Student research bursaries

Choose from the list of research projects for 2024 listed below and then submit an Expression of Interest to Dan Rust using the subject heading "STUDENT RESEARCH BURSARY APPLICATION" in capitals by 4 December 2023.

Your Expression of Interest should be no longer than 500 words and should contain:

• your name, Personal Identifier and preferred email address
• your choice of projects, in order of preference (at most two)
• a summary of how you meet the eligibility criteria above and why you are suitable for your project choice(s)
• a list of grades for all university modules taken at the Open University (a screenshot of your academic transcript is acceptable)
• a brief statement on if you are considering PhD study and why.

Title: Position Problems: Colouring, Games and Transport

Supervisor: James Tuite

Summary:

In 1900 the famous creator of mathematical puzzles Henry Dudeney posed the following chessboard conundrum: how many pawns can be placed on a n x n chessboard if we require that no straight line in the plane passes through three or more pawns? This problem has been generalised to the setting of graph theory. A graph is a combinatorial object consisting of vertices that are connected by edges. The general position problem asks for the number of vertices in a largest set S such that no shortest path in the graph contains more than two vertices of S. Applications include robotic transport and social network analysis.

Recently there has been a great deal of interest in variations on the general position problem, such as using chordless paths instead of shortest paths, or only requiring the existence of at least one shortest path between any pair of vertices {u,v} in S that contain no vertices of S-{u,v}. The successful candidate would work along with researchers in the OU, Slovenia, Italy and India to extend our knowledge of these variants and explore connections with other areas of mathematics. There are many avenues that could be pursued, depending on the student’s interests. Examples are: colouring problems, connections to robotic transport, extremal questions for graphs with given position numbers, links to domination and Ramsey theory and adversarial games on graphs.

Prerequisite knowledge

Essential:

The candidate should be confident with formulating mathematical proofs and should be familiar with fundamental number theory, linear algebra etc.

Desirable:

Experience with combinatorics and graph theory.

Availability:

July to August

Title: Analysis of student collected air quality data

Supervisor: Carol Calvert

Summary:

Fine particles in the atmosphere can affect the health of individuals and of our environment and there is a growing contribution of “citizen science” projects in the field of pollutants and climate change. In the summer of 2023 around 50 volunteer OU students collected over 600 000 air quality readings. The readings were taken on small, low cost hand held monitors across various geographical locations. The data is all held in a database and a large amount of quality control on the data, including linking to government data, will be undertaken as a part of this project. There are government monitoring stations across the UK and this data is readily available for linkage and analysis.

Prerequisite knowledge

Essential:

Knowledge of Minitab, or R , for analysis; Knowledge of regression

Desirable:

Interest in air quality; Interest in large government datasets on air quality

Availability:

July to September

Title: Optimal swimming strategies for nearly spherical microswimmers: the role of shape and hydrodynamics

Supervisor: Abdallah Daddi-Moussa-Ider

Summary:

A microswimmer, whether it's a living cell or a synthetic entity, harnesses internal or external energy to propel itself through a fluid. When considering the hydrodynamics of active swimmers, we can break it down into two main aspects: the inner problem, which deals with how these swimmers generate the force needed for movement, and the outer problem, which focuses on how they interact with their surrounding environment by modifying the fluid around them. 

For microswimmers, the ability to employ the most efficient propulsion strategies is crucial for their locomotion and survival, especially when operating at low Reynolds numbers. While perfectly spherical swimmers ideally use a neutral swimming approach to minimize energy dissipation, any deviation from this spherical shape may prompt swimmers to adopt different propulsion strategies, such as puller or pusher swimming. In this project, we aim to utilize a newly derived theorem for microswimmers that takes into account both internal and external dissipation to determine the flow pattern of an optimally nearly spherical swimmer. We aim to explore how the swimmer's shape profile influences whether it adopts a puller, pusher, or neutral swimming strategy. By using an asymptotic approach, we seek to identify the primary Legendre mode that predominantly determines the swimmer's preferred swimming type.

Prerequisite knowledge

Essential:

Calculus, differential equations

Desirable:

Fluid mechanics, basic knowledge of computer algebra systems like Mathematica or Maple, as well as LaTeX, is helpful.

Availability:

July to September

Title: Spin Models with Feedback: From Concept to Applications

Supervisor: Ivan Sudakow

Summary:

In this research project, we aim to develop a novel approach utilizing spin models derived from statistical mechanics to simulate critical transitions in pattern formation within complex large-scale systems. We consider cases in which these transitions are intricately linked to interactions between the patterns and the surrounding environment. Our approach will be based on incorporating the effects of random forcing field reconfiguration and spin interactions, taking advantage of the interplay between feedback mechanisms within spin clustering and the environment.

