School of Mathematical Sciences
   
   
  

Postgraduate research

research-new

A top ten UK university for research excellence*

 

Nottingham is committed to the pursuit of excellence in curiosity-driven research and applied research of the highest international standards. The range of research activities in Mathematical Sciences is extremely broad; from theoretical research in Pure Mathematics to generic, methodological research in Applied Mathematics and Statistics, which is often motivated by important applications. 

* Research Excellence Framework (REF) 2014 

Postgraduate Open Day

Information about our open day on Wednesday 21 November 2018 can be found in our postgraduate open day page, which has the full programme available to view.  Please note talk timings are subject to change.

How to apply for research opportunities

The best way to submit your application is to apply online here.

Other ways to apply are outlined below.

If you are unable to apply online please contact our research admissions administrator who will be able to assist you.

Details: t: +44 (0)115 951 4963
             f: +44 (0)115 951 4951
             e: maths-pg-admissions@nottingham.ac.uk

Research areas

There are opportunities in a number of research areas which include:

Funded research vacancies 

Scholarships

Funding your research

You can find out more about funding your research work here.

EPSRC DTP CASE PhD studentship in Applied Mathematics (EU students)

Project title: Communication through complex media: a novel interdisciplinary paradigm to bridge information theory and multiscale flow and transport theory

Supervisors: Dr Matteo Icardi  (Mathematics) and Dr. Gabriele Gradoni  (Engineering)

Project information: A variety of industrial applications are faced with challenges in understanding and control reactive transport processes in complex heterogeneous media. In particular, the oil & gas and renewable energy sector strongly relies on the modelling and simulation of multiscale porous materials, as well as complex downstream refining and chemical processing operations. Extracting valuable data and information from these systems for monitoring and control is crucial to ensure safety and increase efficiencies. Networks of nano-sensors for embedded sensing and actuation are currently being developed and tested to this aim. However, the design of robust and optimal communication strategies, in presence of complex transport phenomena and harsh environments remains challenging.

New communication paradigms, such as the nature-inspired molecular communication, have been developed to study the communication content of chemical simple advection-diffusion processes. However, we currently have no understanding of the potential for communication of more complex transport models. The goal of the project is, therefore, to develop the mathematical basis of an information theoretical framework for transport of particles and waves in complex multiscale environments.

This project is co-funded by TOTAL and will be based at the School of Mathematical Sciences, in the group of Industrial and Applied Mathematics, and in collaboration with the GeoEnergy Research Centre and the Wave Modelling Research Group in Nottingham, and several partners in the UK (Warwick) and Europe (Barcelona, Erlangen).

Summary: EU students - tuition fees paid, and full Stipend at the RCUK rate, which is £14,777 per annum for 2018/19. There will also be some support available for you to claim for limited conference attendance. The scholarship length will be 4 years.

Eligibility/entry requirements: We require an enthusiastic graduate with a 1st class degree in Applied Mathematics (or other field such as Physics or Engineering, showing evidence of deep knowledge of continuum transport models and numerical methods), preferably at MMath/MSc level, or an equivalent overseas degree (in exceptional circumstances a 2:1 class degree, or equivalent, can be considered).

Apply: This studentship is available to start in October 2018 and remains open until April 2019. To apply please visit http://www.nottingham.ac.uk/pgstudy/apply specifying in the application the title and supervisors of the project. Please forward a copy of the full application material to matteo.icardi@nottingham.ac.uk

Informal enquiries: For any enquiries please email: matteo.icardi@nottingham.ac.uk

This studentship is open until filled. Early application is strongly encouraged.

 

EPSRC DTP CASE PhD studentship in Applied Mathematics (UK students)

Project title: Communication through complex media: a novel interdisciplinary paradigm to bridge information theory and multiscale flow and transport theory

Supervisors: Dr Matteo Icardi (Mathematics) and Dr Gabriele Gradoni (Engineering)

Project information: A variety of industrial applications are faced with challenges in understanding and control reactive transport processes in complex heterogeneous media. In particular, the oil & gas and renewable energy sector strongly relies on the modelling and simulation of multiscale porous materials, as well as complex downstream refining and chemical processing operations. Extracting valuable data and information from these systems for monitoring and control is crucial to ensure safety and increase efficiencies. Networks of nano-sensors for embedded sensing and actuation are currently being developed and tested to this aim. However, the design of robust and optimal communication strategies, in presence of complex transport phenomena and harsh environments remains challenging.

New communication paradigms, such as the nature-inspired molecular communication, have been developed to study the communication content of chemical simple advection-diffusion processes. However, we currently have no understanding of the potential for communication of more complex transport models. The goal of the project is, therefore, to develop the mathematical basis of an information theoretical framework for transport of particles and waves in complex multiscale environments.

This project is co-funded by TOTAL and will be based at the School of Mathematical Sciences, in the group of Industrial and Applied Mathematics, and in collaboration with the GeoEnergy Research Centre and the Wave Modelling Research Group in Nottingham, and several partners in the UK (Warwick) and Europe (Barcelona, Erlangen).

Summary: UK residents only - tuition fees paid, and enhanced Stipend (125% of the RCUK rate) of £18,471 per annum for 2018/19. There will also be generous support available for you to claim for training and conference attendance. The scholarship length will be 4 years.

Entry requirements: We require an enthusiastic graduate with a 1st class degree in Applied Mathematics (or other field such as Physics or Engineering, showing evidence of deep knowledge of continuum transport models and numerical methods), preferably at MMath/MSc level, or an equivalent overseas degree (in exceptional circumstances a 2:1 class degree, or equivalent, can be considered). 

Apply: This studentship is available to start in October 2018 and remain open until April 2019. To apply please visit http://www.nottingham.ac.uk/pgstudy/apply specifying in the application the title and supervisors of the project. Please forward a copy of the full application material to matteo.icardi@nottingham.ac.uk

Informal enquiries: For any enquiries please email matteo.icardi@nottingham.ac.uk

This studentship is open until filled. Early application is strongly encouraged.

 
Energy storage bed dynamics- the ever-expanding magnesium bed conundrum 

Project title: Energy storage bed dynamics- the ever-expanding magnesium bed conundrum 

Supervisor: John King (Mathematics), Gavin Walker (Engineering), Richard Wheatley (Chemistry)

Energy Research Accelerator 

The Energy Research Accelerator (ERA) is a cross-disciplinary energy hub, fostering business-academica collaboration to accelerate solutions to global energy challenges. It will provide new buildings, skilled people, job products and services to transform the energy sector. Building on existing programmes and academic expertise across the partnership, universities within ERA have committed over £2m for doctoral students for the ERA skills agenda. Through Innovate UK, the government has committed a capital investment of £60m, and ERA has secured private sector co-investment of £120m. ERA's priorities of Geo-Energy Systems, Integrated Energy Systems and Thermal Energy will help deliver new technologies and behavious, enabling ERA to have a transformative effect across the energy spectrum. 

ERA is a key programme within Midlands Innovation - a consortium of research intensive universities that harnesses the Midlands' combined research excellence and industry expertise to tackle the biggest challenges facing the UK.

The Project:

In order to facilitate high penetration of renewable energy in to the grid, energy storage is needed to in order to better manage the supply and demand for the grid. Hydrogen offers a high energy density solution and, rather than storing the hydrogen as a gas at high pressures, solid state storage of hydrogen in a metal like magnesium offers a low pressure and low cost technology. The hydrogenation of magnesium is very exothermic (74.5 kJ mol-1) and the material is also being investigated as a thermal energy store (i.e. using the exotherm of hydrogenation to liberate the stored thermal energy back as heat at 400C).

A fear was that cycling a magnesium bed at high temperatures would lead to sintering and a loss of void space. However, the startling result was that the powdered magnesium bed when cycled at temperatures of 350-400C, rather than losing porosity, gained porosity. The form of the bed had changed from a loose powder to a metal porous plug which had swelled in dimensions to fill the available head space in the vessel. Further cycling at temperature below 350C results in the bed resorting back to a more densely packed loose powder.

The intriguing question is to uncover the fundamental mechanism(s) behind this process and to develop a predicative model based on the physical and chemical processes occurring. For the application, understanding these processes will enable optimisation of the porous structure for heat and mass flow; moreover, there is also concern the expanding bed may exert significant stress on the wall of the storage vessel eventually leading to failure of the vessel.

This challenging research project will develop new mathematical models based on the chemical and physical processes occurring in order to develop a model that simulates the expanding porous bed phenomenon. Some of these processes include: nucleation, growth of the metal hydride phase, crystal lattice expansion leading to defect formation, decrepitation, atomic diffusion and surface energy minimisation, annealing. The models developed will thus need to encompass a wide range of physical phenomena; the focus will be on partial-differential-equation/moving-boundary formulations, building on the established sintering literature but, for the reasons described above (specifically, to generate increased, rather than decreased, porosity), of necessity raising significant additional challenges. The project will accordingly equip the student with an unusually wide experience of experimental and modelling questions and of mathematical techniques, as applied in a context with clear energy and sustainability implications.

Summary: UK/EU students - Tuition Fees paid, and full Stipend at the RCUK rate, which is £14,600 per annum for 2017/18. The scholarship length will be 3.5 years and the successful applicant will be part of the Energy Research Accelerator at the University of Nottingham (http://www.era.ac.uk/)

Entry Requirements: Starting September 2018, we require an enthusiastic graduate with a 1st class degree in Mathematics or a relevant discipline, preferably at Masters level, or an equivalent overseas degree (in exceptional circumstances a 2:1 degree can be considered).

