Stochastic dynamics of complex systems: from glasses to evolution
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London
Imperial College Press
[2013]
|
| Series: | Series on complexity science
2 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xviii, 281 Seiten Illustrationen |
| ISBN: | 9781848169937 |
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MARC
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| 100 | 1 | |a Sibani, Paolo |d 1954- |e Verfasser |0 (DE-588)1111793220 |4 aut | |
| 245 | 1 | 0 | |a Stochastic dynamics of complex systems |b from glasses to evolution |c Paolo Sibani, Henrik Jeldtoft-Jensen |
| 264 | 1 | |a London |b Imperial College Press |c [2013] | |
| 300 | |a xviii, 281 Seiten |b Illustrationen | ||
| 336 | |b txt |2 rdacontent | ||
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-025746370 | ||
Record in the Search Index
| _version_ | 1804150097091493888 |
|---|---|
| adam_text | Contents
Preface v
Acknowledgements
ix
Index
of Figures
xvii
1.
Introduction
1
I Complex Dynamics: Tools and Applications
11
2.
Characterization of Collective Dynamics
13
2.1.
Introduction
13
2.2.
Basic Considerations
14
2.3.
Time Series and their Statistical Properties
17
2.3.1.
Stationary Time Series
18
2.3.2.
Non-stationary Time Series
29
2.3.3.
Stationary or Non-stationary?
33
3.
Markovian Stochastic Processes
35
3.1.
Introduction
35
3.2.
Langevin
Equations
37
3.2.1.
Solution Techniques for the
Langevin
Equation
37
3.2.2.
Ballistic and Diffusive Limit
39
xi
xii
Stochastic Dynamics of Complex Systems
3.3.
General Properties of Markov Processes
41
3.3.1.
Master Equations and Markov Chains
43
3.3.2.
The Propagator and its Moments
46
3.3.3.
Fluctuation-dissipation Theorems
48
3.4.
Relaxation Properties
54
3.4.1.
Relaxation to a Prescribed Stationary State
54
3.4.2.
Eigenvalue Expansions of the Moments
60
3.5.
Markov Chains
61
3.6.
Six Examples of Master Equations
63
3.6.1.
Random Walks in Euclidean Space
65
3.7.
Continuous Time Random Walks
72
3.7.1.
Subordination
72
3.7.2.
Scaling Properties of CTRW
74
3.8.
Fokker-Planck Equations
78
3.8.1.
Stationary Behaviour
82
4.
Monte Carlo Methods
85
4.1.
Introduction
85
4.2.
Importance Sampling
86
4.3.
The Metropolis Algorithm
90
4.4.
Event Driven Algorithms
96
4.4.1.
Standard KMC Methods
98
4.4.2.
Waiting Time Method
99
5.
Record Statistics and Extremal Statistics
101
5.1.
Introduction
101
5.2.
Records in White Noise
102
5.3.
Records and First Passage in Brownian Motion
107
5.4.
Extremal Value Statistics 111
5.4.1.
Relation between Record and Extreme
Value Statistics
118
5.5.
Summary
120
6.
Complexity and Hierarchies
121
6.1.
Introduction
121
Contents xiii
6.2. Kinetically
Constrained Hierarchical
Dynamics 124
6.3.
Dynamical Hierarchies in Thermal Relaxation
128
7.
Energy Landscapes
131
7.1.
Introduction
131
7.2.
Modelling Energy Landscapes
133
7.2.1.
Coarse-graining and the Kramers
Approximation
133
7.2.2.
Applying the Kramers Approximation
to a Hierarchical Landscape Model
137
7.3.
Exploring Energy Landscapes
143
8.
Record Dynamics and Marginal Stability
149
8.1.
Introduction
149
8.2.
Coarse-Graining Complex Dynamics
150
8.3.
Marginal Stability
152
8.4.
Homogeneity of Record Dynamics
in Logarithmic Time
153
8.5.
Scaling Behaviour in Record Dynamics
158
II Complex Systems with Similar Dynamics
161
9.
Ageing of Spin Glasses
163
9.1.
Introduction
163
9.2.
Spin Glasses
164
9.2.1.
The Order Parameter
166
9.2.2.
Are Spin Glasses in Equilibrium?
167
9.2.3.
Ageing: Experimental and Numerical
Observations
170
9.3.
