Schadschneider / Chowdhury / Nishinari Stochastic Transport in Complex Systems

From Molecules to Vehicles
1. Auflage 2010
ISBN: 978-0-08-056052-6
Verlag: Elsevier Science & Techn.
Format: EPUB
Kopierschutz: 6 - ePub Watermark

E-Book, Englisch, 582 Seiten

The first part of the book provides a pedagogical introduction to the physics of complex systems driven far from equilibrium. In this part we discuss the basic concepts and theoretical techniques which are commonly used to study classical stochastic transport in systems of interacting driven particles. The analytical techniques include mean-field theories, matrix product ansatz, renormalization group, etc. and the numerical methods are mostly based on computer simulations. In the second part of the book these concepts and techniques are applied not only to vehicular traffic but also to transport and traffic-like phenomena in living systems ranging from collective movements of social insects (for example, ants) on trails to intracellular molecular motor transport. These demonstrate the conceptual unity of the fundamental principles underlying the apparent diversity of the systems and the utility of the theoretical toolbox of non-equilibrium statistical mechanics in interdisciplinary research far beyond the traditional disciplinary boundaries of physics. - Leading industry experts provide a broad overview of the interdisciplinary nature of physics - Presents unified descriptions of intracellular, ant, and vehicular traffic from a physics point of view - Applies theoretical methods in practical everyday situations - Reference and guide for physicists, engineers and graduate students

Dr. Andreas Schadschneider is Professor at the Institute for Theoretical Physics at the University of Cologne. His research covers various aspects of condensed matter physics ranging from solid state physics to interdisciplinary problems in statistical and biological physics. He has published more than hundred research papers in leading international journals.

Autoren/Hrsg.

