Simulation of Complex Systems

Web Copy This book deals with the most fundamental and essential techniques to simulate complex systems, from the dynamics of molecules to the spreading of diseases, from optimization using ant colonies to the simulation of the Game of Life. Several natural systems found in physics, biology and engineering can be considered complex systems, because their behaviour is not easily predictable and is the result of complex interactions among their constituents. Examples of complex systems are a cell with its organelles, an organ, the human brain, social networks, transportation and communication systems, the stock market, ecosystems, systems with prey and predators, a swarm of bees. There are several specialized books focusing on different simulation methods, but there is not one fully devoted to complex systems. The “bottom-up” approach is innovative and allows the reader to conduct numerical experiments to explore the system's behaviour. Key Features 1. Composed of self-contained, independent chapters 2. Illustrates simulation techniques in a broad range of fields from physics and biology to engineering, social science and economics 3. Provides a hands-on approach with guided exercises 4. Covers the fundamental numerical techniques in complex systems 5. Ideal for self-study 6. Contains supplementary example codes and video tutorials PRELIMS.pdf Preface Author biography Aykut Argun Agnese Callegari Giovanni Volpe CH001.pdf Chapter 1 Molecular dynamics 1.1 Single particle 1.2 Time reversibility 1.3 Multiple particles 1.4 Randomness 1.5 Further reading 1.6 Problems 1.7 Challenges References CH002.pdf Chapter 2 Ising model 2.1 Monte Carlo method 2.2 Ising model 2.3 Critical temperature 2.4 Critical mixtures 2.5 Further reading 2.6 Problems 2.7 Challenges References CH003.pdf Chapter 3 Forest fires 3.1 Forest growth and fire ignition 3.2 Power-law behavior 3.3 Further reading 3.4 Problems 3.5 Challenges References CH004.pdf Chapter 4 The Game of Life 4.1 One-dimensional cellular automata 4.2 Conway’s Game of Life 4.3 Majority rule 4.4 Further reading 4.5 Problems 4.6 Challenges References CH005.pdf Chapter 5 Brownian dynamics 5.1 Random walks and universality 5.2 Discrete white noise 5.3 Brownian motion 5.4 Optical tweezers 5.5 Further reading 5.6 Problems 5.7 Challenges References CH006.pdf Chapter 6 Anomalous diffusion 6.1 Anomalous diffusion exponent 6.2 Regularization and normalization 6.3 Models of anomalous diffusion 6.4 Anomalous diffusion in a non-homogeneous force field 6.5 Further reading 6.6 Problems 6.7 Challenges References CH007.pdf Chapter 7 Multiplicative noise 7.1 A minimal discrete-time model 7.2 Position-dependent noise 7.3 Stochastic integrals 7.4 The spurious drift 7.5 Drift and diffusion measurement 7.6 Particles close to an interface 7.7 Further reading 7.8 Problems 7.9 Challenges References CH008.pdf Chapter 8 The Vicsek model 8.1 The standard Vicsek model 8.2 The effect of delay 8.3 Non-metric and non-reciprocal interactions 8.4 Further reading 8.5 Problems 8.6 Challenges References CH009.pdf Chapter 9 Living crystals 9.1 Active Brownian motion 9.2 Mean square displacement 9.3 Living crystals 9.4 Aligning interactions 9.5 Further reading 9.6 Problems 9.7 Challenges References CH010.pdf Chapter 10 Sensory delay 10.1 A light-sensitive robot 10.2 Single robot with a sensory delay 10.3 Multiple robots with sensory delay 10.4 Further reading 10.5 Problems 10.6 Challenges References CH011.pdf Chapter 11 Disease spreading 11.1 The agent-based SIR model 11.2 Disease transmission as a function of the infection rate 11.3 Extended SIR models 11.4 Lockdown strategies 11.5 Further reading 11.6 Problems 11.7 Challenges References CH012.pdf Chapter 12 Network models 12.1 The adjacency matrix 12.2 Path length, diameter, and clustering coefficient 12.3 Erdős–Rényi random graphs 12.4 Watts–Strogatz small-world graphs 12.5 Albert–Barabási preferential-growth graphs 12.6 Further reading 12.7 Problems 12.8 Challenges References CH013.pdf Chapter 13 Evolutionary games 13.1 The prisoner’s dilemma 13.2 Evolutionary games on a lattice 13.3 Multiple strategies 13.4 Further readings 13.5 Problems 13.6 Challenges References CH014.pdf Chapter 14 Ecosystems 14.1 Lotka–Volterra model 14.2 The logistic growth model 14.3 Mutualism 14.4 Competition 14.5 Further reading 14.6 Problems 14.7 Challenges References CH015.pdf Chapter 15 Ant-colony optimization 15.1 The minimum path length problem 15.2 Ants at work 15.3 Interruptions, accidents, and randomness 15.4 Further reading 15.5 Problems 15.6 Challenges References CH016.pdf Chapter 16 The Sugarscape 16.1 Models of segregation 16.2 The Sugarscape 16.3 Further reading 16.4 Problems 16.5 Challenges References