Random and restricted walks: theory and applications
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Gordon and Breach
1970
|
| Schriftenreihe: | Mathematics and its applications
10 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 176 S. Illustrationen |
| ISBN: | 067702620X |
Internformat
MARC
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| 245 | 1 | 0 | |a Random and restricted walks |b theory and applications |c Michael N. Barber and B. W. Ninham |
| 264 | 1 | |a New York [u.a.] |b Gordon and Breach |c 1970 | |
| 300 | |a XIII, 176 S. |b Illustrationen | ||
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Datensatz im Suchindex
| _version_ | 1804118308986814464 |
|---|---|
| adam_text | Contents
Chapter 1—Introduction .......... 1
PART A THEORY 3
Chapter 2—Problem of random walk 5
2.1 Concept of Random Walk 5
2.2 Probability Distribution and Characteristic Functions ... 6
2.3 General Solution of Random Walk Problem ..... 8
2.4 Gaussian Distribution 9
2.5 Pearson s Walk 10
2.6 Asymptotic Behavior 13
Chapter 3—Lattice walks 16
3.1 Lattice Walk Generating Functions. ...... 16
3.2 One Dimensional Walk 20
3.3 Polya s Theorem and Escape Probabilities 21
3.4 Number of Points Visited in n step Walk 26
3.5 Repeated Occupancy ......... 28
Chapter 4—Walks in continuous time ......•• 31
4.1 Lattice Walks in Continuous Time ....... 31
4.2 Master Equation .......•• 33
4.3 ID Walk in Continuous Time 34
4.4 Random Walks and Bessel Functions ...... 36
Chapter 5—Spatial restrictions .......•• 37
5.1 Absorbing and Reflecting Barriers ¦ ¦ 37
5.2 A Perturbation Theory 39
5.3 Walks on Defective Lattices 41
Chapter 6—Correlated walks ......... 46
6.1 Effect of Correlations 46
6.2 Mean Square Displacement of a Correlated Walk .... 48
6.3 Walks with Restricted Reversals 52
6.4 Walk with Excluded Origin 56
6.5 Gaussian Walk and Overlaps 58
xi
Xli CONTENTS
Chapter 7—Self avoiding walks 60
7.1 Analytic Results 60
7.2 Numerical Results 62
7.3 Probability Distribution and Mean Square Displacement ... 65
7.4 A Soluble Problem 69
PART B APPLICATIONS 73
Chapter 8—Diffusion and Brownian motion ....... 75
8.1 Diffusion Equation 75
8.2 Brownian Motion ......... 78
8.3 Percolation Processes 79
Chapter 9—Configurational statistics of polymers 81
9.1 Random Flight Chains 82
9.2 Chains with Hindered Rotations and The Equivalent Chain . . 84
9.3 Excluded Volume Problem 86
9.4 Self Consistent Field and Excluded Volume Problem ... 91
Chapter 10—Polymers in solution ......... 96
10.1 Polymer Configurations with Solvent Interaction .... 96
10.2 Thermodynamic Functions 99
10.3 Virial Coefficients 101
Chapter 11—Polymer adsorption ......... 103
11.1 Random Walk Models of Adsorption 104
11.2 Statistical Mechanical Formulation 107
11.3 Effect of Self Exclusion Ill
Chapter 12—Solid state applications 113
12.1 Lattice Vibrations 113
12.2 Luminescence 116
12.3 Diffusion in Solids 117
12.4 Spin Waves 118
Chapter 13—Relation to Ising problem 119
Chapter 14—Other applications 122
14.1 Chemical Kinetics 122
14.2 Astronomy 124
14.3 Numerical Analysis 126
14.4 Rubber Elasticity 127
14.5 Network Theory and Exciton Trapping on Photosynthetic Units . 128
t
CONTENTS Xiii
References 130
Addendum ............ 141
Appendix A—Evaluation of the Watson integrals ...... 147
Appendix At—Asymptotic analysis of Kasteleyn s product .... 158
Appendix B—An argument of M. E. Fisher 163
Appendix C — Distribution function for freely jointed chain of finite length . . 167
Appendix D—Mean square distance of a chain element from center of mass . 170
Appendix E—Perturbation theory of excluded volume effects .... 172
|
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| id | DE-604.BV004083462 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:08:15Z |
| institution | BVB |
| isbn | 067702620X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002550497 |
| oclc_num | 630880850 |
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| physical | XIII, 176 S. Illustrationen |
| psigel | TUB-www |
| publishDate | 1970 |
| publishDateSearch | 1970 |
| publishDateSort | 1970 |
| publisher | Gordon and Breach |
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| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Barber, Michael N. 1947- Verfasser (DE-588)1065211651 aut Random and restricted walks theory and applications Michael N. Barber and B. W. Ninham New York [u.a.] Gordon and Breach 1970 XIII, 176 S. Illustrationen txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 10 Irrfahrtsproblem (DE-588)4162442-7 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 s DE-604 Irrfahrtsproblem (DE-588)4162442-7 s Ninham, Barry W. Verfasser aut Mathematics and its applications 10 (DE-604)BV008163334 10 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002550497&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Barber, Michael N. 1947- Ninham, Barry W. Random and restricted walks theory and applications Mathematics and its applications Irrfahrtsproblem (DE-588)4162442-7 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4162442-7 (DE-588)4057630-9 |
| title | Random and restricted walks theory and applications |
| title_auth | Random and restricted walks theory and applications |
| title_exact_search | Random and restricted walks theory and applications |
| title_full | Random and restricted walks theory and applications Michael N. Barber and B. W. Ninham |
| title_fullStr | Random and restricted walks theory and applications Michael N. Barber and B. W. Ninham |
| title_full_unstemmed | Random and restricted walks theory and applications Michael N. Barber and B. W. Ninham |
| title_short | Random and restricted walks |
| title_sort | random and restricted walks theory and applications |
| title_sub | theory and applications |
| topic | Irrfahrtsproblem (DE-588)4162442-7 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Irrfahrtsproblem Stochastischer Prozess |
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