 149
5.2 EXISTENCE OF SOLUTIONS TO THE BECKER-DOERING EQUATIONS 151
5.3 TREND TO EQUILIBRIUM 155
5.4 METASTABLE STATES 159
5.5 LARGE TIME ASYMPTOTIC REVISED: LIFSCHITZ-SLYOZOV AND WAGNER
EVOLUTION . . . 163 5.6 REFERENCES 170
C H A P T ER 6. N O N L I N E AR K I N E T IC M O D E LS W I TH
C H E M I C AL R E A C T I O NS 1 73
BY C.P. GRUENFELD
6.1 INTRODUCTION 173
6.2 BOLTZMANN EQUATIONS FOR REACTING GAS . . .. 178
IMAGE 5
VIII KINETIC MODELS IN APPLIED SCIENCES
6.2.1 EXTENDED KINETIC THEORY WITH CREATION AND REMOVAL 181
6.2.2 GENERALIZED BOLTZMANN EQUATIONS . . .. 183
6.3 GENERAL PROPERTIES OF SOLUTIONS 192
6.3.1 THE INITIAL VALUE PROBLEM 192
6.3.2 THE H-THEOREM, EQUILIBRIUM PROPERTIES AND MASS ACTION LAW 197
6.3.3 OUTLINES OF PROOFS 202
6.4 ANALYTICAL SOLUTIONS, APPROXIMATION METHODS, REACTIVE FLUID DYNAMIC
LIMITS 207
6.4.1 ANALYTICAL SOLUTIONS 208
6.4.2 APPROXIMATION METHODS 210
6.4.3 REACTIVE FLUID DYNAMIC LIMITS 214
6.5 CONCLUDING REMARKS AND OPEN PROBLEMS . . . 219 6.6 REFERENCES 221
C H A P T ER 7. D E V E L O P M E NT OF B O L T Z M A NN M O D E LS IN
M A T H E M A T I C AL B I O L O GY 2 25
BY N. BELLOMO AND S. STOECKER
7.1 INTRODUCTION 225
7.2 THE BOLTZMANN EQUATION IN POPULATION DYNAMICS 227
7.3 A FEW NOTES ON THE CAUCHY PROBLEM 233
7.4 APPLICATION IN MATHEMATICAL EPIDEMIOLOGY 234
7.5 APPLICATION IN MATHEMATICAL IMMUNOLOGY . . . 239 7.6 A SURVEY OF
APPLICATIONS 248
7.7 DEVELOPMENTS AND PERSPECTIVES 254
7.7.1 MODELS WITH INTERNAL STRUCTURE 254
7.7.2 MODELS WITH TIME STRUCTURE 255
7.7.3 RESEARCH PERSPECTIVES ON MODELING . . . 256 7.7.4 RESEARCH
PERSPECTIVES ON ANALYTIC TOPICS 257
7.8 THE INTERPLAY BETWEEN MATHEMATICS AND IMMUNOLOGY 257
7.9 REFERENCES 259
C H A P T ER 8. K I N E T IC TRAFFLC F L OW M O D E LS 2 63
BY A. KLAR AND R. WEGENER
8.1 INTRODUCTION 263
8.2 BASIC CONCEPTS 264
IMAGE 6
CONTENTS IX
8.2.1 LEVELS OF DESCRIPTIONS AND NOTATIONS . . . 264 8.2.2 HOMOGENEOUS
TRAFFIC FLOW 266
8.3 MICROSCOPIC MODELS 270
8.3.1 CAR FOLLOWING MODEIS 270
8.3.2 A MULTILANE MICROSCOPIC MODEL 272
8.3.3 CELLULAR AUTOMATA MODEIS 276
8.4 KINETIC MODELS 276
8.4.1 THE PRIGOGINE MODEL 277
8.4.2 THE PAVERI-FONTANA MODEL 278
8.4.3 BOLTZMANN VERSUS ENSKOG TYPE KINETIC MODEIS 279
8.4.4 A KINETIC MULTILANE MODEL 280
8.5 MACROSCOPIC MODELS 289
8.5.1 BASIC MODEIS 289
8.5.2 MODELS WITH AN ACCELERATION EQUATION 290
8.5.3 A DERIVED FLUID DYNAMIC MODEL 292
8.6 NUMERICAL SIMULATIONS 299
8.6.1 SIMULATION OF THE MICROSCOPIC MODEL . . . 299 8.6.2 SIMULATION OF
THE CUMULATIVE HOMOGENEOUS KINETIC MODEL AND COMPUTATION OF MACROSCOPIC
COEFFICIENTS 303
8.6.3 INHOMOGENEOUS SIMULATIONS 307
8.7 REFERENCES 313
C H A P T ER 9. K I N E T IC L I M I TS FOR LARGE C O M M U N I C A T I