Informal enquiries: please email John.King@nottingham.ac.uk 

To apply, visit: http://www.nottingham.ac.uk/pgstudy/apply/apply-online.aspx 

This studentship is open until filled. Early application is strongly encouraged. 

 
Multi-scale modelling of flow through heterogeneous geo-materials

Project title: Multi-scale modelling of flow through heterogeneous geo-materials

Supervisor: Dr Kris van der Zee (Mathematical Sciences), Dr Xia Li (Engineering)

Project information: 

Do you have a passion for sustainability?

Would you like to apply mathematical research to help improve resource security?

Modelling and Analytics for a Sustainable Society (MASS) is a Leverhulme Doctoral Scholarships programme at the University of Nottingham that aims to tackle the ongoing global problems of food shortages, water scarcity and insufficient clean energy by using mathematics to help understand and optimise resource use through predictive modelling and statistical analysis.

Permeability of geomaterials is critical in predicting pollutant contamination and nitriation transport in groundwater. However, geo-materials are often heterogenous. The micro-defects and rock fractures provide channels for rapid groundwater flow, and consequently, the effective in-situ permeability could be larger than the lab measurement by several orders of magnitude.

This research will develop mathematical models to simulate the groundwater flow through heterogeneous geo-materials and the multi-scale homogenisation techniques that connects the field-scale permeability to intact rock properties and the statistics of micro-defects and fractures. The findings will inform and support effect groundwater management.

For more information, including details of other available research projects, please visit: www.nottingham.ac.uk/mathematics/prospective/research/leverhulme-doctoral-scholarships.aspx

The Leverhulme Doctoral Scholars, who will be based in the new £7m Mathematical Sciences Building, will be exposed to an outstanding and vibrant research environment in mathematics, resource science, engineering and social sciences, with excellent opportunities for international engagement. At the end of their PhD, the Scholars will be eligible to apply for an additional one-year post-doctoral prize, funded by The University of Nottingham, to help establish their independent research careers.

Summary: The scholarships are for four years and will cover PhD tuition fees for UK/EU students, plus a tax-free stipend of £14,553 per annum (2017/18 rate). While the scholarships may be held by students of all nationalities, the Leverhulme Trust has a particular interest in supporting UK or EU students. International students would be expected to cover the difference between international and UK/EU tuition fees (currently approximately £9,500 per annum).

Eligibility: Appropriately motivated students should have, or expect to obtain, a first-class or good 2:1 honours degree and/or a distinction or high merit at MSc level in Mathematics or a subject with a strong mathematical component (e.g. physics, engineering, computer science).

Apply: Please visit the MASS web page and identify up to three projects of interest. Then apply via the University of Nottingham application page, using the personal statement section to indicate that you are applying to the “Mathematics for A Sustainable Society” programme, making sure to list your preferred projects, and uploading a CV of no more than two pages.

Informal enquiries: please email PM-pg-admissions@exmail.nottingham.ac.uk

Studentships are available from September 2018 and will remain open until filled. Early application is strongly encouraged.

 
Numerical upscaling and model identification for lithium-ion batteries

Project title: Numerical upscaling and model identification for lithium-ion batteries

Supervisor: Dr Matteo Icardi

Project information:  This project will be based at the University of Nottingham in the School of

Mathematical Sciences in the group of Industrial and Applied Mathematics, and in collaboration with the GeoEnergy Research Centre. The increasing usage of batteries needs to be supported by more accurate and faster mathematical models. Rechargeable battery models for control applications are typically defined by system identification techniques. Despite their computational simplicity, these models fail to capture the physical meaning and the dependence of the parameters on the underlying chemical-physical processes. Another mostly unresolved issue is the simulation of irreversible and complex non-linear phenomena such as fast (dis)charge and degradation. In this project, we aim to develop new mathematical techniques to develop simple and efficient reduced-order models, as an alternative to classical equivalent circuit models, to enable the fast, yet accurate, simulation of short and long-term behaviour of lithium-ion cells. Starting from the well-known porous electrode theory and PDE continuum models, we aim to derive simple differential equations that can retain the interesting features of the full model (e.g., polarisation, non-linearities). This will be integrated with data coming from both micro- and system scale experimental data into via machine-learning approaches.

The project is part of a wider research effort that sees the collaboration of several UK and international academic partners, and industrial partners in the Automotive and Manufacturing sector.

Funding summary: UK/EU students - tuition fees paid, and full stipend at the RCUK rate, which is £14,296 per annum for 2016/17. There will also be some support available for you to claim for limited conference attendance. The scholarship length will be 3 or 3.5, depending on the qualifications and training needs of the successful applicant.

Eligibility/Entry Requirements: We require an enthusiastic graduate with a 1st class degree in Applied Mathematics (or other field such as Physics or Engineering, showing evidence of deep knowledge of continuum transport models and numerical methods), preferably at MMath/MSc level, or an equivalent overseas degree (in exceptional circumstances a 2:1 class degree, or equivalent, can be considered). 

Application procedure: This studentship is available to start in January or September 2018. To apply please visit the University of Nottingham application page: http://www.nottingham.ac.uk/pgstudy/apply/apply-online.aspx

Informal enquiries: please email Matteo Icardi

This studentship is open until filled. Early application is strongly encouraged.

 
Data-driven coarse-graining and multiscale model reduction for ODEs and PDEs

Project title: Data-driven coarse-graining and multiscale model reduction for ODEs and PDEs

Supervisor: Dr Matteo Icardi

Project information: This project will be based at the University of Nottingham in the School of Mathematical Sciences in the group of Industrial and Applied Mathematics.

Many theoretical tools have been recently developed to reduce the complexity of high-dimensional non-linear ODEs or three-dimensional PDEs in complex environments. These have now an enormous importance in computational chemistry, continuum mechanics, fluid dynamics, and dynamical systems in general. One of these bottom-up formal approaches is the Mori-Zwanzig projection formalism for dynamical systems. At the same time, also data-driven top-down methods, have been widely studied in machine learning and in numerical analysis. In this project, we aim to connect these theoretical and numerical tools to make them applicable for practical applications, such as the molecular dynamics simulation of complex molecule chains, or the relaxation to equilibrium of non-linear reaction-diffusion equations. In the first case, we can rely on the Hamiltonian structure of the full-resolution model, while the latter can be analysed, for example, through their discrete (particle- or mesh-based) counterparts, or through classical spectral analysis. The objective of this project is to develop and implement flexible numerical approaches to deal with the model reduction, multi-scale approximation, and/or coarse-graining of a limited number of model problems, by combining analytical derivations with numerical simulation data. Real-world applications in complex fluids and porous media will be considered.

Funding summary: UK/EU students - tuition fees paid, and full stipend at the RCUK rate, which is £14,296 per annum for 2016/17. There will also be some support available for you to claim for limited conference attendance. The scholarship length will be 3 or 3.5, depending on the qualifications and training needs of the successful applicant.

Eligibility/Entry Requirements: We require an enthusiastic graduate with a 1st class degree in Applied Mathematics (or other field such as Physics or Engineering, showing evidence of deep knowledge of continuum transport models and numerical methods), preferably at MMath/MSc level, or an equivalent overseas degree (in exceptional circumstances a 2:1 class degree, or equivalent, can be considered). 

Application procedure: This studentship is available to start in January or September 2018. To apply please visit the University of Nottingham application page: http://www.nottingham.ac.uk/pgstudy/apply/apply-online.aspx

Informal enquiries: please email Matteo Icardi

This studentship is open until filled. Early application is strongly encouraged.

 
Quantifying uncertainties in multiphase flows through porous media

Project title: Quantifying uncertainties in multiphase flows through porous media

Supervisor: Dr Matteo Icardi

Project information: 

This project will be based at the University of Nottingham in the School of Mathematical Sciences in the group of Industrial and Applied Mathematics, and in collaboration with the GeoEnergy Research Centre. Despite the recent significant developments in Digital Rock Physics (DRP), two-phase flows in complex pore geometries are still not fully predictable, understood, and quantitatively reproducible. This is due to a number of factors including imperfect physical models, insufficient mesh resolution, unknown parameters and pore heterogeneity. The qualitative and quantitative effects of these uncertainties have not been studied yet. In this project, we aim to develop a modelling and simulation workflow to quantify uncertainty and assess the validity of simplified multiphase flow models in digitalised porous media images. Deterministic and Monte-Carlo techniques, together with two-phase flow solvers, will be used to perform a global sensitivity analysis of the problem. 

The project is part of a wider research effort that sees the collaboration of several UK and international academic partners, and industrial partners in the Automotive and Oil&Gas sector.

Funding summary: UK/EU students - tuition fees paid, and full stipend at the RCUK rate, which is £14,296 per annum for 2016/17. There will also be some support available for you to claim for limited conference attendance. The scholarship length will be 3 or 3.5, depending on the qualifications and training needs of the successful applicant.

Eligibility/Entry Requirements: We require an enthusiastic graduate with a 1st class degree in Applied Mathematics (or other field such as Physics or Engineering, showing evidence of deep knowledge of continuum transport models and numerical methods), preferably at MMath/MSc level, or an equivalent overseas degree (in exceptional circumstances a 2:1 class degree, or equivalent, can be considered). 

