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Wave scattering in finite metamaterials: application of complex analysis, PDEs and numerical analysis

Department of Mathematics

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Dr A Kisil Applications accepted all year round Funded PhD Project (Students Worldwide)

About the Project

This project is for potential PhD students who had enjoyed courses on complex analysis, PDEs or numerical analysis. There is an opportunity to do long term placements in various parts of the world and receive an extra stipend of 2100€/month.

The project concerns analytical methods of wave scattering problems in metamaterials with edges. Research work on the project will involve new mathematical analysis of the wave propagation problems and implementation of the developed analytical methods.

Metamaterials are usually defined as engineered materials which exhibit properties not usually found in nature such as negative refractive index, acoustic filters and even cloaking. In other words they can control, direct, and manipulate sound waves in ways that were not
possible before. Metamaterials are usually modelled through the periodic arrangement of some unit cells in a 3-D (metamaterials) or a 2-D fashion (metasurfaces). Many different unit cells can be created and they can be arranged in different manner in order to suit the particular application. It is a major challenge to pick the optimum configuration. Analytic mathematical methods are particularly suited to this challenge being an inexpensive way of rapidly exploring different possibilities of design. They also offer insights into the underlining physical mechanism and hence the key to tailored adaptations.

The advertised post is for a PhD student to work with Dr Anastasia Kisil within the Waves in Complex Continua Group in the Department of Mathematics at Manchester. The appointee will develop new a theoretical framework for understanding the effects of edges in acoustic metamaterials. There has been extensive research into how waves propagate within a metamaterial (periodic materials) but there has been substantially less theoretical results about the way waves interact with the edges of the metamaterials. These results are important, have many applications in noise reduction and naturally build upon the mathematical methods used for canonical scattering problems. There is also the possibility to explore the aeroacoustic uses of these metamaterials.

Entry requirements:
We are looking for an enthusiastic and highly-motivated graduate with
- obtained or working towards a 1st class degree in Mathematics or a closely related discipline with strong mathematical component (Master’s level or equivalent);
- a solid background in some of the following: complex methods, partial differential equations, wave scattering or numerical analysis;
- good programming skills;
- good communication skills (oral and written).

Informal email queries should be directed to Dr Kisil at [Email Address Removed] in the first instance. Formal applications can then be submitted online. As well as transcripts and references, applicants should supply a cover letter describing their academic background and motivation for the project, as well as a complete CV (two pages maximum).

Funding Notes

There is full funding available and an opportunity to do long term placements in various parts of the world and receive an extra stipend of 2100€/month.
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