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PhD in mathematical modelling of viscous wrinkling

PhD position
Date - 28/02/2023
University of Limerick
Ireland
Mathematics and statistics
Mechanical engineering
Physics

Structured PhD in Applied Mathematics (4-years full-time)

Project topic: Mathematical models for wrinkle technology [Fluid Mechanics]

Project supervisors: Dr. Doireann O’Kiely

Project location: MACSI, Department of Mathematics and Statistics, University of Limerick

Application deadline: 28 February 2023

Start date: Summer/Autumn 2023

PhD structure: This project is a full-time 4-year structured PhD project based in the Mathematics Applications Consortium for Science and Industry (MACSI) in the Department of Mathematics and Statistics at University of Limerick. The funding includes a tax-free stipend along with expenses for computing equipment, conference travel and materials. Home/EU fees are provided for in the funding; international students will need to apply for a fee waiver from the University of Limerick

PhD topic: Wrinkles appear in many situations where thin sheets undergo direct or indirect compression. Everyday examples include deflating balloons and stretched plastic wrapping. In technology, wrinkles can be used to redirect light in photovoltaics, they can act as microchannels for microfluidic devices, and they provide flexibility in electronic circuits. They also appear in as an unwanted by-product in the manufacture of glass screens and metal parts. Mathematical modelling plays a key role in improving our understanding of wrinkles, allowing them to be avoided when they are problematic, and exploited where they are useful.

Currently, mathematical modelling of wrinkles focuses on idealized, purely elastic behaviour. Many real-world materials display other behaviours, such as plasticity or viscous flow. The goal of this PhD project is to develop a mathematical framework for modelling and controlling wrinkles in sheets of viscous fluid. This will involve the use of differential equations together with dimensional analysis and/or scaling analysis to create a mathematical model, and the use of perturbation methods/asymptotic analysis together with scientific computation/numerical methods to make predictions.

Requirements: Applicants should have (or expect to attain prior to project start) at least a 2.1 honours degree or equivalent applied mathematics, physics, mechanical engineering or a closely-related discipline. Applicants must demonstrate proficiency in high-level mathematics and continuum mechanics. Applicants for whom English is a second language will be required to demonstrate their competence in the English language in line with University of Limerick requirements.

Funding notes: Stipend of €19,000 per year for four years, with budget for travel and laptop. Fees for Home/EU students will be covered automatically, while international students can apply for a fee waiver from the university.

Application: Applicants should email Dr Doireann O’Kiely (doireann.okiely@ul.ie) before 28 February 2023 to apply with a 2-page CV and a short cover letter/statement of purpose (2-pages max) indicating how their skills align with the project and their motivation for applying. Please include “PhD Application” followed by your name in the subject line. The application CV should, at minimum, include the applicant’s name, education institution, qualification stating overall grade/percentage (predicted grades are acceptable for those still studying) and contact details of two academic referees.

Informal queries can be made to: doireann.okiely@ul.ie. Please include “PhD Query” followed by your name in the subject line.

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