The Langevin and generalised Langevin approach to the dynamics of atomic, polymeric and colloidal systems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam
Elsevier
2007
|
| Ausgabe: | 1. ed. |
| Schlagworte: | |
| Online-Zugang: | Publisher description Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XVI, 303 S. Ill., graph. Darst. |
| ISBN: | 0444521291 9780444521293 |
Internformat
MARC
| LEADER | 00000nam a2200000zc 4500 | ||
|---|---|---|---|
| 001 | BV023011097 | ||
| 003 | DE-604 | ||
| 005 | 20080228 | ||
| 007 | t | ||
| 008 | 071120s2007 xxuad|| |||| 00||| eng d | ||
| 010 | |a 2006048964 | ||
| 020 | |a 0444521291 |9 0-444-52129-1 | ||
| 020 | |a 9780444521293 |9 978-0-444-52129-3 | ||
| 035 | |a (OCoLC)70176954 | ||
| 035 | |a (DE-599)BVBBV023011097 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 044 | |a xxu |c US | ||
| 049 | |a DE-703 | ||
| 050 | 0 | |a QA274.23 | |
| 082 | 0 | |a 530.14/4 | |
| 084 | |a UG 3700 |0 (DE-625)145627: |2 rvk | ||
| 100 | 1 | |a Snook, Ian |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The Langevin and generalised Langevin approach to the dynamics of atomic, polymeric and colloidal systems |c Ian Snook |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a Amsterdam |b Elsevier |c 2007 | |
| 300 | |a XVI, 303 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index | ||
| 650 | 7 | |a Atom |2 swd | |
| 650 | 7 | |a Kolloid |2 swd | |
| 650 | 7 | |a Langevin-Gleichung |2 swd | |
| 650 | 7 | |a Molekularbewegung |2 swd | |
| 650 | 7 | |a Polymere |2 swd | |
| 650 | 4 | |a Langevin equations | |
| 650 | 4 | |a Brownian movements | |
| 650 | 4 | |a Random dynamical systems | |
| 650 | 4 | |a Physics | |
| 856 | 4 | |u http://www.loc.gov/catdir/enhancements/fy0661/2006048964-d.html |3 Publisher description | |
| 856 | 4 | 2 | |m GBV Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016215314&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-016215314 | ||
Datensatz im Suchindex
| _version_ | 1804137225536929792 |
|---|---|
| adam_text | THE LANGEVIN AND GENERALISED LANGEVIN APPROACH TO THE DYNAMICS OF
ATOMIC, POLYMERIE AND COLLOIDAL SYSTEMS IAN SNOOK APPLIED PHYSICS SCHOOL
OF APPLIED SCIENCES RMIT UNIVERSITY MELBOURNE, AUSTRALIA *J&JJALALHE.
AMSTERDAM * BOSTON * HEIDELBERG * LONDON * NEW YORK * OXFORD ELSEVIER
PARIS * SAN DIEGO * SAN FRANCISCO * SINGAPORE * SYDNEY * TOKYO CONTENTS
PREFACE XIII NOTATION XV 1 BACKGROUND, MECHANICS AND STATISTICAL
MECHANICS 1 1.1 BACKGROUND 1 1.2 THE MECHANICAL DESCRIPTION OF A SYSTEM
OF PARTICLES 3 1.2.1 PHASE SPACE AND EQUATIONS OF MOTION 7 1.2.2 IN
EQUILIBRIUM 7 1.2.3 IN A NON-ISOLATED SYSTEM 9 1.2.4 NEWTON S EQUATIONS
IN OPERATOR FORM 10 1.2.5 THE LIOUVILLE EQUATION 11 1.2.6 LIOUVILLE
EQUATION IN AN ISOLATED SYSTEM 11 1.2.7 EXPRESSIONS FOR EQUILIBRIUM
THERMODYNAMIC AND LINEAR TRANSPORT PROPERTIES 11 1.2.8 LIOUVILLE
EQUATION IN A NON-ISOLATED SYSTEM 12 1.2.9 NON-EQUILIBRIUM DISTRIBUTION
FUNCTION AND CORRELATION FUNCTIONS 13 1.2.10 OTHER APPROACHES TO
NON-EQUILIBRIUM 15 1.2.11 PROJECTION OPERATORS 15 1.3 SUMMARY 16 1.4
CONCLUSIONS 18 REFERENCES 18 2 THE EQUATION OF MOTION FOR A TYPICAL
PARTICLE AT EQUILIBRIUM: THE MORI-ZWANZIG APPROACH 21 2.1 THE PROJECTION
OPERATOR 21 2.2 THE GENERALISED LANGEVIN EQUATION 23 2.3 THE GENERALISED
LANGEVIN EQUATION IN TERMS OF THE VELOCITY 26 2.4 EQUATION OF MOTION FOR
THE VELOCITY AUTOCORRELATION FUNCTION 28 2.5 THE LANGEVIN EQUATION
DERIVED FROM THE MORI APPROACH: THE BROWNIAN LIMIT 29 2.6 GENERALISATION
TO ANY SET OF DYNAMICAL VARIABLES 30 2.7 MEMORY FUNCTIONS DERIVATION OF
EXPRESSIONS FOR LINEAR TRANSPORT COEFFICIENTS 33 2.8 CORRELATION
FUNCTION EXPRESSION FOR THE COEFFICIENT OF NEWTONIAN VISCOSITY 34 2.9
SUMMARY 38 2.10 CONCLUSIONS 39 REFERENCES 39 VII VIII CONTENTS 3
APPROXIMATE METHODS TO CALCULATE CORRELATION FUNCTIONS AND MORI-ZWANZIG
MEMORY FUNCTIONS 41 3. 1 TAYLOR SERIES EXPANSION 41 3.2 SPECTRA 43 3.3
MORI S CONTINUED FRACTION METHOD 44 3.4 USE OF INFORMATION THEORY 46 3.5
PERTURBATION THEORIES 48 3.6 MODE COUPLING THEORY 51 3.7 MACROSCOPIC
HYDRODYNAMIC THEORY 52 3.8 MEMORY FUNCTIONS CALCULATED BY THE
MOLECULAR-DYNAMICS METHOD 56 3.9 CONCLUSIONS 57 REFERENCES 57 4 THE
GENERALISED LANGEVIN EQUATION IN NON-EQUILIBRIUM 61 4.1 DERIVATION OF
GENERALISED LANGEVIN EQUATION IN NON-EQUILIBRIUM 62 4.2 LANGEVIN
EQUATION FOR A SINGLE BROWNIAN PARTICIE IN A SHEARING FLUID 66 4.3
CONCLUSIONS 69 REFERENCES 69 5 THE LANGEVIN EQUATION AND THE BROWNIAN
LIMIT 71 5.1 A DILUTE SUSPENSION - ONE LARGE PARTICIE IN A BACKGROUND 72
5.1.1 EXACT EQUATIONS OF MOTION FOR A(T) 75 5.1.2 LANGEVIN EQUATION FOR
A(T) 77 5.1.3 LANGEVIN EQUATION FOR VELOCITY 80 5.2 MANY-BODY LANGEVIN
EQUATION 83 5.2.1 EXACT EQUATIONS OF MOTION FOR A(T) 87 5.2.2 MANY-BODY
LANGEVIN EQUATION FOR A(T) 89 5.2.3 MANY-BODY LANGEVIN EQUATION FOR
VELOCITY 90 5.2.4 LANGEVIN EQUATION FOR THE VELOCITY AND THE FORM OF THE
FRICTION COEFFICIENTS 92 5.3 GENERALISATION TO NON-EQUILIBRIUM . . 94
5.4 THE FOKKER-PLANCK EQUATION AND THE DIFFUSIVE LIMIT 95 5.5 APPROACH
TO THE BROWNIAN LIMIT AND LIMITATIONS 97 5.5.1 A BASIC LIMITATION OF THE
LE AND FP EQUATIONS 98 5.5.2 THE FRICTION COEFFICIENT 98 5.5.3
SELF-DIFFUSION COEFFICIENT (DJ 99 5.5.4 THE INTERMEDIATE SCATTERING
FUNCTION F(Q,T) 102 5.5.5 SYSTEMS IN A SHEAR FIELD 102 5.6 SUMMARY 104
5.7 CONCLUSIONS 104 REFERENCES 105 CONTENTS IX 6 LANGEVIN AND
GENERALISED LANGEVIN DYNAMICS 107 6.1 EXTENSIONS OF THE GLE TO
COLLECTIONS OF PARTICLES 107 6.2 NUMERICAL SOLUTION OF THE LANGEVIN
EQUATION 110 6.2.1 GAUSSIAN RANDOM VARIABLES 111 6.2.2 A BD ALGORITHM TO
FIRST-ORDER IN AF 113 6.2.3 A SECOND FIRST-ORDER BD ALGORITHM 116 6.2.4
A THIRD FIRST-ORDER BD ALGORITHM 118 6.2.5 THE BD ALGORITHM IN THE
DIFFUSIVE LIMIT 120 6.3 HIGHER-ORDER BD SCHEMES FOR THE LANGEVIN
EQUATION 120 6.4 GENERALISED LANGEVIN EQUATION 121 6.4.1 THE METHOD OF
BERKOWITZ, MORGAN AND MCCAMMON 122 6.4.2 THE METHOD OF ERMAK AND
BUCKHOLZ 123 6.4.3 THE METHOD OF CICCOTTI AND RYCKAERT 125 6.4.4 OTHER
METHODS OF SOLVING THE GLE 126 6.5 SYSTEMS IN AN EXTERNAL FIELD 127 6.6
BOUNDARY CONDITIONS IN SIMULATIONS 128 6.6.1 PBC IN EQUILIBRIUM 128
6.6.2 PBC IN A SHEAR FIELD 129 6.6.3 PBC IN ELONGATIONAL FLOW 129 6.7
CONCLUSIONS 131 REFERENCES 131 7 BROWNIAN DYNAMICS 133 7.1 FUNDAMENTALS
133 7.2 CALCULATION OF HYDRODYNAMIC INTERACTIONS 135 7.3 ALTERNATIVE
APPROACHES TO TREAT HYDRODYNAMIC INTERACTIONS 137 7.3.1 THE LATTICE
BOLTZMANN APPROACH 138 7.3.2 DISSIPATIVE PARTICLE DYNAMICS 138 7.4
BROWNIAN DYNAMICS ALGORITHMS 138 7.4.1 THE ALGORITHM OF ERMAK AND
MCCAMMON 138 7.4.2 APPROXIMATE BD SCHEMES 142 7.5 BROWNIAN DYNAMICS IN A
SHEAR FIELD 146 7.6 LIMITATIONS OF THE BD METHOD 148 7.7 ALTERNATIVES TO
BD SIMULATIONS 149 7.7.1 LATTICE BOLTZMANN APPROACH 149 7.7.2
DISSIPATIVE PARTICLE DYNAMICS 150 7.8 CONCLUSIONS 152 REFERENCES 153 8
POLYMER DYNAMICS 157 8.1 TOXVAERD APPROACH 159 8.2 DIRECT USE OF
BROWNIAN DYNAMICS 160 8.3 RIGID SYSTEMS 163 8.4 CONCLUSIONS 166
REFERENCES 166 X CONTENTS 9 THEORIES BASED ON DISTRIBUTION FUNCTIONS,
MASTER EQUATIONS AND STOCHASTIC EQUATIONS 169 9.1 FOKKER-PLANCK EQUATION
170 9.2 THE DIFFUSIVE LIMIT AND THE SMOLUCHOWSKI EQUATION 171 9.2.1
SOLUTION OF THE N-BODY SMOLUCHOWSKI EQUATION 173 9.2.2 POSITION-ONLY
LANGEVIN EQUATION 174 9.3 QUANTUM MONTE CARLO METHOD 176 9.4 MASTER
EQUATIONS 180 9.4.1 THE IDENTIFICATION OF ELEMENTARY PROCESSES 184 9.4.2
KINETIC MC AND MASTER EQUATIONS 186 9.4.3 KMC PROCEDURE WITH CONTINUUM
SOLIDS 187 9.5 CONCLUSIONS 189 REFERENCES 191 10 AN OVERVIEW 197
APPENDIX A: EXPRESSIONS FOR EQUILIBRIUM PROPERTIES, TRANSPORT
COEFFICIENTS AND SCATTERING FUNCTIONS 201 A. 1 EQUILIBRIUM PROPERTIES
201 A.2 EXPRESSIONS FOR LINEAR TRANSPORT COEFFICIENTS 202 A.3 SCATTERING
FUNCTIONS 204 A.3.1 STATIC STRUCTURE 204 A.3.2 DYNAMIC SCATTERING 204
REFERENCES 206 APPENDIX B: SOME BASIC RESULTS ABOUT OPERATORS 20 9
APPENDIX C: PROOFS REQUIRED FOR THE GLE FOR A SELECTED PARTICLE 213
APPENDIX D: THE LANGEVIN EQUATION FROM THE MORI-Z WANZIG APPROACH 217
APPENDIX E: THE FRICTION COEFFICIENT AND FRICTION FACTOR 221 APPENDIX F:
MORI COEFFICIENTS FOR A TWO-COMPONENT SYSTEM 223 EL BASICS 223 E2 SHORT
TIME EXPANSIONS 224 F.3 RELATIVE INITIAL BEHAVIOUR OF C(T) 224 CONTENTS
XI APPENDIX G: TIME-REVERSAL SYMMETRY OF NON-EQUILIBRIUM CORRELATION
FUNCTIONS 225 REFERENCES 227 APPENDIX H: SOME PROOFS NEEDED FOR THE
ALBERS, DEUTCH AND OPPENHEIM TREATMENT 229 APPENDIX I: A PROOF NEEDED
FOR THE DEUTCH AND OPPENHEIM TREATMENT 233 APPENDIX J: THE CALCULATION
OF THE BULK PROPERTIES OF COUOIDS AND POLYMERS 235 J.L EQUILIBRIUM
PROPERTIES 235 J.2 STATIC STRUCTURE 235 J.3 TIME CORRELATION FUNCTIONS
236 J.3.1 SELF-DIFFUSION 236 J.3.2 TIME-DEPENDENT SCATTERING 236 J.3.3
BULK STRESS 237 J.3.4 ZERO TIME (HIGH FREQUENCY) RESULTS IN THE
DIFFUSIVE LIMIT 237 REFERENCES 239 APPENDIX K: MONTE CARLO METHODS 241
K.L METROPOLIS MONTE CARLO TECHNIQUE 241 K.2 AN MC ROUTINE 243
REFERENCES 248 APPENDIX L: THE GENERATION OF RANDOM NUMBERS 249 L. 1
GENERATION OF RANDOM DEVIATES FOR BD SIMULATIONS 249 REFERENCES 250
APPENDIX M: HYDRODYNAMIC INTERACTION TENSORS 251 M.L THE OSEEN TENSOR
FOR TWO BODIES 251 M.2 THE ROTNE-PRAGER TENSOR FOR TWO BODIES 251 M.3
THE SERIES RESULT OF JONES AND BURFIELD FOR TWO BODIES 251 M.4 MAZUR AND
VAN SAARLOOS RESULTS FOR THREE BODIES 252 M.5 RESULTS OF LUBRICATION
THEORY 252 M.6 THE ROTNE-PRAGER TENSOR IN PERIODIC BOUNDARY CONDITIONS
253 REFERENCES 253 APPENDIX N : CALCULATION OF HYDRODYNAMIC INTERACTION
TENSORS 255 REFERENCES 259 APPENDIX O: SOME FORTRAN PROGRAMS 261 INDEX
301
|
| adam_txt |
THE LANGEVIN AND GENERALISED LANGEVIN APPROACH TO THE DYNAMICS OF
ATOMIC, POLYMERIE AND COLLOIDAL SYSTEMS IAN SNOOK APPLIED PHYSICS SCHOOL
OF APPLIED SCIENCES RMIT UNIVERSITY MELBOURNE, AUSTRALIA *J&JJALALHE.