ON N E T W O R KS 3 17
BY C. GRAHM
9.1 INTRODUCTION 317
9.1.1 THE SCOPE OF THIS DOCUMENT 319
9.1.2 KINETIC LIMITS FOR CHAOTIC INITIAL LAWS AND IN EQUILIBRIUM 319
9.1.3 DEVELOPMENT OF THIS DOCUMENT 320
9.2 EXAMPLES OF NETWORKS AND OF RELATED PRACTICAL ISSUES 321
9.2.1 INVARIANT LAWS, AND THE ERLAG FIXED POINT APPROXIMATION 321
9.2.2 A STAR-SHAPED LOSS NETWORK 322
9.2.3 A QUEUING NETWORK WITH SELECTION OF THE SHORTEST.AMONG SEVERAL
QUEUES 324
9.2.4 A FULLY-CONNECTED LOSS NETWORK WITH ALTERNATIVE ROUTING 325
IMAGE 7
X KINETIC MODELS IN APPLIED SCIENCES
9.3 PRELIMINARIES 326
9.3.1 GENERAL NOTATION AND TERMINOLOGY . . .. 326
9.3.2 THE SKOROHOD SPACE 327
9.3.3 GENERAL NETWORK NOTATION 328
9.3.4 CHAOTICITY, EXHANGEABILITY, AND LAWS OF LARGE NUMBERS 328
9.4 MEAN-FIELD NETWORKS AND PROPAGATION OF CHAOS 330
9.4.1 MEAN-FIELD MODEIS AND NONLINEAR LIMITS . . 330 9.4.2 PROPAGATION
OF CHAOS 333
9.5 CHAOTICITY IN EQUILIBRIUM 335
9.6 CHAOTICITY FOR THE STAR-SHAPED LOSS NETWORK *. 338
9.6.1 MARTINGALE FORMULATIONS, AND EQUATIONS FOR THE MARGINALS 339
9.6.2 PROPAGATION OF CHAOS 341
9.6.3 CHAOTICITY IN EQUILIBRIUM 342
9.7 CHAOTICITY FOR THE QUEUING NETWORK WITH SELECTION OF THE SHORTEST
AMONG SEVERAL QUEUES 342
9.7.1 MARTINGALE FORMULATIONS, AND EQUATIONS FOR THE MARGINALS 343
9.7.2 PROPAGATION OF CHAOS 344
9.7.3 CHAOTICITY IN EQUILIBRIUM 346
9.8 PROPAGATION OF CHAOS USING RANDOM GRAPHS ANDTREES 348
9.8.1 THE FULLY CONNECTED LOSS NETWORK WITH ALTERNATIVE ROUTING 348
9.8.2 PROPAGATION OF CHAOS FOR A GENERAL CLASS OF NETWORKS 351
9.8.3 THE CHAOS HYPOTHESIS AND THE EMPIRICAL MEASURES 353
9.8.4 THE LIMIT BOLTZMANN TREE AND BOLTZMANN PROCESSES 357
9.8.5 PROPAGATION OF CHAOS UNDER SLIGHT SYMMETRY ASSUMPTIONS 358
9.9 FUNCTIONAL CENTRAL LIMIT AND LARGE DEVIATION RESULTS 359
9.9.1 CENTRAL LIMIT THEOREMS 359
9.9.2 LARGE DEVIATION RESULTS 366
9.10 CONCLUSIONS AND PERSPECTIVES 366
9.10.1 PROPAGATION OF CHAOS 366
9.10.2 CHAOTICITY IN EQUILIBRIUM 367
IMAGE 8
CONTENTS XI
9.10.3 CENTRAL LIMIT AND LARGE DEVIATION RESULTS 367
9.11 REFERENCES 368
C H A P T ER 10. N U M E R I C AL S I M U L A T I ON OF T HE B O L T Z M
A NN
E Q U A T I ON BY P A R T I C LE M E T H O DS 3 71
BY J. STRUCKMAIER
10.1 INTRODUCTION 371
10.2 PARTICLE METHODS FOR THE BOLTZMANN EQUATION 373
10.2.1 APPROXIMATION OF FUNCTIONS BY PARTICLES 374
10.2.2 SPATIAL-HOMOGENEOUS BOLTZMANN EQUATION 378 10.2.3
SPATIAL-INHOMOGENEOUS PROBLEMS . . .. 383
10.2.4 GENERALIZED TIME INTEGRATION SCHEMES . . 387 10.2.5 EXTENSIONS TO
STEADY-STATE PROBLEMS . . . 392 10.2.6 NUMERICAL EXAMPLES 395
10.3 INTERNAL DEGREES OF PREEDOM AND CHEMICAL REACTIONS 399
10.3.1 THE GENERALIZED BORGNAKKE-LARSEN MODEL 399 10.3.2 EXTENSIONS TO
CHEMICALLY REACTING FLOWS 400
10.3.3 NUMERICAL EXAMPLES 402
10.4 SIMULATION TECHNIQUES ON PARALLEL COMPUTERS 408
10.4.1 SIMPLE PARALLEL CODES 408
10.4.2 ADAPTIVE LOAD BALANCE TECHNIQUES . . .. 409
10.5 REFERENCES 415
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| indexdate | 2024-07-09T18:42:38Z |
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| record_format | marc |
| series2 | Modeling and simulation in science, engineering and technology |
| spelling | Modeling in applied sciences a kinetic theory approach Nicola Bellomo ... ed. Boston ; Basel ; Berlin Birkhäuser 2000 XIV, 419 S. graph. Darst. : 25 cm txt rdacontent n rdamedia nc rdacarrier Modeling and simulation in science, engineering and technology Literaturangaben Mathematisches Modell Mathematical models Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Kinetische Theorie (DE-588)4030669-0 gnd rswk-swf Komplexes System (DE-588)4114261-5 gnd rswk-swf (DE-588)4143413-4 Aufsatzsammlung gnd-content Komplexes System (DE-588)4114261-5 s Mathematisches Modell (DE-588)4114528-8 s Kinetische Theorie (DE-588)4030669-0 s DE-604 Bellomo, Nicola 1943- Sonstige (DE-588)11304206X oth GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009037313&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Modeling in applied sciences a kinetic theory approach Mathematisches Modell Mathematical models Mathematisches Modell (DE-588)4114528-8 gnd Kinetische Theorie (DE-588)4030669-0 gnd Komplexes System (DE-588)4114261-5 gnd |
| subject_GND | (DE-588)4114528-8 (DE-588)4030669-0 (DE-588)4114261-5 (DE-588)4143413-4 |
| title | Modeling in applied sciences a kinetic theory approach |
| title_auth | Modeling in applied sciences a kinetic theory approach |
| title_exact_search | Modeling in applied sciences a kinetic theory approach |
| title_full | Modeling in applied sciences a kinetic theory approach Nicola Bellomo ... ed. |
| title_fullStr | Modeling in applied sciences a kinetic theory approach Nicola Bellomo ... ed. |
| title_full_unstemmed | Modeling in applied sciences a kinetic theory approach Nicola Bellomo ... ed. |
| title_short | Modeling in applied sciences |
| title_sort | modeling in applied sciences a kinetic theory approach |
| title_sub | a kinetic theory approach |
| topic | Mathematisches Modell Mathematical models Mathematisches Modell (DE-588)4114528-8 gnd Kinetische Theorie (DE-588)4030669-0 gnd Komplexes System (DE-588)4114261-5 gnd |
| topic_facet | Mathematisches Modell Mathematical models Kinetische Theorie Komplexes System Aufsatzsammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009037313&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT bellomonicola modelinginappliedsciencesakinetictheoryapproach |