PhD, MPhil, MRes Mathematics & statistics

This project will develop effective solvers for linear systems in these RBF methods. In particular, we will focus on certain iterative methods (Krylov subspace methods) that start with an initial guess of the solution that is improved at each step.

The proposed project will use a variety of analytical and numerical methods to bring new understanding into a range of real-world problems involving thin films of both simple and complex fluids.

In recent years there has been an explosive growth of interest in the behaviour and control of fluids at small (typically sub-millimetre) scales motivated by a range of novel applications including ink-jet printing and lab-on-a-chip technologies.

Matrix balancing aims to transform a nonnegative matrix A by a diagonal scaling by matrices D and E so that P = DAE has prescribed row and column sums. Historical motivation for achieving the balance has included interpreting economic data, preconditioning sparse matrices and understanding traffic circulation.

The aims of this PhD is to develop the truncated EM method are to study the strong convergence in finite-time for SDEs under the generalised Khasminskii condition and its convergence rate and to investigate the numerical stability of the nonlinear SDEs.

This project is to perform the stochastic and numerical analysis on the stock market linked savings accounts in order to establish the theory on the mean percentage of return (MPR).

Time dependent wave propagation and scattering is important in acoustics, electromagnetics and seismology.

The purpose of this project is to conduct a comprehensive extraction and synthesis of all the relevant data for demersal fish species in the Firth of Clyde.

There is currently great interest in self-rewetting fluids whose surface tension exhibits a local minimum with temperature. The aim of the project is bring new insight into the understanding of these novel fluids, and hence to harness the properties of droplets of such fluids in a range of technological applications.

Many problems are described by partial differential equations that are too difficult to solve analytically. Numerical solutions must be used, which typically require the solution of linear systems. This project will look at how to solve these linear systems efficiently.

Study permutation tableaux such as the Le- and EW-tableaux, their connections to Abelian Sandpile Model and Asymmetric Exclusion Processes, and the connection between these two models afforded by the tableaux.

Graph representations became crucial with the advent of the computer era for storing graphs in computer memory. However, graph representations, e.g. those involving patterns in words, are also useful in solving problems on graphs as they may allow transferring a graph problem to that on other objects hence solving it.

To ensure that a person taking any route in a city has the same experience, e.g. seeing a city map, we need methods to cover the routes without over-deploying resources. We will use tools in Graph Theory and Combinatorics to optimally deploy resources across a city to have maximum effect on those navigating it.

Liquid crystals are fluids that show local orientational order. The interplay between orientation and flow in these substances is very intricate and can lead to interesting macroscopic phenomena, many of which are not yet fully understood. This project will study such phenomena using mathematical and numerical models.

The goal of this project is the exact enumeration of classes of permutations that can be plotted on monotone curves in grids. At present, an effective procedure is only known for so-called “skinny” classes. The general problem is challenging because permutations have multiple ways of being plotted on the curves.

Effective methods have been derived for dividing a network into coherent communities using spectral information obtained from the network. Biclustering has received far less attention. We will develop new methods and analysis for this problem, starting from recent work using a bistochastic representation of a network.

The goal of this project is to explore fundamental structural questions concerning sets of permutations that avoid a single pattern. The study of these combinatorial objects was initiated by Donald Knuth in the 1960s when he investigated which permutations could be sorted by being passed through a stack.

The aim of this project is the generalise the existing molecular-statistical theory of elasticity of nematic liquid crystals to the case of bent-core nematics, composed of biaxial and polar molecules, using the preliminary results obtained in recent years.

The aim of this project is to develop a molecular-statistical theory of chirality transfer in cholecteric nanorod phase, determined by steric and electrostatic chiral interactions, and quantitatively describe the variation of helix pitch as a function of rod length, concentration, dispersity and temperature.

The aim of this project is to build and analyse a new generation of spectral preconditioners based on generalised eigenvalue problems allowing a robust behaviour with respect to the physical properties of the medium. This requires a combination of numerical analysis and spectral analysis tools.

Nematic liquid crystals are exciting materials that are intermediate between solid and liquid phases of matter. Nematics have widespread applications in science and technology, notably the thriving liquid crystal display industry. This project focuses on the mathematical modelling and analysis of nematics in prototype systems in an interdisciplinary framework, for potential advances in materials technologies.

Soft Matter is a broad umbrella term for easily deformable materials that are susceptible to external stimulus. In this project, we focus on soft materials with both orientational/nematic order and magnetic order, and study how the two types of order interact with each other to stabilise exotic morphologies. We use analytic and numerical methods to explore these soft matter systems theoretically and hope to propose new experimental systems for tailor-made applications.

Noise is known to be helpful in two models of quantum computing: quantum walks and quantum annealing. You'll investigate how it works and extend the principles to other models of quantum computing.

You'll tackle some of the many open problems that stand in the way of using quantum computers to speed up scientific computing, and test your ideas on real quantum computers.