School of Mathematical Sciences

Leverhulme Doctoral Scholarships


Modelling and Analytics for a Sustainable Society  


MASS: 'Modelling and Analytics for a Sustainable Society’ is an interdisciplinary doctoral training centre that aims to tackle the ongoing global problems of food shortages, water scarcity and insufficient clean energy. It brings together mathematicians with researchers from across the University developing improved crops, bioenergy sources and biological methods to clean contaminated water; renewable energy sources, storage and distribution.

Mathematics plays a crucial role in helping to understand resource use by quantifying and predicting the effects of alternative approaches through predictive modelling, statistical analysis and uncertainty quantification.

High-quality funded PhD opportunities

The programme will fund 15 fully-funded four-year PhD scholarships over three intakes; the first cohort of four students started their scholarships in September 2015. The second cohort of five students have just started their scholarships in September 2016. We are currently recruiting for the third cohort of five scholarships to commence in Autumn 2017.

The scholarships will cover PhD tuition fees for UK/EU students, plus a tax-free stipend of £14,296 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 £11,387 per annum). Students will be based within the School of Mathematical Sciences, and co-supervised by one or more academics from partner schools.


To apply for a scholarship on the programme, please consult the project list below and:

  • identify three projects of interest;
  • apply online via the University of Nottingham application page (for question 1a please select PhD in Mathematics - G10N);
  • in the personal statement section indicate that you are applying to the 'Modelling and Analytics for a Sustainable Society' programme;
  • make sure to include a ranked list of your three preferred projects, together with a CV of no more than two pages.

Applications will remain open until the scholarships are filled.

Available projects

For queries in relation to a particular project, please contact the supervisors associated with that project.

Energy projects

Bayesian inverse problems in the built environment

Supervisors: Dr Marco Iglesias (Mathematical Sciences), Dr Christopher Wood (Engineering)

Policy-making relies on modelling and simulation of the energy demand and performance of buildings. However, inaccurate predictions can arise from the uncertainty of thermal properties of structures such as walls. The student will develop fast and robust Bayesian inverse methods for characterisation of thermal properties of walls, using in-situ experimental data.

Sustainability applications of first-principles calculation of physical properties, via machine learning

Supervisors: Dr Richard Graham (Mathematical Sciences), Dr Richard Wheatley (Chemistry)

Carbon capture and storage (CCS) has the potential to hugely reduce CO2 emissions. However, CO2 from combustion contains many impurities, which affect the cost and safety of CCS. This PhD project will develop a fundamental understanding of impure CO2 by modeling the interactions between the constituent molecules. These interactions can be calculated from first-principles, but such calculations are too expensive numerically for most applications. We have recently developed a machine-learning technique that, via a small number of ab-initio calculations, can efficiently model the entire energy surface. This project will exploit this technique to create first-principles predictions of properties that are important to the safety, design and cost of CO2 pipelines.

Form, function and utility in small community energy networks

Supervisors: Prof Mark Gillott (Architecture & Built Environment), Dr Keith Hopcraft (Mathematical Sciences),
Dr Parham Mirzaei Ahrnjani (Architecture & Built Environment)

This is a unique and exciting opportunity to undertake research that spans across the disciplines of energy engineering and mathematical sciences. Successful applicants will be joining a strong interdisciplinary team from academia and industry who are currently working on the delivery of the Energy Research Accelerator (ERA) Community Energy System (CES) demonstrator at the 15 acre Trent Basin site in Nottingham. The project will investigate the energy challenges and complexity science issues associated with heat and electrical power generation, storage and use arising from the connections between micro-generation output, grid/heat loads, weather, and energy/power demands (including occupant behavior) combined with variable load energy storage devices in order to provide energy stability, a reduction of cost and associated carbon emissions from fossil fuel use.  The PhD research will develop new multi-vector CES models that utilise ‘big data’ obtained from a dedicated onsite monitoring platform at the housing development applied to a heterogeneous network of users. The work will ultimately help inform the design, implementation and operation of local community energy schemes in the UK. Applicants should have a Bachelor Science or Engineering (at least 2i) and/or a Master of Science or Engineering in Mathematical Sciences, Engineering or Energy related disciplines.

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

Supervisors: Prof John King (Mathematical Sciences), Prof Gavin Walker (Engineering), Dr Richard Wheatley (Chemistry)

In order to facilitate high penetration of renewable energy in to the grid, energy storage is needed 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 400°C).

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 350-400°C, 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 350°C 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. 

