Mathematical Sciences


Mathematical modelling

Members of the group apply a variety of techniques from Applied Mathematics to diverse problems in Medicine, Biology, Fluid Dynamics, Materials and Soft Matter Science. The biological systems studied range from intracellular processes to those at the scale of organisms and populations. The fluid flows studied range from environmental buoyancy-driven flows to technologically important micro- and nanofluidic flows. The modelling of materials involves the use of mathematical and computational techniques to solve a wide and varied class of problems; this includes nanoscale devices where the fate of individual atoms is important. It spans length scales and time scales that vary over many orders of magnitude and involves the solution of equations that range from continuum to quantum mechanical descriptions.

Academic staff within this group are:

  • Professor Andrew Archer: Soft condensed matter, with particular interests in the behavior of (colloidal) fluids at interfaces, the statistical mechanics of solvation, in developing and applying dynamical density functional theories and in investigating novel freezing, clustering and pattern forming behavior in model fluids.
  • Dr Marco Discacciati: Mathematical analysis and numerical approximation of partial differential equations, domain decomposition methods especially for heterogeneous (multi-physics) problem, finite elements method, computational fluid mechanics, simulation of filtration processes through porous media
  • Dr Natalia Janson: Nonlinear dynamics, synchronization, noise-induced phenomena in nonlinear systems (including neural models) and their control, systems with time delay, nonlinear time series analysis, applications to the cardiovascular system.
  • Dr Anthony Kay: Theoretical analyses of buoyancy-driven flows, particularly in fresh water near its temperature of maximum density; these flows include thermal bars, plumes and gravity currents. Asymptotic and perturbation methods are used extensively to solve the governing equations, supported by numerical solutions and by laboratory experiments done by collaborators.
  • Dr David Sibley: Multiscale and multiphase flow, dynamics of contact lines, interfacial phenomena, matched asymptotic methods.
  • Professor Roger Smith: Materials modelling, particularly of semi-conductor processing and nanotechnology. Biofilm growth; Continuum and cellular models of surface propagation; Particle ejection from ion-bombarded surfaces; Diamond growth and two-phonon absorption; Molecular dynamics simulations of metals, polymers and covalent materials; Nanoindentation and nanofriction; Cluster applications in nanotechnology.
  • Dr Dmitri Tseluiko: Analytical and computational studies of liquid-film flows, including analysis of mathematical problem arising in interfacial electrohydrodynamics, thin-film flows over topographical substrates, nonlinear waves and low-dimensional complexity and self-organisation in interfacial flows, viscous dispersion effects on bound-state formation in falling liquid films, two-phase flows with one phase laminar and another one turbulent.
  • Dr John Ward: Mathematical biology and medicine: bacterial physiology (particularly biofilms and quorum sensing); tumour growth and drug transport; wound infections and healing; immunological responses to irritants; invasive spread of Japanese Knotweed.

Research Associates:

Research students: