Applied Mathematics
University of Strathclyde
About the Project Induction heating is present in diverse industrially-relevant processes such as heating for forging operation, quenching, hardening, brazing, etc. A typical industrial induction heating line consists of a series of spiral-shaped coils energised by high-frequency alternating current that generates a time-varying magnetic field, where a cylindrical bar travels through the coils in order to be heated by resistive losses of the eddy currents.
- Location
- Glasgow, United Kingdom, United Kingdom
- Deadline
- 30 September 2026
- Funding
- Funded PhD Project (UK Students Only)
Applied Mathematics
University of Southampton
About the Project Supervisory Team: Prof. Ben Waterson and Dr Ioannis Kaparias About the project This project will create a simulated road environment game, to understand how people prioritise different road users, and train the next generation of artificial intelligence based control algorithms to make traffic lights operate the way that people want them to.
- Location
- Southampton, United Kingdom, United Kingdom
- Deadline
- 30 September 2026
- Funding
- Competition Funded PhD Project (Students Worldwide)
Applied Mathematics
University of Leeds
About the Project Please note the start date for this project is Monday 1 February 2027. Join an international team developing scalable algorithms to solve numerical linear algebra challenges on supercomputers. Modern high-performance computing increasingly relies on hardware accelerators originally designed for artificial intelligence.
- Location
- Leeds, United Kingdom, United Kingdom
- Deadline
- 30 September 2026
- Funding
- Funded PhD Project (Students Worldwide)
Applied Mathematics
University of Southampton
About the Project Supervisory team: Prof. Ben Waterson This project will use artificial intelligence (machine learning) techniques to establish new models of pedestrian, cyclist and scooter rider path prediction for use in complex urban environments. Established models of crowd movements predict the paths that pedestrians take based on a cumulative set of forces resulting from forecast future interactions.
- Location
- Southampton, United Kingdom, United Kingdom
- Deadline
- 30 September 2026
- Funding
- Competition Funded PhD Project (Students Worldwide)
Applied Mathematics
University of Warwick
About the Project Sudden cardiac arrest (SCA) accounts for approximately 15-20% of reported deaths in the UK. Mostly, these deaths are linked to cardiac arrhythmias. One of the most common and dangerous is Ventricular Tachycardia (VT), a rapid and unstable heart rhythm that often arises from regions of diseased or scarred heart tissue. VT can lead directly to sudden cardiac death if not treated immediately.
- Location
- Coventry, University of Warwick, United Kingdom
- Deadline
- 30 September 2026
- Funding
- Funded PhD Project (UK Students Only)
Applied Mathematics
Loughborough University
About the Project Since the discovery of graphene, various two-dimensional (2D) materials have been the focus of intense research and important applications. They have potential to induce disruptive technology change in chemical, energy, electronics and quantum industries. The aim of this project is to carry out multiscale modelling of selected 2D materials, including binary systems and stacked layers of them, and databases for machine learning and computer simulations.
- Location
- Loughborough, United Kingdom, United Kingdom
- Deadline
- 1 October 2026
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
University of Birmingham
About the Project A fully-funded 3.5-year PhD studentship (covering UK home student fees and an annual stipend of £21,805) is available in Applied Mathematics for Formulated Products. The PhD will be under the supervision of Professor Rosemary Dyson, in the School of Mathematics (in the College of Engineering and Physical Sciences), and interface with the SUM4Products Network.
- Location
- Birmingham, United Kingdom
- Deadline
- 1 October 2026
- Funding
- UK Students; annual stipend of £21,805
Applied Mathematics
King’s College London
About the Project Gravitational wave (GW) astronomy is approaching a paradigm shift: within the next decade, next-generation observatories such as the Einstein Telescope and LISA will be sensitive enough to reveal not only every binary black hole (BBH) merger in the observable universe, but potentially entirely new, exotic sources of gravitational waves — including compact objects, such as boson stars, which are predicted by dark matter models.
- Location
- London, United Kingdom, United Kingdom
- Deadline
- 12 October 2026
- Funding
- Funded PhD Project (Students Worldwide)
Applied Mathematics
The University of Manchester
About the Project This PhD project addresses the "calibration problem" in particulate continuum models and particle simulations. Specifically, it focuses on developing robust methodologies for selecting and parameterising contact models, a crucial but challenging task due to the lack of standardised measurement techniques.
- Location
- Manchester, United Kingdom
- Deadline
- 13 October 2026
- Funding
- UK Students; £21,805 annual tax-free stipend set at the UKRI rate and tuition fees will be paid
Applied Mathematics
The University of Manchester
About the Project High energy density lasers now sit at the heart of advanced manufacturing, joining and materials processing, and underpin a growing range of defence and energy applications. When a focused beam meets a surface, the material can melt, flow, vapourise and eject within microseconds, while the expanding vapour plume alters how the remaining energy reaches the substrate.
- Location
- Manchester, United Kingdom, United Kingdom
- Deadline
- 14 October 2026
- Funding
- Competition Funded PhD Project (UK Students Only)
Applied Mathematics
Queen’s University Belfast
About the Project Intensive livestock farming is a major contributor to environmental degradation, including nutrient runoff, water pollution, and greenhouse gas emissions. Existing regulatory frameworks often rely on fixed calendar-based rules and retrospective measurements, which fail to reflect the dynamic nature of farm systems.
- Location
- Belfast, United Kingdom, United Kingdom
- Deadline
- 16 October 2026
- Funding
- Funded PhD Project (Students Worldwide)
Applied Mathematics
Cardiff University
About the Project About this project: Decoding calcium signalling during fertilization: a data-driven mathematical modelling framework for a non-invasive IVF diagnostic tool (Cardiff University, School of Computational and Mathematical Sciences) In vitro fertilization (IVF) is the primary treatment for infertility, with over 2.5 million cycles performed annually worldwide.
- Location
- Cardiff, United Kingdom, United Kingdom
- Deadline
- 21 October 2026
- Funding
- Competition Funded PhD Project (Students Worldwide)
Applied Mathematics
University College London
About the Project A fully-funded PhD is available from February 2027 to work with Professors Sonya Crowe , Christina Pagel and Nici Zimmermann on an Operational Research / System Dynamics project as part of the NIHR/EPSRC-funded SPROCKET Hub (Systems and Process Redesign and Optimisation at Childhood Key Events and Transitions).
- Location
- London, United Kingdom, United Kingdom
- Deadline
- 25 October 2026
- Funding
- Competition Funded PhD Project (Students Worldwide)
Applied Mathematics
University of Edinburgh
About the Project This project aims to investigate the capabilities of adaptive structures that change their geometry and mechanical properties to accommodate operational loading and damage management. The core objective of this project is to engineer an adaptive structure that adjusts to the prescribed loading conditions. This adaptation is achieved by integrating local structures that accommodate stiffness variations along the global structure.
- Location
- Edinburgh, United Kingdom, United Kingdom
- Deadline
- 30 October 2026
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
University of Sheffield
About the Project Precision measurements of the Cosmic Microwave Background (CMB) from Planck have established ΛCDM as the standard cosmological model. However, significant tensions have emerged—most notably the Hubble constant discrepancy between early- and late-universe determinations, now exceeding 7σ.
- Location
- Sheffield, United Kingdom, United Kingdom
- Deadline
- 31 October 2026
- Funding
- Competition Funded PhD Project (UK Students Only)
Applied Mathematics
The University of Manchester
About the Project Phase-contrast magnetic resonance imaging (Flow MRI) is a powerful and non-invasive imaging technique that measures blood flow in time and space. It provides vital insights into key metrics for cardiovascular disease diagnosis and management, such as velocity, wall shear stress, and turbulence. However, its clinical application is currently severely limited by high noise (low signal-to-noise ratio) and low spatial and temporal resolution.
- Location
- Manchester, United Kingdom, United Kingdom
- Deadline
- 31 October 2026
- Funding
- Funded PhD Project (UK Students Only)
Applied Mathematics
University of Birmingham
Parametric integrators approximate solutions of (high-dimensional) partial differential equations by restricting the numerical approximation to a closed form that nonlinearly depends on, and is identified by, a set of parameters. Such methods are a popular choice in quantum dynamics, where the wavefunctions of many-body systems are approximated by multiple Gaussians.
- Location
- Birmingham, United Kingdom
- Deadline
- 6 November 2026
- Funding
- UK Students, EU Students, International Students, Self-funded Students; Not Specified
Applied Mathematics
University of Birmingham
About the Project PhD studentship: Physical intelligence in robotic materials Join us! Are you a curiosity-driven scientist with a background in physics, engineering, or a related discipline, who wants to lead work at the intersection of robotics and metamaterials? Join us!
- Location
- Birmingham, United Kingdom
- Deadline
- 6 November 2026
- Funding
- Funded PhD Project (UK Students Only)
Applied Mathematics
University of Southampton
About the Project Supervisory Team: Professor Paul Kemp and Dr Andrew Vowles Freshwater ecosystems are the most degraded on the planet and the species they support the most threatened. Innovative technology can help halt biodiversity loss and degradation of freshwater habitats. This project will employ computer science to solve challenges in identifying and managing dams and weirs that fragment critical river habitat.
- Location
- Southampton, United Kingdom, United Kingdom
- Deadline
- 30 November 2026
- Funding
- Competition Funded PhD Project (UK Students Only)
Applied Mathematics
University of East Anglia
About the Project Primary Supervisor: Dr. Robert Whittaker This is a one-year MSc by Research project. Find out more about this programme here . Manufacturers of thin potato-based snacks are interested in developing healthier cooking methods than the traditional oil frying. One option they are keen to explore is using microwaves. Experiments with circular potato disks running on a belt through a microwave field show some promise.
- Location
- Norwich, United Kingdom, United Kingdom
- Deadline
- 30 November 2026
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
University of East Anglia
About the Project Primary Supervisor: Prof. Mark Blyth Inviscid liquid jets subject to surface tension and in the absence of gravity are known to be unstable under long-wave perturbations, a phenomenon described by the classical Rayleigh–Plateau instability. However, when vorticity and swirl are included, Erhard et al.
- Location
- Norwich, United Kingdom, United Kingdom
- Deadline
- 30 November 2026
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
University of East Anglia
About the Project Primary Supervisor: Dr. Davide Proment A supersolid is one of the most intriguing recently realised phases of quantum matter, simultaneously exhibiting the crystalline structure of solids and the frictionless flow of superfluids. In recent years, dipolar Bose–Einstein condensates (dBECs) have emerged as an ideal platform for creating and studying supersolid states in ultracold atomic systems.
- Location
- Norwich, United Kingdom, United Kingdom
- Deadline
- 30 November 2026
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
University of East Anglia
About the Project Primary Supervisor: Dr. Robert Whittaker Foams, comprising thin liquid films surrounding many small gas bubbles, have many domestic and industrial applications. These often rely on properties such as a high interfacial area, surface activity and yield stress. Foams can also be used as proxies for the structure of more complicated biological systems. The structure of a foam us largely determined by the minimization of the interfacial surface area.
- Location
- Norwich, United Kingdom, United Kingdom
- Deadline
- 30 November 2026
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
University of East Anglia
About the Project Primary Supervisor: Dr. Davide Proment Come and join the research group of Dr Davide Proment at the University of East Anglia (UK, Norwich) to investigate how nonlinear waves propagate, interact, and self-organise on complex networks and graph structures.
- Location
- Norwich, United Kingdom, United Kingdom
- Deadline
- 30 November 2026
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
University of Edinburgh
About the Project Reconstructing 3D gas concentration and temperature profiles within dynamic, turbulent plumes from sparse optical measurements is a classic ill-posed inverse problem. Positioned at the intersection of radiative transfer, fluid dynamics, and statistical physics, this project aims to push the boundaries of computational imaging in extreme, harsh environments.
- Location
- Edinburgh, United Kingdom, United Kingdom
- Deadline
- 11 December 2026
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
University of Birmingham
Advances in manufacturing science have resulted in unprecedented research and development in the design of ‘micro-swimmers’: microscopic entities that navigate fluid environments by converting some form of energy–e.g. electrical, magnetic, acoustic, or chemical–into mechanical motion.
- Location
- Birmingham, United Kingdom
- Deadline
- 25 December 2026
- Funding
- Funded PhD Project (UK Students Only)
Applied Mathematics
Loughborough University
About the Project Over recent years the modelling and understanding of complex phases, and their interfacial interactions, has developed at pace. Phases can be a solution of components, a mixture including colloidal particles, or different states such as in a frozen or vapour state.
- Location
- Loughborough, United Kingdom, United Kingdom
- Deadline
- 1 January 2027
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
University of Glasgow
About the Project Motivated by marine and industrial applications, this project concerns nonlinear resonant sloshing of confined water waves. Nonlinear resonance is a mechanism by which energy is continuously exchanged between a small number of linear wave modes, a phenomenon common to many dispersive fluid systems.
- Location
- Glasgow, United Kingdom, United Kingdom
- Deadline
- 1 January 2027
- Funding
- Competition Funded PhD Project (Students Worldwide)
Applied Mathematics
University of Glasgow
About the Project The aim of this project involves applying techniques across mathematical modelling, analysis, fluid mechanics and/or computation to examine the efficiency of novel methodologies for enhanced and sustainable blood filtration technologies for patients undergoing dialysis treatment.
