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Pattern Formation (Applied Nonlinear Dynamics)

PGR-P-252

Key facts

Type of research degree
PhD
Application deadline
Ongoing deadline
Country eligibility
International (open to all nationalities, including the UK)
Funding
Competition funded
Supervisors
Professor Alastair Rucklidge
Schools
School of Mathematics
Research groups/institutes
Applied Mathematics
<h2 class="heading hide-accessible">Summary</h2>

Pattern Formation (Applied Nonlinear Dynamics) - understanding the formation and stability of complex patterns such as quasipatterns, spatio-temporal chaos or turbulent spirals Regular patterns, such as stripes, squares and hexagons, are ubiquitous in nature, and their formation and stability are governed by the intricate and complex interactions of symmetry and nonlinearity. Nonlinear interaction of waves in different directions can lead to the formation much more complicated and beautiful patterns: quasipatterns, spatio-temporal chaos and other forms of chaotic dynamics, depending on just how the waves interact. This project will involve using ideas from nonlinear dynamics: bifurcation theory, stability theory, three-wave interactions, chaos, symmetry and heteroclinic cycles, to understand the formation and stability of complex patterns such as quasipatterns, spatio-temporal chaos or turbulent spirals. The distinct aspect of this project is that it will involve problems with two length scales, where waves of two different wavelengths can interact in many different ways. There will be emphasis on deep understanding of the underlying dynamics in the problem, using computational tools, bifurcation theory, asymptotic theory, weakly nonlinear theory, symbolic algebra, group theory, or whatever is needed. While the project will focus on solving a particular set of partial differential equations using asmptotic and numerical methods, one of the beauties of the nonlinear dynamics approach is that it can have wide applicability in different areas of mathematics, physics, chemistry or biology. The ideas that this project will explore have application to understanding patterns in fluid dynamics (the Faraday Wave experiment), soft matter physics (the formation of polymer quasicrystals) and chemistry (two-layer reaction-diffusion systems).

<h2 class="heading hide-accessible">Full description</h2>

<p>The earliest start date for this project is 1 October 2020.</p>

<h2 class="heading">How to apply</h2>

<p>Formal applications for research degree study should be made online through the&nbsp;<a href="https://www.leeds.ac.uk/info/130206/applying/91/applying_for_research_degrees">University&#39;s website</a>. Please state clearly in the research information section&nbsp;that the research degree you wish to be considered for is &lsquo;Pattern Formation (Applied Nonlinear Dynamics)&rsquo; as well as&nbsp;<a href="https://physicalsciences.leeds.ac.uk/staff/75/professor-alastair-m-rucklidge">Professor Alastair&nbsp;Rucklidge</a>&nbsp;as your proposed supervisor.</p> <p>If English is not your first language, you must provide evidence that you meet the University&#39;s minimum English language requirements (below).</p> <p><em>We welcome applications from all suitably-qualified candidates, but UK black and minority ethnic (BME) researchers are currently under-represented in our Postgraduate Research community, and we would therefore particularly encourage applications from UK BME candidates. All scholarships will be awarded on the basis of merit.</em></p>

<h2 class="heading heading--sm">Entry requirements</h2>

Applicants to research degree programmes should normally have at least a first class or an upper second class British Bachelors Honours degree (or equivalent) in an appropriate discipline. The criteria for entry for some research degrees may be higher, for example, several faculties, also require a Masters degree. Applicants are advised to check with the relevant School prior to making an application. Applicants who are uncertain about the requirements for a particular research degree are advised to contact the School or Graduate School prior to making an application.

<h2 class="heading heading--sm">English language requirements</h2>

The minimum English language entry requirement for research postgraduate research study is an IELTS of 6.0 overall with at least 5.5 in each component (reading, writing, listening and speaking) or equivalent. The test must be dated within two years of the start date of the course in order to be valid. Some schools and faculties have a higher requirement.

<h2 class="heading">Funding on offer</h2>

<p><strong>Self-Funding Students</strong></p> <p><strong>Funding Eligibility</strong></p> <p><strong>UK/EU</strong> &ndash;&nbsp;Leeds Doctoral Scholarship Award paying Academic Fees and Maintenance matching EPSRC rate of &pound;15,009 per year for 3 years, School of Mathematics Scholarship award paying Academic Fees and Maintenance matching EPSRC rate of &pound;15,009 per year for 3 years.&nbsp; Alumni Bursary is available to previous University of Leeds graduates offering 10% discount on Academic Fees.</p> <p><strong>International Students</strong> &ndash;&nbsp;China Scholarship Council-University of Leeds Scholarship Award paying Academic Fees for 3 years,&nbsp;School of Mathematics Scholarship award paying Academic Fees for 3 years, Commonwealth Scholarship and Commonwealth Split Site Scholarships.&nbsp; Alumni Bursary is available to previous University of Leeds graduates offering 10% discount on Academic Fees.</p>

<h2 class="heading">Contact details</h2>

<p>For further information regarding your application, please contact Doctoral College Admissions by&nbsp;email:&nbsp;<a href="mailto:maps.pgr.admissions@leeds.ac.uk">maps.pgr.admissions@leeds.ac.uk</a>, or telephone: +44 (0)113 343 5057.</p> <p>For further information regarding the project, please contact Professor Ricklidge by email:&nbsp;&nbsp;<a href="mailto:A.M.Rucklidge@leeds.ac.uk">A.M.Rucklidge@leeds.ac.uk</a></p>


<h3 class="heading heading--sm">Linked funding opportunities</h3>
<h3 class="heading heading--sm">Linked research areas</h3>