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.
Author(s): Professor Giovanni Volpe, Agnese Callegari, Aykut Argun
Publisher: IOP Publishing
Year: 2021
Language: English
Pages: 226
City: Bristol
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
