Solving differential equations in chemical engineering

In a compartment model, the total volume in a chemical process is divided in multiple compartments that are assumed to be well mixed. The process is then described as a big system of ordinary differential equations (ODEs) specifying the concentrations of the chemical reactants in each compartment and other quantities like temperature. Prior research led to a tool that construct the ODEs from a high-level description of the chemical process. However, standard implementations of ODE solvers do not work as well as we had hoped.<br /> <br /> We have some ideas on potential issues. The vastly different time scales in chemical reactions mean that the ODEs are usually stiff; however, this is quite a classical problem and there are standard methods (implicit solvers) that should be able to handle this. Quantities like concentration and volume can get very small but they have to remain positive throughout the computation, otherwise the equations and results do not make sense. The equations also have discontinuities in them (for instance, an overflow may activate when the volume in a tank exceed some level), which may also require special handling. However, it is not clear at this point which of these is the main bottleneck, or whether it is a combination or even something completely different.<br /> <br /> The aim of the project is to investigate the performance issues with standard ODE solvers, identify some ways to resolve them, and incorporate this in our tool. This project requires some knowledge of numerical methods for solving ODEs and some programming experience. An interest in chemistry is also needed.

<p>Formal applications for research degree study should be made online through the&nbsp;<a href="https://www.leeds.ac.uk/research-applying/doc/applying-research-degrees">University&#39;s website</a>. Please state clearly in the Planned Course of Study section that you are applying for <em><strong>PHD Applied Mathematics FT</strong></em> and&nbsp;in the research information section&nbsp;that the research degree you wish to be considered for is <em><strong>Solving differential equations in chemical engineering</strong></em>&nbsp;as well as <a href="https://eps.leeds.ac.uk/maths/staff/4067/dr-jitse-niesen">Jitse Niesen</a> 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>As an international research-intensive university, we welcome students from all walks of life and from across the world. We foster an inclusive environment where all can flourish and prosper, and we are proud of our strong commitment to student education. Across all Faculties we are dedicated to diversifying our community and we welcome the unique contributions that individuals can bring, and particularly encourage applications from, but not limited to Black, Asian, people who belong to a minority ethnic community, people who identify as LGBT+ and people with disabilities. Applicants will always be selected based on merit and ability.</em></p> <p class="MsoNoSpacing" style="text-align:start; margin-bottom:24px"><strong>Applications will be considered on an ongoing basis. &nbsp;Potential applicants are strongly encouraged to contact the supervisors for an informal discussion before making a formal application. &nbsp;We also advise that you apply at the earliest opportunity as the application and selection process may close early, should we receive a sufficient number of applications or that a suitable candidate is appointed.</strong></p> <p><strong>Please note that you must provide the following documents when you submit your application:</strong></p> <ul> <li><strong>Full Transcripts of all degree study or if in final year of study, full transcripts to date</strong></li> <li><strong>Personal Statement outlining your interest in the project</strong></li> <li><strong>CV</strong></li> </ul>

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.

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.

<p class="MsoNoSpacing" style="text-align:start; margin-bottom:24px">A highly competitive EPSRC Doctoral Training Partnership Studentship consisting of the award of fees with a maintenance grant (currently &pound;16,062 per year for session 2022/23) for 3.5 years.</p> <p>This opportunity is open to all applicants. All candidates will be placed into the EPSRC Doctoral Training Partnership Studentship Competition and selection is based on academic merit.<br /> <br /> Please refer to the&nbsp;<a href="https://www.ukcisa.org.uk/">UKCISA</a>&nbsp;website for&nbsp;information regarding Fee Status for Non-UK Nationals.</p> <p><strong>Self-Funded or externally sponsored students are welcome to apply.</strong></p> <p>UK&nbsp;&ndash;&nbsp;The&nbsp;<a href="https://phd.leeds.ac.uk/funding/209-leeds-doctoral-scholarships-2022">Leeds Doctoral Scholarships</a>,&nbsp;<a href="https://phd.leeds.ac.uk/funding/234-leeds-opportunity-research-scholarship-2022">Leeds Opportunity Research Scholarship</a>,&nbsp;<a href="https://phd.leeds.ac.uk/funding/198-akroyd-and-brown-scholarship-2022">Akroyd &amp; Brown</a>,&nbsp;<a href="https://phd.leeds.ac.uk/funding/199-frank-parkinson-scholarship-2022">Frank Parkinson</a>&nbsp;and&nbsp;<a href="https://phd.leeds.ac.uk/funding/204-boothman-reynolds-and-smithells-scholarship-2022">Boothman, Reynolds &amp; Smithells</a>&nbsp;Scholarships are available to UK applicants. &nbsp;<a href="https://phd.leeds.ac.uk/funding/60-alumni-bursary">Alumni Bursary</a>&nbsp;is available to graduates of the University of Leeds.</p> <p>Non-UK &ndash; The&nbsp;<a href="https://phd.leeds.ac.uk/funding/48-china-scholarship-council-university-of-leeds-scholarships-2021">China Scholarship Council - University of Leeds Scholarship</a>&nbsp;is available to nationals of China. The&nbsp;<a href="https://phd.leeds.ac.uk/funding/73-leeds-marshall-scholarship">Leeds Marshall Scholarship</a>&nbsp;is available to support US citizens.&nbsp;&nbsp;<a href="https://phd.leeds.ac.uk/funding/60-alumni-bursary">Alumni Bursary</a>&nbsp;is available to graduates of the University of Leeds.</p>

<p>For general enquiries about applications, contact our admissions team at&nbsp;<a href="mailto:maps.pgr.admissions@leeds.ac.uk">maps.pgr.admissions@leeds.ac.uk</a><br /> For questions about the research project, contact Jitse Niesen at <a href="mailto:j.niesen@leeds.ac.uk">j.niesen@leeds.ac.uk</a></p>