The aim of this project is to understand the properties of composites by approximating them with “effective” (homogeneous) materials.
The problem of effective properties of heterogeneous materials (composites) goes back to the works of Maxwell, Rayleigh and Einstein.
In the second half of the past century the theory of homogenisation became a distinct mathematical discipline. Today understanding the properties of composites and search for novel composite materials is a major direction of research in industry and science.
Project aims and methods
Depending on your interests, the project will deal with problems in one of the following two important areas of Homogenisation Theory:
Spectral properties of linear differential operators with heterogeneous (high-contrast) coefficients. This includes understanding of the band-gap structure of the essential spectrum of an operator, localisation of eigenmodes in the gaps of the spectrum, wave propagation phenomenon, resolvent estimates.
Homogenisation problems in non-linear elasticity. In particular, questions of simultaneous homogenisation and dimension reduction, such as homogenisation of thin elastic rods, plates and shells.
You will learn about ideas from mathematical analysis and differential equations which exploit modern techniques of analysis of heterogeneous problems and deal with multi-scale analysis, dimension reduction, asymptotic approximation. Some of the problems have direct applications to the design and engineering of composite materials (metamaterials). If you are a new PhD student, you will be required to take a number of advanced postgraduate level courses as part of the training.
HOW TO APPLY
Applicants should submit an application for postgraduate study via the online application service: http://www.cardiff.ac.uk/study/postgraduate/research/programmes/programme/mathematics
In the research proposal section of your application, please specify the project title and supervisors of this project.
If are applying for more than one Cardiff University project please note this in the research proposal section.