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Transfer Operator Methods for Vibrational Transport Problems


   School of Mathematical Sciences

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  Dr Martin Richter  Applications accepted all year round  Funded PhD Project (UK Students Only)

About the Project

This project will be based at the University of Nottingham in the School of Mathematical Sciences. We require an enthusiastic graduate with a 1st class degree in Mathematics or Physics, preferably at MMath/MSc level, or an equivalent overseas qualification (in exceptional circumstances a 2:1 class degree, or equivalent, can be considered).

We are looking for a bright and curious mind interested in applying mathematical tools and theories to interesting and challenging problems. This work will apply numerical and analytic tools to describe transport phenomena from mechanical engineering and physics, more specifically vibro acoustics and electronic transport. What we can offer is lots of insight and interesting discussions, plenty of things to learn for the curious mind and a very friendly environment. The topics will touch on functional analysis to understand operators describing transport phenomena [1] as well as numerical tools to describe them using computers [2]. We will cover bifurcation theory and stability analysis to understand real data from measurements and try to understand certain features seen in experiments [3].

What we would like you to bring is a curious mind, a good understanding of the relevant mathematical subjects and no fear of asking questions. If you are able to write and run small programs (for example in Python), that would be beneficial. The relevant subjects would be mainly analysis, theory of ordinary differential equations, partial differential equations, operators between Banach spaces, numerical analysis, and Hamiltonian dynamics. If that sounds like a lot, do not worry. We will get you up to speed quickly, see the comments about a friendly atmosphere and culture of asking questions above.

It is highly desirable that the successful applicant is familiar with one or several of the following topics: A solid understanding of classical mechanics, mathematical modelling, numerical methods. While experience with more than one of the aforementioned mathematical fields would be beneficial, the willingness to learn and engage with all of them is an absolute necessity. The project requires the student to have experience with a scientific computing software package or programming language such as Python or C/C++.


Funding Notes

Tuition Fees will be paid, and a full stipend provided at the RCUK rate (£15,609 per annum for 2021/22) There will also be some funds available to support conference attendance. The scholarship length will be 3.5 years.
Start date: 01.10.2021

References

A few references for further scientific details:
[1] Slipantschuk et.~al., Nonlinearity *33*, 2020, 5773-5790 https://doi.org/10.1088/1361-6544/ab9dca
[2] Hartmann et.~al., Wave Motion *87*, 2019, 132-150 https://doi.org/10.1016/j.wavemoti.2018.09.012
[3] Maryenko et.~al., Phys.~Rev.~B *85*, 2012, 195329 https://doi.org/10.1103/PhysRevB.85.195329
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