AMSTERDAM * BOSTON * HEIDELBERG * LONDON * NEW YORK * OXFORD ELSEVIER
PARIS * SAN DIEGO * SAN FRANCISCO * SINGAPORE * SYDNEY * TOKYO CONTENTS
PREFACE XIII NOTATION XV 1 BACKGROUND, MECHANICS AND STATISTICAL
MECHANICS 1 1.1 BACKGROUND 1 1.2 THE MECHANICAL DESCRIPTION OF A SYSTEM
OF PARTICLES 3 1.2.1 PHASE SPACE AND EQUATIONS OF MOTION 7 1.2.2 IN
EQUILIBRIUM 7 1.2.3 IN A NON-ISOLATED SYSTEM 9 1.2.4 NEWTON'S EQUATIONS
IN OPERATOR FORM 10 1.2.5 THE LIOUVILLE EQUATION 11 1.2.6 LIOUVILLE
EQUATION IN AN ISOLATED SYSTEM 11 1.2.7 EXPRESSIONS FOR EQUILIBRIUM
THERMODYNAMIC AND LINEAR TRANSPORT PROPERTIES 11 1.2.8 LIOUVILLE
EQUATION IN A NON-ISOLATED SYSTEM 12 1.2.9 NON-EQUILIBRIUM DISTRIBUTION
FUNCTION AND CORRELATION FUNCTIONS 13 1.2.10 OTHER APPROACHES TO
NON-EQUILIBRIUM 15 1.2.11 PROJECTION OPERATORS 15 1.3 SUMMARY 16 1.4
CONCLUSIONS 18 REFERENCES 18 2 THE EQUATION OF MOTION FOR A TYPICAL
PARTICLE AT EQUILIBRIUM: THE MORI-ZWANZIG APPROACH 21 2.1 THE PROJECTION
OPERATOR 21 2.2 THE GENERALISED LANGEVIN EQUATION 23 2.3 THE GENERALISED
LANGEVIN EQUATION IN TERMS OF THE VELOCITY 26 2.4 EQUATION OF MOTION FOR
THE VELOCITY AUTOCORRELATION FUNCTION 28 2.5 THE LANGEVIN EQUATION
DERIVED FROM THE MORI APPROACH: THE BROWNIAN LIMIT 29 2.6 GENERALISATION
TO ANY SET OF DYNAMICAL VARIABLES 30 2.7 MEMORY FUNCTIONS DERIVATION OF
EXPRESSIONS FOR LINEAR TRANSPORT COEFFICIENTS 33 2.8 CORRELATION
FUNCTION EXPRESSION FOR THE COEFFICIENT OF NEWTONIAN VISCOSITY 34 2.9
SUMMARY 38 2.10 CONCLUSIONS 39 REFERENCES 39 VII VIII CONTENTS 3
APPROXIMATE METHODS TO CALCULATE CORRELATION FUNCTIONS AND MORI-ZWANZIG
MEMORY FUNCTIONS 41 3. 1 TAYLOR SERIES EXPANSION 41 3.2 SPECTRA 43 3.3
MORI'S CONTINUED FRACTION METHOD 44 3.4 USE OF INFORMATION THEORY 46 3.5
PERTURBATION THEORIES 48 3.6 MODE COUPLING THEORY 51 3.7 MACROSCOPIC
HYDRODYNAMIC THEORY 52 3.8 MEMORY FUNCTIONS CALCULATED BY THE
MOLECULAR-DYNAMICS METHOD 56 3.9 CONCLUSIONS 57 REFERENCES 57 4 THE
GENERALISED LANGEVIN EQUATION IN NON-EQUILIBRIUM 61 4.1 DERIVATION OF
GENERALISED LANGEVIN EQUATION IN NON-EQUILIBRIUM 62 4.2 LANGEVIN
EQUATION FOR A SINGLE BROWNIAN PARTICIE IN A SHEARING FLUID 66 4.3
CONCLUSIONS 69 REFERENCES 69 5 THE LANGEVIN EQUATION AND THE BROWNIAN
LIMIT 71 5.1 A DILUTE SUSPENSION - ONE LARGE PARTICIE IN A BACKGROUND 72
5.1.1 EXACT EQUATIONS OF MOTION FOR A(T) 75 5.1.2 LANGEVIN EQUATION FOR
A(T) 77 5.1.3 LANGEVIN EQUATION FOR VELOCITY 80 5.2 MANY-BODY LANGEVIN
EQUATION 83 5.2.1 EXACT EQUATIONS OF MOTION FOR A(T) 87 5.2.2 MANY-BODY
LANGEVIN EQUATION FOR A(T) 89 5.2.3 MANY-BODY LANGEVIN EQUATION FOR
VELOCITY 90 5.2.4 LANGEVIN EQUATION FOR THE VELOCITY AND THE FORM OF THE
FRICTION COEFFICIENTS 92 5.3 GENERALISATION TO NON-EQUILIBRIUM . . 94
5.4 THE FOKKER-PLANCK EQUATION AND THE DIFFUSIVE LIMIT 95 5.5 APPROACH
TO THE BROWNIAN LIMIT AND LIMITATIONS 97 5.5.1 A BASIC LIMITATION OF THE
LE AND FP EQUATIONS 98 5.5.2 THE FRICTION COEFFICIENT 98 5.5.3
SELF-DIFFUSION COEFFICIENT (DJ 99 5.5.4 THE INTERMEDIATE SCATTERING
FUNCTION F(Q,T) 102 5.5.5 SYSTEMS IN A SHEAR FIELD 102 5.6 SUMMARY 104
5.7 CONCLUSIONS 104 REFERENCES 105 CONTENTS IX 6 LANGEVIN AND
GENERALISED LANGEVIN DYNAMICS 107 6.1 EXTENSIONS OF THE GLE TO
COLLECTIONS OF PARTICLES 107 6.2 NUMERICAL SOLUTION OF THE LANGEVIN
EQUATION 110 6.2.1 GAUSSIAN RANDOM VARIABLES 111 6.2.2 A BD ALGORITHM TO
FIRST-ORDER IN AF 113 6.2.3 A SECOND FIRST-ORDER BD ALGORITHM 116 6.2.4
A THIRD FIRST-ORDER BD ALGORITHM 118 6.2.5 THE BD ALGORITHM IN THE
DIFFUSIVE LIMIT 120 6.3 HIGHER-ORDER BD SCHEMES FOR THE LANGEVIN
