Applied and Industrial Mathematics

The Applied and Industrial Mathematics research group employs a vast range of mathematical and statistical techniques, supplemented with the application of extensive modern computing methods, to investigate a diverse range of fundamental and real world problems.

The interdisciplinary nature of the work and the constraints imposed by dealing with genuine practical problems make this a challenging and rewarding area for research.

The quality and impact of the research undertaken is recognised by the group’s success in obtaining competitive grants and in its extensive publications that appear in important international journals. The group is also successful in attracting and graduating high quality HDR students.  The group regularly collaborates with national and international researchers which enhances the group’s world-wide reputation.

Specific strengths of the Group lie in the following three areas with significant overlap among them:

1. Bushfire Dynamics and Combustion Modelling (Jason Sharples, Harvi Sidhu, Isaac Towers, Zlatko Jovanoski, Leesa Sidhu, Ben O’Neill);

      • To better understand the dynamics and impact of large bushfires driven by extreme fire weather.
      • To better understand the complex behaviour of flame fronts, particularly at the onset of instabilities.

2. Ecological Modelling (Leesa Sidhu, Ben O’Neill, Zlatko Jovanoski, Isaac Towers, Harvi Sidhu)

      • Statistical: Modelling the survival of Little Penguins – impact of climate change and banding; Tag recovery studies of Southern Bluefin Tuna.
      • Deterministic and Stochastic: Developed and analysed models for stressed ecosystems and environments with nutrient enrichment/depletion.

3. Nonlinear Dynamics (Tristram Alexander, Harvi Sidhu, Zlatko Jovanoski, Isaac Towers);

      • Nonlinear Optics – Investigate optical effects in nonlinear materials
      • Nonlinear excitations in Bose-Einstein condensates (BECs) – manipulate and control of BECs for possible applications, such as metrology.
      • Chemical and Bio-reactor Engineering – Determine efficient operating conditions for reactors using nonlinear dynamical systems theory.
      • Emergent phenomena – Control of chaotic systems through the use of increased dimensionality; energy transport and localisation in systems with many nonlinearly coupled degrees of freedom.