Institute for Mathematical Innovation

Undergraduate Research Internship Projects 2018

Please contact the supervisor directly if you are interested in working on any of these projects.
New projects will be added when we receive them, so please check this page regularly. 


Analysis of inhaler formulations

Project title: Structural and chemical analysis of inhaler formulations.
Subject area: Pharmaceutical materials science.   
Details: Dry powder inhalers can effectively deliver active pharmaceutical ingredients to the airways. They are, however, notoriously difficult to formulate due to the unpredictability of particle deagglomeration, aerosolisation and entrainment into inspiratory air flow. This project involves the measurement of chemical and structural properties of collected aerosol particles by spectroscopy, microscopy and other physicochemical techniques. The data will be analysed using multivariate statistical tools to establish links between formulation structure and performance.    
Supervisor: Mr William Ganley, Department of Pharmacy & Pharmacology


Artificial hearts

Project title: Multiscale mathematical modelling for artificial hearts.
Subject area: Cardiovascular biomechanics. 
Details: Patients with end stage heart failure really need a heart transplant. However, waiting times are long, so in the meantime they may have the option of an artificial heart, more correctly called a Ventricular Assist Device (VAD), a pump which can help their heart supply blood to the body. Rotary VADs have become the gold standard therapy for end-stage heart failure. However, the relationship between design parameters and physiological benefit is still not well understood. In this project different mathematical models will be used to understand: 1) The relationship between geometrical parameters and pressure-flow characteristics of the VAD, and 2) The relationship between the unsteady pressure-flow characteristics of the VAD and the cardiac support given to the patient. There is also the opportunity for some experimental testing of the results using a flow rig and 3D printed prototypes.
Supervisor: Dr Katherine Fraser, Department of Mechanical Engineering


Canonical metrics and automorphism groups

Project title: Canonical metrics and automorphism groups of surfaces.
Subject area: Algebraic and differential geometry, group theory. 
Details: Canonical metrics are a way measuring on surfaces which allow us to homogeneously measure on all points of the surface. Unfortunately, not all surfaces admit such a metric. One of the basic impediments to the existence of canonical metrics are the symmetries of the surface. In this project, you will learn how to modify a surface to obtain a new one using a technique called “blow-up” which is the basic step to construct surfaces in birational geometry. Furthermore, you will learn basic intersection theory of curves in surfaces and the classification of rational surfaces. Finally, you will learn how to describe the symmetry group of some rational surface and identify how to this group can obstruct the existence of a canonical metric.
Supervisor: Dr Jesus Martinez Garcia, Department of Mathematical Sciences


Clinical and sport biomechanics

Project title: Spinal muscles synergies: how do muscles work synergistically in physiological and pathological movement?  
Details: Muscles activation patterns can reveal underpinning mechanisms related to physiological movements, and can be used as 'biomarkers' to preventively diagnose musculoskeletal diseases. The synergetic behaviour of muscles is particularly key for spinal movement, as anatomically there are many muscles that, if activated, generate similar spinal movement. This project aims to: 1) Understand the mechanical function of individual spinal muscles and spinal muscle groups in relation to their geometrical (i.e. muscle attachments) and anatomical (i.e. muscles volume and strength) characteristics, and 2) Mathematically or statistically explain the function of specific synergies. Experimental data of spinal muscles activation and spinal kinematics are available for the analysis, as well as computer simulation model (i.e. musculoskeletal models) for accessing muscles architecture data.
Supervisor: Dario Cazzola, Department for Health 


Coordination and coordination variability in human movement

Project title: How can we assess coordination and coordination variability in human movement?
Subject area: Biomechanics and Motor Control 
Details: Dynamical system approaches have been used over the last 2-3 decades to characterise coordination and coordination variability in human movement. However, the assessment of movement coordination and of how it changes due to motor skill learning/adaptations (e.g. due to pain, injury or disease) still presents a number of issues. This project will explore existing (e.g. vector coding, multivariate 1D analyses) and new data analysis techniques.    
Supervisor: Dr Ezio Preatoni, Department for Health


Decoding the nervous system

Project title: Decoding the nervous system: A model based approach.
Details: Recent advances in array based neural interfaces have, for the first time, enabled long term recordings of the electrical signals that travel throughout our nervous system. Decoding these signals is key to expanding our fundamental understanding of the nervous system, answering questions about how our bodies and our brain process information, make decisions and form memories. The recorded data are a composite of many individual signals that have been summed together. In this project we will aim to use time series analysis techniques – coupled with statistical models – to pull apart these waveforms and extract the underlying information.
Supervisor: Dr Ben Metcalfe, Department of Electronic & Electrical Engineering


