Using maths to understand the world
Research in mathematics contributes to advances in a wide range of disciplines. From understanding how cells divide to predicting extreme weather to the development of new financial tools, many of today’s challenges are being addressed using applied and industrial mathematics. Using mathematical models and techniques, applied mathematics is used for real-world problem-solving. It can help explain observed phenomena and predict new, unobserved phenomena that may occur in the future.
In almost all industries mathematics opens the way to virtual experiments, the analysis and simulation of multiple scenarios for a given phenomenon and control and optimisation. Applied mathematicians working alongside industry may develop or enhance mathematical methods to solve industrial problems. Using mathematical modelling and numerical analysis, possible solutions to these problems can be identified and tested for accuracy, validity, and reliability and interpreted in relation to the original real-world problem. By breaking down the problem into mathematical variables, organisations can optimise efficiencies, maximise profitability, improve safety outcomes and reduce uncertainty.
Associated schools, institutes & centres
Impact and successful applications
We employ a vast range of mathematical and statistical techniques and computational science to investigate a diverse range of fundamental and real-world problems. The interdisciplinary nature of our work and the constraints imposed by dealing with genuine practical problems make this a challenging and rewarding area for research.
Our strengths lie in:
- Combustion modelling:
- to better understand the complex behaviour of flame fronts, particularly at the onset of instabilities.
- to better understand the complex behaviour of flame fronts, particularly at the onset of instabilities.
- Ecological modelling:
- statistical: modelling the survival of Little Penguins noting the impact of climate change and banding and tag recovery studies of Southern Bluefin Tuna
- deterministic and stochastic: developed and analysed models for stressed ecosystems and environments with nutrient enrichment and depletion.
- Nonlinear dynamics
- chemical and bio-reactor engineering – determine efficient operating conditions for reactors using nonlinear dynamical systems theory
- complex warfighting – the development, simulation, and analysis of mathematical models of warfighting to provide insight into the organisational design best suited to optimise Command and Control and success in contested environments.
Competitive advantage
The quality and impact of our research is made possible by our success in obtaining competitive grants and attracting graduating HDR students. We regularly collaborate with national and international researchers who enhance our world-wide reputation. An extensive number of our publications appear in important international journals.
Research for complex warfighting is done in collaboration with the Defence Science and Technology Group (DST) of Australia and is linked to the DST STaR Shots (Science, Technology and Research Shots) strategy, specifically the agile Command and Control STaR shot.
Our researchers
-
- Ali Ebadi
- Sahar Masoudian
- Caleb Wilson
- William Swedosh
- Rongnan Yang
- Chiara Bellotti
- Tanvir Mahmud Saurav
- Ali Edalatinejad
- Shashi Chourasiya
- Jordan Pertile
- Daniel Johnston
- Nusrat Mehnaz
- Zakir Hossine
- Wenyuan Ma
- En Ci Nicol Leong
-
McRae, R.H.D., Sharples, J.J., Fromm, M. (2015). Linking local wildfire dynamics to pyroCb development. Natural Hazards and Earth System Sciences, 15(3), 417-428. DOI:10.5194/nhess-15-417-2015
Sharples, J.J., Cary, G.J., Fox-Hughes, P., Mooney, S., Evans, J.P., Fletcher, M.S., Fromm, M., Grierson, P.F., McRae, R.H.D., Baker, P. (2016). Natural hazards in Australia: extreme bushfire. Climatic Change, 139(1), 85-99. DOI:10.1007/s10584-016-1811-1
Sharples, J. J., McRae, R., & Wilkes, S. (2012). Wind-terrain effects on the propagation of wildfires in rugged terrain: fire channelling. International Journal of Wildland Fire, 21(3), 282-296.
T.A. McLennan-Smith, D.O. Roberts, H.S Sidhu, ‘Emergent behavior in an adversarial synchronization and swarming model’, Submitted to Physical Review E (2020)
T.A. McLennan-Smith, A.C. Kalloniatis, Z. Jovanoski, H.S. Sidhu, D.O. Roberts, S. Watt, I.N. Towers ‘A mathematical model of humanitarian aid agencies in attritional conflict environments', Submitted to Operations Research (2020)
Chambers MS; Sidhu LA; O'Neill B; Sibanda N, 2017, 'Evidence of separate subgroups of juvenile southern bluefin tuna', Ecology and Evolution, vol. 7, pp. 9818 - 9844, http://dx.doi.org/10.1002/ece3.3500
Quill R; Sharples JJ; Sidhu LA, 2020, 'A Statistical Approach to Understanding Canopy Winds over Complex Terrain', Environmental Modeling and Assessment, vol. 25, pp. 231 - 250, http://dx.doi.org/10.1007/s10666-019-09674-w
Huang Z; Sidhu HS; Towers IN; Jovanoski Z; Watt S; Gubernov VV, 2020, 'Properties of nonadiabatic combustion waves in competitive exothermic reactions', Applied Mathematical Modelling, vol. 77, pp. 1216 - 1228, http://dx.doi.org/10.1016/j.apm.2019.09.010
Sanni S; Jovanoski Z; Sidhu HS, 2020, 'An economic order quantity model with reverse logistics program', Operations Research Perspectives, vol. 7, http://dx.doi.org/10.1016/j.orp.2019.100133
Towers I; Gubernov V; Kolobov AV; Polezhaev AA; Sidhu HS, 2013, 'Bistability of flame propagation in a model with competing exothermic reactions', Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences, vol. 469, pp. 20130315-1 - 20130315-19, http://dx.doi.org/10.1098/rspa.2013.0315
Sutherland, D., Sharples, J.J. and Moinuddin, K.A., 2020. The effect of ignition protocol on grassfire development. International Journal of Wildland Fire, 29(1), pp.70-80.
-
- Effects of flipper bands and injected transponders on the survival of adult Little Penguins
- Living in stressed environments: using mathematics to understand ecosystems’ dynamics
- Computational mathematical analysis of dynamic fire propagation
- Humanitarian aid agencies in attritional conflict environments
-
- Caleb Wilson
- Rongnan Yang
- Tanvir Mahmud Saurav
- Nusrat Mehnaz
- Zakir Hossine
-
- Students undertaking a Bachelor of Science majoring in mathematics can undertake several courses related to Applied and Industrial Mathematics including:
- ZPEM 2311 Mathematical Modelling
- ZPEM2302 Mathematical Tools for Science
- ZPEM3306 Waves & Fluids
- ZPEM3311 Mathematical Methods for Differential Equations