Application procedure: This studentship is available to start in January or September 2018. To apply please visit the University of Nottingham application page: http://www.nottingham.ac.uk/pgstudy/apply/apply-online.aspx

Informal enquiries: please email Matteo Icardi

This studentship is open until filled. Early application is strongly encouraged.

 
Model reduction and homogenisation for filtration and adsorption

Project title: Model reduction and homogenisation for filtration and adsorption

Supervisor: Dr Matteo Icardi

Project information: This project will be based at the University of Nottingham in the School ofMathematical Sciences in the group of Industrial and Applied Mathematics, and in collaboration with the GeoEnergy Research Centre.

Porous media are ubiquitous in natural and engineered transport processes. When colloids or diffusive particles flows through their complex geometrical structure, non-trivial interactions arise between the advection, diffusion, particle-particle and particle-wall interactions. These processes can be modelled and simulated with computationally intensive three-dimensional simulations. In this project, a combination of rigorous multiscale analytical and numerical techniques will be used to derive and calibrate faster and simple models for filtration and adsorption processes. Extensions to include additional phenomena, such as particle-particle interactions, electrostatic forces and electrochemical reactions will be also considered.

The project is part of a wider research effort that sees the collaboration of several UK and international academic partners, and industrial partners in the Automotive and Oil&Gas sector.

Funding summary: UK/EU students - tuition fees paid, and full stipend at the RCUK rate, which is £14,296 per annum for 2016/17. There will also be some support available for you to claim for limited conference attendance. The scholarship length will be 3 or 3.5, depending on the qualifications and training needs of the successful applicant.

Eligibility/Entry Requirements: We require an enthusiastic graduate with a 1st class degree in Applied Mathematics (or other field such as Physics or Engineering, showing evidence of deep knowledge of continuum transport models and numerical methods), preferably at MMath/MSc level, or an equivalent overseas degree (in exceptional circumstances a 2:1 class degree, or equivalent, can be considered). 

Application procedure: This studentship is available to start in January or September 2018. To apply please visit the University of Nottingham application page: http://www.nottingham.ac.uk/pgstudy/apply/apply-online.aspx

Informal enquiries: please email Matteo Icardi

This studentship is open until filled. Early application is strongly encouraged.

 
Optimising experiments for developing ion channel models

Project title: Optimising experiments for developing ion channel models

Supervisors: Dr Gary Mirams and Dr Simon Preston

Project information: This project will be based at the University of Nottingham in the School of Mathematical Sciences. 

Mathematical Background: A major challenge in developing mathematical models is parameterising them – using real experimental data to inform the values of things like rates within our models. Getting the correct information can be facilitated by doing the optimal experiment. An even greater challenge is working out the likelihood that the model you have written down is most appropriate from the range of alternative models that could be constructed.

Biological Background: in biological systems ion channel proteins sit in cell membranes and selectively allow the passage of particular types of ions, creating currents. Ion currents are important for many biological processes, for instance: regulating ionic concentrations within cells; passing signals (such as nerve impulses); or co-ordinating contraction of muscle (skeletal muscle and also the heart, diaphragm, gut, uterus etc.). Mathematical ion channel electrophysiology models have been used for thousands of studies since their development by Hodgkin & Huxley in 1952 [1], and are the basis for whole research fields, such as cardiac modelling and brain modelling [2]. It has been suggested that there are problems in identifying which set of equations is most appropriate as an ion channel model. Often it appears different structures and/or parameter values could fit the training data equally well, but may make different predictions in new situations [3].

Aim: we have been developing novel experimental designs to provide more information about ion channel behaviour from shorter experiments. We would like to improve our techniques – to describe the ion current and also to characterise drug binding to ion channels (which can physically block them and reduce the current that flows to zero, sometimes leading to fatal heart rhythm changes). It is difficult to measure the rate at which drug/ion channel binding occurs and whether it occurs when the channels are open, closed, or both. These factors may be crucial in determining whether novel pharmaceutical compounds are likely to have side effects or not, and there is a need to develop efficient ways to measure them.

Approach: this project will involve computational biophysical modelling (efficient numerical solution of nonlinear ODE systems); the application of statistical techniques to quantify our uncertainty in model parameters and model equations/structure; and some wet-lab laboratory electrophysiology experiments. We will design more information-rich experiments to reduce our uncertainty in the models we develop [4] and work closely with labs to test out experiments we design and improve them.

Relevant Publications:[1] A. L. Hodgkin and A. F. Huxley, “A quantitative description of membrane current and its application to conduction and excitation in nerve,” J. Physiol., 117: 500–544, 1952. [2] D. Noble, A. Garny, and P. J. Noble, “How the Hodgkin – Huxley equations inspired the Cardiac Physiome Project,” 11: 2613–2628, 2012. [3] M. Fink and D. Noble, “Markov models for ion channels : versatility versus identifiability and speed,” Philos. Trans. A., 367(1896): 2161–79, 2009. [4] G. R. Mirams, P. Pathmanathan, R. A. Gray, P. Challenor, and R. H. Clayton, “White paper: Uncertainty and variability in computational and mathematical models of cardiac physiology.,” J. Physiol., 594(23), 6833–47, 2016.

Application procedure: To apply please visit the University of Nottingham application page: http://www.nottingham.ac.uk/pgstudy/apply/apply-online.aspx

Informal enquiries: please email Gary Mirams

Students will be provided with an excellent training environment within the Centre for Mathematical Medicine and Biology and collaborating departments. Students will undertake tailored training, complemented by broadening, soft-skills, wet-lab (where appropriate) and student-led activities. There will also be opportunities for training and exchanges with world-leading partners.

This studentship is open until filled. Early application is strongly encouraged.

 

Statistical analysis of risk, failure, and extreme event propagation in the airline industry using multi-level networks

Enhanced stipend of £17,553 per annum plus additional support for computing equipment and travel

Project title: Statistical analysis of risk, failure, and extreme event propagation in the airline industry using multi-level networks

Supervisors: Dr Yves van Gennip and Dr Gilles Stupfler

Project information: The goal of this project is to build a mathematical model for the spread of risk due to extreme events on multi-level networks and use advanced mathematical tools such as extreme value theory, modern results of mathematical statistics, and network theory, to analyse the model and compare the quantitative outcomes to real data. In particular, we will study this in the setting of the airline industry where failure of an electronic or mechanical component of an aircraft has an impact at the level of the component supply network, the airline network, and the airlines' insurer network. In the airline industry, each airline forms relationships with component manufacturers and insurers.

The key goals of this project are to

  • estimate the probability that an extreme event on one level of the network has significant consequences on another level;
  • model the costs of such extreme events for the different actors in the various layers of the network.

Of particular interest is the estimation of the probability of failure of a critical component in an aircraft and the frequency with which such a failure results in a catastrophic event for an airline and ultimately in an extreme loss for insurers.

The work will be conducted in close collaboration with Russell Group, a company providing leading risk management software and service to insurers and reinsurers, especially in the airline industry. The company will provide data from the airline industry to incorporate in this project. The student will therefore benefit from a lively working environment combining academic life and the vision and ambitions of the private sector. The student should be prepared to spend some time at the company as part of the project, if necessary.

The project is open to UK students as well as non-UK EU students under certain conditions (enquire at the email addresses below) - Tuition fees paid, and an enhanced stipend of £17,553 per annum. There will also be some support available for you to claim for travel and computing equipment costs. The scholarship length will be 4 years. This project will be based at the University of Nottingham in the School of Mathematical Sciences.

Eligibility: We require an enthusiastic graduate with a 1st class degree in Mathematics, preferably of the MMath/MSc level, or an equivalent overseas qualification. This project will heavily use network modelling, statistical analysis of networks, and extreme value analysis, and as such, familiarity with one or several of these topics is highly desirable. Let us emphasise that while experience with more than one of the aforementioned mathematical fields would be beneficial, the willingness to learn and engage with all of them is an absolute necessity. The project also requires the student to have experience with a scientific computing software package or programming language such as MATLAB, R, C++, and/or Python.

Application procedure: 

The studentship is to start as soon as possible or at the latest by 1 October 2018. To apply please visit the University of Nottingham application page: http://www.nottingham.ac.uk/pgstudy/apply/apply-online.aspx

Informal enquiries: please email: y.vangennip@nottingham.ac.uk and/or gilles.stupfler@nottingham.ac.uk.

This studentship is open until filled. Early application is strongly encouraged.

 

Statistical analysis of fibre variability in composites manufacture

PhD Scholarship on Mathematics for Manufacturing

Project Title: Statistical analysis of fibre variability in composites manufacture 

Supervisors: Prof. Frank Ball and Prof. Michael Tretyakov, School of Mathematical Sciences (Nottingham)

Project Information: Multidisciplinary collaborations are a critical feature of material science research enabling integration of data collection with computational and/or mathematical modelling. This PhD study provides an exciting opportunity for an individual to participate in a project spanning research into composite manufacturing, stochastic modelling, statistical analysis and scientific computing. The project is integrated into the EPSRC Centre for Innovative Manufacturing in Composites, which is led by the University of Nottingham and delivers a co-ordinated programme of research in composites manufacturing.

