- UCAS course code
- F305
- UCAS institution code
- M20
Course unit details:
Introduction to Non-linear Physics
Unit code | PHYS30471 |
---|---|
Credit rating | 10 |
Unit level | Level 3 |
Teaching period(s) | Semester 1 |
Available as a free choice unit? | No |
Overview
Introduction to Nonlinear Physics (M)
Pre/co-requisites
Unit title | Unit code | Requirement type | Description |
---|---|---|---|
Dynamics | PHYS10101 | Pre-Requisite | Compulsory |
Vibrations & Waves | PHYS10302 | Pre-Requisite | Compulsory |
Mathematics 2 | PHYS10372 | Pre-Requisite | Compulsory |
Mathematics of Waves and Fields | PHYS20171 | Pre-Requisite | Compulsory |
Aims
To introduce the concepts required for understanding 'real world' nonlinear phenomena using a variety of mathematical and laboratory models.
Learning outcomes
Learning outcomes
On completion successful students will be able to:
1. describe the key concepts of nonlinear dynamics.
2. analyse simple one and two-dimensional nonlinear systems.
3. apply the basic numerical methods relevant to nonlinear systems
4. explain the origin and key features of chaotic behaviour
Syllabus
1. Introduction - overview of the course introducing some of the basic ideas. (1 lecture)
General introduction and motivation; examples of linearity and nonlinearity in physics and the other sciences; modelling systems using iterated maps or differential equations.
2. General features of dynamical systems - the structures that may arise in the analysis of ordinary differential equations. (10 lectures)
Systems of differential equations with examples; control parameters; fixed points and their stability; phase space; linear stability analysis; numerical methods for nonlinear systems; properties of limit cycles; nonlinear oscillators and their applications; the impossibility of chaos in the phase plane; bifurcations: their classification and physical examples; spatial systems, pattern formation and the Turing mechanism; strange attractors and chaotic behaviour.
3. The logistic map - period doubling and chaos in a simple iterated map. (4 lectures)
Linear and quadratic maps; graphical analysis of the logistic map; linear stability analysis and the existence of 2-cycles; numerical analysis of the logistic map; universality and the Feigenbaum numbers; chaotic behaviour and the determination of the Lyapunov exponent; other examples of iterated maps.
4. Fractals - complex geometrical objects of which strange attractors are examples. (4 lectures)
How long is the coastline of Britain? Artificial fractals: the Cantor set and von Koch curve; fractal dimensions; iterations of the complex plane and the Mandelbrot set; how fractals arise in the description of dynamical systems.
5. Further aspects of chaotic dynamics - exploring the basic ingredients of chaos. (3 lectures)
Fractal structures in simple maps; how strange attractors come about; the evolution of phase space volumes in chaotic and non-chaotic systems; mixing and information entropy.
Assessment methods
Method | Weight |
---|---|
Written exam | 100% |
Feedback methods
While students will not be required to hand in solutions to example sheets, I will give feedback on written solutions, should students wish to hand in work. Model answers will be issued. One or two Question & Answer sessions may be arranged.
Recommended reading
Recommended texts:
Strogatz, S.H. Nonlinear Dynamics and Chaos, (Addison Wesley 1994).
Useful references:
Baker, G.L. & Gollub, J.P. Chaotic Dynamics: An Introduction, (CUP 1996), Second edition
Jordan, D.W. & Smith, P. Nonlinear Ordinary Differential Equations, (OUP 1999), Third edition
Supplementary reading:
Gleick, J. Chaos: Making a New Science, (Heinmann 1998)
Stewart, I. Does God play Dice? The Mathematics of Chaos, (Penguin 1990)
Study hours
Scheduled activity hours | |
---|---|
Assessment written exam | 1.5 |
Lectures | 22 |
Independent study hours | |
---|---|
Independent study | 76.5 |
Teaching staff
Staff member | Role |
---|---|
Draga Pihler-Puzovic | Unit coordinator |
Additional notes
. *Note - scheduled teaching hours:
11 weeks of teaching times 2 lectures plus the exam.
All material for the unit, such as videos, example scripts and notes, is available online via Blackboard