On a broader scale, our study seeks to explore the applicability of universal characteristics of critical transition phenomena to socioecological issues. This includes investigating how climate feedback mechanisms might act as triggers for tipping points and how feedback processes are influencing people's opinions within social networks.

Prerequisite knowledge

Essential:

Differential equations, statistics and probabilities, and programming.

Desirable:

Dynamical systems, computational mathematics, and stochastic processes.

Availability:

July and August

Title: Computational Fluid Dynamics of Biologically Active Fluids

Supervisor: Elsen Tjhung

Summary:

Biologically active fluids, such as bacterial suspensions, biofilms and cell cytoplasm, are driven far-from-equilibrium due to the internal driving forces/stresses, which are generated by each constituent particle. For example, in the case of bacterial suspensions, each single bacterium `stirs’ the fluid around it, and therefore continuously injects energy to the fluid locally (this energy is then subsequently dissipated as heat). Consequently, biological active fluid cannot be described by Navier-Stokes equation (since the fluid is alive). Instead, we have to modify the Navier-Stokes equation to take into account of this `internal’ stress generation. In this project, we will explore some of the hydrodynamics models, used to study these systems and discover new phenomena using computational fluid dynamics simulations. 

Desirable knowledge:

Mathematical Methods and Fluid Dynamics (MST326); Python programming (e.g.: Python Crash Course, 3rd Edition, by Eric Matthes)

Availability:

July to September. Project length 8-12 weeks. Full time/part time.

Title: Exploring the architecture of our appearance using AI

Supervisor: Kaustubh Adhikari

Summary:

Our appearance is a major component of our social and personal identity. Human appearance is multi-faceted, with many different aspects such as skin colour, facial shape, body height, and so on. Unfortunately, some aspects of our appearance have also been the subject of societal misunderstandings, including discrimination and racism.

Researchers in the area of genetics are using various methods to understand the architecture (including but not limited to the biological basis) of several aspects of our appearance. For example, many genes have been identified that explain the huge variability observed between ethnicities and also within any group of people.

Underlying all this are mammoth efforts in generating data and analysing it with various statistical techniques. In particular, AI (artificial intelligence) and machine learning models have been popular approaches. But understanding and interpreting the underlying architecture of complex AI models is challenging.

The student will be working as part of a research team to work with a dataset to investigate a specific aspect of the diversity of our appearance and its representation through AI models. The immediate goal is to produce a research output, but the broader goal is to have a better understanding of the latest research and delicate issues around this area, and to support the student in their own journey in academic research and public engagement. It will be a useful experience for someone planning to do further study in applied statistics, AI and machine learning, or biomedical fields.

Prerequisite knowledge

Essential:

Basic understanding of probability and statistics. Some familiarity with programming (Python / R etc.) or data analysis software (such as MS Excel) would be helpful. Prior knowledge of AI models is not necessary.

Desirable:

Some basic knowledge of biology or genetics (high school level) would be helpful to grasp the context of the problem easily, but is not essential.

Availability:

July to September

Title: The proof is in the pudding: a historical view of proof from ancient to modern times

Supervisors: Brigitte Stenhouse & Andrew Potter

Summary:

For almost every maths student, an undergraduate course is where they first meet the idea of a rigorous mathematical proof. Initially, proofs can be unfamiliar, intimidating, and confusing, but they are also the source of beauty and certainty that many find in studying mathematics. Recent scholarship in the history of mathematics - especially by scholars such as Karine Chemla and Agathe Keller on the history of proof in Chinese and Sanskrit traditions - has explored how the idea of proof emerged and became widespread within mathematical practice across the globe. Such studies help us to explore why we prove things – and afterwards, why we search for shorter, cleaner, or different proofs of the same result.

In this project, the successful student will survey literature on mathematical proof in order to produce an introduction and historical overview aimed at undergraduate students. This introduction will aim to inspire and encourage students who might lack confidence around using proofs, demonstrating the many uses that proofs have and the many different forms in which they come.

Prerequisite knowledge

Essential:

Have completed Stage 1 of a maths degree, or equivalent modules in mathematics; interest in the history of mathematics, especially outside of Europe and North America; ability to clearly summarise texts and write with a friendly tone; enthusiasm for reading.

Desirable:

Experience of study in history at A-Level / AS-Level (England, Wales, Northern Ireland), Higher (Scotland), or at an equivalent level or above. Interest in studying mathematical proof outside of the university curriculum. The ability to read French would be helpful but is NOT necessary.

Availability:

August to September