Pattern formation in large domains

We have been made aware of a convincing email scam that is focusing on our Programme and Workshop participants. Participants may receive an email from a firm called Expo Hotel Services (ehotelservices.org) to arrange accommodation for workshops and/or programmes. This might include a request to provide them with credit card information.

Please note, INI will never ask for your card details. We take all payments via the University of Cambridge Online store https://onlinesales.admin.cam.ac.uk/.

If you have been contacted by this company please contact us as soon as possible.

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 field Authors: Jonathan Dawes Download PDF	2005	PFD
Rayleigh-Benard convection in the presence of a radial ramp of the Rayleigh number Authors: N Mukolobwiez, J Oh, ET Al, KMS Bajaj Download PDF	2005	PFD
Invariants, equivariants and characters in symmetric bifurcation theory Authors: F Antoneli, PC Matthews, Ana Dias Download PDF	2005	PFD
Charge transport scalings in turbulent electroconvection Authors: ZA Daya, Peichun Tsai, Stephen Morris Download PDF	2005	PFD
Codimension-two points in annular electroconvection as a function of aspect ratio Authors: VB Deyirmenjian, ZA Daya, Stephen Morris Download PDF	2005	PFD
The role of initial conditions in the decay of spatially periodic patterns in a nematic liquid crystal Authors: L Kramer, N Eber, ET Al, Werner Pesch Download PDF	2005	PFD
Localized states in the generalized Swift-Hohenberg equation Authors: E Knobloch, J Burke Download PDF	2005	PFD

Workshops

PFDW01

Seminars

Tuesday 16th August 2005
10:00 to 11:00	Michael Tribelsky Degenerate dissipative systems and a new scenario for transition to turbulence	Room 1

Thursday 18th August 2005
10:00 to 11:00	Karen Daniels North Carolina State University Localized bursts in inclined layer convection	Room 1

Tuesday 23rd August 2005
10:00 to 11:00	Ralf Wittenberg Simon Fraser University One-dimensional spatiotemporal chaos	Room 2
14:00 to 15:00	Ian Stewart University of Warwick Phase relations and symmetry in periodic dynamics of networks	Room 2

Thursday 25th August 2005
10:00 to 11:00	Mark Paul New physical insights from experimentally realistic simulations of Rayleigh-Benard convection	Room 2

Tuesday 30th August 2005
10:00 to 11:00	Chemically driven self-propelled running droplets	Room 1

Thursday 1st September 2005
10:00 to 11:00	Bjorn Sandstede University of Surrey The absolute spectrum and spiral waves	Room 1

Tuesday 6th September 2005
10:00 to 11:00	Stephen Morris University of Toronto Oscillations and subdiffusion in a granular segregation experiment	Room 1

Thursday 8th September 2005
10:00 to 11:00	How does flow in a pipe become turbulent?	Room 1

Tuesday 13th September 2005
10:00 to 11:00	Symmetry-breaking from a degenerate orbit	Room 1

Thursday 15th September 2005
10:00 to 11:00	Reiner Lauterbach Steady state bifurcation with symmetry	Room 1

Thursday 6th October 2005
10:00 to 11:00	Claire Postlethwaite Aalborg Universitet Cycling cycles: Dynamics near a heteroclinic network	Room 1

Tuesday 11th October 2005
10:00 to 11:00	Elaine Crooks University of Oxford On the convergence of travelling-front speeds as diffusion vanishes in reaction-diffusion equations with non-convex flux	Room 1

Thursday 13th October 2005
10:00 to 11:00	Sergey Zelik Universität Stuttgart Sinai-Bunimovich space-time chaos in PDEs	Room 1

Tuesday 18th October 2005
14:00 to 15:00	Arjen Doelman Stability of spatially periodic pulse patterns	Room 1

Thursday 20th October 2005
10:00 to 11:00	A normal form for excitable media	Room 1

Tuesday 25th October 2005
10:00 to 11:00	Buckling of long, thin cylinders	Room 1

Thursday 27th October 2005
10:00 to 11:00	Kostyantyn Blyuss University of Exeter Spatio-temporal dynamics in a phase-field model with phase-dependent heat absorption	Room 1

Friday 28th October 2005
14:00 to 15:00	Jens Rademacher Essential and absolute spectra, and their computation by continuation	Room 1

Thursday 3rd November 2005
10:00 to 11:00	Alastair Rucklidge University of Leeds Boundary effects and the onset of Taylor vortices	Room 1

Tuesday 8th November 2005
10:00 to 11:00	David Lloyd University of Surrey Nucleation of localised patterns in the 2D Swift-Hohenberg equation	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 Hopf bifurcation on hemispheres	Room 1

Thursday 17th November 2005
10:00 to 11:00	Conservation laws, large-scale modes and localised patterns	Room 1

Tuesday 22nd November 2005
10:00 to 11:00	Alan Champneys University of Bristol Localised pattern formation	Room 1

Wednesday 23rd November 2005
11:00 to 14:00	Lunch	Discussion Room

Tuesday 29th November 2005
10:00 to 11:00	Elena Beatriz Martín Universidad de Vigo Viscous mean flows in nearly inviscid Faraday waves	Room 1

Thursday 1st December 2005
10:00 to 11:00	Modulational instabilities due to strong spatial resonances	Room 1

Tuesday 6th December 2005
10:00 to 11:00	Serafim Kalliadasis Three-dimensional wave dynamics in falling liquid films: formation of lattices of interacting stationary solitary pulses	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 Duke 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 University of Cambridge
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

Show All

Programme theme

Preprints

Localised convection cells in the presence of a vertical magnetic field

Rayleigh-Benard convection in the presence of a radial ramp of the Rayleigh number

Invariants, equivariants and characters in symmetric bifurcation theory

Charge transport scalings in turbulent electroconvection

Codimension-two points in annular electroconvection as a function of aspect ratio

The role of initial conditions in the decay of spatially periodic patterns in a nematic liquid crystal

Localized states in the generalized Swift-Hohenberg equation

Workshops

Training course: pattern formation in large domains

Developments in experimental pattern formation

Theoretical aspects of pattern formation

Theory and applications of coupled cell networks

Pattern formation in growing domains

Lorenz Kramer day

Pattern formation in fluid dynamics

Seminars

Organisers

Speakers

Supported By

Pattern formation in large domains

Programme theme

Preprints

Localised convection cells in the presence of a vertical magnetic field

Rayleigh-Benard convection in the presence of a radial ramp of the Rayleigh number

Invariants, equivariants and characters in symmetric bifurcation theory

Charge transport scalings in turbulent electroconvection

Codimension-two points in annular electroconvection as a function of aspect ratio

The role of initial conditions in the decay of spatially periodic patterns in a nematic liquid crystal

Localized states in the generalized Swift-Hohenberg equation

Workshops

Training course: pattern formation in large domains

Developments in experimental pattern formation

Theoretical aspects of pattern formation

Theory and applications of coupled cell networks

Pattern formation in growing domains

Lorenz Kramer day

Pattern formation in fluid dynamics

Seminars

Organisers

Speakers

Supported By

Register for updates