Mathematical Modelling of Structures, Solids and Fluids

Overview

The group's interests cover diverse problems in solid and fluid mechanics, rheology and meteorology. They include elasticity and related multiphysics problems; biomechanics; transmission problems in non-smooth domains; plasticity and viscoplasticity; flow behaviour of elastico-viscous liquids, including polymer solutions; the structure and dynamics of foams and related materials; linear analysis of complex fluids; optimal mass transfer problems and their applications; measure theory and convex analysis.  Our approaches include modelling, accurate mathematical analysis, numerical simulation and experiment.

Areas of Research

Gennady Mishuris and Adam Vellender's interests include singular fields, imperfect interfaces and thin interphases in composite materials, mathematical modelling of fracture in inhomogeneous media, dynamical problems in solids and structures, plastic and visco-plastic materials. Of particular interest are asymptotic analysis of the solutions near irregular points, crack and failure propagation, waves in complex media, justification of the dimensional reduction, contact problems in biomechanics, and new effects resulting from specific material behaviour in the presence of thin interfaces and defects.

Rob Douglas's main research interest is optimal mass transfer problems and their applications, proving rigorous results using measure theory and convex analysis (and its generalisations). Some of the problems are motivated by meteorology, such as finding more sophisticated ways of measuring weather forecast error, whilst others are concerned with properties of systems of pdes. He is also interested in linear analysis of complex fluids.

Dave Binding and Ken Walters are interested in the flow behaviour of elastico-viscous liquids such as polymer solutions. Analytical and numerical techniques are used to solve flow problems in an attempt to predict the important flow characteristics which are likely to be present in the behaviour of real liquids. The theoretical work is supported by a corresponding experimental programme within the Complex Fluids Laboratory.

Simon Cox and Tudur Davies are interested in modelling the structure and dynamics of foams and related materials, including rheology. They work with Edwin Flikkema on determining the geometric and topological structure of static foams. The research involves the solution of partial differential equations, numerical simulation of cellular structures in physics and biology and devising related experiments. Cox is also interested in potential flow applied to problems in wave-breaking, and works with Mishuris on mean curvature flows. Adil Mughal studies the effects of topology and geometry in condensed matter physics.  In particular, he is interested in packing problems, foams and the role played by conformal geometries in these systems.

The group has close links with the WIMCS clusters concerned with Computational Modelling and Mathematical Analysis and Modern Applications. This includes membership of the Computational Modelling cluster steering committee and organising workshops, e.g. on optimal mass transfer. Members of the research group also pursue research in collaboration with European partners, with FP7 and Horizon2020 funding