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

Loughborough University - Department of Mathematical Science

Application details:

Reference number: GT/MA/2018
Start date of studentship: 1st October 2018
Closing date of advert: 16th February 2018


Primary supervisor: Dr. Gyula I. Tóth
Secondary supervisor: Professor Andrew J. Archer

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.

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 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.

Full Project Detail:

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.

Find out more:

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.

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. Gyula I. Tóth
Tel: (+44)1509-227162

How to apply:

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

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Midlands of England