This project focuses on the development of a manufacturing route for composite materials capable of producing complex components in a single process chain based on advancements in the knowledge, measurement and prediction of uncertainty in processing. The outcome of this work will enable a step change in the capabilities of composite manufacturing technologies to be made, overcoming limitations related to part thickness, component robustness and manufacturability as part of a single process chain, whilst yielding significant developments in mathematics and statistics with generic application in the fields of stochastic modelling and inverse problems.

The specific aims of this project are: (i) statistical analysis of fibber placements based on textile and composite material data sets; (ii) statistical analysis and stochastic modelling of permeability of textiles and composites; (iii) efficient sampling techniques of stochastic permeability. A student will obtain an excellent grasp of various statistical and stochastic techniques (e.g., spatial statistical methods, use of random fields, Monte Carlo methods), how to apply them, how to work with real data and how to do related modelling and simulation. This knowledge and especially experience are transferable to other applications of statistics and probability.

The PhD programme contains a training element, the exact nature of which will be mutually agreed by the student and their supervisors.

Eligibility: The studentship is available for a period of three and a half years from and provides a stipend and full payment of Home/EU Tuition Fees. Students must meet the EPSRC eligibility criteria. We require an enthusiastic graduate with a 1st class honours in Mathematics (in exceptional circumstances a 2(i) class degree can be considered), preferably at the MMath/MSc level, with good programming skills and williness to work as a part of an interdisciplinary team. A candidate with a solid background in statistics and stochastic processes will have an advantage. 

Informal Enquiries: should be addressed to Prof. Michael Tretyakov

Application Procedure: To apply please use The University of Nottingham online application form.  Please ensure you quote ref: SCI/1262X1.

Application Deadline: This studentship is open until filled. Early application is strongly encouraged.

 

Chemokine gradient development around lymphatic vessels during immune and inflammatory responses

Project Title: Chemokine gradient development around lymphatic vessels during immune and inflammatory responses.

Supervisors: Assistant Professor Bindi Brook

Project Information: The precisely orchestrated migration of leukocytes is a key feature of all immune and inflammatory responses, including those that occur in infectious diseases. Rapid leukocyte transport around the body is facilitated by fluid delivery in the blood and lymphatic vessels. However, their guidance to key destinations in tissues, lymph nodes or other tissue spaces is driven by a family of small secreted proteins called chemokines. Despite major advances in understanding chemokine function, it is still unclear how chemokine gradients are formed, maintained and regulated in tissues. Chemokines are known to bind to extra-cellular matrix (ECM) components and this adhesion is likely to play a key role. Interstitial fluid flow will also contribute to chemokine gradient formation, and in the case of chemokine production near blood or lymphatic vessels, the transmural movement of fluid is likely to advect chemokines further into tissues than would be possible by pure diffusion. ‘Atypical’ chemokine receptors (ACKRs), a small family of molecules that scavenge and destroy extracellular chemokines are also likely to play a critical role in establishing, stabilizing and regulating chemokine gradients. The type of leukocyte migration induced depends on chemokine context, with soluble chemokine gradients directing chemotactic cell movement (migration up concentration gradients), while immobilized chemokine gradients induce integrin-dependent haptotaxis (migration up adhesion gradients). 

The mechanisms that set up these gradients include diffusion, advection (fluid movement), cell-mediated scavenging, and selective binding to extracellular matrix (ECM), some of which may be modified during inflammation. The aim of this project will therefore be to develop mathematical models of chemokine gradient development during an immune or inflammatory response. The models will be developed in collaboration with immunologists based at the University of Glasgow (Profs Nibbs and Graham) [1], and a bioengineer at Imperial College London (Prof James Moore) who will be quantifying chemokine transport dynamics using a novel microfluidic platform to obtain a better understanding of chemokine transport and distribution in interstitial tissues around lymphatic vessels. 

[1] Immune regulation by atypical chemokine receptors. Nibbs and Graham. Nature Reviews Immunology 13:815-829, 2013.

Informal Enquires: should be addressed to Postgraduate Admissions.

Funding Summary: UK/EU students - Tuition Fees paid, and full Stipend of £14,296 (2016/17 rate). There will also be some support available for you to claim for limited conference attendance.

Eligibility: We require an enthusiastic graduate with a 1st class degree in Mathematics (other highly mathematical field), preferably of the MMath/MSc level, or an equivalent overseas degree (in exceptional circumstances a 2:1 class degree, or equivalent, can be considered).

Application Procedure: To apply please visit The University of Nottingham application page.

Application Deadline: This studentship is open now and will be available until it is filled.

 

Analysing how hormone dynamics create plant root branches

School of Mathematical Sciences & School of Biosciences

Fully funded PhD studentship in Applied Mathematics/Mathematical Modelling/Mathematical Biology

Project Title: Analysing how hormone dynamics create plant root branches

Supervisors: Supervised by Dr Leah Band, Prof John King and Prof Malcolm Bennett
In collaboration with Prof. Tom Beeckman, University of Ghent.

Project Information: Plant roots transport water and nutrients from the soil to the rest of the plant, enabling it to grow. Therefore understanding the processes regulating root growth and branching could enable us to produce root structures that maximise water and nutrient uptake and hence improve global food security. In this project, we shall focus on the role of the plant hormone auxin, which is known to control both the direction of the root growth (typically in the direction of gravity) and the formation of root branches.

Auxin moves between plant cells in a complicated manner, due to the spatial distribution of proteins on the cell membranes. This project will involve developing and analysing multicellular models that investigate how the auxin dynamics depend on both this cell-to-cell transport, and hence how these processes regulate root growth. In particular, we shall analyse some new experimental findings on the regulation of root branching, which cannot be explained with our existing models. We shall focus on deterministic models and use a range of techniques, including asymptotic analysis and numerical simulations (exploiting recent modelling developments within our groups).

This project will be based at the Centre for Plant Integrative Biology, a world-renowned centre for plant modelling, and will involve close collaboration with researchers from other disciplines. By working closely with Prof. Tom Beeckman at the University of Ghent and with other researchers within the University of Nottingham, we shall develop models that reflect the latest experimental findings and that generate novel predictions for testing by these experimental collaborators.

We require an enthusiastic graduate with a 1st class degree in Mathematics (in exceptional circumstances a 2(i) class degree can be considered), preferably of the MMath/MSc level. Candidates would need to be keen to work in an interdisciplinary environment and interested in learning about plant science; any experience in this field, or in mathematical biology more generally, would be a distinct advantage.

The studentship is available for immediate start and provides an annual stipend at the standard rate (currently £14,296 per annum) and full payment of Home/EU Tuition Fees. The studentship period will depend on the training needs of the successful applicant.

Informal enquiries: should be addressed to Dr Leah Band

Application: To apply, please use the online postgraduate application form , quoting reference: SCI/1233.

Application Deadline: This studentship is open until filled. Early application is strongly encouraged.

 

Bottom-up development of multi-scale models of airway remodelling in asthma: from cell To tissue

School of Mathematical Sciences

PhD Scholarship in Mathematical Medicine and Biology

Bottom-up development of multi-scale models of airway remodelling in asthma: from cell to tissue

Supervisors:
Bindi Brook, School of Mathematical Sciences (Nottingham)
Co-supervisors: Reuben O’Dea, School of Mathematical Sciences (Nottingham) Amanda Tatler, Respiratory Medicine (Nottingham)

Project details: Airway remodelling in asthma has until recently been associated almost exclusively with inflammation over long time-scales. Current experimental evidence suggests that broncho-constriction (as a result of airway smooth muscle contraction) itself triggers activation of pro-remodelling growth factors that causes airway smooth muscle growth over much shorter time-scales. This project will involve the coupling of sub-cellular mechano-transduction signalling pathways to biomechanical models of airway smooth muscle cells and extra-cellular matrix proteins with the aim of developing a tissue-level biomechanical description of the resultant growth in airway smooth muscle.

The mechano-transduction pathways and biomechanics of airway smooth muscle contraction are extremely complex. The cytoskeleton and contractile machinery within the cell and ECM proteins surrounding it are thought to rearrange dynamically (order of seconds). The cell is thought to adapt its length (over 10s of seconds). To account for all these processes from the bottom-up and generate a tissue level description of biological growth will require the combination of agent-based models to biomechanical models governed by PDEs. The challenge will be to come up with suitably reduced models with elegant mathematical descriptions that are still able to reproduce observed experimental data on cell and tissue scales, as well as the different time-scales present. Initially models will be informed by data from on-going experiments in Dr Amanda Tatler's lab in Respiratory Medicine but there will also be the opportunity to design new experiments based on model results.

While this study will be aimed specifically at airway remodelling, the methodology developed will have application in multi-scale models of vascular remodelling and tissue growth in artificially engineered tissues.

The PhD programme contains a training element, which includes research work as well as traditional taught material. The exact nature of the training will be mutually agreed by the student and their supervisors and will have a minimum of 30 credits (approximately ¼ of a Master course/taught component of an MSc course) of assessed training. The graduate programmes at the School of Mathematical Sciences provide a variety of appropriate training courses.

We require an enthusiastic graduate with a 1st class degree in Mathematics (in exceptional circumstances a 2(i) class degree can be considered), preferably of the MMath/MSc level, with good programming skills and willing to work as a part of an interdisciplinary team. A candidate with a solid background in continuum mechanics (fluid, solid or both) will have an advantage.