- Location
- Glasgow, United Kingdom, United Kingdom
- Deadline
- 1 January 2027
- Funding
- Competition Funded PhD Project (Students Worldwide)
Applied Mathematics
University of Edinburgh
About the Project This PhD tackles a fundamental open problem in soft matter physics that sits at the heart of multiple industries and natural systems: the rheology of dense suspensions of elongated particles. Why does a slurry packed with cellulose fibres flow so differently from one packed with spherical particles?
- Location
- Edinburgh, United Kingdom, United Kingdom
- Deadline
- 1 March 2027
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
University of Edinburgh
About the Project Context Reverse osmosis (RO) holds significant promise in alleviating global water scarcity through seawater desalination. But shortages of increasing frequency and intensity now demand treatment of unconventional waters beyond seawater, such as wastewater, to expand supply. RO is also increasingly deployed to treat industrial streams in microelectronics, pharmaceutical, and food & drink manufacturing, which must meet stringent water quality standards.
- Location
- Edinburgh, United Kingdom, United Kingdom
- Deadline
- 2 March 2027
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
University of Southampton
About the Project Supervisory Team: Dr Yasir Noori This project aims to shape the future of semiconductor manufacturing by using deep learning to predict nanoscale defects before they occur. It combines nano lithography, plasma etching, material deposition, with deep learning (AI) modelling, with access to Southampton’s cleanrooms, IRIDIS supercomputing, collaboration with global leaders in chip manufacturing and commercialisation opportunities.
- Location
- Southampton, United Kingdom, United Kingdom
- Deadline
- 1 June 2027
- Funding
- Competition Funded PhD Project (Students Worldwide)
Applied Mathematics
Loughborough University
About the Project The impact of two bodies of liquid, such as droplets, is a phenomenon occurring widely in nature and in engineering applications, from waves breaking onto layers of marine biological matter to streams of different inks in additive manufacturing. Impacts are notoriously complicated problems to study, with rapid topological changes occurring over disparate lengthscales.
- Location
- Loughborough, United Kingdom, United Kingdom
- Deadline
- 31 July 2027
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
Durham University
About the Project Pollinating insects are essential to agriculture and biodiversity, yet monitoring wild bees in natural environments remains extremely difficult. Bees are small, fast-moving and visually diverse, and must be detected against complex vegetation under changing illumination, weather and seasonal conditions.
- Location
- Durham, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
The University of Manchester
About the Project The modelling of laser-material interactions is a complex multi-physics problem, very computationally intensive and often relies on detailed and expensive characterisation of the material's thermo-physical properties. This makes this type of analysis inaccessible for industrial applications that can require a wide range of modelling parameters, over large spatial and temporal spaces and where inputs are stochastic in nature.
- Location
- Manchester, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Funded PhD Project (UK Students Only)
Applied Mathematics
University of Birmingham
About the Project PhD Studentship in Numerical Analysis and Scientific Computing The project concerns the numerical solution of partial differential equations (PDEs) with uncertain inputs (e.g., material properties, external forces, geometry of the computational domain). It will focus on developing adaptive algorithms for efficient solution of such problems.
- Location
- Birmingham, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Competition Funded PhD Project (UK Students Only)
Applied Mathematics
University of Birmingham
About the Project This project will develop advanced computational and experimental tools to support the safe, efficient, and scalable manufacture of materials critical to UK and European security, with a particular focus on resonant acoustic mixing (RAM) - a relatively novel and increasingly important class of process equipment attracting growing industrial interest across multiple sectors.
- Location
- Birmingham, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Funded PhD Project (UK Students Only)
Applied Mathematics
University of Aberdeen
About the Project These projects are open to students worldwide, but have no funding attached. Therefore, the successful applicant will be expected to fund tuition fees at the relevant level (home or international) and any applicable additional research costs. Please consider this before applying.
- Location
- Aberdeen, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
Cardiff University
About the Project Electroencephalography (EEG) is a technique that measures the electric potential originating from the brain using electrodes located on the scalp. Its main purpose is to characterise the neural sources that give rise to such potentials. To this end, it is necessary to build approximation models of the head and the brain sources involved, which allow us to study electrical propagation through the head tissues.
- Location
- Cardiff, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
The University of Manchester
About the Project With the growing use of non-metallic structural materials, such as glass fibre-reinforced plastic in the marine and renewable energy sectors and polymers for instance, high-density polyethylene in pipelines, non-destructive evaluation (NDE) of these materials is becoming a growing and pressing challenge.
- Location
- Manchester, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Funded PhD Project (UK Students Only)
Applied Mathematics
Imperial College London
About the Project Student Background: Theoretical Physics, Mathematics/Statistics, Bioinformatics, Electrical Engineering, Computing (Biological knowledge not required). We have been investigating (genetic) variation in cellular power stations (mitochondria), an article about our work is here: https://www.imperial.ac.uk/news/264393/cryptic-mitochondrial-dna-mutations-reveal-hidden/ Our group's goal is to understand human ageing and to develop therapies to combat disease.
- Location
- London, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Competition Funded PhD Project (European/UK Students Only)
Applied Mathematics
University of Strathclyde
About the Project This project represents a development in a truly sparse capability within the UK. With the current, very rapid development of requirements for future timing systems, in both the military and civil arenas, there is a keen and growing demand for suitably qualified and experienced persons in these areas to which the work in this proposal will contribute significantly. Only one studentship is available, recruitment will close on selection of a suitable student.
- Location
- Glasgow, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Funded PhD Project (UK Students Only)
Applied Mathematics
University of Sheffield
About the Project The way the smart grid is envisioned in the near future is as a constantly changing system where intermittent renewable sources and non stationary loads impose a turbulent system. If we intend to understand what is the statistical structure of the electric grid that is coming, we need to confront the dynamism of the network and discard the widespread linearized static model.
- Location
- Sheffield, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
University of Liverpool
About the Project This project develops and validates AI-derived retinal, ECG, echocardiographic, and serum biomarkers to enable early detection and risk prediction of heart failure in patients with hypertension and diabetes.
- Location
- Liverpool, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
University of Sheffield
About the Project In classical general relativity, Einstein’s equations involve the curvature of space-time on the left-hand-side, and the stress-energy tensor of matter on the right-hand-side. In a quantum theory of gravity, both sides of Einstein’s equations (that is, both the geometry and the matter) will be quantum in nature.
- Location
- Sheffield, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
University of Birmingham
About the Project The human brain is commonly represented as a network in which brain regions are nodes and connections between pairs of regions are edges. But is a pairwise network really enough to describe how the brain works? Many neural processes arise from the coordinated activity of groups of brain regions , meaning that important information may be lost when complex interactions are reduced to pairs.
