Pattern formation in large domains
PFD
1 August 2005 to 23 December 2005
Programme theme
Pattern formation occurs in a wide variety of natural contexts, from animal coat markings to convection cells in the Sun. Experimentally, patterns have been studied in many different systems, including Rayleigh-Bénard convection, solidification, chemical reactions and Faraday waves. Despite the physical differences between these systems, the patterns that appear display common features, indicating some kind of universal underlying structure. There are currently many different mathematical approaches to the study of patterns, including numerical simulation, amplitude equations and equivariant bifurcation theory, and this programme will bring together mathematicians and experimentalists for an interchange and fusion of ideas. This synthesis of techniques will be needed to tackle current problems in the theoretical foundation of the subject, and to explain recent experimental results. A short instructional course aimed at younger researchers will introduce the central topics and current approaches.
In small domains, simple regular patterns are observed, and these can be understood through the application of methods from symmetric bifurcation theory. But as the domain size increases, the range of validity of this approach shrinks to zero and so other methods are required. Similar difficulties are encountered in large networks of coupled oscillators. Patterns in one space dimension can, generically, be described by the Ginzburg-Landau equation, but this has not been rigorously generalised to two dimensions, because of the problem of orientational degeneracy. There are therefore many fascinating aspects of two-dimensional patterns that are currently not well understood. Specifically, the programme will address the following topics.
- Recent experimental and numerical results on pattern formation in large domains.
- Bifurcation theory and symmetry in extended systems, including the validity of amplitude equations and phase equations in two dimensions.
- Networks of coupled oscillators and synchronisation.
- Complex spatial structures such as giant spirals, quasipatterns, spiral defect chaos, localised states, defects and domain boundaries.
- Systems where, even in one dimension, the Ginzburg-Landau equation does not apply, for example because of the presence of a large-scale neutral mode.
- Applications, including convection, Faraday waves and neuroscience.
Click here to download the programme's final scientific report
Preprints
| Title | Year | Programme | |
|---|---|---|---|
Localised convection cells in the presence of a vertical magnetic fieldAuthors: Jonathan Dawes |
2005 | PFD | 21 October 2016 |
Rayleigh-Benard convection in the presence of a radial ramp of the Rayleigh numberAuthors: N Mukolobwiez, J Oh, ET Al, KMS Bajaj |
2005 | PFD | 21 October 2016 |
Invariants, equivariants and characters in symmetric bifurcation theoryAuthors: Ana Dias, PC Matthews, F Antoneli |
2005 | PFD | 21 October 2016 |
Charge transport scalings in turbulent electroconvectionAuthors: ZA Daya, Stephen Morris, Peichun Tsai |
2005 | PFD | 21 October 2016 |
Codimension-two points in annular electroconvection as a function of aspect ratioAuthors: ZA Daya, Stephen Morris, VB Deyirmenjian |
2005 | PFD | 21 October 2016 |
The role of initial conditions in the decay of spatially periodic patterns in a nematic liquid crystalAuthors: N Eber, ET Al, Werner Pesch, L Kramer |
2005 | PFD | 21 October 2016 |
Localized states in the generalized Swift-Hohenberg equationAuthors: E Knobloch, J Burke |
2005 | PFD | 21 October 2016 |
Workshops
Training course: pattern formation in large domains
1 August 2005 to 5 August 2005
Developments in experimental pattern formation
8 August 2005 to 12 August 2005
Theoretical aspects of pattern formation
19 September 2005 to 23 September 2005
Theory and applications of coupled cell networks
26 September 2005 to 30 September 2005
Pattern formation in growing domains
31 October 2005 to 1 November 2005
Lorenz Kramer day
11 December 2005 to 11 December 2005
