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.
Journal Article: Chord-length distributions cannot generally be obtained from small-angle scattering
Gommes, Cedric J., Jiao, Yang, Roberts, Anthony P. and Jeulin, Dominique (2020) Chord-length distributions cannot generally be obtained from small-angle scattering. Journal of Applied Crystallography, 53 1: 127-132. doi:10.1107/S1600576719016133
Journal Article: An optimised family of anisotropic microstructures with application to functionally graded materials
Challis, V.J., Cramer, A.D. and Roberts, A.P. (2019) An optimised family of anisotropic microstructures with application to functionally graded materials. International Journal of Solids and Structures, 171 17-29. doi:10.1016/j.ijsolstr.2019.05.009
Journal Article: Dynamic visualization of line integrals of vector fields: a didactic proposal
Ponce Campuzano, J. C., Roberts, A. P., Matthews, K. E., Wegener, M. J., Kenny, E. P. and McIntyre, T. J. (2018) Dynamic visualization of line integrals of vector fields: a didactic proposal. International Journal of Mathematical Education in Science and Technology, 1-16. doi:10.1080/0020739x.2018.1510554
(2017–2019) University of Western Australia
(2011–2019) University of Western Australia
(2011–2012) UWA-UQ Bilateral Research Collaboration Award
Microstructure Interpolation for Macroscopic Optimisation
(2017) Doctor Philosophy
Continuum diffusion on networks
(2010) Doctor Philosophy
Multi-property topology optimisation with the level-set method
(2009) Doctor Philosophy
Topology Optimisation
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).
Structure-Property Relationships in Complex Materials
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
modelling x-ray scattering from Kratky line sources is available, and will tie
in with new experiments being undertaken at the University of Queensland.
elasticity and fluid transport. A specific project in modelling properties
and degradation of ceramic fuel cells is available.
Modeling structure-property relationships in random cellular materials
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.
Chord-length distributions cannot generally be obtained from small-angle scattering
Gommes, Cedric J., Jiao, Yang, Roberts, Anthony P. and Jeulin, Dominique (2020) Chord-length distributions cannot generally be obtained from small-angle scattering. Journal of Applied Crystallography, 53 1: 127-132. doi:10.1107/S1600576719016133
An optimised family of anisotropic microstructures with application to functionally graded materials
Challis, V.J., Cramer, A.D. and Roberts, A.P. (2019) An optimised family of anisotropic microstructures with application to functionally graded materials. International Journal of Solids and Structures, 171 17-29. doi:10.1016/j.ijsolstr.2019.05.009
Dynamic visualization of line integrals of vector fields: a didactic proposal
Ponce Campuzano, J. C., Roberts, A. P., Matthews, K. E., Wegener, M. J., Kenny, E. P. and McIntyre, T. J. (2018) Dynamic visualization of line integrals of vector fields: a didactic proposal. International Journal of Mathematical Education in Science and Technology, 1-16. doi:10.1080/0020739x.2018.1510554
Stochastic analysis of capillary condensation in disordered mesopores
Gommes, Cedric J. and Roberts, Anthony P. (2018) Stochastic analysis of capillary condensation in disordered mesopores. Physical Chemistry Chemical Physics, 20 19: 13646-13659. doi:10.1039/c8cp01628c
Physically realizable three-dimensional bone prosthesis design with interpolated microstructures
Cramer, Andrew D. , Challis, Vivien J. and Roberts, Anthony P. (2017) Physically realizable three-dimensional bone prosthesis design with interpolated microstructures. Journal of Biomechanical Engineering, 139 3: 031013. doi:10.1115/1.4035481
