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 Tapio Ala-Nissilä: Theoretical and Computational Physics: Polymers, Colloids, Nanostructures, Functional Nanomaterials, Polymer Translocation, Diffusion, Surface and Interface Physics, Chemical Reactions, Fluctuation Relations, Quantum and Classical Thermodynamics, Open Quantum Systems, Electromagnetic Radiation.
  • 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 of elliptic and parabolic partial differential equations and their numerical approximation; domain decomposition methods; finite elements; preconditioning.
  • 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 Achilleas Lazarides: Out-of-equilibrium dynamics in open and closed quantummany-body systems: non-equilibrium phases, numerical and analytical techniques, disorder; universal features of non-equilibrium systems.
  • Dr Marco Mazza: Theoretical and computation soft matter physics in nonequilibrium, with particular interest in (i) active matter --such as bacterial motility modes, biofilms, and planktonic dynamics; (ii) dynamics of granular matter --such as driven systems, and granular gases; and (iii) liquid crystal flow and the interactions of topological defects, self-assembly in confinement, and dynamics.
  • Dr Tyler Shendruk: Numerical simulations of biophysics and flowing soft condensed matter; developing coarse-grained algorithms; biopolymer dynamics; active matter and complex fluids; microbe motility; cytoplasmic streaming
  • Dr David Sibley: Multiscale and multiphase flow, dynamics of contact lines, interfacial phenomena, matched asymptotic methods.
  • Professor Roger Smith: Materials modelling, bridging length and time scales and especially the use and development of long time scale dynamics to investigate atomistic growth at surfaces and radiation damage on the atomic scale.
  • Dr Gyula Toth: Mean-field theories of the crystal-liquid phase transition, continuum models of crystal nucleation, nucleation precursors and amorphous solids, hydrodynamics of solids, pattern formation in multicomponent complex liquids, deriving continuum theories from classical microscopic models, developing and implementing advanced numerical techniques for massively parallel HPC devices.
  • 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:

  • Shaho Abdalla: Classical density functional theory for amorphous solids
  • Amal Al-Harbi: Radiation studies of borosilicate glass
  • Mounirah Areshi: Modelling spreading/dewetting and evaporation of liquids and the interplay of diffusion and advection
  • Jonas Dieterich: Modelling foam electrokinetic separation and liquids on surfaces
  • Iain Brown
  • Peter Hatton:
  • Louise Holford: Modelling evaporation, condensation and pattern formation of liquids on surfaces
  • Juliet Ojiako:
  • Antonios Parasyris: Modelling filtration
  • Morgan Tudball: Electrohydrodynamics, thin films, the modelling of fluid flow over inclined topography
  • Hanyu Yin: Dynamics of dropplet spreading and bubble formation.