Advanced stability assessment methods for power grids dominated by renewable energy sources

Supervisors: Dr Stephen Cox (Mathematical Sciences), Dr Alessandro Costabeber (Electrical and Electronic Engineering), Prof Pericle Zanchetta (Electrical and Electronic Engineering)

One of the key actions to meet the targets of the 2020 climate and energy package [1] to reduce greenhouse emissions and improve the exploitation of renewable energy is the redefinition of the paradigm behind electrical power generation. The electrical system has been recently moving from a top-down structure with centralised production mainly based on coal and nuclear to a new concept of the Smart Grid, in which distributed generation, based on renewable sources such as photovoltaic (PV) and wind, is connected at different levels [2].

In this scenario, Power Electronics represents a key enabling technology, since power converters are essential to interface renewable sources with the AC grid. When looking at renewables from a system perspective, it is often assumed that power converters are functional building blocks with an established technology. In reality, a power converter is a complex entity, with several and often non-linear control algorithms. When several converters are connected to the same power network, complex interactions occur, that might lead to instability of the electrical system.

The aim of this project is to explore advanced mathematical modelling approaches that can be applied to predict instability and define actions to mitigate the risk of undesired behaviours of networks of power converters. Different techniques have been proposed in literature, but none of them with general validity. The ideal outcome of this project is the development of a generalised modelling and stability assessment framework. The method will be used to predict the impact on stability of a new renewable generator, as well as to assess the capability of a network to accommodate a new generator.

Theoretical findings will be validated in simulation and on laboratory-scale experiments representative of practical application scenarios.

[2] S. Bifaretti, P. Zanchetta, A. J. Watson, L. Tarisciotti, and J.C. Clare, “Advanced Power Electronic Conversion and Control System for Universal and Flexible Power Management,” IEEE Trans. On Smart Grid, vol. 2, no.2, pp. 231 - 243, 2011


Food projects

Modelling the physical and biological properties of soil

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

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.

Bacterial infections in food animals as a problem for food security

Supervisors: Professor Michael Tretyakov (Mathematical Sciences), Dr Michael Jones (Veterinary Medicine and Science)

Campylobacter jejuni is a major cause of food-borne infections, and consequently a problem for food security. This project will develop stochastic models for C. jejuni mutation and selection and the evolution of antibiotic resistance. A significant mathematical challenge will be to estimate model parameters using a relatively small amount of in vitro and in vivo data. The student will be trained in foundations of microbiology and genetics as well as becoming an expert in stochastic modelling of biological processes and associated modern statistical techniques.

Mathematical modelling of the effect of temperature stress on crop fertility

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

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.

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

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

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.


Water projects

Multi-scale modelling of flow through heterogeneous geo-materials

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

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.


Society projects

The following project link specific resources to their societal context, and hence also appear in the resource sections above.

Engaging school teachers and learners in the mathematics of sustainability

Supervisors: Dr Ria Symonds (Mathematical Sciences), Dr Stephen Hibberd (Mathematical Sciences), Professor Andrew Noyes (Education)

In partnership with a small number of school mathematics departments, the student will design, develop and assess the effectiveness of curriculum materials that engage teachers and learners in the mathematics of sustainability [1]. The materials would support specific curricular goals (e.g. learning of algebra, proportional reasoning). The project will also investigate young people's understanding of sustainability and the effectiveness of the materials in enhancing this understanding and developing critical-mathematical literacy. 

[1] Maths Awareness Month, Sustainability Counts.  



 DatesEvent Further information

Wednesday 4 November 2015

Sir Clive Granger Building, University Park

 Leverhulme Launch Meeting

Read further about the Leverhulme Launch meeting

Friday 14 October 2016

Hockerton Housing Project

 Hockerton Housing Project - MASS visit Read about our experiences at the Hocketon Housing Project

Thursday 24 November 2016

B27, Energy Technology Building, Jubilee Campus

Maths challenges for a Sustainable Energy future -PhD Collaboration scoping workshop Registration for this event is now closed

Wednesday 7 December 2016

B07, Engineering and Science Learning Centre (ESLC), University Park

Modelling and Analytics for the Water-Energy-Food Nexus - PhD Collaboration scoping workshop Registration for this event is now closed
Leverhulme Trust logo

The Leverhulme Trust

The centre is funded through the Leverhulme Doctoral Scholarships scheme by the Leverhulme Trust

a philanthropic organisation established by William Hesketh Lever, the founder of Lever Brothers, in 1925. MASS is one of 14 such centres funded around the UK.

Contact Us

For general enquiries about the MASS programme, please contact the admissions team.

School of Mathematical Sciences

The University of Nottingham
University Park
Nottingham, NG7 2RD

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