EQUATION 120 6.4 GENERALISED LANGEVIN EQUATION 121 6.4.1 THE METHOD OF
BERKOWITZ, MORGAN AND MCCAMMON 122 6.4.2 THE METHOD OF ERMAK AND
BUCKHOLZ 123 6.4.3 THE METHOD OF CICCOTTI AND RYCKAERT 125 6.4.4 OTHER
METHODS OF SOLVING THE GLE 126 6.5 SYSTEMS IN AN EXTERNAL FIELD 127 6.6
BOUNDARY CONDITIONS IN SIMULATIONS 128 6.6.1 PBC IN EQUILIBRIUM 128
6.6.2 PBC IN A SHEAR FIELD 129 6.6.3 PBC IN ELONGATIONAL FLOW 129 6.7
CONCLUSIONS 131 REFERENCES 131 7 BROWNIAN DYNAMICS 133 7.1 FUNDAMENTALS
133 7.2 CALCULATION OF HYDRODYNAMIC INTERACTIONS 135 7.3 ALTERNATIVE
APPROACHES TO TREAT HYDRODYNAMIC INTERACTIONS 137 7.3.1 THE LATTICE
BOLTZMANN APPROACH 138 7.3.2 DISSIPATIVE PARTICLE DYNAMICS 138 7.4
BROWNIAN DYNAMICS ALGORITHMS 138 7.4.1 THE ALGORITHM OF ERMAK AND
MCCAMMON 138 7.4.2 APPROXIMATE BD SCHEMES 142 7.5 BROWNIAN DYNAMICS IN A
SHEAR FIELD 146 7.6 LIMITATIONS OF THE BD METHOD 148 7.7 ALTERNATIVES TO
BD SIMULATIONS 149 7.7.1 LATTICE BOLTZMANN APPROACH 149 7.7.2
DISSIPATIVE PARTICLE DYNAMICS 150 7.8 CONCLUSIONS 152 REFERENCES 153 8
POLYMER DYNAMICS 157 8.1 TOXVAERD APPROACH 159 8.2 DIRECT USE OF
BROWNIAN DYNAMICS 160 8.3 RIGID SYSTEMS 163 8.4 CONCLUSIONS 166
REFERENCES 166 X CONTENTS 9 THEORIES BASED ON DISTRIBUTION FUNCTIONS,
MASTER EQUATIONS AND STOCHASTIC EQUATIONS 169 9.1 FOKKER-PLANCK EQUATION
170 9.2 THE DIFFUSIVE LIMIT AND THE SMOLUCHOWSKI EQUATION 171 9.2.1
SOLUTION OF THE N-BODY SMOLUCHOWSKI EQUATION 173 9.2.2 POSITION-ONLY
LANGEVIN EQUATION 174 9.3 QUANTUM MONTE CARLO METHOD 176 9.4 MASTER
EQUATIONS 180 9.4.1 THE IDENTIFICATION OF ELEMENTARY PROCESSES 184 9.4.2
KINETIC MC AND MASTER EQUATIONS 186 9.4.3 KMC PROCEDURE WITH CONTINUUM
SOLIDS 187 9.5 CONCLUSIONS 189 REFERENCES 191 10 AN OVERVIEW 197
APPENDIX A: EXPRESSIONS FOR EQUILIBRIUM PROPERTIES, TRANSPORT
COEFFICIENTS AND SCATTERING FUNCTIONS 201 A. 1 EQUILIBRIUM PROPERTIES
201 A.2 EXPRESSIONS FOR LINEAR TRANSPORT COEFFICIENTS 202 A.3 SCATTERING
FUNCTIONS 204 A.3.1 STATIC STRUCTURE 204 A.3.2 DYNAMIC SCATTERING 204
REFERENCES 206 APPENDIX B: SOME BASIC RESULTS ABOUT OPERATORS 20 9
APPENDIX C: PROOFS REQUIRED FOR THE GLE FOR A SELECTED PARTICLE 213
APPENDIX D: THE LANGEVIN EQUATION FROM THE MORI-Z WANZIG APPROACH 217
APPENDIX E: THE FRICTION COEFFICIENT AND FRICTION FACTOR 221 APPENDIX F:
MORI COEFFICIENTS FOR A TWO-COMPONENT SYSTEM 223 EL BASICS 223 E2 SHORT
TIME EXPANSIONS 224 F.3 RELATIVE INITIAL BEHAVIOUR OF C(T) 224 CONTENTS
XI APPENDIX G: TIME-REVERSAL SYMMETRY OF NON-EQUILIBRIUM CORRELATION
FUNCTIONS 225 REFERENCES 227 APPENDIX H: SOME PROOFS NEEDED FOR THE
ALBERS, DEUTCH AND OPPENHEIM TREATMENT 229 APPENDIX I: A PROOF NEEDED
FOR THE DEUTCH AND OPPENHEIM TREATMENT 233 APPENDIX J: THE CALCULATION
OF THE BULK PROPERTIES OF COUOIDS AND POLYMERS 235 J.L EQUILIBRIUM
PROPERTIES 235 J.2 STATIC STRUCTURE 235 J.3 TIME CORRELATION FUNCTIONS
236 J.3.1 SELF-DIFFUSION 236 J.3.2 TIME-DEPENDENT SCATTERING 236 J.3.3
BULK STRESS 237 J.3.4 ZERO TIME (HIGH FREQUENCY) RESULTS IN THE
DIFFUSIVE LIMIT 237 REFERENCES 239 APPENDIX K: MONTE CARLO METHODS 241
K.L METROPOLIS MONTE CARLO TECHNIQUE 241 K.2 AN MC ROUTINE 243
REFERENCES 248 APPENDIX L: THE GENERATION OF RANDOM NUMBERS 249 L. 1
GENERATION OF RANDOM DEVIATES FOR BD SIMULATIONS 249 REFERENCES 250
APPENDIX M: HYDRODYNAMIC INTERACTION TENSORS 251 M.L THE OSEEN TENSOR
FOR TWO BODIES 251 M.2 THE ROTNE-PRAGER TENSOR FOR TWO BODIES 251 M.3
THE SERIES RESULT OF JONES AND BURFIELD FOR TWO BODIES 251 M.4 MAZUR AND
VAN SAARLOOS RESULTS FOR THREE BODIES 252 M.5 RESULTS OF LUBRICATION
