## Imperial College London 4 year phd

## 4 year PhD

The 4 year PhD programme in Theory and Simulation of Materials combines the one year MSc in TSM with a 3 year PhD research project.

The first year provides a rigorous training in the required theoretical methods and simulation techniques through the taught MSc programme and includes a 24 week research project which normally acts as an introduction to the PhD research project that follows.

On completion of the MSc in TSM, students undertake their PhD research project, which occupies years 2-4. Each student has at least two supervisors (one of whom may be based in industry or at another university) whose combined expertise spans multiple length- and/or time-scales of materials theory and simulation. Students do not have to make a choice of their research project until May of year 1 and there will be a large range of projects to choose from (view a representative sample of projects).

A key emphasis of all research projects is the development and implementation of new theory and code for materials simulation. Research projects being undertaken by current students in the TSM-CDT can be found here. Find out more about what a TSM-CDT research project is all about.

Students in the TSM-CDT are active participants in the Thomas Young Centre (TYC), the London Centre for the Theory and Simulation of Materials, which brings researchers in theory and simulation of materials from all over London (Imperial, UCL, King’s College, and Queen Mary’s), for an exciting programme of scientific events, workshops and visiting professors from across the globe.

### Imperial College London 4 year phd

### Academic Requirements

The principal requirement for entry to the TSM-CDT is a **first class** Bachelor’s or Master’s degree in an appropriate subject within the physical sciences or engineering. The course is multidisciplinary in nature, so applicants from a wide range of backgrounds are encouraged to apply. However the theoretical nature of the course means that the study of mathematics to a high level is required. The list below gives the minimum mathematical pre-requisites for the course.

- Complex algebra: roots of polynomials, de Moivre’s theorem, hyperbolic functions.
- Vector algebra: scalar, vector and triple products; basis vectors; vector geometry.
- Matrix algebra: representation of simultaneous linear equations, matrix inversion, determinants, eigenproblems and diagonalisation.
- Ordinary differential equations: solution of separable first-order and linear first-order equations; solution of linear second-order equations with constant coefficients.
- Fourier analysis: Fourier series and transforms; Dirac delta function; convolution theorem.
- Partial differential equations: solution of second-order equations by separation of variables; Fourier methods for applying boundary conditions.
- Vector calculus: gradient, divergence, curl and Laplacian in Cartesians; line, surface and volume integrals’ divergence and Stokes’ theorems; spherical and cylindrical polar coordinates.