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Preface
Contents
Complexity
A Course
by
Rajesh R. Parwani
usprrp@nus.edu.sg
Preface
Contents
Introduction
Overview
Examples
Schooling of Fish
Bacterial Colonies
Forest Fires
The Double Pendulum
The Leopard Spots
Summary
Exercises
References
Fractals
Mathematical Fractals
The Koch Curve and Snowflake
Dimensions
Random Fractals
Dynamical generation of fractals: Diffusion Limited Aggregation
Occurrence and uses of Fractals
Summary
Exercises
References
Chaos
Introduction
Dynamical Systems and Iterative Maps
A Simple Example of an Iterative Map
An Intuitive Analysis
A Graphical Analysis
The Analytical Approach
A Discrete Model of Population Growth
Varying the control parameter in the logistic map
Bifurcation Diagrams
The Feigenbaum Constant and Universality
Experimental Tests
The Rossler System
The Lorenz map
Noise versus Chaos
Summary
Exercises
References
Equilibrium Systems
Thermodynamics and Kinetic Theory
State Variables
The Ideal Gas
Statistical Mechanics
The Second Law
The First Law
Entropy for Open Systems
Phase Transitions
Second Order Transitions
Correlation Function
The Scaling Hypothesis
The Ising Model
Critical Opalescence
Percolation
Summary
Exercises
References
Systems Far From Equilibrium
Order in Nature
Vortices
Benard Cells
Non-Equilibrium Pattern Formation vs Equilibrium Phase Transitions
The Belousov-Zhabotinski Reaction
Turing Structures
Predator-Prey Systems
War and Love
Summary
Exercises
References
Self-Organisation
Game of Life
Termites
Boids
Ants
Herd Behaviour in Humans
Evolving Complex Networks
Summary
Exercises
References
Self-Organised Criticality
Power Laws in Nature
Models
Experiments
Life
Zipf's Law
War and Peace
Summary
Exercises
References
Measures of Complexity
Exercises
References
Conclusion
Summary
Exercises
References
About this document ...
Rajesh Parwani 2002-01-03
