PhD, MPhil, MRes Mathematics & statistics

The PhD student will work closely with our industrial partners to develop innovative digital tools and methodologies for improving the resilience and sustainability of critical infrastructure. These will include but not limited to the development of: mathematical models to address the performance of critical functions and critical hazards; new uncertainty methods with quantifiable confidence; fast simulation tools based on machine learning and engineering-physics based automatic learning.

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).

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.

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.

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 evaporation of sessile droplets is a fundamental scientific problem that is key to numerous physical and biological processes, and, as a result, has been the subject of an explosion of analytical, experimental, and numerical investigations in recent years. However, despite its intrinsic complexity and multidisciplinary nature, considerable insight can be gained into many fascinating aspects of the problem by developing and solving a range of mathematical models.