THEORY 252 M.6 THE ROTNE-PRAGER TENSOR IN PERIODIC BOUNDARY CONDITIONS
253 REFERENCES 253 APPENDIX N : CALCULATION OF HYDRODYNAMIC INTERACTION
TENSORS 255 REFERENCES 259 APPENDIX O: SOME FORTRAN PROGRAMS 261 INDEX
301 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Snook, Ian |
| author_facet | Snook, Ian |
| author_role | aut |
| author_sort | Snook, Ian |
| author_variant | i s is |
| building | Verbundindex |
| bvnumber | BV023011097 |
| callnumber-first | Q - Science |
| callnumber-label | QA274 |
| callnumber-raw | QA274.23 |
| callnumber-search | QA274.23 |
| callnumber-sort | QA 3274.23 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | UG 3700 |
| ctrlnum | (OCoLC)70176954 (DE-599)BVBBV023011097 |
| dewey-full | 530.14/4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.14/4 |
| dewey-search | 530.14/4 |
| dewey-sort | 3530.14 14 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| discipline_str_mv | Physik |
| edition | 1. ed. |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01698nam a2200481zc 4500</leader><controlfield tag="001">BV023011097</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20080228 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">071120s2007 xxuad|| |||| 00||| eng d</controlfield><datafield tag="010" ind1=" " ind2=" "><subfield code="a">2006048964</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0444521291</subfield><subfield code="9">0-444-52129-1</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780444521293</subfield><subfield code="9">978-0-444-52129-3</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)70176954</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV023011097</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">xxu</subfield><subfield code="c">US</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-703</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA274.23</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">530.14/4</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">UG 3700</subfield><subfield code="0">(DE-625)145627:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Snook, Ian</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">The Langevin and generalised Langevin approach to the dynamics of atomic, polymeric and colloidal systems</subfield><subfield code="c">Ian Snook</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">1. ed.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Amsterdam</subfield><subfield code="b">Elsevier</subfield><subfield code="c">2007</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XVI, 303 S.</subfield><subfield code="b">Ill., graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references and index</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Atom</subfield><subfield code="2">swd</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Kolloid</subfield><subfield code="2">swd</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Langevin-Gleichung</subfield><subfield code="2">swd</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Molekularbewegung</subfield><subfield code="2">swd</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Polymere</subfield><subfield code="2">swd</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Langevin equations</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Brownian movements</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Random dynamical systems</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Physics</subfield></datafield><datafield tag="856" ind1="4" ind2=" "><subfield code="u">http://www.loc.gov/catdir/enhancements/fy0661/2006048964-d.html</subfield><subfield code="3">Publisher description</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">GBV Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016215314&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-016215314</subfield></datafield></record></collection> |
