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Lecture Courses


PX391 Nonlinearity, Chaos, Complexity

Lectures are second half of spring term- past papers and solutions to the (four) problem sheets are available from the Physics Undergraduate office. Problem sheet solutions are available here and in hard copy from the Undergraduate Office.

Handouts:

Course Description

Problem Sheet 1

Problem Sheet 2

Problem Sheet 3

Problem Sheet 4


phase transitions

classification of fixed points

Buckingham Pi theorem


The Netlogo website, home to Netlogo free-to-download package for modelling complex systems

My (not so elegant or fast) Matlab routine for flocking birds (Vicsek model) .

There are some fun movie clips courtesy MIT, eg the coupled pendulum:

Takens theorem movies, see the supplimentary info of Sugihara et al (2012)

Forgotten the maths? Have a look on Khan Academy:

How to sketch curves: Derivative applications

What is a Taylor expansion

How to Solve quadratics by formula

Basic Trig Identities


Lecture notes- these are verbatim as given in the lectures- not textbook quality! Note I may not stick to this exact schedule.

Lecture 1

Lecture 2

Lecture 3

Lecture 4

Lecture 5+6 see also handout on classification of fixed points

Lecture 7

Lecture 8

Lecture 9

Lecture 10

Lectures 11-12

Lecture 13

Lecture 14

Lecture 15



MPAGS Module : Time Series Analysis- an Introduction to Advanced Methods


Given in Autumn Term.

Course Description

Lecture Notes

These are written to supplement, not replace, the lectures, and so are terse in style.

lecturenotes-dftsummary.pdf

lecturenotes-spectralestimates.pdf

lecturenotes-scaling.pdf

lecturenotes-stationarity.pdf

lecturenotes-generalizingfourier.pdf

lecturenotes_wavelets.pdf

lecturenotes_structurefunctions.pdf

lecturenotes_complex_measures.pdf

Project and Assessment

To take part in this course for credit you will need to do the exercise in data analysis- this will be described in detail in the lectures. You will need to look at the RXTE websites:

The Readme files on RXTE Quicklook datafiles and the datasets are: RXTE ASM Lightcurves

For what is expected in the report: report.pdf

Reference material

Matlab's own demos (both in Matlab and in the signal processing and wavelets toolboxes) are highly recommended.

Basic Fourier theory: basicfourierintro.pdf (courtesy The Math Forum@Drexel Library) and Matlab intro basicfouriermatlab.pdf

Higher Order Spectra: ddw_review_hos_2003.pdf

Wavelets: torrence_compo_wavelets_1998.pdf farge_wavelets_turb1996.pdf farge_wavelets_turb2002.pdf

Observing power laws: clausetpowerlaws.pdf

Pi theorem, Buckingham's original paper: buckingham1914.pdf and an application to turbulence and SOC: chapmanpitheorem.pdf