Brownian motion: fluctuations, dynamics, and applications
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford [u.a.]
Oxford Univ. Press
2009
|
| Ausgabe: | 1. publ. in paperback |
| Schriftenreihe: | The international series of monographs on physics
112 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 289 S. graph. Darst. |
| ISBN: | 9780199556441 9780198515678 |
Internformat
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| 100 | 1 | |a Mazo, Robert M. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Brownian motion |b fluctuations, dynamics, and applications |c Robert M. Mazo |
| 250 | |a 1. publ. in paperback | ||
| 264 | 1 | |a Oxford [u.a.] |b Oxford Univ. Press |c 2009 | |
| 300 | |a XII, 289 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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Datensatz im Suchindex
| _version_ | 1804138115362717696 |
|---|---|
| adam_text | CONTENTS
Historical Background
1
1.1
Robert Brown
1
1.2
Between Brown and Einstein
3
1.3
Albert Einstein
5
1.4
Marian
von Smoluchowski 7
1.5
Molecular Reality
8
1.6
The Scope of this Book
10
Probability Theory
11
2.1
Probability
11
2.2
Conditional Probability and Independence
14
2.3
Random Variables and Probability Distributions
16
2.4
Expectations and Particular Distributions
18
2.5
Characteristic Function; Sums of Random Variables
23
2.6
Conclusion
25
Stochastic Processes
26
3.1
Stochastic Processes
26
3.2
Distribution Functions
27
3.3
Classification of Stochastic Processes
29
3.4
The Fokker-Planck Equation
33
3.5
Some Special Processes
35
3.6
Calculus of Stochastic Processes
37
3.7
Fourier Analysis of Random Processes
40
3.8
White Noise
43
3.9
Conclusion
45
Einstein—Smoluchowski Theory
46
4.1
What is Brownian Motion?
46
4.2
Smoluchowski s Theory
48
4.3
Smoluchowski Theory Continued
52
4.4
Einstein s Theory
54
4.5
Diffusion Coefficient and Friction Constant
57
4.6
The
Langevin
Theory
59
Stochastic Differential Equations and Integrals
62
5.1
The
Langevin
Equation Revisited
62
5.2
Stochastic Differential Equations
64
5.3
Which Rule Should Be Used?
67
5.4
Some Examples
69
ix
CONTENTS
6
Functional
Integrals 71
6.1
Functional
Integrals 71
6.2 The Wiener Integral 72
6.3 Wiener
Measure
74
6.4 The Feynman-Kac
Formula
76
6.5
Feynman Path
Integrals 78
6.6 Evaluation
of
Wiener Integrals 79
6.7 Applications
of Functional
Integrals 82
7
Some Important
Special
Cases
83
7.1
Several Cases of Interest
83
7.2
The Free Particle
83
7.3
The Distribution of Displacements
85
7.4
The Harmonically Bound Particle
87
7.5
A Particle in a Constant Force Field
92
7.6
The
Uniaxial
Rotor
93
7.7
An Equation for the Distribution of Displacements
94
7.8
Discussion
95
8
The Smoluchowski Equation
97
8.1
The Kramers-Klein Equation
97
8.2
The Smoluchowski Equation
98
8.3
Elimination of Fast Variables
101
8.4
The Smoluchowski Equation Continued
104
8.5
Passage over Potential Barriers
105
8.6
Concluding Remarks
108
9
Random Walk 111
9.1
The Random Walk 111
9.2
The One-Dimensional Pearson Walk
112
9.3
The Biased Random Walk
114
9.4
The Persistent Walk
117
9.5
Boundaries and First Passage Times
120
9.6
Random Remarks on Random Walks
125
10
Statistical Mechanics
127
10.1
Molecular Distribution Functions
127
10.2
The Liouville Equation
129
10.3
Projection Operators
—
The
Zwanzig
Equation
131
10.4
Projection Operators
—
The Mori Equation
133
10.5
Concluding Remarks
136
11
Stochastic Equations from a Statistical Mechanical
Viewpoint
138
11.1
The
Langevin
Equation A Heuristic View
138
11.2
The Fokker-Planck Equation—A Heuristic View
141
CONTENTS
11.3
What is Wrong with these Derivations?
