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.

Climate change can disrupt the synchronicity between annual ecological events. This project will explore the ecosystem level consequences of organisms drifting out of step in the marine environment, failing to match reproduction and migration with the availability of food.

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.

Predictions based on numerical simulations of complex real-world engineering systems cannot be considered reliable if the simulation tool does not include the nondeterministic features of the system into account. The aim of this exciting project is to design and analyse cutting-edge numerical schemes to approximate high-dimensional problems and quantify uncertainty in multiphysics engineering systems.

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 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.

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.

High-dimensional problems are crucial across science and engineering, appearing in areas such as climate modelling and machine learning, where computational costs increase dramatically with each added dimension. This project investigates low-rank methods to address these challenges, aiming to simplify complex problems. The goal is to establish a dynamical low-rank method as a practical, well-understood tool for analysing uncertainty in large datasets and complex scenarios.

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.

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.

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.

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.

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.

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 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.

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.

John Anderson Research Studentship Scheme (JARSS) doctoral studentships are available annually for excellent students and excellent research projects.

There are two main sources of funding:

• Central University funding
• Engineering and Physical Sciences Research Council - Doctoral Training Partnership (EPSRC - DTP) funding.

The JARSS 2023/2024 competition will open in October 2023 and students successful in this competition will commence studies in October 2024. Faculties will set their own internal deadlines for the competition.

Academics/Supervisors make the applications for this scheme and there are various deadlines across the Department and Faculties, therefore, in the first instance, all interested students should contact the Department where they would like to carry out their research.