Designing robust and sustainable biomass value chains

Project title: Optimisation-based approach for the design of robust and sustainable biomass value chains that are synergistic with the food-energy-water-environment nexus.
Subject area: Optimisation of large-scale systems, operational research, supply chain modelling and optimisation, mathematical programming, optimisation under uncertainty. 
Details: Biomass can be used to produce biofuels, energy, chemicals and other valuable products. The biomass supply chain involves numerous activities and complex systems that can span entire countries and even continents. It also involves many interdependent decisions such as: what biomass to grow, where to grow them; what energy services/products to generate; what processing technologies to use, how to transport and distribute biomass products. The vast number of interdependent decisions, relating to the design and operation of biomass value chains, are too numerous to permit optimal configurations to be determined using heuristics or intuition. Approaches such as supply chain optimisation, which systematically and efficiently search the whole solution space, are the only way to guarantee optimal or near optimal designs.

The aim of this project is to develop a biomass value chain optimisation model to determine the combinations of crops grown and technologies used to convert biomass to energy and other high-value products, including detailed logistics, that provide the greatest benefits with the lowest impact on the nexus. This model will be used to identify the robust and sustainable value chains that are synergistic with the nexus and have the potential for deployment over a wide range of scenarios with different combinations of socio-economic and environmental objectives and constraints, including those for ecosystem services and biodiversity.    
Supervisor: Dr Sheila Samsatli, Department of Chemical Engineering


Fuzzy cognitive maps

Project title: Using fuzzy cognitive maps to test neuroscience models of psychiatric disorders.
Project aim: I am working on a new line of research which uses Fuzzy Cognitive Maps (FCM) to create models of large-scale brain networks comprised of brain regions and their connection. First, a model is created and then simulated using a new FCM program to test the dynamic activity of the brain regions and model, based on fuzzy logic. This research involves literature reviews of models and brain research on a given topic or disorder towards developing a model of relevant brain regions, then to run simulations to initially test normal model stability and activity. Then to add a dysfunction in the model to simulate a lesion or disorder to test out theories and compare results to research literature. The aim of the summer research is to develop and test some new FCM models, and to write up the results to be published in relevant journals in the field.           
Supervisor: Dr Chris Ashwin, Department of Psychology


Hollow-core optical fibres

Project title: Guidance of light in hollow-core optical fibres.
Subject area: Theoretical / Computational Physics
Details: One of the key properties of an optical fibre is its loss - it is important that light entering one end of the fibre gets to the other end without losing too much intensity along the way. For a number of applications it is useful to have light travelling in air rather than glass but, to date, hollow-core fibres have had a much larger loss than conventional fibres. Over the past five years there has been a lot of interest generated by a new class of hollow-core fibre, because these have the potential to have a lower loss than previous designs. I am interested in developing theoretical and computational models to gain a deeper understanding of why these fibres guide light so effectively, and to use this to support the design of new structures. There are a range of projects that are available, both analytic and computational, that could be tailored to suit the student's interests.   
Supervisor: Professor David Bird, Department of Physics


Hybrid models of reaction-diffusion processes

Project title: Developing hybrid models of reaction-diffusion processes.
Project aim: To develop a continuum-discrete, stochastic-deterministic hybrid modelling framework for reaction-diffusion processes.
Details: Mathematical modelling of reaction-diffusion processes has until recently been dominated by continuum models in the form of partial differential equations (PDEs). In some situations, there will be sufficiently many molecules to make these deterministic. For some model systems there may exist regions of the domain in which a PDE may be acceptable whereas in other regions it may be more appropriate to use a discrete model. One possibility is to use a hybrid model that simulates cell density using a PDE in one region and an individual-based model in the other. This raises non-trivial questions as to how to appropriately couple the two models and what should be the condition we use to determine where to segue between the models. However, if the molecules are more sparsely distributed then the inherent stochasticity of the system may become important, thereby rendering such continuum models redundant. One way to incorporate noise into such systems is to discretise the domain into ‘compartments’ in which molecules can reside and move between. This is known as a position-jump model.     
Supervisor: Dr Kit Yates, Department of Mathematical Sciences


Manufacturing processes

Project title: Innovative manufacturing processes.
Details: This project involves investigation and development of new techniques for improving manufacturing processes for exotic alloys used in medical and aerospace industries. The project can be followed in different ways either experimental work or theoretical modelling using finite element methods. Suitable for undergraduate students with a background and interest in mechanical engineering, electrical engineering, material science or mathematical science. 
Supervisor: Dr Alborz Shokrani, Department of Mechanical Engineering