Coburn, Luke, Lopez, Hender, Caldwell, Benjamin J., Moussa, Elliott, Yap, Chloe, Priya, Rashmi, Noppe, Adrian, Roberts, Anthony P., Lobaskin, Vladimir, Yap, Alpha S., Neufeld, Zoltan and Gomez, Guillermo A. (2016) Contact inhibition of locomotion and mechanical cross-talk between cell-cell and cell-substrate adhesion determine the pattern of junctional tension in epithelial cell aggregates. Molecular Biology of the Cell, 27 22: 3436-3448. doi:10.1091/mbc.E16-04-0226
Microstructure interpolation for macroscopic design
Cramer, Andrew D., Challis, Vivien J. and Roberts, Anthony P. (2015) Microstructure interpolation for macroscopic design. Structural and Multidisciplinary Optimization, 53 3: 1-12. doi:10.1007/s00158-015-1344-7
Modelling wound closure in an epithelial cell sheet using the cellular Potts model
Noppe, Adrian R., Roberts, Anthony P., Yap, Alpha S., Gomez, Guillermo A. and Neufeld, Zoltan (2015) Modelling wound closure in an epithelial cell sheet using the cellular Potts model. Integrative Biology (United Kingdom), 7 10: 1253-1264. doi:10.1039/c5ib00053j
High specific strength and stiffness structures produced using selective laser melting
Challis, Vivien J., Xu, Xiaoxue, Zhang, Lai Chang, Roberts, Anthony P., Grotowski, Joseph F. and Sercombe, Timothy B. (2014) High specific strength and stiffness structures produced using selective laser melting. Materials & Design, 63 783-788. doi:10.1016/j.matdes.2014.05.064
High resolution topology optimization using graphics processing units (GPUs)
Challis, Vivien J., Roberts, Anthony P. and Grotowski, Joseph F. (2014) High resolution topology optimization using graphics processing units (GPUs). Structural and Multidisciplinary Optimization, 49 2: 315-325. doi:10.1007/s00158-013-0980-z
A mathematics support programme for first-year engineering students
Hillock, Poh Wah, Jennings, Michael, Roberts, Anthony and Scharaschkin, Victor (2013) A mathematics support programme for first-year engineering students. International Journal of Mathematical Education in Science and Technology, 44 7: 1030-1044. doi:10.1080/0020739X.2013.823251
Challis, Vivien J., Guest, James K., Grotowski, Joseph F. and Roberts, Anthony P. (2012) Computationally generated cross-property bounds for stiffness and fluid permeability using topology optimization. International Journal of Solids And Structures, 49 23-24: 3397-3408. doi:10.1016/j.ijsolstr.2012.07.019
Roberts, A. P., Grayson, G., Challis, V. J., Zhang, L. C., Grotowski, J. F., Schaffer, G. B. and Sercombe, T. B. (2011) Elastic moduli of sintered powders with application to components fabricated using selective laser melting. Acta Materialia, 59 13: 5257-5265. doi:10.1016/j.actamat.2011.05.002
Electrostatic approximation of source-to-target mean first-passage times on networks
Roberts, Anthony P. and Haynes, Christophe P. (2011) Electrostatic approximation of source-to-target mean first-passage times on networks. Physical Review E, 83 3: 031113. doi:10.1103/PhysRevE.83.031113
Diffusion on asymmetric fractal networks
Haynes, Christopher P. and Roberts, Anthony P. (2010) Diffusion on asymmetric fractal networks. Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), 82 6: 061121-1-061121-5. doi:10.1103/PhysRevE.82.061121
Challis, VJ, Roberts, AP, Grotowski, JF, Zhang, LC and Sercombe, TB (2010) Prototypes for bone implant scaffolds designed via topology optimization and manufactured by solid freeform fabrication. Advanced Engineering Materials, 12 11: 1106-1110. doi:10.1002/adem.201000154
Generalization of the fractal Einstein law relating conduction and diffusion on networks
Haynes, Christophe P. and Roberts, Anthony P. (2009) Generalization of the fractal Einstein law relating conduction and diffusion on networks. Physical Review Letters, 103 2: 020601-1-020601-4. doi:10.1103/PhysRevLett.103.020601
Continuum diffusion on networks: Trees with hyperbranched trunks and fractal branches