144
11.4
Eliminating Fast Processes
146
11.5
The Distribution Function
153
11.6
Discussion
157
12
Two Exactly Treatable Models
159
12.1
Two Illustrative Examples
159
12.2
Brownian Motion in a Dilute Gas
159
12.3
Discussion
162
12.4
The Particle Bound to a Lattice
163
12.5
The One-Dimensional Case
167
12.6
Discussion
169
13
Brownian Motion and Noise
170
13.1
Limits on Measurement
170
13.2
Oscillations of a Fiber
171
13.3
A Pneumatic Example
174
13.4
Electrical Systems
178
13.5
Discussion
181
14
Diffusion Phenomena
183
14.1
Brownian Motion in Configuration Space
183
14.2
Diffusion Controlled Reactions
183
14.3
The Effect of Forces
187
14.4
The Coagulation of Colloids
191
14.5
Taylor Diffusion
192
15
Rotational Diffusion
197
15.1
Rotational Diffusion
197
15.2
Fluorescence Depolarization
201
15.3
Non-Spherical Brownian Particles
204
15.4
Concluding Remarks
207
16
Polymer Solutions
208
16.1
A Model for Dilute Solutions of Polymers
208
16.2
Hydrodynamic Interaction
210
16.3
The Equation of Motion
212
16.4
Diffusion and Intrinsic Viscosity
214
16.5
Historical Remarks and Additional Reading
219
17
Interacting Brownian Particles
222
17.1
Effects of Concentration
222
17.2
The Fokker-Planck Equation
223
17.3
The Multiparticle Smoluchowski Equation
226
17.4
The Diffusion Coefficient
228
17.5
The Viscosity
235
17.6
Concluding Remarks
238
xii CONTENTS
18 Dynamics,
Fractals, and
Chaos 240
18.1 Brownian Dynamics 240
18.2 Brownian
Paths as Fractals
246
18.3 Brownian Motion and Chaos 251
18.4
Concluding Remarks
257
A The Applicability of Stokes Law
258
В
Functional Calculus
260
С
An Operator Identity
263
D
Euler
Angles
264
E
The
Oseen
Tensor
266
F
Mutual Diffusion and Self-Diffusion
268
F.I Mutual Diffusion
268
F.2 Self-Diffusion
269
F.3 Relation between Dm and Ds
269
References
271
Index
285
|
| adam_txt |
CONTENTS
Historical Background
1
1.1
Robert Brown
1
1.2
Between Brown and Einstein
3
1.3
Albert Einstein
5
1.4
Marian
von Smoluchowski 7
1.5
Molecular Reality
8
1.6
The Scope of this Book
10
Probability Theory
11
2.1
Probability
11
2.2
Conditional Probability and Independence
14
2.3
Random Variables and Probability Distributions
16
2.4
Expectations and Particular Distributions
18
2.5
Characteristic Function; Sums of Random Variables
23
2.6
Conclusion
25
Stochastic Processes
26
3.1
Stochastic Processes
26
3.2
Distribution Functions
27
3.3
Classification of Stochastic Processes
29
3.4
The Fokker-Planck Equation
33
3.5
Some Special Processes
35
3.6
Calculus of Stochastic Processes
37
3.7
Fourier Analysis of Random Processes
40
3.8
White Noise
43
3.9
Conclusion
45
Einstein—Smoluchowski Theory
46
4.1
What is Brownian Motion?
46
4.2
Smoluchowski's Theory
48
4.3
Smoluchowski Theory Continued
52
4.4
Einstein's Theory
54
4.5
Diffusion Coefficient and Friction Constant
57
4.6
The
Langevin
Theory
59
Stochastic Differential Equations and Integrals
62
5.1
The
Langevin
Equation Revisited
62
5.2
Stochastic Differential Equations
64
5.3
Which Rule Should Be Used?