Mechanical face seals

Project title: Dynamics of a non-contacting face seal.
Subject area: Applied mathematics, mathematical modelling, nonlinear dynamics, uncertainty quantification. 
Details: In rotating machinery, used in aerospace, industrial and automotive industries, mechanical face seals are used to prevent the leakage of fluid from one part of the machine to another, whilst operating under challenging conditions. To improve the seal efficiency, performance and prevent premature seal failure, a comprehensive understanding of the dynamic seal response is needed. This project will focus on the derivation of a mathematical model for a simplified non-contacting face seal to investigate the dynamics of the seal and identify safe operating conditions. There is the option to include uncertainty quantification in the analysis as the operating conditions are not know exactly.    
Supervisor: Dr Nicola Bailey, Department of Mechanical Engineering


Metal forming

Project title: Combining finite element analysis with machine learning for metal forming applications.
Details: Analytical modelling of metal forming is often intractable. Hence, numerical methods are often used to evaluate processes. Those, however, cannot always be used in real-time design problems or for process control, since they are slow and inflexible. Machine Learning methods can potentially be trained using the volumes of data available through parametric FEA studies, and thus provide fast, predictive models on demand. This project will both aim at running the necessary simulations based on existing models, as well as training and testing ML algorithms.      
Supervisor: Dr Evripides Loukaides, Department of Mechanical Engineering


Modelling air pollution

Project titleModelling air pollution for West of England Combined Authority spatial planning.
Details: The newly-formed West of England Combined Authority (WECA), which is constituted of the local authorities of Bath & North East Somerset, Bristol and South Gloustershire, has developed an ambitious housing and infrastructure plan for the next twenty years. This project will work in partnership with the Institute for Policy Research (IPR) at the University of Bath and with WECA to model the impact of these developments on air pollution, a significant public health challenge. Air pollution is responsible for an estimated 400,000 premature deaths per year in Europe. The aim of this project is to collect and merge geographical subsets of data in multiple forms and from multiple sources to create state-of-the-art air pollution models and visualisations which can provide actionable insights for WECA on this pressing policy issue.      
SupervisorProfessor Julie Barnett, Department of Psychology 


Modelling skin absorption

Project title: Modelling skin absorption from in vitro – flow through diffusion cells permeation data.
Project aim: To develop a continuum-discrete, stochastic-deterministic hybrid modelling framework for reaction-diffusion processes.
Details: Skin in vitro permeation data using flow-through diffusion cells is becoming progressively more accepted by regulators such as the FDA and EMA as part of the dossier required to establish bioequivalence and quality of topical products. However, when finite doses of creams and ointments are applied, as to mimic real application by patients, the experimental set-up can introduce artefacts that could lead to wrong conclusions or to inconclusive results. This is because the contributions of factors such as the flow of the subdermal receptor fluid, the receptor volume and dead-volume effects have on the estimated flux of drugs across the skin have not been addressed. Available experimental data with the drug acyclovir (apparent skin flux measured at two different flow rates) indicates that the effect of the different flow rate must be addressed before it is possible to assess whether the results in the two cases are meaningfully different.

This project will utilize a mathematical model of the flow-through diffusion cell system to relate the apparent drug flux (estimated from the drug concentrations in the collected samples of the receptor fluid) to the actual (intrinsic) flux through the skin, which is the desired outcome.  A regression analysis will be developed to derive a functional representation of the drug flux from the input data; i.e., the drug concentrations measured in the collected samples of the receptor fluid over the duration of the experiment. This function in combination with the diffusion cell model is solved using Laplace transforms to give the actual flux as a function of time. The goal is to incorporate the computational steps (data input, data regression to the functional representation, Laplace inversion of the resulting model, and output of the actual flux through skin over time) into a convenient app that provides reliable estimates of the actual drug flux through the skin. The outcome will be an app that can be used by skin scientists and industry to provide improved estimations of skin absorption from flow-through diffusion cell data that can be compared across laboratories using different experimental conditions. 
Supervisors: Dr Jane White, Department of Mathematical Sciences, Dr Begoña Delgado-Charro, Department of Pharmacy and Pharmacology and Professor Annette Bunge, Colorado School of Mines
Email: or


Natural loading effects

Project title: Deciphering small fluctuations in groundwater piezometer data at a coastal landslide to measure natural loading effects.
Details: Recent field trials have shown that ground water piezometers at a coastal landslide site show very small, periodic changes in pore water pressure. These are thought to be due to external loading (e.g. atmospheric loading, moisture loading, and earth tides). These will be interpreted to determine the stiffness, permeability and water storage of the subsurface soil and rock formations.    
Supervisor: Dr Kevin Briggs, Department of Architecture & Civil Engineering