Haynes, C. P. and Roberts, A. P. (2009) Continuum diffusion on networks: Trees with hyperbranched trunks and fractal branches. Physical Review E, 79 3: 031111-1-031111-11. doi:10.1103/PhysRevE.79.031111
Global first-passage times of fractal lattices
Haynes, C. P. and Roberts, A. P. (2008) Global first-passage times of fractal lattices. Physical Review E, 78 4: 041111-1-041111-9. doi:10.1103/PhysRevE.78.041111
Fracture resistance via topology optimization
Challis, Vivien J., Roberts, Anthony P. and Wilkins, Andrew H. (2008) Fracture resistance via topology optimization. Structural and Multidisciplinary Optimization, 36 3: 263-271. doi:10.1007/s00158-007-0160-0
Structure development of resorcinol-formaldehyde gels: Microphase separation or colloid aggregation
Gommes, Cedric J. and Roberts, Anthony P. (2008) Structure development of resorcinol-formaldehyde gels: Microphase separation or colloid aggregation. Physical Review E, 77 4: 041409.1-041409.13. doi:10.1103/PhysRevE.77.041409
Design of three dimensional isotropic microstructures for maximized stiffness and conductivity
Challis, V. J., Roberts, A. P. and Wilkins, A. H. (2008) Design of three dimensional isotropic microstructures for maximized stiffness and conductivity. International Journal of Solids and Structures, 45 14-15: 4130-4146. doi:10.1016/j.ijsolstr.2008.02.025
Yield functions for porous materials with cubic symmetry using different definitions of yield
McElwain, D. L. S., Roberts, A. P. and Wilkins, A. H. (2006) Yield functions for porous materials with cubic symmetry using different definitions of yield. Advanced Engineering Materials, 8 9: 870-876. doi:10.1002/adem.200600075
Yield criterion of porous materials subjected to complex stress states
McElwain, D. L. S., Roberts, A. P. and Wilkins, A. H. (2006) Yield criterion of porous materials subjected to complex stress states. Acta Materialia, 54 8: 1995-2002. doi:10.1016/j.actamat.2005.12.028
The effect of the lipid layer on tear film behaviour
Jones, MB, McElwain, DLS, Fulford, GR, Collins, MJ and Roberts, AP (2006) The effect of the lipid layer on tear film behaviour. Bulletin of Mathematical Biology, 68 6: 1355-1381. doi:10.1007/s11538-006-9105-9
Dynamics of tear film deposition and draining
Jones, M. B., Please, C. P., McElwain, D. L. S., Fulford, G. R., Roberts, A. P. and Collins, M. J. (2005) Dynamics of tear film deposition and draining. Mathematical Medicine and Biology - a Journal of The Ima, 22 3: 265-288. doi:10.1093/imammb/dqi012
Roberts, AP and Garboczi, EJ (2002) Computation of the linear elastic properties of random porous materials with a wide variety of microstructure. Proceedings of The Royal Society of London Series A-mathematical Physical And Engineering Sciences, 458 2021: 1033-1054. doi:10.1098/rspa.2001.0900
Elastic Properties of Model Random Three-dimensional Open-cell Solids
Roberts, A. P. and Garboczi, E. J. (2002) Elastic Properties of Model Random Three-dimensional Open-cell Solids. Journal of The Mechanics And Physics of Solids, 50 1: 33-55. doi:10.1016/S0022-5096(01)00056-4
Roberts, AP, Henry, BM, Sutton, AP, Grovenor, CRM, Briggs, GAD, Miyamoto, T, Kano, A, Tsukahara, Y and Yanaka, M (2002) Gas permeation in silicon-oxide/polymer (SiOx/PET) barrier films: role of the oxide lattice, nano-defects and macro-defects. Journal of Membrane Science, 208 1-2: 75-88. doi:10.1016/S0376-7388(02)00178-3
How cracks in SiOx-coated polyester films affect gas permeation
Yanaka, M., Henry, B. M., Roberts, A. P., Grovenor, C. R., Briggs, G. A. D., Sutton, A. P., Miyamoto, T., Tsukahara, Y., Takeda, N. and Chater, R. J. (2001) How cracks in SiOx-coated polyester films affect gas permeation. Thin Solid Films, 397 1-2: 176-185. doi:10.1016/S0040-6090(01)01473-0
Elastic moduli of model random three-dimensional closed-cell cellular solids
Roberts, AP and Garboczi, EJ (2001) Elastic moduli of model random three-dimensional closed-cell cellular solids. Acta Materialia, 49 2: 189-197. doi:10.1016/S1359-6454(00)00314-1