- Location
- Birmingham, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Competition Funded PhD Project (UK Students Only)
Applied Mathematics
University of Aberdeen
About the Project These projects are open to students worldwide, but have no funding attached. Therefore, the successful applicant will be expected to fund tuition fees at the relevant level (home or international) and any applicable additional research costs. Please consider this before applying. Complex systems are everywhere — from swarming birds and interacting cells to the spread of ideas or diseases through society.
- Location
- Aberdeen, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
University of Sheffield
About the Project Precision measurements of the Cosmic Microwave Background (CMB) from Planck have established ΛCDM as the standard cosmological model. However, significant tensions have emerged—most notably the Hubble constant discrepancy between early- and late-universe determinations, now exceeding 5σ. Recent results from DESI also suggest a preference for dynamical dark energy over a cosmological constant, further challenging the standard framework.
- Location
- Sheffield, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
University of Sheffield
About the Project Pairs of black holes generate distinctive 'chirp' signals as they coalesce. These signals have been successfully detected at gravitational-wave observatories since 2015. Using these signals, we can test the theory of relativity in the strong-field regime and we can learn more about the "zoo" of black holes that populate our universe. The next decade will see the launch of the first detector in space: the Laser Interferometer Space Antenna (LISA) satellite.
- Location
- Sheffield, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
University of Bath
About the Project This PhD is one of a number of projects hosted by the Centre for Doctoral Training in Green Industrial Futures (CDT-GIF). We are offering pioneering research projects that will enable PhD researchers to explore key technologies and solutions that will support UK industry to reach net zero.
- Location
- Bath, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Funded PhD Project (Students Worldwide)
Applied Mathematics
University of Strathclyde
About the Project Develop advanced causal inference and uncertainty-aware models to identify hidden root causes and predict long-term risk in nuclear infrastructure and associated assets.
- Location
- Glasgow, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Funded PhD Project (UK Students Only)
Applied Mathematics
University of Aberdeen
About the Project These projects are open to students worldwide, but have no funding attached. Therefore, the successful applicant will be expected to fund tuition fees at the relevant level (home or international) and any applicable additional research costs. Please consider this before applying. We all live today in a cyber world. Much of the world data traffic is encrypted because of security threats, occurring among different societies, and within several societal levels.
- Location
- Aberdeen, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
Cardiff University
About the Project The characterisation of biological tissue microstructure in vivo and non-invasively is of outmost interest in science. If successful, it could reveal unique insights into biological processes, including aging and cancer. In this regard, MRI plays a crucial role due to its superb flexibility to depict soft tissues.
- Location
- Cardiff, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
University of Sheffield
About the Project This project is concerned with quantum field theory in curved space-time, a semiclassical approach to the as-yet-elusive theory of quantum gravity. In this set-up, the space-time geometry is fixed and classical, while the matter is quantized (and described by a quantum field). In this project the background space-time is a charged Reissner-Nordstrom black hole, and the quantum field is a charged fermion field. There are three key aspects to the project.
- Location
- Sheffield, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
University of Salford
About the Project Background and rationale. Multi-agent large language model (LLM) systems are increasingly used for reasoning, evaluation, simulation and decision support. However, adding more agents does not automatically create collective intelligence.
- Location
- Manchester, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
University of Liverpool
About the Project Background Age-related macular degeneration (AMD) is the leading cause of blindness globally. Current treatments involve the injection of anti-vascular endothelial growth factor. However, many individuals do not respond to treatment, with regular visits required placing a large burden on healthcare systems and patients.
- Location
- Liverpool, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
Durham University
About the Project High-dimentional data is central to many computer vision research. Such data includes videos, 3D motions and trajectories, LiDAR, RADAR, medical images, meshes, time series, etc. They inform real-world applications such as healthcare, suivellience and monitoring. This project focuses on deep learning based computer vision methods to understand high-dimensional data, with a particular focus on artificial intelligence that makes responsible decisions.
- Location
- Durham, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
University of Aberdeen
About the Project These projects are open to students worldwide, but have no funding attached. Therefore, the successful applicant will be expected to fund tuition fees at the relevant level (home or international) and any applicable additional research costs. Please consider this before applying.
- Location
- Aberdeen, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
University of Reading
About the Project Decarbonisation of heating and cooling in buildings can be achieved through switching fuels and transferring the demand from Natural Gas to low-carbon electricity. It is generally agreed that heat pump and thermal storage technologies can make a significant contribution to this decarbonisation process.
- Location
- Reading, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
Durham University
About the Project This project aims at deep learning based machine vision and/or robotics methods to facilitate space-related applications. There is a wide range of projects within this scope. Some examples include: Satellite image analysis for earth observation and climate change monitoring. Computer vision on telescopic imagery for satellite detection, tracking and characterisation. Robotics-informed active machine vision system.
- Location
- Durham, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
Edinburgh Napier University
About the Project Mathematical systems and control theory “represents an attempt to codify, in mathematical terms, the principles and techniques used in the analysis and design of control systems” [1]. It concerns itself with “the basic theoretical principles underlying the analysis of feedback and the design of control systems [and] differs from the more classical study of dynamical systems in its emphasis on inputs (or controls) and outputs (or measurements)” [2].
- Location
- Edinburgh, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
University of Liverpool
About the Project Lung cancer is the leading cause of cancer-related death worldwide. We aim to develop and validate blood-borne diagnostic biomarkers to enable early detection to save lives. In Liverpool, we have collected a unique cohort in which matched proteomic, miRNA, and metabolomic profiles were generated from pre-diagnostic plasma samples collected 1–10 years before diagnosis. This offers an exciting PhD opportunity.
- Location
- Liverpool, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
University of Sheffield
About the Project The production of flares and Coronal Mass Ejections (CMEs) from solar active regions (ARs) is still not well understood in spite of their huge importance to Sun-Earth connections, in particular, to protect mankind and our sophisticated technological systems that might be at considerable risk from high-speed charged particles blowing often abruptly off the Sun. These most energetic eruptions of the entire Solar System follow the 11-year solar cycle.
- Location
- Sheffield, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
University of Aberdeen
About the Project These projects are open to students worldwide, but have no funding attached. Therefore, the successful applicant will be expected to fund tuition fees at the relevant level (home or international) and any applicable additional research costs. Please consider this before applying.
- Location
- Aberdeen, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
University of Strathclyde
About the Project Polymers and turbulence are two of the most difficult problems in statistical physics. In the past, the study of polymeric liquids was divided in two categories: rheological investigations, where coarse- grained molecular models of polymers are interacting with a prescribed velocity field, hence the effects of the polymers on fluid motion are not taken into account, and fluid dynamics investigations, where the polymeric fluid is modeled at large/slow enough…
- Location
- Glasgow, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
The University of Manchester
About the Project The mechanical properties of plant and animal tissues are strongly influenced by the arrangement of their constituent cells. Discrete models, in which cells are represented as polygons or polyhedra, provide a popular and powerful modelling framework for understanding tissue biomechanics. Such models often capture features that are hard to resolve using traditional continuum approaches.