The studentship is available for a period of three years and provides an annual stipend of £14,296 and full payment of Home/EU Tuition Fees.

Informal enquiries: should be addressed to Dr Bindi Brook.

To apply: please use the online application form and ensure you quote ref: SCI/.

Closing date: This studentship is open until filled. Early application is strongly encouraged.

 

Multiscale Computational Methods for Complex Granular Systems

School of Mathematical Sciences
PhD studentship in Mathematical Sciences

Supervisors: Dr Kris van der Zee, Dr Donald Brown and Dr Xia Li

This project will be based at the University of Nottingham in the School of Mathematical Sciences and the Department of Chemical and Environmental Engineering.

Granular media are materials consisting of a large collection of solid particles, examples being coffee, corn, coal, sand and tablets. Research into such materials is crucial to the operation and efficiency in many industrial sectors, and it is also particularly important to geo-hazardous processes such as erosion, landslide disasters and plate tectonics. Emergent phenomena are a paramount characteristic of general complex systems of interacting discrete entities. Granular media exhibit a range of such phenomena when observed at macroscopic length scales: nonlinear stress-strain behaviour, static and dynamic arching, and shear banding. It is extremely important to predict these critical emergent phenomena as they are often the trigger or companion to system failure or process blockage. However, uncertainties in the underlying material makes computational modelling very challenging. On the one hand, macroscale computational methods completely neglect the discrete nature of granular media. On the other hand, microscale discrete models demand massive particle-scale inputs and, moreover, they are computationally intractable. The PhD project aims to address these challenges by developing multiscale computational methods for complex granular systems, which will allow for accurate, and computationally tractable, predictions of critical failure mechanisms in granulate systems. 

Summary: UK/EU students: Tuition Fees paid, and full Stipend at the RCUK rate, which is £14,296 per annum for 2016/17. There will also be some support available for you to claim for limited conference attendance. The scholarship length will be 3 or 3.5, depending on the qualifications and training needs of the successful applicant. 

Eligibility/Entry Requirements: We require an enthusiastic graduate with a 1st class degree in Mathematics (or other related mathematical field such as Engineering, Physics or Natural Sciences), preferably at MMath/MSc level, or an equivalent overseas degree (in exceptional circumstances a 2:1 class degree, or equivalent, can be considered).

Apply: This studentship is available to start from September 2017 and remains open until it is filled. To apply please visit The University of Nottingham application page.

For any enquiries please email:  kg.vanderzee@nottingham.ac.uk

This studentship is open until filled. Early application is strongly encouraged.

 

Experimental and mathematical models for avalanche fronts

School of Mathematical Sciences
PhD studentship in Mathematical Sciences

Experimental and mathematical models for avalanche fronts

Supervisors: Dr Paul Matthews and Dr Barbara Turnbull

This project will be based at the University of Nottingham in the School ofMathematical Sciences and the Department of Civil Engineering.

Powder snow avalanches are suspensions of ice particles in air that can flow down mountainsides at tens to hundreds of metres per second. The higher bulk density of the suspension compared with its surrounding generates the gravitational force that drives the avalanche. As it passes over the snow cover, the avalanche density can increase as loose snow along the path is fed into the head, but mixing between the suspension and the surrounding air dilutes the flow to slow it down. These competing mechanisms of snow erosion and air entrainment are critical to the longevity of an avalanche and potential stresses it can exert on an obstacle.

This project examines instabilities at the front of an avalanche, where the majority of snow and air is entrained. We propose an experiment to model a powder snow avalanche that will release high density fluid into a lower density fluid from a central reservoir to propagate down a cone. This symmetry, with its periodic boundary condition, will permit relatively straightforward comparison with mathematical models predicting the front behaviour. Computational and analytical work will be carried out to investigate whether simple mathematical models for the shape of the front provide an accurate description of the experiment. We will then explore the links to real avalanches by investigating steeper slopes, increased density ratios and particle-driven currents.

Summary: UK/EU students - Tuition Fees paid, and full Stipend at the RCUK rate, which is £14,296 per annum for 2016/17. There will also be some support available for you to claim for limited conference attendance. The scholarship length will be 3 or 3.5, depending on the qualifications and training needs of the successful applicant. 

Eligibility/Entry Requirements: We require an enthusiastic graduate with a 1st class degree in Mathematics (or other highly mathematical field such as Physics or Engineering), preferably at MMath/MSc level, or an equivalent overseas degree (in exceptional circumstances a 2:1 class degree, or equivalent, can be considered).

Apply: This studentship is available to start from September 2017 and remain open until it is filled. To apply please visit The University of Nottingham application page.

For any enquiries please email:  Paul.Matthews@nottingham.ac.uk

This studentship is open until filled. Early application is strongly encouraged.

 

Modelling energy localisation and propagation in nonlinear lattices

School of Mathematical Sciences
PhD studentship in Mathematical Sciences

Modelling energy localisation and propagation in nonlinear lattices

Supervisors: Dr Jonathan Wattis and Dr Dmitrios Chronopoulos

This project will be based at the University of Nottingham in the School of Mathematical Sciences and the Department of Mechanical Engineering.

The aim of this project is to investigate the frequencies and type of wave which permit the transfer of energy through a lattice. 

In a nonlinear lattice, nodes are connected to nearest neighbouring nodes by force interactions which are nonlinear in local displacements. In addition, there may be internal degrees of freedom in which complicate the dynamics. Such systems can be modelled mathematically using large systems of coupled differential equations. Depending on the form of interaction and internal modes at lattice sites, energy can propagate through a structure, or be prevented from being transported, depending on the frequency of oscillations.  The aim of this project is to use asymptotic analysis and numerical simulations to investigate these systems. The engineering applications of this work include the transport of energy from earthquakes across foundation piles which support buildings, as well as the propagation of such energy up a towerblock.

Summary: UK/EU students - Tuition Fees paid, and full Stipend at the RCUK rate, which is £14,296 per annum for 2016/17. There will also be some support available for you to claim for limited conference attendance. The scholarship length will be 3 or 3.5, depending on the qualifications and training needs of the successful applicant.

Eligibility/Entry Requirements: We require an enthusiastic graduate with a 1st class degree in Mathematics (or other related mathematical field such as Natural Sciences or Physics), preferably at MMath/MSc level, or an equivalent overseas degree (in exceptional circumstances a 2:1 class degree, or equivalent, can be considered).

Apply: This studentship is available to start from September 2017 and remain open until it is filled. To apply please visit The University of Nottingham application page.

For any enquiries please email:  jonathan.wattis@nottingham.ac.uk

This studentship is open until filled. Early application is strongly encouraged.

 

Modelling flow and crystallisation in polymers

Modelling flow and crystallisation in polymers

Reference
: SCI1646

Supervisor: Dr Richard Graham

This project will be based at the University of Nottingham in the School of Mathematical Sciences and the School of Chemistry.

Polymers are very long chain molecules and many of their unique properties depend upon their long chain nature. Like simple fluids many polymer fluids crystallise when cooled. However, the crystallisation process is complicated by the way the constituent chains are connected, leading to a multitude of unexplained phenomena. Furthermore, if a polymer fluid is placed under flow, this strongly affects both the ease with which the polymer crystallises and the arrangement of the polymer chains within the resulting crystal. This project will develop molecular models and simulations for polymer dynamics and phase transitions using a range of analytical, numerical and stochastic techniques, with the ultimate aim of improving our understanding of polymer crystallisation.

This studentship will support the EPSRC funded Design by Science project "Flow induced crystallisation in polymers: from molecules to processing". This major project on the molecular understanding of polymer crystallization involves the Universities of Nottingham, Leeds and Bradford, along with multinational industrial partners Dow, SCG and Autodesk.

Summary: UK/EU students - Tuition Fees paid, and full Stipend at the RCUK rate, which is £14,296 per annum for 2016/17. There will also be some support available for you to claim for limited conference attendance. The scholarship length will be 3 or 3.5, depending on the qualifications and training needs of the successful applicant.

This scholarship can be extended to cover full international fees. Interested full international students must apply by 15th January 2017, at the latest.

Eligibility/Entry Requirements: We require an enthusiastic graduate with a 1st class degree in Mathematics (or other highly mathematical field such as Physics or Chemistry), preferably at MMath/MSc level, or an equivalent overseas degree (in exceptional circumstances a 2:1 class degree, or equivalent, can be considered).

Apply: This studentship is available to start from September 2017 and remain open until it is filled. To apply please visit The University of Nottingham application page.

For any enquiries please email: Richard.Graham@nottingham.ac.uk

This studentship is open until filled. Early application is strongly encouraged.

 

Machine learning for first-principles calculation of physical properties

Reference: SCI1647

Supervised by: Dr Richard Graham (Maths) and Dr Richard Wheatley (Chemistry)

This project will be based at the University of Nottingham in the School of Mathematical Sciences and the School of Chemistry.

The physical properties of all substances are determined by the interactions between the molecules that make up the substance. The energy surface corresponding to these interactions can be calculated from first-principles, in theory allowing physical properties to be derived ab-initio from a molecular simulation; that is by theory alone and without the need for any experiments. Recently we have focussed on applying these techniques to model carbon dioxide properties, such as density and phase separation, for applications in Carbon Capture and Storage. However, there is enormous potential to exploit this approach in a huge range of applications. A significant barrier is the computational cost of calculating the energy surface quickly and repeatedly, as a simulation requires. In collaboration with the School of Chemistry we have recently developed a machine-learning technique that, by using a small number of precomputed ab-initio calculations as training data, can efficiently calculate the entire energy surface. This project will involve extending the approach to more complicated molecules and testing its ability to predict macroscopic physical properties.

