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. 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.