Mechanical structure-property relationship of aerogels
Ma, Hang-Shing, Roberts, Anthony P., Prevost, Jean-H., Jullien, Rémi and Scherer, George W. (2000) Mechanical structure-property relationship of aerogels. Journal of Non-Crystalline Solids, 277 2-3: 127-141. doi:10.1016/S0022-3093(00)00288-X
Chronostratigraphy of the CRP-2/2A Drillcore, Ross Sea, Antarctica
Bohaty, S. M., Fielding, C. R., Florindo, F., Hannah, M., Harwood, D. M., McIntosh, W. C., Naish, T. R., Roberts, A. P., Sagnotti, R. P., Scherer, C. P., Strong, C. K. L., Verosub, K. L., Villa, G., Watkins, D. K., Webb, P., Wilson, G. S. and Woolfe, K. J. (2000) Chronostratigraphy of the CRP-2/2A Drillcore, Ross Sea, Antarctica. Terra Antartica. An Antarctic Earth Sciences Journal, 7 4: 647-657.
Elastic properties of model porous ceramics
Roberts, Anthony P. and Garboczi, Edward J. (2000) Elastic properties of model porous ceramics. Journal of the American Ceramic Society, 83 12: 3041-3048. doi:10.1111/j.1151-2916.2000.tb01680.x
A microstructural study of transparent metal oxide gas barrier films
Henry, B. M., Dinelli, F., Zhao, K. Y., Grovenor, C. R., Kolosov, O. V., Briggs, G. A., Roberts, A., Kumar, R. S. and Howson, R. P. (1999) A microstructural study of transparent metal oxide gas barrier films. Thin Solid Films, 355-356 500-505. doi:10.1016/S0040-6090(99)00461-7
Roberts, A. P. and Torquato, S. (1999) Chord-distribution functions of three-dimensional random media: Approximate first-pasage times of Gaussian processes. Physical Review E, 59 5: 4953-4963. doi:10.1103/PhysRevE.59.4953
Elastic properties of a tungsten-silver composite by reconstruction and computation
Roberts, A. P. and GarbocziEJ (1999) Elastic properties of a tungsten-silver composite by reconstruction and computation. Journal of the Mechanics and Physics of Solids, 47 10: 2029-2055. doi:10.1016/S0022-5096(99)00016-2
Morphology, continuity, and conductive properties of anisotropic polymer blends
Arns, C. H., Knackstedt, M. A., Roberts, A. P. and Pinczewski, V. W. (1999) Morphology, continuity, and conductive properties of anisotropic polymer blends. Macromolecules, 32 18: 5964-5966. doi:10.1021/ma981476u
Cross-property correlations for disordered materials
Roberts, Anthony P. and Knackstedt, Mark A. (1997) Cross-property correlations for disordered materials. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 130 377-385. doi:10.1016/S0927-7757(97)00054-X
Statistical reconstruction of three-dimensional porous media from two-dimensional images
Roberts, Anthony P. (1997) Statistical reconstruction of three-dimensional porous media from two-dimensional images. Physical Review E, 56 3: 3203-3212. doi:10.1103/PhysRevE.56.3203
Morphology and thermal conductivity of model organic aerogels
Roberts, Anthony P. (1997) Morphology and thermal conductivity of model organic aerogels. Physical Review E, 55 2: R1286-R1289. doi:10.1103/PhysRevE.55.R1286
Transport and elastic properties of fractal media
Roberts, Anthony P. and Knackstedt, Mark A. (1996) Transport and elastic properties of fractal media. Physica A: Statistical Mechanics and its Applications, 233 3-4: 848-858. doi:10.1016/S0378-4371(96)00198-7
Structure-property correlations in model composite materials
Roberts, Anthony and Knackstedt, Mark (1996) Structure-property correlations in model composite materials. Physical Review E, 54 3: 2313-2328. doi:10.1103/PhysRevE.54.2313
Morphology and macroscopic properties of conducting polymer blends
Knackstedt, Mark A. and Roberts, A. P. (1996) Morphology and macroscopic properties of conducting polymer blends. Macromolecules, 29 4: 1369-1371. doi:10.1021/ma951295h
Mechanical and transport properties of model foamed solids
Roberts, A. P. and Knackstadt, M. A. (1995) Mechanical and transport properties of model foamed solids. Journal of Materials Science Letters, 14 19: 1357-1359. doi:10.1007/BF00270727
