Brownian Agents and Active Particles (eBook)

Foreword 6
Preface 10
Contents 13
1. Complex Systems and Agent Models 17
1.1 Introduction to Agent-Based Modeling 17
1.2 Brownian Agents 38
1.3 Brownian Motion 55
2. Active Particles 66
2.1 Active Motion and Energy Consumption 66
2.2 Active Motion in One-Dimensional Systems 80
2.3 Active Motion in Two-Dimensional Systems 110
2.4 Swarming of Active Particles 129
3. Aggregation and Physicochemical Structure Formation 147
3.1 Indirect Agent Interaction 147
3.2 Aggregation of Brownian Agents 159
3.3 Pattern Formation in Reaction–Diffusion Systems 178
4. Self-Organization of Networks 188
4.1 Agent-Based Model of Network Formation 188
4.2 Estimation of Network Connectivity 195
4.3 Construction of a Dynamic Switch 205
5. Tracks and Trail Formation in Biological Systems 215
5.1 Active Walker Models 215
5.2 Discrete Model of Track Formation 224
5.3 Track Formation and Aggregation in Myxobacteria 237
5.4 Trunk Trail Formation of Ants 244
6. Movement and Trail Formation by Pedestrians 258
6.1 Movement of Pedestrians 258
6.2 Trail Formation by Pedestrians 262
7. Evolutionary Optimization Using Brownian Searchers 278
7.1 Evolutionary Optimization Strategies 278
7.2 Evaluation and Optimization of Road Networks 290
7.3 Asymptotic Results on the Optimization Landscape 300
8. Analysis and Simulation of Urban Aggregation 305
8.1 Spatial Structure of Urban Aggregates 305
8.2 Rank–Size Distribution of Urban Aggregates 317
8.3 Kinetic Models of Urban Growth 328
9. Economic Agglomeration 344
9.1 Migration and Agglomeration of Workers 344
9.2 Dynamic Model of Economic Concentration 354
10. Spatial Opinion Structures in Social Systems 365
10.1 Quantitative Sociodynamics 365
10.2 Collective Opinion Formation of Brownian Agents 371
10.3 Spatial Opinion Patterns in a Model of Direct Interactions 383
Bibliography 394
Index 421