- Location
- Manchester, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
Durham University
About the Project A funded PhD studentship is available under the supervision of Peter Davies-Peck , part of the Network Engineering Science and Theory in Durham (NESTiD) group in the Department of Computer Science at Durham University, UK. We are seeking a bright and motivated student interested in working on any aspects of distributed and parallel algorithms.
- Location
- Durham, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Funded PhD Project (UK Students Only)
Applied Mathematics
University of Aberdeen
About the Project These projects are open to students worldwide, but have no funding attached. Therefore, the successful applicant will be expected to fund tuition fees at the relevant level (home or international) and any applicable additional research costs. Please consider this before applying. Distributed Hybrid Renewable Energy Systems (DHRES) are critical enablers of the energy transition.
- Location
- Aberdeen, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
The University of Manchester
About the Project The detection and characterisation of damage, material properties and foreign objects by Non-Destructive Evaluation (NDE) is crucial to society and throughout industry. These technologies underpin the safe operation of critical structures and equipment, which are essential to modern life.
- Location
- Manchester, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Funded PhD Project (UK Students Only)
Applied Mathematics
University of Liverpool
About the Project Infertility is a disease of the reproductive system defined as a failure to achieve a clinical pregnancy after 12 months or more of regular unprotected intercourse. Infertility is common, affecting 1 in 6 heterosexual couples, and rates are rising, especially with the current trend of delayed childbearing. Infertility can lead to distress, depression, discrimination and ostracism.
- Location
- Liverpool, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
University of Aberdeen
About the Project These projects are open to students worldwide, but have no funding attached. Therefore, the successful applicant will be expected to fund tuition fees at the relevant level (home or international) and any applicable additional research costs. Please consider this before applying. The space agencies NASA and ESA both plan to send spacecraft to explore Venus in the early 2030s [1].
- Location
- Aberdeen, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
University of Strathclyde
About the Project Develop rapid, uncertainty-aware surrogate models that replace expensive simulations with results in seconds, while preserving mathematical rigour.
- Location
- Glasgow, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Funded PhD Project (UK Students Only)
Applied Mathematics
University of Reading
About the Project Project Overview: Meeting Net Zero targets will require fully utilizing smart solutions at all levels of the electricity network. This includes home energy management systems, optimal operation of battery storage systems, and local area energy trading. However, progress at implementing these solutions is hindered by the lack of data at the low voltage level.
- Location
- Reading, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
University of Aberdeen
About the Project These projects are open to students worldwide, but have no funding attached. Therefore, the successful applicant will be expected to fund tuition fees at the relevant level (home or international) and any applicable additional research costs. Please consider this before applying. Fifty years on from the first spacecraft fly-by of a giant planet in 1973, many aspects of giant planet atmospheres remain poorly understood.
- Location
- Aberdeen, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
University of Aberdeen
About the Project These projects are open to students worldwide, but have no funding attached. Therefore, the successful applicant will be expected to fund tuition fees at the relevant level (home or international) and any applicable additional research costs. Please consider this before applying.
- Location
- Aberdeen, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
University of Bristol
About the Project Why we sleep and what happens to the brain during sleep remain very open questions. However, we now know that many different physiological processes take place during sleep, thanks to a large recent increase in available experimental data, for example through measurements of brain blood flow, electrical activity and other parameters. We also know that poor sleep patterns are related to higher risks of brain diseases such as dementia.
- Location
- Bristol, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Competition Funded PhD Project (Students Worldwide)
Applied Mathematics
University of Strathclyde
About the Project An exciting opportunity for a fully-funded 42-months PhD studentship co-funded by EPSRC is available at the Department of Biomedical Engineering at the University of Strathclyde.
- Location
- Glasgow, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- See advert
Applied Mathematics
The University of Manchester
About the Project Foams are used across industries—from aerospace to packaging—providing cushioning during transit, thermal insulation, and structural reinforcement in a range of applications. However, the mechanisms underpinning transport and reactions within some of these materials are still not well understood and there is a lack of effective mathematical modelling.
- Location
- Manchester, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Funded PhD Project (UK Students Only)
Applied Mathematics
University of Southampton
About the Project Supervisory team: Haris Moazam Sheikh This project will develop a multi-scale surrogate modeling framework to optimize passive surface textures (like dimples) for maximum fluid drag reduction. By enabling efficient shape optimization and identifying critical flow parameters, this research seeks to resolve conflicting results and advance the theoretical understanding and practical application of cost-effective flow control in transportation.
- Location
- Southampton, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Competition Funded PhD Project (Students Worldwide)
Applied Mathematics
King’s College London
About the Project The threat of large-scale, general-purpose quantum computers to existing public-key cryptographic solutions has led to global efforts to standardise post-quantum cryptography as a replacement. One of the front-runners for problems to base post-quantum cryptography on are hard problems on lattices.
- Location
- London, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Funded PhD Project (Students Worldwide)
Applied Mathematics
University of Liverpool
About the Project Infertility is a disease of the reproductive system defined as a failure to achieve a clinical pregnancy after 12 months or more of regular unprotected intercourse. Infertility is common, affecting 1 in 6 heterosexual couples, and rates are rising, especially with the current trend of delayed childbearing.
- Location
- Liverpool, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
University of Sheffield
About the Project This PhD project focuses on using topological data analysis (TDA) in machine learning (ML) to study (exotic) quantum matter systems defined on a lattice.
- Location
- Sheffield, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
University of Aberdeen
About the Project These projects are open to students worldwide, but have no funding attached. Therefore, the successful applicant will be expected to fund tuition fees at the relevant level (home or international) and any applicable additional research costs. Please consider this before applying. This project aims to elucidate the mechanisms by which histone chaperones function.
- Location
- Aberdeen, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
University of Sheffield
About the Project State-of-the-art high-resolution ground- and spaced-based telescopes routinely observe magnetohydrodynamic (MHD) waves that are ubiquitous in the solar atmosphere. MHD waves and oscillations are very important as they have dominant contribution to the local plasma heating in the solar atmosphere, that is one of the key and unsolved puzzles of modern plasma-astrophysics.
- Location
- Sheffield, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
University of Birmingham
About the Project In order to answer the myriad of specific research questions related to the brain as observed with fNIRS, current fNIRS analysis is based on ad-hoc models, whether from statistics e.g. like the general linear model, or other branches of maths e.g. graph theory, differential equations, etc in each case with associate and causal variants.