Schadschneider, Andreas

Chowdhury, Debashish

Nishinari, Katsuhiro

Inhaltsverzeichnis

1;Front cover;1
2;Stochastic Transport in Complex Systems;4
3;Copyright page;5
4;Dedication ;6
5;Table of contents;8
6;Preface ;16
7;Acknowledgments ;20
8;Part One: Methods and Concepts;22
8.1;Chapter 1. Introduction to Nonequilibrium Systems and Transport Phenomena;24
8.1.1;1.1. Introduction ;24
8.1.2;1.2. Classification of Nonequilibrium Phenomena;25
8.1.3;1.3. Hierarchy of Description at Different Levels;27
8.1.4;1.4. Individual-Based Models;28
8.1.5;1.5. Population-Based Models;31
8.1.6;1.6. Fluid Flow: Theoretical Descriptions at Different Levels;35
8.1.7;1.7. Back to Discrete Models: Mimicking Hydrodynamics with Fictitious Particles;40
8.1.8;1.8. Phase Transitions, Critical Dynamics, and Kinetics of Phase Ordering;43
8.2;Chapter 2. Methods for the Description of Stochastic Models;48
8.2.1;2.1. Quantum Formalism ;49
8.2.2;2.2. Mean-Field and Cluster Methods;58
8.2.3;2.3. Bethe Ansatz ;62
8.2.4;2.4. Matrix-Product Ansatz;64
8.2.5;2.5. Other Methods;73
8.2.6;2.6. Numerical Methods;78
8.2.7;2.7. Appendices ;87
8.3;Chapter 3. Particle-Hopping Models of Transport Far from Equilibrium;92
8.3.1;3.1. Elements of Random Walk Theory;93
8.3.2;3.2. Asymmetric Simple Exclusion Process ;95
8.3.3;3.3. Zero-Range Process and Exact Results;96
8.3.4;3.4. Extensions and Generalizations;102
8.3.5;3.5. Physics of the ZRP;111
8.3.6;3.6. Particle-Hopping Models with Factorized Stationary States;118
8.3.7;3.7. Generalized Mass Transport Models;123
8.3.8;3.8. Appendix ;127
8.4;Chapter 4. Asymmetric Simple Exclusion Process – Exact Results;130
8.4.1;4.1. ASEP with Periodic Boundary Conditions;132
8.4.2;4.2. ASEP with Open Boundary Conditions;152
8.4.3;4.3. Partially Asymmetric Version;166
8.4.4;4.4. Extension of the ASEP to Other Update Types;172
8.4.5;4.5. Boundary-Induced Phase Transitions;179
8.4.6;4.6. Extensions of ASEP;184
8.4.7;4.7. Multispecies Models;202
8.4.8;4.8. Other Related Models;206
8.4.9;4.9. Appendices ;216
9;Part Two: Applications ;228
9.1;Chapter 5. Modeling of Traffic and Transport Processes;230
9.1.1;5.1. Introduction ;230
9.1.2;5.2. Classification of Models;233
9.2;Chapter 6. Vehicular Traffic I: Empirical Facts;236
9.2.1;6.1. Measurement Techniques and Detectors;236
9.2.2;6.2. Observables and Data Analysis;237
9.2.3;6.3. Formation and Characterization of Traffic Jams;242
9.2.4;6.4. Fundamental Diagram ;247
9.2.5;6.5. Metastability and Hysteresis;249
9.2.6;6.6. Phases of Traffic Flow;251
9.2.7;6.7. Ramps, Intersections, and Other Inhomogeneities;256
9.2.8;6.8. Headway Distributions ;257
9.2.9;6.9. Optimal-Velocity Function;259
9.2.10;6.10. Correlation Functions;260
9.2.11;6.11. Psychological Effects ;261
9.3;Chapter 7. Vehicular Traffic II: The Nagel–Schreckenberg Model;264
9.3.1;7.1. Definition of the Model;265
9.3.2;7.2. Fundamental Diagram and Limiting Cases of the NaSch Model;269
9.3.3;7.3. Analytical Theories for NaSch Model with Vmax > 1;276
9.3.4;7.4. Spatio-Temporal Organization of Vehicles;281
9.3.5;7.5. Appendices ;293
9.4;Chapter 8. Vehicular Traffic III: Other CA Models;302
9.4.1;8.1. Slow-to-Start Rules, Metastability, and Hysteresis;303
9.4.2;8.2. Cruise-Control Limit;312
9.4.3;8.3. CA Models of Synchronized Traffic;315
9.4.4;8.4. Other CA Models;325
9.4.5;8.5. CA from Ultradiscrete Method;334
9.4.6;8.6. CA Models of Multilane Traffic;340
9.4.7;8.7. Effects of Quenched Disorder;345
9.4.8;8.8. Bus-Route Model;350
9.4.9;8.9. Accidents ;353
9.5;Chapter 9. Vehicular Traffic IV: Non-CA Approaches;356
9.5.1;9.1. Fluid-Dynamical Theories;357
9.5.2;9.2. Second-Order Fluid Dynamical Theories;363
9.5.3;9.3. Gas-Kinetic Models;372
9.5.4;9.4. Car-Following Models;378
9.5.5;9.5. Coupled-Map Models;392
9.5.6;9.6. Other Approaches ;398
9.6;Chapter 10. Transport on Networks;404
9.6.1;10.1. Networks and Transport;404
9.6.2;10.2. BML Model of City Traffic;405
9.6.3;10.3. Chowdhury–Schadschneider Model;411
9.6.4;10.4. Highway and City Networks;419
9.6.5;10.5. Computer Networks and Internet Traffic;423
9.7;Chapter 11. Pedestrian Dynamics;428
9.7.1;11.1. Introduction ;429
9.7.2;11.2. Empirical Observations and Collective Phenomena;430
9.7.3;11.3. Cellular Automata Models;444
9.7.4;11.4. Floor Field CA;451
9.7.5;11.5. Other Models;468
9.8;Chapter 12. Traffic Phenomena In Biology;482
9.8.1;12.1. Introduction ;482
9.8.2;12.2. TASEP for Hard Rods: Minimal Model of Transcription and Translation;483
9.8.3;12.3. TASEP for Particles with Langmuir Kinetics: Minimal Model of Kinesin Traffic;487
9.8.4;12.4. Traffic in Social Insect Colonies: Ant-Trails;493
10;Guide To The Literature ;510
11;Bibliography ;512
12;Index ;570