Phase Transitions

Overview

"This ambitious book provides an elegant and much-needed synthesis to many of the ideas that have come to define the field of complex systems and their applications to nature and society. It makes an important contribution to the field, especially for researchers and students looking for an overview of the literature and entry points for research."?Luis Bettencourt, Los Alamos National Laboratory and the Santa Fe Institute

"This clear and easy-to-follow book is a valuable compilation of systems showing phase ...

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Phase Transitions

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Overview

"This ambitious book provides an elegant and much-needed synthesis to many of the ideas that have come to define the field of complex systems and their applications to nature and society. It makes an important contribution to the field, especially for researchers and students looking for an overview of the literature and entry points for research."—Luis Bettencourt, Los Alamos National Laboratory and the Santa Fe Institute

"This clear and easy-to-follow book is a valuable compilation of systems showing phase transition phenomena that have become more and more important in understanding natural and man-made complex systems. It is a useful addition to the already existing literature."—Stefan Thurner, Medical University of Vienna

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Editorial Reviews

Journal of Artificial Societies and Social Simulation
Solé has compiled an interesting overview of the vast amount of real world systems in which phases play a role. It is a good introduction to the topic and the great variety of applications is inspirational. Phase Transitions is a good read for the JASSS audience interested in if, how, and when abrupt changes may occur—either as risks for collapse or as opportunities for salvation.
— Emile Chappin
BioScience
Mean-field approaches constitute an elegant and considerable contribution to complex systems studies, and I commend Sole for his rigorous presentation.
— Lael Parrott
Journal of Artificial Societies and Social Simulation - Emile Chappin
Solé has compiled an interesting overview of the vast amount of real world systems in which phases play a role. It is a good introduction to the topic and the great variety of applications is inspirational. Phase Transitions is a good read for the JASSS audience interested in if, how, and when abrupt changes may occur—either as risks for collapse or as opportunities for salvation.
BioScience - Lael Parrott
Mean-field approaches constitute an elegant and considerable contribution to complex systems studies, and I commend Sole for his rigorous presentation.
From the Publisher
"Solé has compiled an interesting overview of the vast amount of real world systems in which phases play a role. It is a good introduction to the topic and the great variety of applications is inspirational. Phase Transitions is a good read for the JASSS audience interested in if, how, and when abrupt changes may occur—either as risks for collapse or as opportunities for salvation."—Emile Chappin, Journal of Artificial Societies and Social Simulation

"Mean-field approaches constitute an elegant and considerable contribution to complex systems studies, and I commend Sole for his rigorous presentation."—Lael Parrott, BioScience

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Product Details

  • ISBN-13: 9780691150758
  • Publisher: Princeton University Press
  • Publication date: 8/14/2011
  • Series: Primers in Complex Systems Series
  • Pages: 264
  • Sales rank: 1,400,750
  • Product dimensions: 5.40 (w) x 8.40 (h) x 0.70 (d)

Meet the Author

Ricard V. Solé is research professor and head of the Complex Systems Lab at Pompeu Fabra University and external professor at the Santa Fe Institute. He is the coauthor of "Signs of Life" (Basic) and "Self-Organization in Complex Ecosystems" (Princeton).

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Table of Contents

Preface xi

Chapter 1. Phase Changes 1
1.1 Complexity 1
1.2 Phase diagrams 4
1.3 Interactions make a difference 7
1.4 The Ising model: From micro to macro 11
1.5 Monte Carlo simulation 13
1.6 Scaling and universality 17
1.7 Mean field Ising model 18
1.8 Nonequilibrium transitions 23

Chapter 2. Stability and Instability 25
2.1 Dynamical systems 25
2.2 Attractors 27
2.3 Nonlinear dynamics 30
2.4 Linear stability analysis 33

Chapter 3. Bifurcations and Catastrophes 37
3.1 Qualitative changes 37
3.2 Symmetry breaking 38
3.3 Catastrophes and breakpoints 43
3.4 Critical slowing down 49
3.5 Multiple broken symmetries 51

Chapter 4. Percolation 53
4.1 Systems are connected 53
4.2 Percolation thresholds 54
4.3 Percolation is widespread 57
4.4 Bethe lattices 59

Chapter 5. Random Graphs 63
5.1 The Erdos-Renyi model 63
5.2 Statistical patterns 64
5.3 Percolation at critical connectivity 65
5.4 Real networks are heterogeneous 68

Chapter 6. Life Origins 70
6.1 Prebiotic evolution 70
6.2 Replicators and reproducers 71
6.3 Autocatalysis and cooperation 72
6.4 Prebiotic reaction networks 75

Chapter 7. Virus Dynamics 78
7.1 Molecular parasites 78
7.2 Exploring the hypercube 80
7.3 Swetina-Schuster quasispecies model 84
7.4 Critical genome size 87
7.5 Beyond the threshold 88

Chapter 8. Cell Structure 91
8.1 The architecture of cells 91
8.2 States and transitions 94
8.3 Dynamical instability model 95
8.4 Tensegrity 97

Chapter 9. Epidemic Spreading 99
9.1 Spreading diseases 99
9.2 SIS model 102
9.3 Vaccination thresholds 105
9.4 Pathogens and networks 107

Chapter 10. Gene Networks 109
10.1 Genes and cell types 109
10.2 Boolean dynamics 112
10.3 Percolation analysis 113
10.4 Is cell dynamics Boolean? 118

Chapter 11. Cancer Dynamics 120
11.1 Abnormal growth 120
11.2 Tumor decay under immune attack 122
11.3 Thresholds in cancer instability 128
11.4 Cancer as an evolving system 132

Chapter 12. Ecological Shifts 134
12.1 Change in ecology 134
12.2 Green-desert transitions 136
12.3 Continuous transitions 138
12.4 Sudden shifts 140
12.5 Metapopulation dynamics 143
12.6 Warning signals 146

Chapter 13. Information and Traffic Jams 148
13.1 Internet and computer networks 148
13.2 Mean field model of traffic flow 150
13.3 Fluid flow and congestion explosion 152
13.4 Self-regulated traffic 154

Chapter 14. Collective Intelligence 157
14.1 Swarm behavior 157
14.2 Foraging and broken symmetry 159
14.3 Order-disorder transitions in ant colonies 162
14.4 Structure and evolution in social insects 165

Chapter 15. Language 167
15.1 Lexical change 167
15.2 Words: Birth and death 169
15.3 String models 171
15.4 Symmetric model 174
15.5 Language thresholds 176

Chapter 16. Social Collapse 179
16.1 Rise and fall 179
16.2 Slow responses and sunk-cost effects 181
16.3 Ecological model of social collapse 182
16.4 Historical dynamics 186

References 189
Index 213

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