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CARMA Research Group

Mathematical Modelling and Industrial Applications

About us

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.


  • Mathematics in Industry Public Lecture

    5:00 pm, Friday, 31st Jan 2020
    Newcastle City Hall (Newcastle, NSW)

    A special public event in conjunction with the Mathematics in Industry Workshop. Please register for free to attend this public lecture. Please arrive by 5:00 pm for 5:30 pm. PLEASE NOTE NEW VENUE: Hunter Room, Newcastle City Hall (290 King Street, Newcastle).

    "Mathematics in Industry: Optimisation in Action - Unlocking Value in the Mining, Energy, and Agriculture Industries"
       Prof. Ryan Loxton
    Optimisation is a branch of applied mathematics that focuses on using mathematical techniques to optimise complex systems. Real-world optimisation problems are typically enormous in scale, with hundreds of thousands of inter-related variables and constraints, multiple conflicting objectives, and numerous candidate solutions that can easily exceed the total number of atoms in the solar system, overwhelming even the fastest supercomputers. Mathematical optimisation has numerous applications in business and industry, but there is a big mismatch between the optimisation problems studied in academia (which tend to be highly structured problems) and those encountered in practice (which are non-standard, highly unstructured problems). This lecture gives a non-technical overview of the presenter's recent experiences in building optimisation models and practical algorithms in the oil and gas, mining, and agriculture sectors. Some of this practical work has led to academic journal articles, showing that the gap between industry and academia can be overcome.