Summary: UK/EU students - Tuition Fees paid, and full Stipend at the RCUK rate, which is £14,296 per annum for 2016/17. There will also be some support available for you to claim for limited conference attendance. The scholarship length will be 3 or 3.5, depending on the qualifications and training needs of the successful applicant. There is also the option to carry this project with the Leverhulme Doctoral Scholarships programmeMathematics for A Sustainable Society, which provides 4 years of funding.

Eligibility/Entry Requirements: We require an enthusiastic graduate with a 1st class degree in Mathematics (or other highly mathematical field such as Physics or Chemistry), preferably at MMath/MSc level, or an equivalent overseas degree (in exceptional circumstances a 2:1 class degree, or equivalent, can be considered).

Apply: This studentship is available to start from September 2017 and remain open until it is filled. To apply please visit The University of Nottingham application page.

For any enquiries please email: Richard.Graham@nottingham.ac.uk

This studentship is open until filled. Early application is strongly encouraged. 

 

Thermal characterisation of the building fabric under uncertainty

Reference: SCI1650

Department: Mathematical Sciences Supervisors: Dr Marco Iglesias (Mathematical Sciences), Dr Yupeng Wu (Engineering)

Do you have a passion for sustainability?

Would you like to apply mathematical research to help improve resource security?

Modelling and Analytics for a Sustainable Society (MASS) is a Leverhulme Doctoral Scholarships programme at the University of Nottingham that aims to tackle the ongoing global problems of food shortages, water scarcity and insufficient clean energy by using mathematics to help understand and optimise resource use through predictive modelling and statistical analysis.

The built environment is responsible for 45% of all UK carbon emissions with approximately 27% attributed to the domestic sector and 18% to non-domestic buildings. Reducing the energy demand in the built-environment is thus essential for the UK decarbonisation policy which legislates an 80% reduction of its 1990 green house gas emissions by 2050. The existing housing stock is a primary target for reductions of the energy demand since it is estimated that up to 85% of existing buildings will be standing by 2050. An accurate characterisation of the thermal performance of the existing housing stock in the UK is thus needed to inform large-scale cost-effective policies for retrofit intervention that can effectively contribute towards achieving those decarbonisation targets. Unfortunately, existing approaches for the in-situ characterisation of the building fabric (including ISO standards) cannot accurately characterise the thermal performance of buildings in the presence of thermal bridge effects that arise from heterogeneities, irregularities and/or abrupt changes and discontinuities in the thermophysical properties of the building fabric. In particular, these approaches cannot capture thermal bridge effects due to fabric degradation and moisture condensation which are likely to be found in existing dwellings.

This challenging research will develop novel thermal imaging algorithms capable of characterising, with an accurate measure of uncertainty, the thermal performance of the building fabric in the presence of a general class of thermal bridge effects. This project will build upon state-of-the-art Bayesian algorithms for inverse problems that have been successfully applied for tomographic inversions in the context of groundwater flow [1], electrical impedance tomography [1], resin transfer moulding [2], and the characterisation of thermophysical properties of walls [3,4]. The techniques developed in this project will be validated with real experiments. Although highly ambitious, this proposed research has enormous potential to revolutionise current approaches for in-situ characterisation of the thermal performance of buildings thereby enhancing the predictive capabilities of existing housing stock models.

[1] Iglesias, M.A. 2016. “A Regularizing Iterative Ensemble Kalman Method for PDE-Constrained Inverse Problems.” Inverse Problems 32 (2):025002. http://stacks.iop.org/0266-5611/32/i=2/a=025002.

[2] Iglesias, M.A., M. Park, and M. Tretyakov. 2017. “Bayesian Inverse Problems in Resin Transfer Molding.” Submitted Preprint available at: https://arxiv.org/abs/1707.03575.

[3] Iglesias, M.A., Sawlan Z., Scavino M., Tempone R., and C. Wood. 2018. “Bayesian Inferences of the Thermal Properties of a Wall Using Temperature and Heat Flux Measurements.” International Journal of Heat and Mass Transfer 116 (Supplement C):417–31.

[4] De Simon,L. M. A. Iglesias, B. Jones and C. Wood. 2017. “Quantifying Uncertainty in Thermal Properties of Walls by Means of Bayesian Inversion.” Submitted Preprint available at: (https://arxiv.org/abs/1710.02976).

For more information, including details of other available research projects, please visit our MASS pages.

The Leverhulme Doctoral Scholars, who will be based in the new £7m Mathematical Sciences Building, will be exposed to an outstanding and vibrant research environment in mathematics, resource science, engineering and social sciences, with excellent opportunities for international engagement. At the end of their PhD, the Scholars will be eligible to apply for an additional one-year post-doctoral prize, funded by The University of Nottingham, to help establish their independent research careers.

Summary: The scholarships are for four years and will cover PhD tuition fees for UK/EU students, plus a tax-free stipend of £14,296per annum (2016/17 rate). While the scholarships may be held by students of all nationalities, the Leverhulme Trust has a particular interest in supporting UK or EU students. International students would be expected to cover the difference between international and UK/EU tuition fees (currently approximately £9,500 per annum).

Eligibility: Appropriately motivated students should have, or expect to obtain, a first-class or good 2:1 honours degree and/or a distinction or high merit at MSc level in Mathematics or a subject with a strong mathematical component (e.g. physics, engineering, computer science).

Apply: Please visit the MASS web page and identify up to three projects of interest. Then apply via The University of Nottingham application page, using the personal statement section to indicate that you are applying to the “Mathematics for A Sustainable Society” programme, making sure to list your preferred projects, and uploading a CV of no more than two pages.

Studentships are available from September 2017 and will remain open until filled, early application is encouraged.

For any enquiries please email: PM-pg-admissions@exmail.nottingham.ac.uk

 

Mathematical modelling of the effect of temperature stress on crop fertility

Reference: SCI1651

Supervisors: Professor John King (Mathematical Sciences), Professor Zoe Wilson (Biosciences)

Do you have a passion for sustainability?

Would you like to apply mathematical research to help improve resource security?

Modelling and Analytics for a Sustainable Society (MASS) is a Leverhulme Doctoral Scholarships programme at the University of Nottingham that aims to tackle the ongoing global problems of food shortages, water scarcity and insufficient clean energy by using mathematics to help understand and optimise resource use through predictive modelling and statistical analysis.

Increased temperatures during flowering have extreme affects on pollen development and thus reproductive success and yield in plants. It has been predicted that this may be the key factor in determining future productivity for many crops, particularly in the temperate cereals such as wheat and barley. This project will model the effects of temperature changes on reproductive success, focusing in particular on the impact this may have on yields for wheat.

It will also explore the influence of this temperature stress on the molecular pathways regulating pollen development by modelling of how the dynamic changes in hormone levels and gene expression are influenced by elevated temperature.

For more information, including details of other available research projects, please visit our MASS pages.

The Leverhulme Doctoral Scholars, who will be based in the new £7m Mathematical Sciences Building, will be exposed to an outstanding and vibrant research environment in mathematics, resource science, engineering and social sciences, with excellent opportunities for international engagement. At the end of their PhD, the Scholars will be eligible to apply for an additional one-year post-doctoral prize, funded by The University of Nottingham, to help establish their independent research careers.

Summary: The scholarships are for four years and will cover PhD tuition fees for UK/EU students, plus a tax-free stipend of £14,296per annum (2016/17 rate). While the scholarships may be held by students of all nationalities, the Leverhulme Trust has a particular interest in supporting UK or EU students. International students would be expected to cover the difference between international and UK/EU tuition fees (currently approximately £9,500 per annum).

Eligibility: Appropriately motivated students should have, or expect to obtain, a first-class or good 2:1 honours degree and/or a distinction or high merit at MSc level in Mathematics or a subject with a strong mathematical component (e.g. physics, engineering, computer science).

Apply: Please visit the MASS web page and identify up to three projects of interest. Then apply via The University of Nottingham application page, using the personal statement section to indicate that you are applying to the “Mathematics for A Sustainable Society” programme, making sure to list your preferred projects, and uploading a CV of no more than two pages.

Studentships are available from September 2017 and will remain open until filled, early application is encouraged.

For any enquiries please email: PM-pg-admissions@exmail.nottingham.ac.uk

 

Neurocomputational models of hippocampus-dependent place learning and navigation

Reference: SCI1652

Supervised by: Prof Stephen Coombes (Mathematical Sciences) and Dr Tobias Bast (Psychology)

This project will be based at the University of Nottingham in the School of Mathematical Sciences and the School of Psychology.

