Richard Graham

Professor of Applied Mathematics

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Prof Richard Graham,
School of Mathematical Sciences,
University of Nottingham,
NG7 2RD, UK.

Tel: (+44) (115) 951 3850
Fax: (+44) (115) 951 4951


Researcher ID: C-9196-2011
ORCID 0000-0002-5530-8120
Google Scholar Link
Researchgate Richard_Graham13
Github RichGraham


Areas of research

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Equations of state for Carbon Capture and Storage

Carbon capture and storage is a crucial technology in the international efforts to meet carbon dioxide emission targets. Capturing carbon dioxide from industrial sources can lead to a 90% reduction in emissions. However, no gas separation process is 100% efficient, and as a result the carbon dioxide generated contains a number of different impurities, depending on its source. These impurities can, depending on their composition and concentration, greatly influence the physical properties of the fluid compared to pure CO2. They have important design, safety and cost implications for the compression and transport of carbon dioxide and its storage location, for example geological sequestration. A descriptive sentence
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My research is designed to tackle one of the key technical challenges facing the development of commercially viable CO2 transport networks: modelling phase behaviour of impure carbon dioxide, under the conditions typically found in carbon capture from power stations, and in high-pressure (liquid phase) and low-pressure (gas phase) pipelines. Accurate modelling of the physical properties of CO2 mixtures is essential for the design and operation of compression and transport systems for CO2. I use a range of techniques, from empirical parametric and non-parameter methods, through to ab initio molecular simulation.

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Flow induced crystallization in polymer melts

Using theories of molecular motion to understand and predict the effect of flow on crystallisation of polymeric materials. I have been developing a series of computational models for anisotropic crystal nucleation and growth in polymer melts and the effect of flow on these processes. I am tackling this problem with a range of techniques, including analytic calculations, numerical solution of closed-form PDEs and kinetic Monte-Carlo simulations.

Machine learning for first-principles calculation of physical properties
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. Ongoing work involves extending the approach to more complicated molecules and testing its ability to predict macroscopic physical properties.Machine learning for first-principles calculation of physical properties. A descriptive sentence about the picture
Electrophoresis of DNA molecules

Developing models and Brownian dynamics simulation algorithms for the motion of DNA molecules under the influence of strong electric fields. Applying these models to understand and improve processes involved in separating and sequencing DNA molecules.

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Dynamics of entangled polymers

Developing quantitative models of polymer dynamics under flow. Using statistical mechanical theories of polymer motion I derive detailed fundamental models for concentrated fluids of branched and linear polymer undergoing rapid flows. In particular, I have constructed a family of coarse-grained models for linear polymers, which allows the level of detail and computation expense to be selected according to the desired application.

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Neutron scattering from polymers under strong flow

Neutron scattering provides a very detailed picture of the dynamics of a polymer chain under flow, and is a very good testing ground for polymer theories. I use molecular models to predict and interpret the results of small angle neutron scattering measurements from polymers subjected to flow and I have shown some successful quantitative predictions of neutron scattering measurements from polymer melts under rapid flows.


For a list of my publications, see my Researcher ID C-9196-2011, ORCID 0000-0002-5530-8120, Google Scholar pgEKg_4AAAAJ or Researchgate Richard_Graham13.


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Graham RS, Molecular and continuum modelling of polymer melt flows, Department of Applied Mathematics and School of Physics and Astronomy, University of Leeds (2002).
[Download: Pdf file (~5.5Mb), Zipped pdf (~1.6Mb), Postscript (~11Mb) , Zipped postscript (~1.8Mb)]

My thesis was awarded the the Vernon Harrison Annual Doctoral prize for “excellence, creativity and novelty in research” by the British Society of Rheology in 2003.