Phase Transitions
1st Edition
Published on 18. November 2019
240 pages
978-1-4008-3892-9 (ISBN)
Description
Phase transitions--changes between different states of organization in a complex system--have long helped to explain physics concepts, such as why water freezes into a solid or boils to become a gas. How might phase transitions shed light on important problems in biological and ecological complex systems? Exploring the origins and implications of sudden changes in nature and society, Phase Transitions examines different dynamical behaviors in a broad range of complex systems. Using a compelling set of examples, from gene networks and ant colonies to human language and the degradation of diverse ecosystems, the book illustrates the power of simple models to reveal how phase transitions occur.
Introductory chapters provide the critical concepts and the simplest mathematical techniques required to study phase transitions. In a series of example-driven chapters, Ricard Solé shows how such concepts and techniques can be applied to the analysis and prediction of complex system behavior, including the origins of life, viral replication, epidemics, language evolution, and the emergence and breakdown of societies.
Written at an undergraduate mathematical level, this book provides the essential theoretical tools and foundations required to develop basic models to explain collective phase transitions for a wide variety of ecosystems.
Introductory chapters provide the critical concepts and the simplest mathematical techniques required to study phase transitions. In a series of example-driven chapters, Ricard Solé shows how such concepts and techniques can be applied to the analysis and prediction of complex system behavior, including the origins of life, viral replication, epidemics, language evolution, and the emergence and breakdown of societies.
Written at an undergraduate mathematical level, this book provides the essential theoretical tools and foundations required to develop basic models to explain collective phase transitions for a wide variety of ecosystems.
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Ricard Sole
Phase Transitions
Book
08/2011
Princeton University Press
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Person
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).
Content
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
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
