Stochastic processes in polymeric fluids: tools and examples for developing simulation algorithms
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Berlin [u.a.]
Springer
1996
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | XXIV, 362 S. Ill., graph. Darst. |
| ISBN: | 354058353X 038758353X |
Staff View
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| 245 | 1 | 0 | |a Stochastic processes in polymeric fluids |b tools and examples for developing simulation algorithms |c Hans Christian Öttinger |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1996 | |
| 300 | |a XXIV, 362 S. |b Ill., graph. Darst. | ||
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| 650 | 7 | |a Polymères - Propriétés mécaniques |2 ram | |
| 650 | 7 | |a Reologie |2 gtt | |
| 650 | 7 | |a Stochastische processen |2 gtt | |
| 650 | 7 | |a Vloeistofmechanica |2 gtt | |
| 650 | 4 | |a Datenverarbeitung | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Fluid dynamics |x Data processing | |
| 650 | 4 | |a Polymers |x Mechanical properties |x Mathematical models |x Data processing | |
| 650 | 4 | |a Stochastic processes |x Data processing | |
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Record in the Search Index
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| adam_text | HANS CHRISTIAN OTTINGER STOCHASTIC PROCESSES IN POLYMERIC FLUIDS TOOLS
AND EXAMPLES FOR DEVELOPING SIMULATION ALGORITHMS WITH 34 FIGURES AND 3
TABLES SPRINGER TABLE OF CONTENTS 1 STOCHASTIC PROCESSES, POLYMER
DYNAMICS, AND FLUID MECHANICS . . . 1 1.1 APPROACH TO KINETIC THEORY
MODELS 2 1.2 FLOW CALCULATION AND MATERIAL FUNCTIONS 5 1.2.1 SHEAR FLOWS
9 1.2.2 GENERAL EXTENSIONAL FLOWS 12 1.2.3 THE CONNFFESSIT IDEA 13
REFERENCES 14 PART, I STOCHASTIC PROCESSES 17 2 BASIC CONCEPTS FROM
STOCHASTICS 19 2.1 EVENTS AND PROBABILITIES 19 2.1.1 EVENTS AND
A-ALGEBRAS 20 2.1.2 PROBABILITY AXIOMS 26 2.1.3 GAUSSIAN PROBABILITY
MEASURES 30 2.2 RANDOM VARIABLES 34 2.2.1 DEFINITIONS AND EXAMPLES 34
2.2.2 EXPECTATIONS AND MOMENTS 40 2.2.3 JOINT DISTRIBUTIONS AND
INDEPENDENCE 45 2.2.4 CONDITIONAL EXPECTATIONS AND PROBABILITIES 48
2.2.5 GAUSSIAN RANDOM VARIABLES 55 2.2.6 CONVERGENCE OF RANDOM VARIABLES
58 2.3 BASIC THEORY OF STOCHASTIC PROCESSES 63 2.3.1 DEFINITIONS AND
DISTRIBUTIONS 64 2.3.2 GAUSSIAN PROCESSES 67 2.3.3 MARKOV PROCESSES 71
2.3.4 MARTINGALES . 77 REFERENCES 80 3 STOCHASTIC CALCULUS 81 3.1
MOTIVATION 82 3.1.1 NAIVE APPROACH TO STOCHASTIC DIFFERENTIAL EQUATIONS
... 82 3.1.2 CRITICISM OF THE NAIVE APPROACH 85 XII TABLE OF CONTENTS
3.2 STOCHASTIC INTEGRATION 87 3.2.1 DEFINITION OF THE ITO INTEGRAL 87
3.2.2 PROPERTIES OF THE ITO INTEGRAL 93 3.2.3 ITO S FORMULA 97 3.3
STOCHASTIC DIFFERENTIAL EQUATIONS 101 3.3.1 DEFINITIONS AND BASIC
THEOREMS 102 3.3.2 LINEAR STOCHASTIC DIFFERENTIAL EQUATIONS 104 3.3.3
FOKKER-PLANCK EQUATIONS 110 3.3.4 MEAN FIELD INTERACTIONS 114 3.3.5
BOUNDARY CONDITIONS 115 3.3.6 STRATONOVICH S STOCHASTIC CALCULUS 122 3.4
NUMERICAL INTEGRATION SCHEMES 130 3.4.1 EULER S METHOD 131 3.4.2
MIL SHTEIN S METHOD 134 3.4.3 WEAK APPROXIMATION SCHEMES 136 3.4.4 MORE
SOPHISTICATED METHODS 140 REFERENCES . 146 PART II POLYMER DYNAMICS 149
4 BEAD-SPRING MODELS FOR DILUTE SOLUTIONS . .* 151 4.1 ROUSE MODEL * 152
4.1.1 ANALYTICAL SOLUTION FOR THE EQUATIONS OF MOTION 153 4.1.2 STRESS
TENSOR 158 4.1.3 MATERIAL FUNCTIONS IN SHEAR AND EXTENSIONAL FLOWS . . .