Humans and other animals can readily remember significant places and associated events and return to these places as appropriate. From an experimental point of view, studies of the neuro-psychological mechanisms underlying place learning and navigation offer unique opportunities, because similar tests can be used in rodent models and human participants. Studies in rodent models have led to a detailed understanding of the neuro-psychological mechanisms of place memory, and the importance of the hippocampus for place learning and navigation in humans and other animals is well-established.  In this project, we aim to develop quantitative models describing how neurons in the hippocampus and associated brain areas give rise to place learning and navigation, and construct an in silicomodel for testing ideas about functional mechanisms. The project brings together behavioural neuroscience expertise on hippocampal function and place learning (Bast, Psychology) with expertise in mathematical and computational neuroscience (Coombes, Mathematical Sciences) to understand rapid place learning.  A particular emphasis will be on the hippocampal learning-behaviour translation: how place information (as encoded, for example, by hippocampal place cells) is related to decision making processes and, ultimately, translated into motor behaviour (for example, by way of interactions with prefrontal and subcortical circuits).  From a mathematical perspective the project will develop new neurocomputational models of hippocampus-dependent place learning and navigation using tools from stochastic optimal control, reinforcement learning theory, dynamical systems and computational neuroscience.

Summary: UK/EU students - Tuition Fees paid, and full Stipend at the RCUK rate, which is £14,296 per annum for 2016/17. There will also be some support available for you to claim for limited conference attendance. The scholarship length will be 3 or 3.5, depending on the qualifications and training needs of the successful applicant.

Eligibility/Entry Requirements: We require an enthusiastic graduate with a 1st class degree in Mathematics (or other highly mathematical field such as Physics or Chemistry), preferably at MMath/MSc level, or an equivalent overseas degree (in exceptional circumstances a 2:1 class degree, or equivalent, can be considered).

Apply: This studentship is available to start from September 2017 and remain open until it is filled. To apply please visit The University of Nottingham application page.

For any enquiries please email: Richard.Graham@nottingham.ac.uk

This studentship is open until filled. Early application is strongly encouraged. 

 

Modelling the physical and biological properties of soil

Reference: SCI1653

Supervisors: Professor Ian Dryden (Mathematical Sciences), Professor Sacha Mooney (Biosciences)

Do you have a passion for sustainability?

Would you like to apply mathematical research to help improve resource security?

Modelling and Analytics for a Sustainable Society (MASS) is a Leverhulme Doctoral Scholarships programme at the University of Nottingham that aims to tackle the ongoing global problems of food shortages, water scarcity and insufficient clean energy by using mathematics to help understand and optimise resource use through predictive modelling and statistical analysis.

Soil quality and structure is critical for crop yield, however it is dynamic, with multiple factors influencing productivity. This project will model the physical and biological properties of soil, determining the impacts of irrigation, no till and environmental inputs. Statistical regression models will be developed in the topical area of Object Data Analysis, where geometrical objects are predicted using functional or geometrical covariates.

For more information, including details of other available research projects, please visit our MASS pages.

The Leverhulme Doctoral Scholars, who will be based in the new £7m Mathematical Sciences Building, will be exposed to an outstanding and vibrant research environment in mathematics, resource science, engineering and social sciences, with excellent opportunities for international engagement. At the end of their PhD, the Scholars will be eligible to apply for an additional one-year post-doctoral prize, funded by The University of Nottingham, to help establish their independent research careers.

Summary: The scholarship is for four years and will cover PhD tuition fees for UK/EU students, plus a tax-free stipend of £14,296per annum (2016/17 rate). While the scholarship may be held by students of all nationalities, the Leverhulme Trust has a particular interest in supporting UK or EU students. International students would be expected to cover the difference between international and UK/EU tuition fees (currently approximately £9,500 per annum).

Eligibility: Appropriately motivated students should have, or expect to obtain, a first-class or good 2:1 honours degree and/or a distinction or high merit at MSc level in Mathematics or a subject with a strong mathematical component (e.g. physics, engineering, computer science).

Apply: Please visit the MASS web page and identify up to three projects of interest. Then apply via The University of Nottingham application page, using the personal statement section to indicate that you are applying to the “Mathematics for A Sustainable Society” programme, making sure to list your preferred projects, and uploading a CV of no more than two pages.

Studentship is available from September 2017 and will remain open until filled, early application is encouraged.

For any enquiries please email: maths-pg-admissions@nottingham.ac.uk

 

Towards sustainable antimicrobial use in agriculture: quantifying the risks of emergence of antimicrobial pathogens

Reference: SCI1655

Supervisors: Professor Michael Tretyakov (Mathematical Sciences), Dr Dov Stekel & Dr Jon Hobman (Biosciences)

Do you have a passion for sustainability?

Would you like to apply mathematical research to help improve resource security?

Modelling and Analytics for a Sustainable Society (MASS) is a Leverhulme Doctoral Scholarships programme at the University of Nottingham that aims to tackle the ongoing global problems of food shortages, water scarcity and insufficient clean energy by using mathematics to help understand and optimise resource use through predictive modelling and statistical analysis.

Antimicrobial resistance is a major threat both to human and animal health. The majority of antibiotic use is in agriculture, thus the threat of antimicrobial resistance, and the appropriate use of antibiotics, are essential to sustainable agriculture and food production. The aim of this project is to develop mathematical models that can improve our capacity to predict the risk of emergence of antimicrobial resistant pathogens within a sustainable agriculture context. Specifically, the student will develop and analyze both spatially homogeneous and heterogeneous stochastic models for the spread of antimicrobial resistance between populations of bacteria in dairy slurry. The model will be based upon the real dairy slurry system in the University of Nottingham farm in Sutton Bonington.

In addition to being based in the sustainability programme, the project will be supported by on-going research in antimicrobial resistance in agriculture and will benefit from experimental measurements carried out by colleagues in Biosciences, Pharmacy and Engineering.

For more information, including details of other available research projects, please visit our MASS pages.

The Leverhulme Doctoral Scholars, who will be based in the new £7m Mathematical Sciences Building, will be exposed to an outstanding and vibrant research environment in mathematics, resource science, engineering and social sciences, with excellent opportunities for international engagement. At the end of their PhD, the Scholar will be eligible to apply for an additional one-year post-doctoral prize, funded by The University of Nottingham, to help establish their independent research careers.

Summary: The scholarship is for four years and will cover PhD tuition fees for UK/EU students, plus a tax-free stipend of £14,296per annum (2016/17 rate). International students would be expected to cover the difference between international and UK/EU tuition fees (currently approximately £9,500 per annum).

Eligibility: Appropriately motivated students should have, or expect to obtain, a first-class or good 2:1 honours degree and/or a distinction or high merit at MSc level in Mathematics or a subject with a strong mathematical component (e.g. physics, engineering, computer science).

Apply: Please visit the MASS web page and identify up to three projects of interest. Then apply via The University of Nottingham application page, using the personal statement section to indicate that you are applying to the “Mathematics for A Sustainable Society” programme, making sure to list your preferred projects, and uploading a CV of no more than two pages.

For any enquiries please email: maths-pg-admissions@nottingham.ac.uk

 

Efficient Techniques for Heterogeneous Non-Local Flow Models

Reference: SCI1665

Supervised by: Dr Donald L. Brown

This project will be based at the University of Nottingham in the School of Mathematical Sciences.

Understanding flow and transport in is critical for mitigating environmental impacts in groundwater flow and improving recovery in conventional oil and gas reservoirs. The central challenges being the heterogeneity and uncertainty of the subsurface properties. Often standard local Darcy flow models are not sufficient to describe the underlying physics, as is the case of the famous MacroDispersion Experiment (MADE).  Non-local fractional flow models have thus been proposed, stimulating a great variety of exciting research, both computationally and mathematically. The challenge with these models is the non-locality coupled with the multiscale nature make them often computationally intractable. However, with the development of efficient multiscale methods to bridge the scales, as well as the addition extra spatial dimensions to localize the problem, allow for possible efficient computational techniques to attack these problems.

This PhD studentship aims to develop efficient techniques to better understand such complicated flow models. For this project, there is flexibility from being very applied with real-data integration to very theoretical, dependent on student background and interests. For this project, persons with experience with numerical methods as well as ability to program in MATLAB or other programming languages would be at an advantage. This project will have considerable interaction with the GeoEnergy Research Centre (GERC) and British Geological Survey (BGS).

Summary: UK/EU students - Tuition Fees paid, and full Stipend at the RCUK rate, which is £14,296 per annum for 2016/17. There will also be some support available for you to claim for limited conference attendance. The scholarship length will be 3 or 3.5, depending on the qualifications and training needs of the successful applicant.

This scholarship can be extended to cover full international fees. Interested full international students must apply by 15 January 2017, at the latest.

Eligibility/Entry Requirements: We require an enthusiastic graduate with a 1st class degree in Mathematics (or other highly mathematical field such as Engineering), preferably at MMath/MSc level, or an equivalent overseas degree (in exceptional circumstances a 2:1 class degree, or equivalent, can be considered).

Apply: This studentship is available to start from September 2017 and remain open until it is filled. To apply please visit The University of Nottingham application page.

For any enquiries please email: Donald.Brown@nottingham.ac.uk

This studentship is open until filled. Early application is strongly encouraged.

 

Next generation neural field models on spherical domains

Reference: SCI1666

Supervised by: Dr Rachel Nicks and Professor Stephen Coombes

This project will be based at the University of Nottingham in the School of Mathematical Sciences.

The number of neurons in the brain is immense (of the order of 100 billion). A popular approach to modelling such cortical systems is to use neural field models which are mathematically tractable and which capture the large scale dynamics of neural tissue without the need for detailed modelling of individual neurons. Neural field models have been used to interpret EEG and brain imaging data as well as to investigate phenomena such as hallucinogenic patterns, short-term (working) memory and binocular rivalry.

