Dr Bryn Davies - Propagation operators for nonlinear metamaterials

Students successfully applying to this grant will be part of the CDT and follow the normal CDT structure. The first year research project will be under the direction of the project supervisor, forming part of the project detailed below.

About / Project Description:

Supervisor:

Dr Bryn Davies

Background:

Although we typically rely on linear models to design metamaterials, harnessing nonlinear phenomena can unlock significant benefits. This includes the freedom to alter the frequency composition of a wave, exploit amplitude-dependent responses and create directionally dependent (e.g. diode-like) behaviour. However, many of the standard tools for metamaterials (e.g. asymptotic homogenisation, transfer matrices, Floquet-Bloch analysis) exploit linearity of the underlying equations.

Objectives:

This project will develop a propagation operator framework that generalises the transfer matrix method to nonlinear wave regimes. We will use concepts from dynamical systems theory (such as attractors and Lyapunov exponents) to develop suitable notions of band gaps and use asymptotic approximation to develop homogenisation strategies. Depending on the student's interests, we could generalise the approach to nonlinear systems including nonlinear acoustics, vibro-elastic systems and nonlinear optics. We will use our methods to unlock the benefits of nonlinearity for applications including

exploiting amplitude-dependent transmission gaps to build sensors;
designing diode-like non-reciprocal phenomena;
reducing energy reflection to improve wave energy harvesters;
exploiting hysteresis to give materials the ability to remember, count and compute.

This would be well suited for a student with an interest in combining mathematical modelling, dynamical systems and numerical simulation. We will study problems with significant engineering applications and collaborate with a range of industrial and experimental colleagues.

Funding:

This project is funded by the Leverhulme Trust through Bryn Davies' Research Leadership Award on developing new imperfection-resilient metamaterials. You will be part of a large research group containing several other PhD students and postdoctoral researchers working on broadly related problems. Particularly given the scope of this project has some flexibility, interested candidates are encouraged to reach out to Bryn via email.

Eligibility:

Level of study: PhD

Mode of study: Full Time

Fee status: Home / Overseas

Department/School: Mathematics Department

Application Process:

To be considered for these scholarships and the CDT please apply in the Admission Portal indicating your interest in this Research Project and the name of the supervisor (Bryn Davies) in your application.

Key Dates:

Application deadline: Ongoing

Application results date: April 2027