Random Walks in Inhomogeneous Media and Their Applications in Mesoscopic Physics and Evolutionary Dynamics - EPSRC DTP funded PhD Studentship

About the award

This project is one of a number funded by the Engineering and Physical Sciences Research Council (EPSRC) Doctoral Training Partnership to commence in September 2018. This project is in direct competition with others for funding; the projects which receive the best applicants will be awarded the funding.

The studentships will provide funding for a stipend which is currently £14,553 per annum for 2017-2018. It will provide research costs and UK/EU tuition fees at Research Council UK rates for 42 months (3.5 years) for full-time students, pro rata for part-time students.

Please note that of the total number of projects within the competition, up to 15 studentships will be filled.

Location: Streatham Campus, Exeter

Project Description
This project explores random walks in inhomogeneous media as a tool to describe both wave propagation in scattering systems and evolutionary dynamics of expanding populations.

Aim: Unify the description of two apparently very different fields: wave propagation in scattering media and evolutionary dynamics of expanding populations.

Background: Very different problems sometimes share a very similar underlying mathematical description: wave propagation in mesoscopic systems, i.e., systems with features comparable in size to the wavelength, can be mapped to a random walk between scattering events, but random walks can also be used to model the evolution of populations expanding into a new environment. In both cases the macroscopic final state and the genetic diversity of the population, respectively, will depend on the distribution of the walker’s path lengths and the correlations between different paths, thus providing a common framework for two otherwise very different topics. In both cases not much is currently known about what happens when the underlying environment is inhomogeneous. Understanding this regime will allow for more realistic models of wave propagation and provide deeper inside into the evolutionary dynamics of expanding populations.

Methods: The following quantities are of special interest: distribution of the walker’s path lengths and correlations between different random walkers. To gain an understanding of how these quantities depend on the spatial structure of the medium or the environment, the student will develop and use simulations extensively. To gain a deep understanding, it is necessary to go beyond simulations in a second step and develop a coarsened analytic understanding. In a third part of the project, the findings will be applied to wave propagation in scattering media and evolutionary dynamics. Thereby, commonalities and differences will be explored in detail.

Funding, training, and experience to be gained: Funding is available for 3.5 years. Over the course of the project the student will be trained both the numerical and analytical techniques used to describe random walks, the physics of wave propagation, and the evolutionary dynamics of expanding populations. The project will be co-supervised by researchers with expertise in the different areas, providing the unique opportunity of training in these different fields of physics and biology.

Suitability: The project is suitable for candidates with a background in the physical sciences. Interest in a wide range of subjects is recommended as this project is highly interdisciplinary in nature, and draws methods from different fields.

Entry Requirements
You should have or expect to achieve at least a 2:1 Honours degree, or equivalent, in a physical science. Experience in theoretical physics is desirable.

If English is not your first language you will need to meet the English language requirements and provide proof of proficiency.

The majority of the studentships are available for applicants who are ordinarily resident in the UK and are classed as UK/EU for tuition fee purposes. If you have not resided in the UK for at least 3 years prior to the start of the studentship, you are not eligible for a maintenance allowance so you would need an alternative source of funding for living costs. To be eligible for fees-only funding you must be ordinarily resident in a member state of the EU.

Applicants who are classed as International for tuition fee purposes are NOT eligible for funding. International students interested in studying at the University of Exeter should search our funding database for alternative options.