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.

This project will use the theories of liquid crystal fluids to model self-organisation and pattern formation in an active fluid - a type of liquid containing active organisms which interact with the fluid by swimming.

This project will use mathematical models of soil water and the growth of plants. Even for plants with complicated root densities we will look for analytical solutions of the models to help understand plant growth.

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 project deals with VISIBILITY GRAPHS. It will involve numerical work as well as methods of network and graph theory, primarily spectral analysis of adjacency matrices and Laplacians of the visibility graphs, and centrality and communicability indices of these graphs.

In this project, you will meet with the challenge of developing and testing an individual based model to simulate the life history and dispersal of Sargassum muticum driven by coastal ocean currents.

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.

In this project, you will meet with the challenge of developing an individual based model to simulate the growth and dispersal of a highly invasive seaweed (Japanese eelgrass) driven by coastal ocean currents.

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.