Roberts, A. P. and Teubner, Max (1995) Transport properties of heterogeneous materials derived from Gaussian random fields: bounds and simulation. Physical Review E, 51 5: 4141-4154. doi:10.1103/PhysRevE.51.4141
Comparative study of large-scale Laplacian growth patterns
Batchelor, M. T., Henry, B. I. and Roberts, A. P. (1995) Comparative study of large-scale Laplacian growth patterns. Physical Review E, 51 1: 807-810. doi:10.1103/PhysRevE.51.807
Comment on ‘Hitting probabilities of diffusion-limited-aggregation clusters’
Roberts, A. P. and Knackstedt, M. A. (1993) Comment on ‘Hitting probabilities of diffusion-limited-aggregation clusters’. Physical Review E, 48 5: 4143-4144. doi:10.1103/PhysRevE.48.4143
Growth in non-Laplacian fields
Roberts, A. P. and Knackstedt, M. A. (1993) Growth in non-Laplacian fields. Physical Review E, 47 4: 2724-2728. doi:10.1103/PhysRevE.47.2724
Using interactive simulations to enhance student engagement in mathematics and physics
Wegener, Margaret J., Kenny, Elise , Ponce Campuzano, Juan , Roberts, Anthony P., Matthews, Kelly and McIntyre, Timothy J. (2017). Using interactive simulations to enhance student engagement in mathematics and physics. In: Australian Conference on Science and Mathematics Education, Melbourne, Australia, (). 27-28 September 2017.
Active learning using interactive simulations
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.
Dynamic, interactive simulations for enhancing student learning
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.
Isotropic, stiff, conducting structures via Topology optimisation
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.
Optimal bone implants and cermets
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.
Elastic properties of model 3-D porous ceramics and foams
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.
Elastic properties of porous materials
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.
Mathematical characterisation of porous materials
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.
(2017–2019) University of Western Australia
(2011–2019) University of Western Australia
(2011–2012) UWA-UQ Bilateral Research Collaboration Award
New-generation parallel-computing cluster for the mathematical and physical sciences
(2011) UQ Major Equipment and Infrastructure
(2008–2010) University of Western Australia
Elastic Properties of Complex Porous Materials.
(2000) ARC Australian Research Council (Small grants)
(1999–2002) ARC Australian Postdoctoral Research Fellowship
"Using systems of partial differential equations to understand changes in tuna fisheries in response to climate change"
Master Philosophy — Associate Advisor
Other advisors:
Using size spectrum models to understand fisheries productivity in the ocean now and in the future
Doctor Philosophy — Associate Advisor
Other advisors:
Microstructure Interpolation for Macroscopic Optimisation
(2017) Doctor Philosophy — Principal Advisor
Continuum diffusion on networks
(2010) Doctor Philosophy — Principal Advisor
Multi-property topology optimisation with the level-set method
(2009) Doctor Philosophy — Principal Advisor
Simulating the collective behaviour of a monolayer of epithelial cells using a cellular Potts model
(2019) Doctor Philosophy — Associate Advisor
Other advisors:
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.
Topology Optimisation
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).
Structure-Property Relationships in Complex Materials
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
modelling x-ray scattering from Kratky line sources is available, and will tie
in with new experiments being undertaken at the University of Queensland.
elasticity and fluid transport. A specific project in modelling properties
and degradation of ceramic fuel cells is available.