- Location
- Birmingham, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Competition Funded PhD Project (UK Students Only)
Applied Mathematics
University of Birmingham
About the Project How does information propagate through the human brain, and what can direct recordings of neural activity tell us about its network organisation? This PhD project will develop and apply network neuroscience methods to invasive electrophysiological recordings , including intracranial EEG (iEEG) and stereo-EEG (SEEG).
- Location
- Birmingham, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Funded PhD Project (UK Students Only)
Applied Mathematics
University of Aberdeen
About the Project These projects are open to students worldwide, but have no funding attached. Therefore, the successful applicant will be expected to fund tuition fees at the relevant level (home or international) and any applicable additional research costs. Please consider this before applying. Haematopoiesis, the lifelong process by which blood cells are produced from haematopoietic stem cells (HSCs), offers a remarkable example of dynamic equilibrium.
- Location
- Aberdeen, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
University of Portsmouth
About the Project Applications are invited for a self-funded, 3 year full-time or 6 year part-time PhD project. The PhD will be based in the School of Electrical and Mechanical Engineering and will be supervised by Dr Katerina Karali , Dr Roxane Bonithon and Pr Gordon Blunn . Project description The menisci are C-shaped, fibrocartilaginous structures in the tibiofemoral joint that play a crucial role in stabilizing and cushioning during weight-bearing activities.
- Location
- Portsmouth, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
The University of Manchester
About the Project This PhD project focuses on the simulation and modelling of wet and cohesive powders, which play a crucial role in industries such as pharmaceuticals, food processing, and additive manufacturing. Despite their importance, the complex behaviour of these materials — driven by capillary forces, adhesion, and particle cohesion — remains challenging to predict and control.
- Location
- Manchester, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Funded PhD Project (UK Students Only)
Applied Mathematics
The University of Manchester
About the Project This collaborative project between the University of Manchester and Aston University, embarks on the challenge of developing predictive modelling for solid oxide cells that are valuable tools for Energy Transition. Solid oxide fuel cells (SOFCs) and solid oxide electrolysis cells (SOECs) are promising technologies for clean energy conversion and storage, but their widespread deployment is hindered by degradation phenomena that limit lifetime and reliability.
- Location
- Manchester, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
University of Sheffield
About the Project (Macro)spicules are one of the longest studied yet unsolved phenomena of small-scale solar atmospheric dynamics. Since the discovery of spicules by Father Secchi about 150 years ago, a number of competing theories have been developed to model the generation, propagation and energy and momentum transport capabilities of spicules.
- Location
- Sheffield, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
Durham University
About the Project This PhD scholarship is offered by the EPSRC CDT in Offshore Wind Energy Sustainability and Resilience, a partnership between the Universities of Durham, Hull, Loughborough and Sheffield. The successful applicant will undertake six-months of training with the rest of the CDT cohort at the University of Hull before continuing their PhD research at Durham University.
- Location
- Durham, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Competition Funded PhD Project (Students Worldwide)
Applied Mathematics
University of Bristol
About the Project Ischaemic stroke, the disease that occurs when a clot blocks a large blood vessel in the brain, causing brain tissue to die, remains a common cause of death and a leading cause of disability. Computational models of stroke development can help to determine the best treatment options, and to understand the specific factors that lead to different outcomes in different patient groups.
- Location
- Bristol, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Competition Funded PhD Project (Students Worldwide)
Applied Mathematics
University of Aberdeen
About the Project These projects are open to students worldwide, but have no funding attached. Therefore, the successful applicant will be expected to fund tuition fees at the relevant level (home or international) and any applicable additional research costs. Please consider this before applying. Sex steroids, including androgens, play a central role in regulating cellular function, metabolism, reproduction and cancer.
- Location
- Aberdeen, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
The University of Manchester
About the Project This PhD project focuses on the development of next-generation high-fidelity modelling, computational fluid dynamics (CFD), and physics-informed artificial intelligence frameworks for particle-based long-duration energy storage (LDES) systems operating under highly variable renewable energy conditions.
- Location
- Manchester, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Funded PhD Project (UK Students Only)
Applied Mathematics
Durham University
About the Project This PhD aims at advanced deep-learning based Artificial Intelligence designs and development for Unmanned Aerial Vehicles (drones or swarms) detection and tracking using multimodal sensing, spatiotemporal analysis, and vision–language models. Unlike conventional object detection research, drone detection systems are often deployed in critical contexts such as airport security, where reliability is paramount.
- Location
- Durham, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
University of Sheffield
About the Project Neuroblastoma is the most common solid tumour of early childhood and, in its aggressive forms, remains hard to treat. These tumours arise when embryonic cells - trunk neural crest cells and their derivatives - fail to differentiate correctly.
- Location
- Sheffield, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Funded PhD Project (UK Students Only)
Applied Mathematics
The University of Manchester
About the Project Fibre networks are ubiquitous in both natural and engineered materials. They are manufactured for many reasons: from the nonwoven fabrics used for insulation, clothing and filtration to the rubberlike polymer-based materials used in applications ranging from plumbing to transport. They are also nature's preferred way of providing structural scaffolding within cells (the cytoskeleton), and within tissues (the extracellular matrix).
- Location
- Manchester, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Funded PhD Project (UK Students Only)
Applied Mathematics
The University of Manchester
About the Project For many years, the resolution of the near-wall turbulent layer is a hot topic in fluid dynamics. Near-wall turbulence modelling is a computationally expensive problem. A major part of the computing time is taken up by the resolution of a thin layer, which includes a laminar sublayer adjacent to the wall.
- Location
- Manchester, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
University of Birmingham
About the Project Details: Dynamical systems are often solved/integrated by a suitable numerical discretisation method in such a way that certain properties of the underlying systems will be preserved. However, it is highly nontrivial to design such a method for complex systems in biology, chemistry, and physics, particularly in high dimensions.
- Location
- Birmingham, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Competition Funded PhD Project (Students Worldwide)
Applied Mathematics
Queensland University of Technology
About the Project We seek a PhD student in applied mathematics to join the Queensland University of Technology node of MACSYS . MACSYS is the Australian Research Council Centre of Excellence for the Mathematical Analysis of Cellular Systems. The PhD student will work with QUT researchers in the development and deployment of mathematical and computational models that describe experimental data generated within the MACSYS ecosystem.
- Location
- Brisbane, Australia, Australia
- Deadline
- Year-round applications
- Funding
- Funded PhD Project (Students Worldwide)
Applied Mathematics
University of Southampton
About the Project Supervisory Team: Dr Dong-Yang WANG This project will be focusing on the research on non-Hermitian topological physics. Frontier research topics of exceptional point/surfaces, non-Hermitian skin effect, and catastrophe theory will be pursued. Topological band theory serves as a fundamental framework to generate new phase of matter with novel material properties.
