PhD Studentship: Fractal Structures in High-dimensional Reactions

Loughborough University

Start date of studentship: 1st October 2018

Closing date for applications: 16th February 2018


Primary supervisor: Dr Thomas Bartsch

Secondary supervisor: Prof Anatoly Neishtadt

The project offers the chance to learn and further develop fundamental methods in dynamical systems that will have applications across a range of fields. The research group maintains collaborations with researchers in mathematics, physics and chemistry in various European countries and the US. The successful applicant will obtain wide-ranging expertise in different fields of science and build a network of contacts that will form an excellent basis for further career development.

Loughborough University is a top-ten rated university in England for research intensity (REF2014). In choosing Loughborough for your research, you’ll work alongside academics who are leaders in their field. You will benefit from comprehensive support and guidance from our Doctoral College, including tailored careers advice, to help you succeed in your research and future career.


The Department of Mathematical Sciences works to deliver innovative research that has the potential to have significant impact on industry. Research students within the department enjoy a vibrant learning community benefitting from a range of resources to support their work, plus the opportunity to undertake training in lecturing/tutoring. 


Full Project Detail:

In many chemical reactions the reaction rate is determined by the crossing of an energy barrier. In order to predict whether a reaction will occur, one must understand the dynamics of the crossing in as much detail as possible. There is a growing interest in high-dimensional systems, which show novel dynamical effects.

Of particular importance are the trapped trajectories near the barrier top, i.e., those that never leave the barrier region. These trajectories organize the surrounding dynamics. They often form fractal structures.

In this project you will study the dynamics of simple chemical reactions with three atoms, which are the smallest systems in which high-dimensional effects occur. You will compute the clusters of trapped trajectories, their fractal dimension and stability properties and relate them to the reaction rate.

Find out more:

Entry requirements:

Applicants should have, or expect to achieve, at least a 2:1 Honours degree (or equivalent) in Mathematics or Physics or a related subject. A relevant Master’s degree and/or experience in one or more of the following will be an advantage: Mathematics, Theoretical Physics.

The project will involve a significant amount of numerical simulation, in particular the numerical solution of ordinary differential equations. It requires familiarity with a suitable programming language of the applicant’s choice.

Funding information:

This studentship will be awarded on a competitive basis to applicants who have applied to this project and/or any of the advertised projects prioritised for funding by the School of Science.

The 3-year studentship provides a tax-free stipend of £14,553 (2017 rate) per annum (in line with the standard research council rates) for the duration of the studentship plus tuition fees at the UK/EU rate.  International (non-EU) students may apply however the total value of the studentship will be used towards the cost of the International tuition fee in the first instance.

Contact details:

Name: Dr Thomas Bartsch


Tel: +44-(0)1509-222858

How to apply:

Applications should be made online at Under programme, select Mathematics.

Please quote reference number: TB/MA/2018

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