| id | DE-604.BV023011097 |
| illustrated | Illustrated |
| index_date | 2024-07-02T19:09:23Z |
| indexdate | 2024-07-09T21:08:55Z |
| institution | BVB |
| isbn | 0444521291 9780444521293 |
| language | English |
| lccn | 2006048964 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016215314 |
| oclc_num | 70176954 |
| open_access_boolean | |
| owner | DE-703 |
| owner_facet | DE-703 |
| physical | XVI, 303 S. Ill., graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Elsevier |
| record_format | marc |
| spelling | Snook, Ian Verfasser aut The Langevin and generalised Langevin approach to the dynamics of atomic, polymeric and colloidal systems Ian Snook 1. ed. Amsterdam Elsevier 2007 XVI, 303 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Atom swd Kolloid swd Langevin-Gleichung swd Molekularbewegung swd Polymere swd Langevin equations Brownian movements Random dynamical systems Physics http://www.loc.gov/catdir/enhancements/fy0661/2006048964-d.html Publisher description GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016215314&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Snook, Ian The Langevin and generalised Langevin approach to the dynamics of atomic, polymeric and colloidal systems Atom swd Kolloid swd Langevin-Gleichung swd Molekularbewegung swd Polymere swd Langevin equations Brownian movements Random dynamical systems Physics |
| title | The Langevin and generalised Langevin approach to the dynamics of atomic, polymeric and colloidal systems |
| title_auth | The Langevin and generalised Langevin approach to the dynamics of atomic, polymeric and colloidal systems |
| title_exact_search | The Langevin and generalised Langevin approach to the dynamics of atomic, polymeric and colloidal systems |
| title_exact_search_txtP | The Langevin and generalised Langevin approach to the dynamics of atomic, polymeric and colloidal systems |
| title_full | The Langevin and generalised Langevin approach to the dynamics of atomic, polymeric and colloidal systems Ian Snook |
| title_fullStr | The Langevin and generalised Langevin approach to the dynamics of atomic, polymeric and colloidal systems Ian Snook |
| title_full_unstemmed | The Langevin and generalised Langevin approach to the dynamics of atomic, polymeric and colloidal systems Ian Snook |
| title_short | The Langevin and generalised Langevin approach to the dynamics of atomic, polymeric and colloidal systems |
| title_sort | the langevin and generalised langevin approach to the dynamics of atomic polymeric and colloidal systems |
| topic | Atom swd Kolloid swd Langevin-Gleichung swd Molekularbewegung swd Polymere swd Langevin equations Brownian movements Random dynamical systems Physics |
| topic_facet | Atom Kolloid Langevin-Gleichung Molekularbewegung Polymere Langevin equations Brownian movements Random dynamical systems Physics |
| url | http://www.loc.gov/catdir/enhancements/fy0661/2006048964-d.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016215314&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT snookian thelangevinandgeneralisedlangevinapproachtothedynamicsofatomicpolymericandcolloidalsystems |