Theoretical Considerations
183
9.3.1.
Theoretical Outlook
192
10.
Magnetic Relaxation in Superconductors
195
10.1.
Introduction I95
10.2.
Magnetic Fields and Type II Superconductors
196
xiv
Stochastic Dynamics of Complex Systems
10.3.
Restricted Occupancy Model
197
10.4.
Intermittent Magnetic Relaxation
200
11.
Ageing of Colloids
207
11.1.
Introduction
207
11.2.
Hard Sphere Colloids
209
11.2.1.
The Critical Density
210
11.2.2.
Non-ergodic Ageing Behaviour
213
11.3.
A Heuristic Model
215
11.4.
Conclusion
218
12.
Evolving Biological Systems
219
12.1.
Introduction
219
12.2.
Models of Biological Evolution
220
12.3.
Quasi-Species Model
222
12.4.
Kauffman Models
224
12.4.1.
NK Model
224
12.4.2.
NKC Model
226
12.5.
Bak-Sneppen Model
227
12.6.
Tangled Nature Model
229
12.6.1.
Model Description
230
12.6.2.
General Qualitative Behaviour
231
12.6.3.
The Time Arrow in the Tangled
Nature Model
233
12.6
A. The Evolution of the Fluctuations
in Birth Rate
237
12.6.5.
The Offspring Probability
and Adaptation
239
12.7.
Conclusions
241
13.
Non-stationary Ageing Dynamics in Ant Societies
245
13.1.
Introduction
245
13.2.
Model Description
246
13.3.
General Considerations
248
Contents xv
13.4. Data
Analysis
251
13.5.
Discussion
254
III Epilogue
257
14.
What is Complexity Science?
259
Bibliography
263
Index
273
|
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| author | Sibani, Paolo 1954- Jensen, Henrik Jeldtoft 1956- |
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| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.23 |
| dewey-search | 519.23 |
| dewey-sort | 3519.23 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV040767938 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:33:30Z |
| institution | BVB |
| isbn | 9781848169937 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025746370 |
| oclc_num | 807040360 |
| open_access_boolean | |
| owner | DE-473 DE-BY-UBG DE-29T DE-188 DE-11 |
| owner_facet | DE-473 DE-BY-UBG DE-29T DE-188 DE-11 |
| physical | xviii, 281 Seiten Illustrationen |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Imperial College Press |
| record_format | marc |
| series | Series on complexity science |
| series2 | Series on complexity science |
| spelling | Sibani, Paolo 1954- Verfasser (DE-588)1111793220 aut Stochastic dynamics of complex systems from glasses to evolution Paolo Sibani, Henrik Jeldtoft-Jensen London Imperial College Press [2013] xviii, 281 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Series on complexity science 2 Stochastisches dynamisches System (DE-588)4305316-6 gnd rswk-swf Stochastisches dynamisches System (DE-588)4305316-6 s DE-604 Jensen, Henrik Jeldtoft 1956- Verfasser (DE-588)131894528 aut Series on complexity science 2 (DE-604)BV039961107 2 Digitalisierung UB Bamberg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025746370&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sibani, Paolo 1954- Jensen, Henrik Jeldtoft 1956- Stochastic dynamics of complex systems from glasses to evolution Series on complexity science Stochastisches dynamisches System (DE-588)4305316-6 gnd |
| subject_GND | (DE-588)4305316-6 |
| title | Stochastic dynamics of complex systems from glasses to evolution |
| title_auth | Stochastic dynamics of complex systems from glasses to evolution |
| title_exact_search | Stochastic dynamics of complex systems from glasses to evolution |
| title_full | Stochastic dynamics of complex systems from glasses to evolution Paolo Sibani, Henrik Jeldtoft-Jensen |
| title_fullStr | Stochastic dynamics of complex systems from glasses to evolution Paolo Sibani, Henrik Jeldtoft-Jensen |
| title_full_unstemmed | Stochastic dynamics of complex systems from glasses to evolution Paolo Sibani, Henrik Jeldtoft-Jensen |
| title_short | Stochastic dynamics of complex systems |
| title_sort | stochastic dynamics of complex systems from glasses to evolution |
| title_sub | from glasses to evolution |
| topic | Stochastisches dynamisches System (DE-588)4305316-6 gnd |
| topic_facet | Stochastisches dynamisches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025746370&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV039961107 |
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