Pattern Formation (Applied Nonlinear Dynamics)

Supervisor(s)

Contact Professor Alastair Rucklidge to discuss this project further informally.

Project description

Pattern Formation (Applied Nonlinear Dynamics) - understanding the formation and stability of complex patterns such as quasipatterns, spatio-temporal chaos or turbulent spirals

Regular patterns, such as stripes, squares and hexagons, are ubiquitous in nature, and their formation and stability are governed by the intricate and complex interactions of symmetry and nonlinearity. Nonlinear interaction of waves in different directions can lead to the formation much more complicated and beautiful patterns: quasipatterns, spatio-temporal chaos and other forms of chaotic dynamics, depending on just how the waves interact.

This project will involve using ideas from nonlinear dynamics: bifurcation theory, stability theory, three-wave interactions, chaos, symmetry and heteroclinic cycles, to understand the formation and stability of complex patterns such as quasipatterns, spatio-temporal chaos or turbulent spirals. 

The distinct aspect of this project is that it will involve problems with two length scales, where waves of two different wavelengths can interact in many different ways. There will be emphasis on deep understanding of the underlying dynamics in the problem, using computational tools, bifurcation theory, asymptotic theory, weakly nonlinear theory, symbolic algebra, group theory, or whatever is needed.

While the project will focus on solving a particular set of partial differential equations using asmptotic and numerical methods, one of the beauties of the nonlinear dynamics approach is that it can have wide applicability in different areas of mathematics, physics, chemistry or biology. The ideas that this project will explore have application to understanding patterns in fluid dynamics (the Faraday Wave experiment), soft matter physics (the formation of polymer quasicrystals) and chemistry (two-layer reaction-diffusion systems).

Entry requirements

Applications are invited from candidates with or expecting a minimum of a UK upper second class honours degree 2:1, and/or a Master's degree in a relevant subject.

If English is not your first language, you must provide evidence that you meet the University’s minimum English Language requirements.

How to apply

Formal applications for research degree study should be made online through the university's website. Please state clearly in the research information section that the PhD you wish to be considered for is the 'Pattern Formation (Applied Nonlinear Dynamics) - understanding the formation and stability of complex patterns such as quasipatterns, spatio-temporal chaos or turbulent spirals’ as well as Professor Alastair Rucklidge as your proposed supervisor.

We welcome scholarship applications from all suitably-qualified candidates, but UK black and minority ethnic (BME) researchers are currently under-represented in our Postgraduate Research community, and we would therefore particularly encourage applications from UK BME candidates. All scholarships will be awarded on the basis of merit.

If you require any further information please contact the Graduate School Office, e: maps.pgr.admissions@leeds.ac.uk