Pattern formation in fluid dynamics
12 December 2005 to 16 December 2005
Seminars
| Tuesday 16th August 2005 | |||
|---|---|---|---|
| 10:00 to 11:00 |
Michael Tribelsky |
Room 1 | |
| Thursday 18th August 2005 | |||
|---|---|---|---|
| 10:00 to 11:00 |
Karen Daniels North Carolina State University |
Room 1 | |
| Tuesday 23rd August 2005 | |||
|---|---|---|---|
| 10:00 to 11:00 |
Ralf Wittenberg Simon Fraser University |
Room 2 | |
| 14:00 to 15:00 |
Ian Stewart University of Warwick |
Room 2 | |
| Thursday 25th August 2005 | |||
|---|---|---|---|
| 10:00 to 11:00 |
Mark Paul |
Room 2 | |
| Tuesday 30th August 2005 | |||
|---|---|---|---|
| 10:00 to 11:00 | Room 1 | ||
| Thursday 1st September 2005 | |||
|---|---|---|---|
| 10:00 to 11:00 |
Bjorn Sandstede University of Surrey |
Room 1 | |
| Tuesday 6th September 2005 | |||
|---|---|---|---|
| 10:00 to 11:00 |
Stephen Morris University of Toronto |
Room 1 | |
| Thursday 8th September 2005 | |||
|---|---|---|---|
| 10:00 to 11:00 | Room 1 | ||
| Tuesday 13th September 2005 | |||
|---|---|---|---|
| 10:00 to 11:00 | Room 1 | ||
| Thursday 15th September 2005 | |||
|---|---|---|---|
| 10:00 to 11:00 |
Reiner Lauterbach |
Room 1 | |
| Thursday 6th October 2005 | |||
|---|---|---|---|
| 10:00 to 11:00 |
Claire Postlethwaite Aalborg Universitet |
Room 1 | |
| Tuesday 11th October 2005 | |||
|---|---|---|---|
| 10:00 to 11:00 |
Elaine Crooks University of Oxford |
Room 1 | |
| Thursday 13th October 2005 | |||
|---|---|---|---|
| 10:00 to 11:00 |
Sergey Zelik Universität Stuttgart |
Room 1 | |
| Tuesday 18th October 2005 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Arjen Doelman |
Room 1 | |
| Thursday 20th October 2005 | |||
|---|---|---|---|
| 10:00 to 11:00 | Room 1 | ||
| Tuesday 25th October 2005 | |||
|---|---|---|---|
| 10:00 to 11:00 | Room 1 | ||
| Thursday 27th October 2005 | |||
|---|---|---|---|
| 10:00 to 11:00 |
Kostyantyn Blyuss University of Exeter |
Room 1 | |
| Friday 28th October 2005 | |||
|---|---|---|---|
| 14:00 to 15:00 |
Jens Rademacher |
Room 1 | |
| Thursday 3rd November 2005 | |||
|---|---|---|---|
| 10:00 to 11:00 |
Alastair Rucklidge University of Leeds |
Room 1 | |
| Tuesday 8th November 2005 | |||
|---|---|---|---|
| 10:00 to 11:00 |
David Lloyd University of Surrey |
Room 1 | |
| Thursday 10th November 2005 | |||
|---|---|---|---|
| 10:00 to 11:00 |
A new perspective on resonance in Hopf bifurcation from relative equilibria |
Room 1 | |
| Tuesday 15th November 2005 | |||
|---|---|---|---|
| 10:00 to 11:00 |
Ana Dias Universidade do Porto |
Room 1 | |
| Thursday 17th November 2005 | |||
|---|---|---|---|
| 10:00 to 11:00 | Room 1 | ||
| Tuesday 22nd November 2005 | |||
|---|---|---|---|
| 10:00 to 11:00 |
Alan Champneys University of Bristol |
Room 1 | |
| Wednesday 23rd November 2005 | |||
|---|---|---|---|
| 11:00 to 14:00 | Discussion Room | ||
| Tuesday 29th November 2005 | |||
|---|---|---|---|
| 10:00 to 11:00 |
Elena Beatriz Martín Universidad de Vigo |
Room 1 | |
| Thursday 1st December 2005 | |||
|---|---|---|---|
| 10:00 to 11:00 | Room 1 | ||
| Tuesday 6th December 2005 | |||
|---|---|---|---|
| 10:00 to 11:00 |
Serafim Kalliadasis |
Room 1 | |
Organisers
- Jon Dawes University of Cambridge
- Martin Golubitsky University of Houston
- Paul Matthews University of Nottingham
- Alastair Rucklidge University of Leeds
Speakers
- Kostyantyn Blyuss University of Exeter
- Alan Champneys University of Bristol
- Elaine Crooks University of Oxford
- Karen Daniels North Carolina State University
- Ana Dias Universidade do Porto
- Arjen Doelman
- Serafim Kalliadasis
- Reiner Lauterbach
- David Lloyd University of Surrey
- Elena Beatriz Martín Universidad de Vigo
- Stephen Morris University of Toronto
- Mark Paul
- Claire Postlethwaite Aalborg Universitet
- Jens Rademacher
- Alastair Rucklidge University of Leeds
- Bjorn Sandstede University of Surrey
- Ian Stewart University of Warwick
- Michael Tribelsky
- Ralf Wittenberg Simon Fraser University
- Sergey Zelik Universität Stuttgart
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