A typical formulation of a neural field equation is an integro-differential equation for the evolution of the activity of populations of neurons within a given domain. Neural field models are nonlinear spatially extended pattern forming systems. That is, they can display dynamic behaviour including spatially and temporally periodic patterns beyond a Turing instability in addition to localised patterns of activity. The majority of research on neural field models has been restricted to the line or planar domains, however the cortical white matter system is topologically close to a sphere. It is relevant to study neural field models as pattern forming systems on spherical domains, particularly as the periodic boundary conditions allow for natural generation (via interference) of the standing waves observed in EEG signals.

This project will build on recent developments in neural field theory, focusing in particular on extending to spherical geometry the neural field equations arising from “Next generation neural mass models” (which incorporate a description of the evolution of synchrony within the system). Techniques from dynamical systems theory, including linear stability analysis, weakly nonlinear analysis, symmetric bifurcation theory and numerical simulation will be used to consider the global and local patterns of activity that can arise in these models.

Summary: UK/EU students - Tuition Fees paid, and full Stipend at the RCUK rate, which is £14,296 per annum for 2016/17. There will also be some support available for you to claim for limited conference attendance. The scholarship length will be 3 or 3.5, depending on the qualifications and training needs of the successful applicant.

This scholarship can be extended to cover full international fees. Interested full international students must apply by 15th January 2017, at the latest.

Eligibility/Entry Requirements: We require an enthusiastic graduate with a 1st class degree in Mathematics, preferably at MMath/MSc level, or an equivalent overseas degree (in exceptional circumstances a 2:1 class degree, or equivalent, can be considered).

Apply: This studentship is available to start from September 2017 and remain open until it is filled. To apply please visit The University of Nottingham application page.

For any enquiries please email: Rachel.Nicks@nottingham.ac.uk

This studentship is open until filled. Early application is strongly encouraged.

 

Multiscale Methods for Hysteresis Effects in Geomechanics

Reference: SCI1667

Supervised by: Dr Donald L. Brown and Dr Savvas Triantafyllou (Faculty of Engineering).

This project will be based at the University of Nottingham in the School of Mathematical Sciences.

During cyclic fluid injections into the subsurface for either Carbon Storage or GeoEnergy applications, the in-situ geomaterials experience complex fluid-rock interactions that may alter the flow and mechanical properties of the subsurface. A key rock mechanics processes in this setting are hysteresis effects on the geomaterial. Simulating and predicting this phenomenon is critical in mitigating environmental risks and is complicated by the multiscale nature of the subsurface. When considering only the flow aspects, multiscale finite elements have proven to be a very efficient way to include microscale information at the coarser flow scales, greatly expediting the computations.

Recently, when considering the case of a heterogeneous solid backbone, smooth hysteretic models in combination with robust multiscale finite element methodologies have proven efficient in providing high-fidelity and rapid simulation of the underlying mechanical processes. This approach has been successfully utilized in the case of mechanical structures.  However, pore pressures evolving within the solid medium are expected to significantly affect its hysteretic response and thus need also to be accounted for. This is a direction not yet explored and has interesting applications in CCS, rock mechanics, and reservoir engineering. This project seeks to develop a coupled stress-pore pressure hysteretic operator to be fused in a multiscale finite element setting.

This PhD studentship aims to develop efficient techniques to better understand such complicated mechanics and flow models. For this project, persons with experience with numerical methods as well as ability to program in MATLAB or other programming languages would be at an advantage. This project will have considerable interaction with the GeoEnergy Research Centre (GERC) and British Geological Survey (BGS). For the interested students, to gain international experience in fluid-rock interactions in geomechanics, a secondment to GERCs partners at Virginia Tech, USA or China University of Mining Technology, Xuzhou, China, may be possible.

Summary: UK/EU students - Tuition Fees paid, and full Stipend at the RCUK rate, which is £14,296 per annum for 2016/17. There will also be some support available for you to claim for limited conference attendance. The scholarship length will be 3 or 3.5, depending on the qualifications and training needs of the successful applicant.

Eligibility/Entry Requirements: We require an enthusiastic graduate with a 1st class degree in Mathematics (or other highly mathematical field such as Physics or Engineering), preferably at MMath/MSc level, or an equivalent overseas degree (in exceptional circumstances a 2:1 class degree, or equivalent, can be considered).

Apply: This studentship is available to start from September 2017 and remain open until it is filled. To apply please visit The University of Nottingham application page.

For any enquiries please email: Donald.Brown@nottingham.ac.uk

This studentship is open until filled. Early application is strongly encouraged.

 

EPSRC DTG studentships, School and University funded studentships

Applications are invited for fully funded PhD studentships in any area of Mathematics, including Statistics and Probability, at the School of Mathematical Sciences, University of Nottingham. In the 2008 Research Assessment Exercise all units of assessment performed well with applied mathematics placed 5th in the research power ranking and statistics ranked 6th for quality. Over 95% of research across the school was judged to be of international standard.

The School of Mathematical Sciences is a large and thriving research centre. Areas of research specialism include Algebra, Number Theory, Analysis, Applied Nonlinear Mathematics, Mathematical Medicine and Biology, Complex and Disordered Systems, Continuum Mechanics, Industrial Mathematics, Quantum Gravity, Quantum Information, Epidemic Modelling, Statistical Shape Analysis, Probability Theory and Financial Mathematics.

EPSRC studentships will cover all study fees for EU nationals. For UK nationals, or EU nationals who can demonstrate a relevant connection with the UK (usually established by being ordinarily resident for a period of 3 years immediately prior to the date of application for an award), it will also provide a stipend for either three or three and a half years, currently £13,726 per annum, increasing in line with the EPSRC rates. Details of eligibility can be found  from the Office of Public Sector Information .

School funded studentships and University funded studentships cover all study fees for EU nationals and also provides a stipend for either three or three and a half years at the EPSRC rate mentioned above.

Applicants should have a First or Upper Second class degree in Mathematics or Statistics, or in a subject with a high mathematical content.

Applications should be made online via the Applicants' Portal.

 

Scholarships available for UK and EU PhD students

The School has available a number of Studentships for students from the UK and the EU, including EPSRC and BBSRC studentships funded through Doctoral Training Grants, Nottingham University Research Scholarships (URSs) and School Scholarships.

URSs and School Scholarships

The URSs and School Scholarships provide full funding (fees and living expenses) for UK and EU students.

EPSRC and BBSRC Scholarships

The EPSRC and BBSRC studentships provide full funding for UK students and for EU students who have been resident in the UK for at least 3 years prior to PhD study, and cover fees only for other EU students.

These studentships are awarded on a competitive basis. 

Vice Chancellor's Scholarship for Research Excellence

EU students are also eligible to apply for the Vice Chancellor's Scholarship for Research Excellence (European Union).To apply for this scholarship you must first apply the school and received an offer of a place and then apply for the scholarship itself. The scholarship deadline is in early March.

 

Scholarships for international students

International Office Scholarships

The university's International Office administers a number of  scholarships and assists with external scholarships. Many of the scholarships require an offer from the School before you can apply so early application is encouraged. Once you have an offer from the School we will assist you in applying for scholarships.

The university's Vice Chancellor's Scholarship for Research Excellence (International)

The University of Nottingham Vice Chancellor's Scholarship for Research Excellence (International) is open to all nationalities. To apply for this scholarship you must first apply the school and received an offer of a place and then apply for the scholarship itself. The scholarship deadline is in early March.

 

Comparison between factorisation algebras and AQFT

School of Mathematical Sciences
PhD studentship in Mathematical Sciences

Supervised by Dr Alexander Schenkel

Quantum gauge theories are not only one of the main cornerstones of fundamental physics, but they also inspired exciting developments in mathematics. The aim of this project is to study a particularly simple, but rich class of topological quantum gauge theories from the perspective of algebraic quantum field theory. For this we shall employ modern mathematical techniques from homotopical algebra and operad theory. The results should be compared to Lurie’s classification of locally constant factorisation algebras by E_n-algebras.

This studentship will be funded by the Royal Society via the Research Fellows Enhancement Award “Comparison between factorisation algebras and AQFT”. It is associated to the Royal Society University Research Fellowship “Homotopical algebra and quantum gauge theories” by Dr Alexander Schenkel.

Summary: UK/EU students - Tuition Fees paid, and full Stipend at the RCUK rate, which is £14,553 per annum for 2017/18. There will also be some support available for you to claim for limited conference attendance. The scholarship length will be 4 years.

Eligibility/Entry Requirements: We require an enthusiastic graduate with a 1st class degree in Mathematics (or Mathematical Physics), preferably at MMath level, or an equivalent overseas degree. Preference will be given to those candidates who already have some experience in a relevant area of pure mathematics, e.g. algebraic topology, category theory or homological algebra.

Apply: This studentship is available to start from October 2018 or earlier. To apply please visit the University of Nottingham application page: http://www.nottingham.ac.uk/pgstudy/apply/apply-online.aspx

For any enquiries please email: alexander.schenkel@nottingham.ac.uk

This studentship is open until filled. Early application is strongly encouraged.

 

 

Current project listings

You can search an illustrative list of projects or filter the results by Research Group:

School of Mathematical Sciences

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For all enquiries please visit:
www.nottingham.ac.uk/enquire