67
5.4
Some Examples
69
ix
CONTENTS
6
Functional
Integrals 71
6.1
Functional
Integrals 71
6.2 The Wiener Integral 72
6.3 Wiener
Measure
74
6.4 The Feynman-Kac
Formula
76
6.5
Feynman Path
Integrals 78
6.6 Evaluation
of
Wiener Integrals 79
6.7 Applications
of Functional
Integrals 82
7
Some Important
Special
Cases
83
7.1
Several Cases of Interest
83
7.2
The Free Particle
83
7.3
The Distribution of Displacements
85
7.4
The Harmonically Bound Particle
87
7.5
A Particle in a Constant Force Field
92
7.6
The
Uniaxial
Rotor
93
7.7
An Equation for the Distribution of Displacements
94
7.8
Discussion
95
8
The Smoluchowski Equation
97
8.1
The Kramers-Klein Equation
97
8.2
The Smoluchowski Equation
98
8.3
Elimination of Fast Variables
101
8.4
The Smoluchowski Equation Continued
104
8.5
Passage over Potential Barriers
105
8.6
Concluding Remarks
108
9
Random Walk 111
9.1
The Random Walk 111
9.2
The One-Dimensional Pearson Walk
112
9.3
The Biased Random Walk
114
9.4
The Persistent Walk
117
9.5
Boundaries and First Passage Times
120
9.6
Random Remarks on Random Walks
125
10
Statistical Mechanics
127
10.1
Molecular Distribution Functions
127
10.2
The Liouville Equation
129
10.3
Projection Operators
—
The
Zwanzig
Equation
131
10.4
Projection Operators
—
The Mori Equation
133
10.5
Concluding Remarks
136
11
Stochastic Equations from a Statistical Mechanical
Viewpoint
138
11.1
The
Langevin
Equation A Heuristic View
138
11.2
The Fokker-Planck Equation—A Heuristic View
141
CONTENTS
11.3
What is Wrong with these Derivations?
144
11.4
Eliminating Fast Processes
146
11.5
The Distribution Function
' 153
11.6
Discussion
157
12
Two Exactly Treatable Models
159
12.1
Two Illustrative Examples
159
12.2
Brownian Motion in a Dilute Gas
159
12.3
Discussion
162
12.4
The Particle Bound to a Lattice
163
12.5
The One-Dimensional Case
167
12.6
Discussion
169
13
Brownian Motion and Noise
170
13.1
Limits on Measurement
170
13.2
Oscillations of a Fiber
171
13.3
A Pneumatic Example
174
13.4
Electrical Systems
178
13.5
Discussion
181
14
Diffusion Phenomena
183
14.1
Brownian Motion in Configuration Space
183
14.2
Diffusion Controlled Reactions
183
14.3
The Effect of Forces
187
14.4
The Coagulation of Colloids
191
14.5
Taylor Diffusion
192
15
Rotational Diffusion
197
15.1
Rotational Diffusion
197
15.2
Fluorescence Depolarization
201
15.3
Non-Spherical Brownian Particles
204
15.4
Concluding Remarks
207
16
Polymer Solutions
208
16.1
A Model for Dilute Solutions of Polymers
208
16.2
Hydrodynamic Interaction
210
16.3
The Equation of Motion
212
16.4
Diffusion and Intrinsic Viscosity
214
16.5
Historical Remarks and Additional Reading
219
17
Interacting Brownian Particles
222
17.1
Effects of Concentration
222
17.2
The Fokker-Planck Equation
223
17.3
The Multiparticle Smoluchowski Equation
226
17.4
The Diffusion Coefficient
228
17.5
The Viscosity
235
17.6
Concluding Remarks
238
xii CONTENTS
18 Dynamics,
Fractals, and
Chaos 240
18.1 Brownian Dynamics 240
18.2 Brownian
Paths as Fractals
246
18.3 Brownian Motion and Chaos 251
18.4
Concluding Remarks
257
A The Applicability of Stokes' Law
258
В
Functional Calculus
260
С
An Operator Identity
263
D
Euler
Angles
264
E
The
Oseen
Tensor
266
F
Mutual Diffusion and Self-Diffusion
268
F.I Mutual Diffusion
268
F.2 Self-Diffusion
269
F.3 Relation between Dm and Ds
269
References
271
Index
285 |
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| author | Mazo, Robert M. |
| author_facet | Mazo, Robert M. |
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| discipline | Chemie / Pharmazie Physik Mathematik |
