Fully-funded PhD Studentship in Applied Nonlinear Dynamics & Mathematical Physics

Summary

We are delighted to offer a fully funded PhD studentship and applications are invited from strongly motivated and academically excellent candidates for PhD study in our large and vibrant Applied Mathematics & Mathematical Physics department, within these strategic priority Research areas:

Applied Nonlinear Dynamics: Dr Cédric Beaume, Professor Mauro Mobilia, Dr Jitse Niesen, Professor Alastair Rucklidge, Professor Rob Sturman, Dr Jon Ward

A vibrant research area lying at the heart of problems of fundamental and practical importance. We employ a wealth of mathematical techniques, from statistical to geometrical, from computational to algebraic, and from qualitative to analytical. The main concern is systems that change with time, where the presence of nonlinearities can produce hugely complicated behaviour. We possess cutting-edge expertise in pattern formation (from quasipatterns to spatial localisation), network dynamics, stochastic processes (e.g. the voter model, agent-based models), physics (from statistical mechanics to fluid dynamics), life sciences and numerical methods. Developments in the basic theory and techniques of Nonlinear Dynamics go hand-in-hand with investigations of particular applications, such as fluid dynamics experiments, dynamics on complex networks and mixing in microfluidics.

Integrable Systems and Mathematical Physics: Dr Vincent Caudrelier, Dr Oleg Chalykh, Professor Alexander Mikhailov

Symmetry is a central unifying theme in Mathematical and Physics which finds its ultimate form in the area of Integrable Systems. These are systems characterised by a very large number of symmetries, which control their dynamics and make them amenable to exact solution methods. Our group in Leeds has been at the forefront of this area of Mathematical Physics for several decades. We offer a research environment based on expertise in geometric and algebraic aspects of integrable systems with applications to physics: classical and quantum integrable many-body systems (e.g. Calogero and Ruijsenaars models), integrable quantum field theories, (in)finite dimensional Lie algebras (e.g. double affine Hecke algebras, affine and Kac-Moody algebras, automorphic Lie algebras), Lagrangian and Hamiltonian formalism of integrable systems, classical and quantum Yang-Baxter equations, soliton theory, quivers and representation theory. There are strong connections with the Geometry and the Algebra groups and we coordinate the UK-wide LMS national network "Classical and Quantum Integrability”.

A list of related PhD projects in this area:

Pattern Formation (Applied Nonlinear Dynamics)

Instabilities in fluid dynamics

Exponential integrators

Particle methods for plasma physics

Solving differential equations with Fourier extension

Quantisation of integrable field theories and Lagrangian multiform

Applicants to research degree programmes should normally have at least a first class or an upper second class British Bachelors Honours degree (or equivalent) in an appropriate discipline. The criteria for entry for some research degrees may be higher, for example, several faculties, also require a Masters degree. Applicants are advised to check with the relevant School prior to making an application. Applicants who are uncertain about the requirements for a particular research degree are advised to contact the School or Graduate School prior to making an application.

The minimum English language entry requirement for research postgraduate research study is an IELTS of 6.0 overall with at least 5.5 in each component (reading, writing, listening and speaking) or equivalent. The test must be dated within two years of the start date of the course in order to be valid. Some schools and faculties have a higher requirement.