If you are interested in joining the group in any capacity, you are encouraged to to reach out to Bryn via email [bryn.davies@warwick.ac.uk]. Informal enquiries of any form are always welcome. It's generally advisable to reach out as early as possible to discuss possible projects and the various options for supporting them.
Warwick students are welcome to join the group for URSS projects, 4th year R-projects and MSc projects.
Some specific open projects are listed below, however this list will never be exhaustive and we may have other opportunities that are better suited to you, so please get in touch.
Background: A latent symmetry (sometimes known as a "hidden" symmetry) is the phenomenon whereby systems are not symmetric in any classical sense (i.e. they don't have any reflectional or rotational symmetries) but they still exhibit properties of symmetric systems. These ideas originate in graph theory [PhysA] and have been extended to wave systems [PRL]. This project will extend these ideas to PDE models.
Objectives: Find an appropriate formulation of latent symmetry for continuous PDE models. Use this to advance applications to imaging, sensing and communication problems. Work with external collaborators to develop experimental realisations.
Collaborators: Malte Röntgen and Wenlong Gao (Eastern Institute of Technology, Ningbo); experts in the physics of latent symmetries.
Background: Metamaterials are formed by combining many small, locally resonant elements in a repeating pattern. This gives materials with exotic properties such as negative effective masses, negative refractive indices or negative Poisson's ratios. The repeating patterns are often either periodic (in which case Floquet-Bloch theory can be applied) or random (in which case ensemble averages can be used). We have been studying metamaterials based on a class of quasiperiodic patterns, which are non-periodic but have long-range order. Our work so far has focused on developing methods to estimate spectra [PRSA] and using these to identify and develop novel applications [PRL].
Objectives: Continue the search for novel applications of quasiperiodic metamaterials, particularly to multi-dimensional systems. This will need new mathematical methods to be developed to facilitate their design. Work with external partners to develop experimental demonstrations of new designs and concepts.
Collaborators: I have various collaborators, both in the UK and overseas, that will support the development of experimental implementations of our results.