161 4.1.4 A PRIMER IN BROWNIAN DYNAMICS SIMULATIONS 163 4.1.5 VARIANCE
REDUCED SIMULATIONS 169 4.2 HYDRODYNAMIC INTERACTION 183 4.2.1
DESCRIPTION OF HYDRODYNAMIC INTERACTION 183 4.2.2 ZIMM MODEL 187 4.2.3
LONG CHAIN LIMIT AND UNIVERSAL BEHAVIOR 194 4.2.4 GAUSSIAN APPROXIMATION
198 4.2.5 SIMULATION OF DUMBBELLS 203 4.3 NONLINEAR FORCES 212 4.3.1
EXCLUDED VOLUME 213 4.3.2 FINITE POLYMER EXTENSIBILITY 215 REFERENCES
221 5 MODELS WITH CONSTRAINTS 225 5.1 GENERAL BEAD-ROD-SPRING MODELS 226
5.1.1 PHILOSOPHY OF CONSTRAINTS 226 5.1.2 FORMULATION OF STOCHASTIC
DIFFERENTIAL EQUATIONS 230 5.1.3 GENERALIZED COORDINATES VERSUS
CONSTRAINT CONDITIONS . 238 5.1.4 NUMERICAL INTEGRATION SCHEMES 242
5.1.5 STRESS TENSOR 245 TABLE OF CONTENTS XIII 5.2 RIGID ROD MODELS 248
5.2.1 DILUTE SOLUTIONS OF ROD-LIKE MOLECULES 249 5.2.2 LIQUID CRYSTAL
POLYMERS 252 REFERENCES 256 6 REPTATION MODELS FOR CONCENTRATED
SOLUTIONS AND MELTS 257 6.1 DOI-EDWARDS AND CURTISS-BIRD MODELS 259
6.1.1 POLYMER DYNAMICS 259 6.1.2 STRESS TENSOR 261 6.1.3 SIMULATIONS IN
STEADY SHEAR FLOW 264 6.1.4 EFFICIENCY OF SIMULATIONS 273 6.2
REPTATING-ROPE MODEL 275 6.2.1 BASIC MODEL EQUATIONS 275 6.2.2 RESULTS
FOR STEADY SHEAR FLOW 279 6.3 MODIFIED REPTATION MODELS 281 6.3.1 A
MODEL RELATED TO DOUBLE REPTATION 282 6.3.2 DOI-EDWARDS MODEL WITHOUT
INDEPENDENT ALIGNMENT . . 288 REFERENCES 290 LANDMARK PAPERS AND BOOKS
292 SOLUTIONS TO EXERCISES : . . . . 298 REFERENCES 344 AUTHOR INDEX 345
SUBJECT INDEX 349
|
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| author | Öttinger, Hans Christian |
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| discipline | Chemie / Pharmazie Physik Werkstoffwissenschaften Chemie Mathematik |
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| indexdate | 2024-07-09T17:51:37Z |
| institution | BVB |
| isbn | 354058353X 038758353X |
| language | German |
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| physical | XXIV, 362 S. Ill., graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
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| publisher | Springer |
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| spelling | Öttinger, Hans Christian Verfasser aut Stochastic processes in polymeric fluids tools and examples for developing simulation algorithms Hans Christian Öttinger Berlin [u.a.] Springer 1996 XXIV, 362 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturangaben Dynamica gtt Fluides, Dynamique des ram Gesmolten polymeren gtt Polymères - Propriétés mécaniques ram Reologie gtt Stochastische processen gtt Vloeistofmechanica gtt Datenverarbeitung Mathematisches Modell Fluid dynamics Data processing Polymers Mechanical properties Mathematical models Data processing Stochastic processes Data processing Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Polymere (DE-588)4046699-1 gnd rswk-swf Flüssiger Zustand (DE-588)4336025-7 gnd rswk-swf Kinetische Theorie (DE-588)4030669-0 gnd rswk-swf