CARMA Research Group
Mathematical Modelling and Industrial Applications
Leader: Mike Meylan
The mathematical modelling and industrial applications group works on the application of mathematics to solving real-world problems. We have particular expertise in the implementation of differential equations to modelling complex problems in fluid dynamics and other processes. Our research can be broadly grouped into the following areas.
1) Mathematical Modelling. We have wide-ranging experience in modelling including extensive applications in fluid flows, wave scattering, material science, and biological processes including interactions between cells and swarming of insects.
2) Nanostructures and their applications in nanotechnology, includeing modelling electrorheologicalfluids, the mechanics of carbon nanostructures, nanomaterials used in biology and medicine and protein and other polymer chain structures using the calculus of variations.
3) Electromaterials in energy applications such as solar cells, energy storage and carbon capture.
4) Finite element methods and numerical solution of complex equations, including Mixed and Hybrid Finite Element Methods, Domain Decomposition Methods, Non-conforming Discretization Techniques, Nearly Incompressible Elasticity, Approximation Theory, Subset Selection & Variational Methods in Image Processing. The group also specialises in computaional techniques such as Dissipative Particle Dynamics (DPD), Molecular Dynamics (MD) and Smoothed Particle Hydrodynamics (SPH) which are used to model a complex system involving micro and nano materials.
Our group also focuses on working with industry to develop mathematical models to solve real industrial-based problems. The major upcoming event for our group is the Mathematics in Industry Study Group (MISG) for 2020-2022.