| discipline_str_mv | Chemie / Pharmazie Physik Mathematik |
| edition | 1. publ. in paperback |
| format | Book |
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| id | DE-604.BV035132703 |
| illustrated | Illustrated |
| index_date | 2024-07-02T22:24:57Z |
| indexdate | 2024-07-09T21:23:03Z |
| institution | BVB |
| isbn | 9780199556441 9780198515678 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016800199 |
| oclc_num | 273500181 |
| open_access_boolean | |
| owner | DE-20 DE-83 DE-11 DE-703 |
| owner_facet | DE-20 DE-83 DE-11 DE-703 |
| physical | XII, 289 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Oxford Univ. Press |
| record_format | marc |
| series | The international series of monographs on physics |
| series2 | The international series of monographs on physics Oxford science publications |
| spelling | Mazo, Robert M. Verfasser aut Brownian motion fluctuations, dynamics, and applications Robert M. Mazo 1. publ. in paperback Oxford [u.a.] Oxford Univ. Press 2009 XII, 289 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier The international series of monographs on physics 112 Oxford science publications Brownian hareket işlemi Olasılık Brownian motion processes Probabilities Brownsche Bewegung (DE-588)4128328-4 gnd rswk-swf Dynamik (DE-588)4013384-9 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Fluktuation Statistik (DE-588)4154794-9 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 s Brownsche Bewegung (DE-588)4128328-4 s DE-604 Fluktuation Statistik (DE-588)4154794-9 s Dynamik (DE-588)4013384-9 s The international series of monographs on physics 112 (DE-604)BV000106406 112 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016800199&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mazo, Robert M. Brownian motion fluctuations, dynamics, and applications The international series of monographs on physics Brownian hareket işlemi Olasılık Brownian motion processes Probabilities Brownsche Bewegung (DE-588)4128328-4 gnd Dynamik (DE-588)4013384-9 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Fluktuation Statistik (DE-588)4154794-9 gnd |
| subject_GND | (DE-588)4128328-4 (DE-588)4013384-9 (DE-588)4057630-9 (DE-588)4154794-9 |
| title | Brownian motion fluctuations, dynamics, and applications |
| title_auth | Brownian motion fluctuations, dynamics, and applications |
| title_exact_search | Brownian motion fluctuations, dynamics, and applications |
| title_exact_search_txtP | Brownian motion fluctuations, dynamics, and applications |
| title_full | Brownian motion fluctuations, dynamics, and applications Robert M. Mazo |
| title_fullStr | Brownian motion fluctuations, dynamics, and applications Robert M. Mazo |
| title_full_unstemmed | Brownian motion fluctuations, dynamics, and applications Robert M. Mazo |
| title_short | Brownian motion |
| title_sort | brownian motion fluctuations dynamics and applications |
| title_sub | fluctuations, dynamics, and applications |
| topic | Brownian hareket işlemi Olasılık Brownian motion processes Probabilities Brownsche Bewegung (DE-588)4128328-4 gnd Dynamik (DE-588)4013384-9 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Fluktuation Statistik (DE-588)4154794-9 gnd |
| topic_facet | Brownian hareket işlemi Olasılık Brownian motion processes Probabilities Brownsche Bewegung Dynamik Stochastischer Prozess Fluktuation Statistik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016800199&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000106406 |
| work_keys_str_mv | AT mazorobertm brownianmotionfluctuationsdynamicsandapplications |