- Location
- Southampton, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Competition Funded PhD Project (Students Worldwide)
Applied Mathematics
University of Aberdeen
About the Project These projects are open to students worldwide, but have no funding attached. Therefore, the successful applicant will be expected to fund tuition fees at the relevant level (home or international) and any applicable additional research costs. Please consider this before applying.
- Location
- Aberdeen, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
University of Aberdeen
About the Project These projects are open to students worldwide, but have no funding attached. Therefore, the successful applicant will be expected to fund tuition fees at the relevant level (home or international) and any applicable additional research costs. Please consider this before applying. Nonlinear analysis of light curves of variable stars has revealed complex patterns in their dynamics [1,2].
- Location
- Aberdeen, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
University of Reading
About the Project The calculus of variations is, roughly speaking, the mathematical theory of how to minimise or maximise magnitudes. Variational problems from science typically require minimisation of an average magnitude over a space-time region depending on unknown quantities. But not all variational problems pertain to an average. For shape or design optimisation problems, for example, it is a maximum that needs to be minimised instead, which leads to minimax problems.
- Location
- Reading, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
University of Birmingham
About the Project Details: Complex systems in biology, chemistry, and physics are often modelled using ordinary/partial/stochastic differential equations. It is desirable and highly nontrivial to design and analyse numerical algorithms that preserve the physical properties of the underlying systems.
- Location
- Birmingham, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Competition Funded PhD Project (Students Worldwide)
Applied Mathematics
University of Birmingham
About the Project Details: Stochastic differential equations (SDEs) are widely used in science and engineering in order to model systems where random effects play a significant role. They arise in many application areas, including molecular dynamics and Bayesian sampling techniques used in emerging machine learning applications.
- Location
- Birmingham, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Competition Funded PhD Project (Students Worldwide)
Applied Mathematics
University of Aberdeen
About the Project These projects are open to students worldwide, but have no funding attached. Therefore, the successful applicant will be expected to fund tuition fees at the relevant level (home or international) and any applicable additional research costs. Please consider this before applying.
- Location
- Aberdeen, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
University of Southampton
About the Project Supervisory Team: Dr Dong-Yang WANG This project will be designing and building topological photonic crystals on silicon chips, aiming to promote important applications such as optical imaging, sensing, and computing. Topological photonics is an intriguing research direction to use topological theory for developing new optical materials.
- Location
- Southampton, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Competition Funded PhD Project (Students Worldwide)
Applied Mathematics
University of Aberdeen
About the Project These projects are open to students worldwide, but have no funding attached. Therefore, the successful applicant will be expected to fund tuition fees at the relevant level (home or international) and any applicable additional research costs. Please consider this before applying. Signal and system modelling, numerical simulation and analysis of Optical Fibre for sensors or lasers or communications. Optical fibres are widely used in many fields.
- Location
- Aberdeen, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
University of Aberdeen
About the Project These projects are open to students worldwide, but have no funding attached. Therefore, the successful applicant will be expected to fund tuition fees at the relevant level (home or international) and any applicable additional research costs. Please consider this before applying.
- Location
- Aberdeen, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
The University of Manchester
About the Project Dynamical systems describe a variety of real-life problems related to evolution over time. It is often the case that the problems are so complicated that mathematical models for them either do not exist or are not accurate enough. Nowadays, there are data-driven techniques that allow us to obtain a mathematical model from measurement data over time. One of such techniques is the method of dynamic mode decomposition (DMD).
- Location
- Manchester, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Competition Funded PhD Project (Students Worldwide)
Applied Mathematics
University of Birmingham
About the Project --> We seek a curiosity-driven candidate with a background in Mathematics, Physics, Engineering or Computer Science who wants to make a difference in pressing environmental problems. --> You will join a vibrant group that develops and uses state-of-the-art models at the University of Birmingham (UK). --> We are seeking self-funded students. --> Projects can include collaborations and placements in public sector or industry.
- Location
- Birmingham, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
University of Derby
About the Project Build a fully physics-based synthetic environment to support the design of nuclear submarine systems, integrating ICME, reliability modelling and AI-assisted digital twins. Lead Supervisor: Angelo R.
- Location
- Derby, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Funded PhD Project (UK Students Only)
Applied Mathematics
University of Sheffield
About the Project Data assimilation combines physical models with experimental or numerical data to produce dynamically consistent flow reconstructions. In turbulence, where full resolution is expensive and measurements are sparse, physics-informed data assimilation integrates data with the Navier–Stokes equations to preserve physical realism.
- Location
- Sheffield, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
University of Southampton
About the Project Supervisory Team: Prof. Austin Taranta, Dr. Gianluca Guerra, Dr. Gregory Jasion and Dr. Ian Davidson Dive into the mysterious world of polarization in antiresonant hollow core fibres, where conventional wisdom is turned on its head, and unexpected phenomena emerge every day. Through your insights and innovation, you will shape the future of this cutting-edge technology from data centres, to high-power lasers, to space systems.
- Location
- Southampton, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Competition Funded PhD Project (Students Worldwide)
Applied Mathematics
The University of Manchester
About the Project This project focuses on developing advanced simulation techniques to optimise the sustainable packaging of granular and complex fluid materials through virtual prototyping. By coupling the open-source software MercuryDPM for discrete particle modelling with oomph-lib for the simulation of complex fluids, the research will create a powerful framework for fluid-particle interaction.
- Location
- Manchester, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Funded PhD Project (UK Students Only)
Applied Mathematics
University of Sheffield
About the Project Many theories of quantum gravity agree that the spacetime geometry of Einstein’s general relativity needs to be replaced by a different underlying structure. In particular, spacetime may fundamentally consist of discrete “atoms”. In this project you will study the group field theory approach to quantum gravity, which posits that spacetime is emergent from microscopic “atoms” of geometry, similar to how a fluid fundamentally consists of atoms and molecules.
- Location
- Sheffield, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
University of Sheffield
About the Project In General Relativity, bodies in freefall follow geodesics in spacetime. For example, the Earth follows a geodesic in the spacetime of the Sun, to a good approximation. However, this is not strictly true for compact bodies with angular momentum. Rapidly spinning bodies, such as neutron stars and black holes, are pushed away from geodesic motion by a spin-curvature force, modelled with the Mathisson-Papapetrou-Dixon equations.
- Location
- Sheffield, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
University of Sheffield
About the Project Chaos may seem like complete disorder, but even chaotic systems can sometimes fall into step — a phenomenon called chaos synchronisation. Two systems that start differently can gradually align their behaviour through a small amount of interaction or shared information, much like pendulum clocks on the same wall eventually ticking together. In turbulent flows, synchronisation is a powerful way to understand and control chaos.
