Random Walks in Inhomogeneous Media and Their Applications in Mesoscopic Physics and Evolutionary Dynamics - EPSRC DTP funded PhD Studentship Ref: 2959

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.

Dr Jacopo Bertolotti
Dr Wolfram Moebius

Streatham Campus

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. Click here for more information and a list of acceptable alternative tests.

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.  For information on EPSRC residency criteria click here.

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.


Application deadline:10th January 2018
Value:3.5 year studentship: UK/EU tuition fees and an annual maintenance allowance at current Research Council rate. Current rate of £14,553 per year.
Duration of award:per year
Contact: Doctoral Collegepgrenquiries@exeter.ac.uk

How to apply

You will be required to upload the following documents:
•       CV
•       Letter of application outlining your academic interests, prior research experience and reasons for wishing to
        undertake the project.
•       Transcript(s) giving full details of subjects studied and grades/marks obtained.  This should be an interim
        transcript if you are still studying.
•       If you are not a national of a majority English-speaking country you will need to submit evidence of your current
        proficiency in English.  For further details of the University’s English language requirements please see

The closing date for applications is midnight (GMT) on Wednesday 10 January 2018.  Interviews will be held at the University of Exeter in late February 2018.

If you have any general enquiries about the application process please email: pgrenquiries@exeter.ac.uk.
Project-specific queries should be directed to the supervisor.

During the application process, the University may need to make certain disclosures of your personal data to third parties to be able to administer your application, carry out interviews and select candidates.  These are not limited to, but may include disclosures to:

• the selection panel and/or management board or equivalent of the relevant programme, which is likely to include staff from one or more other HEIs;
• administrative staff at one or more other HEIs participating in the relevant programme.

Such disclosures will always be kept to the minimum amount of personal data required for the specific purpose. Your sensitive personal data (relating to disability and race/ethnicity) will not be disclosed without your explicit consent.