Anthony Roberts

Anthony Roberts

School of Computer and Mathematical Sciences

Faculty of Sciences, Engineering and Technology

Eligible to supervise Masters and PhD (as Co-Supervisor) - email supervisor to discuss availability.

Areas of research interest include Modelling of complex multiscale dynamical systems, Stochastic differential equations, Centre manifold theory and applications, Free-surface hydrodynamics, Thin film flows, Turbulent floods, Multifractal geometry, Scientific computing, Computer algebra algorithms, and Multiscale modelling of emergent dynamics in complex systems.

A world leading achievement is my development of techniques, based on centre manifold theory, for the rational and complete low-dimensional modelling of complicated multiscale dynamical systems, for both deterministic and stochastic systems. These techniques, born out of the explosion of interest in dynamical systems in the last decades of the 20th century, apply to many physical problems and lead to many new insights—some of which enable us to correct and complete classic approximations. Further, the systematic basis of the techniques allows us to devise new models in ways unimagined before. This endeavour is recognised by the US Department of Energy as a priority area for research.

The significance of the research is that in multiscale systems we need to extract an appropriate summary of the microscale dynamics to form a closure of macroscale dynamics. This empowers us to simulate the emergent behaviour on the large scale with a much simpler model, one that only resolves the macroscale quantities of interest. The whole process of making simplifying approximations, so cen- tral to quantitative science, is vastly improved by my development of these new systematic and accurate techniques. Most physical situations of interest in the world around us have an enormous number of fine details which are of little concern in many situations. For example, the microscopic detail of molecular motion is almost completely irrelevant on our macroscopic scale; consequently we work with the much less informative, but nonetheless much more tractable, continuum approximation. Similarly, when engineers consider a beam they are not overly interested in the detailed distribution of elastic stresses, instead they are primarily concerned with how the beam simply bends in response to a given load—for this, beam theory was developed. In these, and many situations, the equations which scientists deal with are simplifications of the ‘true’ but intractable or overly-complicated equations that describe all the details. Traditionally these simple models of actual physical complexity emerge via specific heuristic arguments which are very limited in scope. The trick has always been to argue cogently that neglected effects are indeed small and to be careful not to ‘throw out the baby with the bath-water’; the ‘baby’ being the important dynamics of interest on the large scale, while the ‘bathwater’ is the uninteresting microscopic fine detail. It is this process of creating simple macroscale approximations for otherwise intractable complex multiscale dynamical systems which my research has addressed

  • DP180100050 A three year Discovery Project Multiscale modelling of systems with complex microscale detail: Mathematical analysis supports systematic and efficient macroscale mod- elling and simulation with Dr. J. Bunder and Prof I.G. Kevrekidis: 2018–20, $327,234.

    DP150102385 A five year Discovery Project Complex Multi- scale Systems: Modeling, Analysis and Scientific Computation with Prof I.G. Kevrekidis: 2015–9, $530,700.

    DP120104260 A three year Discovery Project Accurate modelling of large multiscale dynamical systems for engineering and scientific simulation and analysis with Prof I.G. Kevrekidis: 2012–4, $330,000.

    LP110200799 A four year Linkage Grant, Novel technology for enhanced coal seam gas production utilising mechanisms of stimulated cleat permeability through graded particle injection with Prof Pavel Bedrikovetski, Prof Anthony J Roberts, A/Prof Andrei G Kotooussov, Prof Mark J Biggs, Prof Sheik S Rahman, Dr Yildiray Cinar, Dr Mark R Tin- gay, Dr Manouchehr Haghighi, A/Prof Phillip Pendleton, Dr John D Codrington, Mr Jose T Rodrigues, Mr Imran Abbasy: 2011–14, $360,000.

    LP100100613 A three year Linkage Grant, Development of innovative technologies for oil production based on the advanced theory of suspension flows in porous media with Prof Pavel Bedrikovetski, Prof Anthony J Roberts, Dr Andrei G Kotooussov, A/Prof Phillip Pendleton, Mr Keith S Boyle, Mr Jose T Rodrigues: 2010–12, $448,000.

    DP0988738 A three year ARC Discovery Project grant, Effective and accurate model dynamics, deterministic and stochas- tic, across multiple space and time scales with Dr Strunin: 2009–11, $315,000.

    DP0774311 A four year ARC Discovery Project grant, Mod- elling of multiscale systems in engineering and science sup- ports large-scale equation-free simulations and analysis with Prof. Kevrekidis: 2007–10, $390,000.

    DP0560040 A three year ARC Discovery Project grant, Systematically model the large-scale complexity of turbulent floods and thin film flows with Dr Strunin: 2005–7, $120,000.

    A00000399 A three year ARC Discovery Project grant,  Developing effective and complete low-dimensional modelling of fluid dynamics: 2000–2, $144,000.

    and more in previous decades.

All levels, all topics.

  • Past Higher Degree by Research Supervision (University of Adelaide)
    Date Role Research Topic Program Degree Type Student Load Student Name
    2018 - 2022 Principal Supervisor Accurate multiscale simulation of wave-like systems Doctor of Philosophy Doctorate Full Time Mr Divahar Jayaraman
    2013 - 2017 Principal Supervisor Developing Multiscale Methodologies for Computational Fluid Mechanics Doctor of Philosophy Doctorate Full Time Mr Hammad Mayoof M Alotaibi
    2013 - 2016 Co-Supervisor Analytical Modelling of Two-Phase Multi-Component Flow in Porous Media with Dissipative and Non-equilibrium Effects Doctor of Philosophy Doctorate Full Time Dr Sara Borazjani
    2012 - 2015 Principal Supervisor Multiscale Modelling of Continuum and Discrete Dynamics in Materials with Complicated Microstructure Doctor of Philosophy Doctorate Full Time Dr Chen Chen
    2011 - 2014 Principal Supervisor Modelling environmental turbulent fluids and multiscale modelling couples patches of wave-like system Doctor of Philosophy Doctorate Full Time Mr Meng Cao
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