Associate Professor Tony Roberts

Associate Professor

Mathematics
Faculty of Science
apr@maths.uq.edu.au
+61 7 336 53263

Overview

Mathematical Materials Science

Dr Roberts did an Honours degree in Science (Mathematics) at the University of Queensland (1991), and undertook his doctoral studies at the Australian National University (PhD, 1996). From 1997-2002 he was a post-doctoral fellow at Oxford, a Fulbright fellow at Princeton University and the National Institute of Standards and Technology (USA), and an Australian Research Council postdoctoral fellow at UQ. He was a lecturer at the Queensland University of Technology (2003-2004), before taking up a senior lecturing position in the Mathematics department at UQ.

Research Interests

  • Mathematical Materials Science
    Dr Roberts' research is focused on role that the micro-structure plays in determining the interesting and important properties of natural and manufactured materials. His research fields in applied mathematics include probability theory, contiuum mechanics, electrostatic and diffusive transport, and topology optimization. He has studied the properties of a wide range of materials including; binary alloys, polymers, aerogels, porous ceramics, network models, aggregates, gas barrier films and fractals. Recently he has been studying the design of optimal bone implants and diffusion on networks.

Qualifications

  • Doctor of Philosophy, Australian National University

Publications

View all Publications

Supervision

View all Supervision

Available Projects

  • We are currently working in an exciting new area of mathematics called Topology optimisation. Our aim is to develop the tools to optimize the shape and topology of porous and composite materials to perform specific tasks. In particular we have a current ARC Discovery grant that will provide funding for APA top-ups and research costs for projects relating to optimal design of bone implants. Specific projects involve research in a range of fields from applied mathematics, as well as computational science. There is also scope for projects with an emphasis on pure mathematics (geometric evolution equations).

  • A number of projects are available in the area of predicting the macroscopic

    properties of materials from a knowledge of their microstructure.

    Depending on the background and interests of the student the projects

    can focus on

    1. applied probabilistic modelling of material structures using Gaussian random fields, Boolean processes and Voronoi tessellations. A specific project on

    modelling x-ray scattering from Kratky line sources is available, and will tie

    in with new experiments being undertaken at the University of Queensland.

    1. Large scale computation of material properties such as conductivity,

    elasticity and fluid transport. A specific project in modelling properties

    and degradation of ceramic fuel cells is available.

View all Available Projects

Publications

Book Chapter

  • Roberts, Anthony P. (2005). Modeling structure-property relationships in random cellular materials. In Michael Scheffler and Paolo Colombo (Ed.), Cellular ceramics: Structure, manufacturing, properties and applications (pp. 267-288) Weinheim, Germany; Chichester, U.K.: Wiley-VCH; John Wiley.

Journal Article

Conference Publication

  • McIntyre, T. J., Wegener, M. J., Roberts, A. P., Kenny, E. P., Ponce Campuzano, J. C. and Matthews, K. (2016). Active learning using interactive simulations. In: Joint Asia Pacific Physics Conference and Australian Institute of Physics Conference, Brisbane, Australia, (). 4-8 December 2016.

  • McIntyre, Timothy J., Roberts, Anthony P., Wegener, Margaret J., Juan Ponce Campuzano, Elise Kenny and Matthews, Kelly (2016). Dynamic, interactive simulations for enhancing student learning. In: Australian Conference on Science and Mathematics Education, Brisbane, QLD, Australia, (). 28-29 September 2016.

  • McCredden, Julie E., O'Brien, Katherine R. and Roberts, Tony P. (2013). Applied dimensional problems in mathematics courses: how small-scale partnerships across disciplines can improve mathematical problem-solving skills of engineering students. In: Charles Lemckert, Graham Jenkins and Susan Lang-Lemckert, Proceedings of the 24th Annual Conference of the Australasian Association for Engineering Education: AAEE2013 Proceedings. AAEE 2013: 24th Annual Conference of the Australasian Association for Engineering Education, Gold Coast, QLD, Australia, (1-24). 8-11 December, 2013.

  • Wilkins, A. H., Challis, V. J. and Roberts, A. P. (2007). Isotropic, stiff, conducting structures via Topology optimisation. In: Proceedings of the 7th World Congress on Structural and Multidisciplinary Optimization. 7th World Congress on Structural and Multidisciplinary Optimization, Seoul, Korea, (2236-2245). 21-25 May, 2007.

  • Challis, V. J., Roberts, A. P. and Wilkins, A. H. (2007). Optimal bone implants and cermets. In: Proceedings of the 7th World Congress on Structural and Multidisciplinary Optimization. 7th World Congress on Structural and Multidisciplinary Optimization, Seoul, Korea, (2609-2616). 21-25 May, 2007.

  • Roberts, Anthony and Garboczi, Edward (2000). Elastic properties of model 3-D porous ceramics and foams. In: Proceedings of the American Physical Society, March Meeting. American Physical Society, March Meeting, Minneapolis, Minnesota, U.S.A., (69-69). 20-24 March 2000.

  • Roberts, Anthony P. and Garboczi, Edward J. (2000). Elastic properties of porous materials. In: SIAM - Society for Industrial and Applied Mathematics, Proceedings of the Third SIAM Conference on Mathematical Aspects of Materials Science. Third SIAM Conference on Mathematical Aspects of Materials Science, Philadelphia, USA, (34-34). 22-24 May 2000.

  • Roberts, A. (2000). Mathematical characterisation of porous materials. In: Proceedings of the ANZIAM Meeting, Australian Mathematics Society. ANZIAM Meeting, Australian Mathematics Society, New Zealand, (). February 2000.

PhD and MPhil Supervision

Current Supervision

  • Doctor Philosophy — Principal Advisor

    Other advisors:

  • Doctor Philosophy — Associate Advisor

    Other advisors:

Completed Supervision

Possible Research Projects

Note for students: The possible research projects listed on this page may not be comprehensive or up to date. Always feel free to contact the staff for more information, and also with your own research ideas.

  • We are currently working in an exciting new area of mathematics called Topology optimisation. Our aim is to develop the tools to optimize the shape and topology of porous and composite materials to perform specific tasks. In particular we have a current ARC Discovery grant that will provide funding for APA top-ups and research costs for projects relating to optimal design of bone implants. Specific projects involve research in a range of fields from applied mathematics, as well as computational science. There is also scope for projects with an emphasis on pure mathematics (geometric evolution equations).

  • A number of projects are available in the area of predicting the macroscopic

    properties of materials from a knowledge of their microstructure.

    Depending on the background and interests of the student the projects

    can focus on

    1. applied probabilistic modelling of material structures using Gaussian random fields, Boolean processes and Voronoi tessellations. A specific project on

    modelling x-ray scattering from Kratky line sources is available, and will tie

    in with new experiments being undertaken at the University of Queensland.

    1. Large scale computation of material properties such as conductivity,

    elasticity and fluid transport. A specific project in modelling properties

    and degradation of ceramic fuel cells is available.