Non-linearity in the Solar Wind - Magnetosphere - Earth Systems

Project title: Detecting non-linearity in the Solar Wind - Magnetosphere - Earth System.
Subject area: Heliophysics, geophysics, solar-terrestrial physics, non-linear dynamics and time series analysis.
Details: The sun continuously emits a stream of charged particles known as the solar wind into space at speeds of hundreds of kilometers per second. The Earth moves through this solar wind. We are protected from the energetic particles in the solar wind by Earth's magnetic field, but the interaction between the solar wind and Earth's magnetic field can have many physical and practical technological consequences, including the aurora, damage to satellites, disruption of phone services and even power cuts because of damage to electricity distribution grid infrastructure. Predicting such events is therefore of considerable importance but current forecasting methods have proved unreliable, especially so by failing to predict extreme events. It is believed that one of the reasons this is because the response on Earth to events in the solar wind, mediated by Earth's magnetic field and atmosphere, is non-linear. This project aims to confirm this through statistical analysis of the Auroral Electrojet Index, which measures the disturbance of Earth's magnetic field by events in the solar wind. The project would be suited to students who have an interest in space science, space or infrastructure engineering or statistics.    
Supervisor: Dr Robert Burston, Department of Electronic & Electrical Engineering


Optical properties of atomically thin multilayers

Project title: Modelling optical properties of atomically thin multilayers.
Subject area: Two-dimensional semiconductors.
Details: The isolation of graphene in 2004 (Geim and Novoselov: Physics Nobel Prize 2010) started a huge worldwide activity in nanoscience focuing on the many materials that can exist as layers only a few atoms thick. Around 1000 different materials are either known or expected to belong to this family. In Bath, we have pioneered the study of one particular class of materials which, unusually, show strong anisotropy in the 2D plane of the layers; one way this anisotropy reveals itself is in the propagation of light through the layers. The interaction with light is crucial to many of the applications proposed for these materials (sensors, photodetectors, wearable flexible electronics) and is, in our case, surprisingly complicated to understand. In this project, we aim to develop a model that describes correctly the optical properties of materials that we are studying experimentally.    
Supervisor: Dr Daniel Wolverson, Department of Physics
Contact the researcher


Preserving cultural heritage

Project title: Preserving cultural heritage: regenerating images of damaged items.
Subject area: Computer vision, modelling
Details: The world’s cultural heritage is being lost due to both natural and man-made causes, such as mishandling by excavators/curators or destruction during wars. To help preserve it for the future, there is a need for digitising and regenerating images or 3D models of damaged heritage. The main approach to the project would be as follows: 1) Digitally remove the labels put on the face of the artefacts by the excavators, 2)  Remove signs of bad restorations and 3) Reconstruct the broken parts of the artefacts using various mathematical methods.     
: Dr Gule Saman, Department of Computer Science


Random satisfiability

Project title: A new model for random satifiability.
Subject area: Theoretical computer science, probability.
Details: This project lies at the boundary between theoretical computer science and probability. The aim is to understand a model of random inputs to the satisfiability problem (there is no pre-requisite in probability besides the very basics) and run simulations of these inputs in an efficient way, using the University's supercomputer, in order to establish conjectures about the behaviour of this new model.

A SAT-solver takes as input a Boolean expression, and gives as output the answer to the question “ is this expression satisfiable?” It is known since the work of Cook in 1971 that the satisfiability problem is NP-complete; however, SAT-solvers are surprisingly efficient in practise, suggesting that, although the SAT-solvers have exponential complexity on worst-case inputs, they have polynomial complexity on “typical” inputs. Models of random SAT inputs are a way to try to understand the structure of typical inputs; this has been done in the literature but many exciting problems are still open. The internship will focus on a new model for such inputs: the model of random saturated trees. Read more >>      
: Dr Cécile Mailler, Department of Mathematical Sciences  and Professor James Davenport, Department of Computer Science
Email: or


Sleep behaviour andSleep behaviour and chicken welfare

Project title: Mathematical modelling of sleep behaviour as an indicator of chicken welfare.
Subject area: Non linear dynamical systems,  statistics, mathematical biology. 
Details: The importance of a good night’s sleep is universally acknowledged to underpin good health and to promote effective mental functioning in human beings. Sleep follows a strong circadian rhythm and is controlled by internal clock-like systems and external cues. Some of these effects have been captured in mathematical models applied to humans and to other mammals, but there has been no work to describe sleep quality in birds. Like mammals, birds can sleep with both brain hemispheres simultaneously, but unlike mammals, birds can also sleep with just half of their brain at a time, allowing the other half of the brain to remain active and alert. The aim of this project is to develop a data-informed, mathematical approach to define and model sleep processes in birds, specifically commercially farmed laying hen chicks, under different on-farm rearing conditions. This will enable a preliminary decision about which rearing conditions lead to the best bird welfare. The project could be tailored to suit students with various backgrounds and interests, and could include statistical and/or mathematical modelling, as well as data processing.    
Supervisor: Dr Lorna Wilso, Institute for Mathematical Innovation