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Deriving kinetic equations: from particles to continuum


Department of Mathematical Sciences

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Dr Karsten Matthies No more applications being accepted Funded PhD Project (European/UK Students Only)

About the Project

The University of Bath is inviting applications for a funded PhD project in the Department of Mathematical Sciences https://www.bath.ac.uk/departments/department-of-mathematical-sciences/

Lead supervisor: Dr Karsten Matthies, University of Bath https://researchportal.bath.ac.uk/en/persons/karsten-matthies
Co-supervisor: Dr Florian Theil, University of Warwick https://warwick.ac.uk/fac/sci/maths/people/staff/florian_theil/

The project aims to develop methods for coarse-graining evolution equations in the context of particle systems. Kinetic equations represent an important class of models in Sciences and Mathematics with many formidable challenges such as existence and uniqueness of solutions to application-oriented problems involving long-time asymptotics, stability of patterns etc. We consider the question whether kinetic equations are in fact scaling limits of microscopic particles systems.

The project will include the use of methods from Dynamical Systems, Functional Analysis (Semigroups), Partial Differential Equations and Probability Theory. Advanced training in these areas can be provided as the successful candidate will profit from various training opportunities through courses and seminars offered by the Analysis and Probability groups as well as activities towards applications in the doctoral training centre on ’Statistical Applied Mathematics in Bath’ (SAMBa).

The student will be based in Bath but there will be frequent collaboration with the project partner (Florian Theil) in Warwick.

The studentship is financed by a Leverhulme research project grant, which provides additional travel and computing funds.

Candidate requirements:

Applicants should hold, or expect to receive, a First Class or high Upper Second Class UK Honours degree (or the equivalent qualification gained outside the UK) in Mathematics or a relevant subject and have detailed knowledge in some of the following areas: Analysis, Partial Differential Equations, Dynamical Systems, Probability Theory. A master’s level qualification and research experience would be beneficial.

Non-UK applicants must meet our English language entry requirement http://www.bath.ac.uk/study/pg/apply/english-language/index.html.

Enquiries and applications:

Informal enquiries are welcome and should be addressed to Karsten Matthies ([Email Address Removed]).

Formal applications should be made via the University of Bath’s online application form for a PhD in Mathematics:
https://samis.bath.ac.uk/urd/sits.urd/run/siw_ipp_lgn.login?process=siw_ipp_app&code1=RDUMA-FP03&code2=0014

Please ensure that you quote the supervisor’s name and project title in the ‘Your research interests’ section.

More information about applying for a PhD at Bath may be found here:
http://www.bath.ac.uk/guides/how-to-apply-for-doctoral-study/

IMPORTANT NOTE: Applications will be reviewed from 20/05/2020 until the position is filled. Early application is strongly recommended.

Anticipated start date: 28 September 2020.

Funding Notes

UK and EU citizens applying for this project will be considered for a studentship which will cover UK/EU tuition fees and will provide a tax-free maintenance allowance at the UKRI Doctoral Stipend rate (£15,285 per annum, 2020/21 rate) for a period of up to 3.5 years.

Unfortunately, applicants who are classed as 'Overseas' for fee paying purposes are not eligible for funding and will not be considered unless they can provide documentary evidence of their ability to fully self-fund their studies (Overseas tuition fees, research expenses/bench fees and living costs).

References

Karsten Matthies, George Stone, Florian Theil
The Derivation of the Linear Boltzmann Equation from a Rayleigh Gas Particle Model
http://www.aimsciences.org/article/doi/10.3934/krm.2018008
Kinetic and Related Models 11 (2018), 137 - 177

Karsten Matthies, Florian Theil
A semigroup approach to the justification of kinetic theory
https://epubs.siam.org/doi/10.1137/120865598
SIAM J. Math. Anal. 44 (2012), 4345-4379.

For background:
Isabelle Gallagher, Laure Saint-Raymond, and Benjamin Texier
From Newton to Boltzmann: hard spheres and short-range potentials. Zurich Lectures in Advanced Mathematics. European mathematical society, 2013.
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