- Location
- Sheffield, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
University of Aberdeen
About the Project These projects are open to students worldwide, but have no funding attached. Therefore, the successful applicant will be expected to fund tuition fees at the relevant level (home or international) and any applicable additional research costs. Please consider this before applying.
- Location
- Aberdeen, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
The University of Manchester
About the Project This PhD project aims to develop a virtual tabletting laboratory by creating computational models that capture the multiscale mechanics of die compaction — from individual crystal behaviour to the formation of solid pharmaceutical tablets. Spanning many orders of magnitude in scale, the work will link particle-scale interactions, such as crystal plasticity and fracture, with bulk-scale processes like powder flow, compression, and tablet formation.
- Location
- Manchester, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Funded PhD Project (UK Students Only)
Applied Mathematics
University of Strathclyde
About the Project Process design requires accurate and reliable thermodynamic data for multicomponent mixtures in the system over a wide range conditions (e.g., solvents, impurity concentrations, temperatures, pressures) which are often missing, especially for new compounds.
- Location
- Glasgow, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
The University of Manchester
About the Project Concrete under high temperature is rarely subjected to simple uniaxial loading. In reality, structures such as nuclear systems, tunnels, underground transport infrastructure, and composite columns experience combined compression, tension, and shear while simultaneously undergoing severe thermal gradients. Yet most current material models and design approaches are based on simplified stress states and uniform temperature assumptions.
- Location
- Manchester, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Funded PhD Project (UK Students Only)
Applied Mathematics
University of Birmingham
About the Project Over 50 years ago at Caltech, Richard Feynman stated that Waves easily seen by everyone and which are usually used as an example of waves in elementary courses are water waves.
- Location
- Birmingham, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Funded PhD Project (European/UK Students Only)
Applied Mathematics
University of Birmingham
About the Project Machine learning and statistical algorithms are now implemented at a large scale in almost every aspect of our society, significantly impacting our daily lives through their performance. Hence, there is a soaring demand for the development of trustworthy procedures. Some directions include Robust and private learning in heterogenous and distributed environments.
- Location
- Birmingham, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Competition Funded PhD Project (Students Worldwide)
Applied Mathematics
University of Southampton
About the Project Supervisory Team: Dr Dong-Yang WANG This project will explore the use of photonic quasicrystals in building higher-dimensional topological phases. The research covers the mathematical framework development, photonic quasicrystals design, energy band calculation, sample fabrication, and experimental characterization. Topological photonics is a rising field of research to embed topological invariants in optical materials.
- Location
- Southampton, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Competition Funded PhD Project (Students Worldwide)
Applied Mathematics
Cardiff University
About the Project Magnetoencephalography (MEG) is a non-invasive medical imaging technique that allows characterisation of human brain electrophysiology by measuring magnetic fields generated by neural currents. Since its invention, MEG has shown its value for understanding brain function in health and disease, providing unique insights into neurophysiological processes.
- Location
- Cardiff, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
University of Aberdeen
About the Project These projects are open to students worldwide, but have no funding attached. Therefore, the successful applicant will be expected to fund tuition fees at the relevant level (home or international) and any applicable additional research costs. Please consider this before applying. A mathematical tree is a graph in which any two distinct vertices are connected by a unique path.
- Location
- Aberdeen, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
University of Strathclyde
About the Project This project will expose systematic errors in widely used methods for estimating and translating the efficacy of vaccines and outline a strategy for alleviating those problems. Explicitly, methods that neglect realistic heterogeneities in susceptibility to infection among individuals in a trial, tend to underestimate vaccine efficacy, a bias that is exacerbated with the length of the trial and the intensity of exposure to infection in trial settings.
- Location
- Glasgow, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Funded PhD Project (UK Students Only)
Applied Mathematics
University of Aberdeen
About the Project These projects are open to students worldwide, but have no funding attached. Therefore, the successful applicant will be expected to fund tuition fees at the relevant level (home or international) and any applicable additional research costs. Please consider this before applying.
- Location
- Aberdeen, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
University of Birmingham
About the Project This PhD project with Dr Yeo will focus on understanding how we perform interception. Interceptive movements--such as catching a gently thrown ball, quickly grabbing a tilting cup to avoid spilling or even just handshaking someone--feel like trivial everyday tasks for us that seemingly look too simple to study.
- Location
- Birmingham, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
University of Reading
About the Project Project overview : Functional electrical stimulation (FES) is a treatment that applies small electrical charges to a muscle that has become paralysed or weakened, due to damage in the brain or spinal cord. The electrical charge stimulates the muscle to make its usual movement. FES is a technique that can help with swallowing, hand and arm function, and breathing for people with pulmonary disease or stroke, for example.
- Location
- Reading, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
University of Reading
About the Project There are >18 million new cancer patients worldwide every year, of which >2 million are women with breast cancer. With targeted and newer therapies, survival rates of breast and other cancers are increasing. However, anti-cancer therapies, including those for breast cancer, can be toxic. They can affect the heart, potentially causing heart failure. This creates an additional mental health burden for patients.
- Location
- Reading, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
University of Sheffield
About the Project Black holes have now been observed in detail via astrophysical observations, detections of gravitational waves and pictures of the event horizon. However, their theoretical description within general relativity is incomplete, since it contains a singularity where the laws of physics break down. Quantum theories of gravity may offer a very different perspective on the fundamental description of black holes.
- Location
- Sheffield, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
University of Birmingham
About the Project Brain function arises from a highly complex network of interconnected processes that we still don’t fully understand. Functional near-infrared spectroscopy (fNIRS) is a non-invasive tool that measures changes in brain oxygenation, offering a way to monitor brain activity across different populations across all stages of life.
- Location
- Birmingham, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
The University of Manchester
About the Project Transcriptional gene regulation, or the ability to control the timing and levels of gene expression through binding of transcription factors (TFs) to DNA, is a defining feature of life. It allows organisms to coordinate function internally and to respond to external changes in the environment. The main mechanism through which gene regulation occurs, especially in bacteria, relies on binding between a protein (transcription factor, or TF) and DNA.
- Location
- Manchester, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only
Applied Mathematics
Durham University
About the Project Anomaly detection , and the synonymous topics of novelty and out-of-distribution detection, addresses the computer vision ("visual AI") challenge of automatically identifying outliers within the scene or image based on their appearance, motion or behaviour characteristics. Essentially asking - "what differs and why?" - but doing this algorithmically in the age of Large Language Models (LLM) and Vision Language Models (VLM) tools.
- Location
- Durham, United Kingdom, United Kingdom
- Deadline
- Year-round applications
- Funding
- Self-Funded PhD Students Only