Analytic description of amorphous solids: A classical density functional approach PhD

Mathematical Sciences
Entry requirements:
3 years
not available
Reference number:
Start date:
01 October 2018
Is funding available?
UK/EU fees:
International fees:
Application deadline:
16 February 2018



of research classed as 'internationally recognised'

REF 2014


in the UK for Mathematics

The Complete University Guide 2018


Loughborough University is a top-ten rated university in England for research intensity (REF2014) and an outstanding 66% of the work of Loughborough’s academic staff who were eligible to be submitted to the REF was judged as ‘world-leading’ or ‘internationally excellent’, compared to a national average figure of 43%.

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. 

Project detail

The PhD candidate will be supervised by two academics from the Department of Mathematical Science and Interdisciplinary Centre for Mathematical Modelling who have extensive experience in modelling the structure of matter in both liquid and solid state. The student will gain expertise in mathematical modelling, numerical and analytical techniques and programming, and will also receive training in presentation, teaching, writing and science communications skills.

The Department of Mathematical Sciences is highly regarded and provides an excellent research environment. The mathematical modelling section of the Department consists of 9 full-time research active academics, 3 postdoctoral researchers and 13 PhD students.  With the recent formation of the Interdisciplinary Centre for Mathematical Modelling, further growth in this area is planned.

Although crystal nucleation fundamentally determines the macroscopic physical properties of the material, it is one of the least understood phenomena in science. Recent experimental results suggest that solidification can start with the formation of a non-crystalline solid precursor, which then transforms into the crystal in a subsequent process. The experimental observations are also supported by atomistic simulations and theoretical studies.

During the proposed project the candidate will study the properties of the metastable bulk non-crystalline solid phase and the properties of the equilibrium amorphous-liquid interface using density functional theories, starting from the Phase-Field Crystal model and its variants. This approach is becoming increasingly used to model the thermodynamics, phase behaviour and structure of matter. The specific task is to develop a mathematical methodology of determining the average properties of an infinite set of “random” solutions of the Euler-Lagrange equation.


Primary supervisor: Dr. Gyula I. Tóth

Secondary supervisor: Professor Andrew J. Archer

Find out more

For further project details email Dr. Gyula I. Tóth or register your interest and ask us a question.

To find out more about postgraduate research in the School of Science please visit our website.

Click here to read more about the Computational Materials Science Group.

Entry Requirements

Applicants should have, or expect to achieve, at least a 2:1 Honours degree (or equivalent) in Physics, Mathematics or a related subject. A relevant Master’s degree and/or experience in one or more of the following will be an advantage: Statistical physics and thermodynamics, nucleation theory, pattern formation models, probability theory and statistical methods, Fourier analysis, parallel programming.

Applicants must meet the minimum English Language requirements, details available on the website.

Fees and funding


Tuition fees cover the cost of your teaching, assessment and operating University facilities such as the library, IT equipment and other support services. University fees and charges can be paid in advance and there are several methods of payment, including online payments and payment by instalment. Special arrangements are made for payments by part-time students.

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.

How to apply

All applications should be made online. Under programme name, select ‘Mathematical Sciences’.

Please quote reference number: GT/MA/2018

Application details

Reference number:  GT/MA/2018
Start date: 01 October 2018
Application deadline: 16 February 2018