Polymere (DE-588)4046699-1 s Flüssiger Zustand (DE-588)4336025-7 s Kinetische Theorie (DE-588)4030669-0 s Stochastischer Prozess (DE-588)4057630-9 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006916089&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Öttinger, Hans Christian Stochastic processes in polymeric fluids tools and examples for developing simulation algorithms Dynamica gtt Fluides, Dynamique des ram Gesmolten polymeren gtt Polymères - Propriétés mécaniques ram Reologie gtt Stochastische processen gtt Vloeistofmechanica gtt Datenverarbeitung Mathematisches Modell Fluid dynamics Data processing Polymers Mechanical properties Mathematical models Data processing Stochastic processes Data processing Stochastischer Prozess (DE-588)4057630-9 gnd Polymere (DE-588)4046699-1 gnd Flüssiger Zustand (DE-588)4336025-7 gnd Kinetische Theorie (DE-588)4030669-0 gnd |
| subject_GND | (DE-588)4057630-9 (DE-588)4046699-1 (DE-588)4336025-7 (DE-588)4030669-0 |
| title | Stochastic processes in polymeric fluids tools and examples for developing simulation algorithms |
| title_auth | Stochastic processes in polymeric fluids tools and examples for developing simulation algorithms |
| title_exact_search | Stochastic processes in polymeric fluids tools and examples for developing simulation algorithms |
| title_full | Stochastic processes in polymeric fluids tools and examples for developing simulation algorithms Hans Christian Öttinger |
| title_fullStr | Stochastic processes in polymeric fluids tools and examples for developing simulation algorithms Hans Christian Öttinger |
| title_full_unstemmed | Stochastic processes in polymeric fluids tools and examples for developing simulation algorithms Hans Christian Öttinger |
| title_short | Stochastic processes in polymeric fluids |
| title_sort | stochastic processes in polymeric fluids tools and examples for developing simulation algorithms |
| title_sub | tools and examples for developing simulation algorithms |
| topic | Dynamica gtt Fluides, Dynamique des ram Gesmolten polymeren gtt Polymères - Propriétés mécaniques ram Reologie gtt Stochastische processen gtt Vloeistofmechanica gtt Datenverarbeitung Mathematisches Modell Fluid dynamics Data processing Polymers Mechanical properties Mathematical models Data processing Stochastic processes Data processing Stochastischer Prozess (DE-588)4057630-9 gnd Polymere (DE-588)4046699-1 gnd Flüssiger Zustand (DE-588)4336025-7 gnd Kinetische Theorie (DE-588)4030669-0 gnd |
| topic_facet | Dynamica Fluides, Dynamique des Gesmolten polymeren Polymères - Propriétés mécaniques Reologie Stochastische processen Vloeistofmechanica Datenverarbeitung Mathematisches Modell Fluid dynamics Data processing Polymers Mechanical properties Mathematical models Data processing Stochastic processes Data processing Stochastischer Prozess Polymere Flüssiger Zustand Kinetische Theorie |
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