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Asymptotic Analysis of Nonlinear Lattice Systems

University of Bristol

Qualification Type: PhD
Location: Bristol, Sydney - Australia
Funding for: UK Students, EU Students
Funding amount: Minimum £15,609 p.a. subject to eligibility status
Hours: Full Time
Placed On: 13th September 2021
Closes: 13th December 2021

The project:

Systems of discrete particles often exhibit richer and more complicated behaviour than equivalent continuum systems. This makes them of interest to both mathematicians and materials scientists; as nanoscale fabrication systems improve, opportunities will develop for designing nanostructured materials with finely-tuned mechanical, electrical, acoustic, or optical properties.

The incredible versatility of these lattices stems from nonlinear dynamics in the interactions between lattice components. These enable the impulse response to be highly tunable, allowing for simple design of materials with useful and unusual properties. However, this flexibility comes at a cost: nonlinear lattice systems are particularly challenging to analyse and can make material behaviour difficult to predict and control. Recent developments in modern asymptotic methods (notably exponential asymptotics and discrete-to-continuum asymptotics) have great potential to yield insight into how the micro-scale interactions between lattice particles control macro-scale lattice behaviour.

In this project, we will use state-of-the-art asymptotic methods to understand and predict the behaviour of nonlinear lattice systems, focusing on lattices with physical applications such as nanoelectromechanical lattices and tunable lattices of magnets. This work will both lead to new mathematical results on the analysis of discrete systems and will also provide mathematical underpinnings for designing novel materials and structures with tuned properties.

This is a “cotutelle” PhD that will be jointly supervised between Dr Cameron Hall at the University of Bristol and Dr Christopher Lustri at Macquarie University in Sydney. As part of this PhD programme, you will spend half of your time in Bristol and half of your time in Sydney. The PhD funding includes funds for one return trip between Bristol and Sydney.

How to apply:

The application process will ultimately involve online applications at both the University of Bristol and at Macquarie University. Applicants should apply to the University of Bristol first, following the instructions below. Applicants are also encouraged to contact Dr Cameron Hall at an early stage to discuss the cotutelle PhD structure and how the application process works.

Prior to any application, please contact Dr Cameron Hall to discuss your research proposal.  No indication of an offer can be made until a completed application has been received.

To apply for this studentship, submit a PhD application using our online application system

Please ensure that in the Funding section you tick “I would like to be considered for a funding award from the Engineering Mathematics Department” and specify the title of the scholarship in the “other” box below along with and the name of the supervisor.  Interested candidates should apply as soon as possible.

Candidate requirements: 

Applicants must meet the entry requirements for the PhD Research programme they wish to apply to. Requirements can be found at http://www.bristol.ac.uk/study/postgraduate/2021/eng/phd-eng-maths/ including English Language.

Funding:

Funding is available for 3.25 years of which 18 months will be paid in Australia at the standard Australian Research Council rate.  In the UK this will cover:

  • Minimum £15,609 tax-free stipend per year for living expenses
  • tuition fees at UK student rates

For EPSRC funding, students must meet the EPSRC residency requirements.

Contacts:  

For questions about the research topic please contact Dr Cameron Hall cameron.hall@bristol.ac.uk

For questions about eligibility and the application process please contact sceem-pgr-admissions@bristol.ac.uk

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