Dr Bryn Davies - Predictive models for waves in imperfect periodic media

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:

Periodic small-scale structures are the backbone of metamaterials and other wave control devices. However, manufacturing imperfections or operational damage can alter their intended function. Many of the standard tools we use to model and design these systems rely on geometric periodicity and struggle to predict how they will behave once imperfections are introduced.

Objectives:

This project will develop a range of analytic and numerical methods to model and design imperfect metamaterials. Depending on the student's interests, this could include

perturbative methods for weakly random media;
developing variants of large deviation theory to characterise when imperfections qualitatively alter wave phenomena;
applying localisation landscape techniques to predict the creation of localised modes;
generalising radiative transfer methods to describe propagation in perturbed periodic media;
characterising the statistics of eigenmodes, particularly the creation of localised modes.

This would be well suited for a student with an interest in combining analysis of PDEs, probability theory 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