• Accurate families of multi-continuum micromorphic homogenisations in multi-d space-time via dynamical systems theory. A.~J. Roberts. Transactions of Mathematics and Its Applications, 9(tnaf001):1--72, August 2025.

  • Construct accurate multi-continuum micromorphic homogenisations in multi-d space-time with computer algebra. A.~J. Roberts. Technical report, [http://arxiv.org/abs/2407.03483v3], April 2025.

  • Efficient prediction of static and dynamical responses of functional graded beams using sparse multiscale patches. Thien Tran-Duc, J.~E. Bunder, and A.~J. Roberts. Computational Mechanics, pages 1--22, March 2025.

  • Accurate and efficient multiscale simulation of a heterogeneous elastic beam via computation on small sparse patches. A.~J. Roberts, Thien Tran-Duc, J.~E. Bunder, and I.~G. Kevrekidis. In Elliot Carr, Vivien Challis, Qianqian Yang, Tim Moroney, and Judith Bunder, editors, Proceedings of the 20th Biennial Computational Techniques and Applications Conference, CTAC-2022, volume 64 of ANZIAM J., pages C161--C177, April 2024.

  • Efficient computational homogenisation of {2D} beams of heterogeneous elasticity using the patch scheme. Thien Tran-Duc, J.E. Bunder, and A.~J. Roberts. International Journal of Solids and Structures, 292(112719):1--15, April 2024.

  • Staggered grids for multidimensional multiscale modelling. J. Divahar, A.~J. Roberts, Trent~W. Mattner, J.~E. Bunder, and Ioannis~G. Kevrekidis. Computers and Fluids, 271(106167):1--18, jan 2024.

  • Embed in ensemble to rigorously and accurately homogenise quasi-periodic multi-scale heterogeneous material. A.~J. Roberts. ANZIAM Journal, 66(1):1--34, 2024.

  • Two novel families of multiscale staggered patch schemes efficiently simulate large-scale, weakly damped, linear waves. J. Divahar, A.~J. Roberts, Trent~W. Mattner, J.~E. Bunder, and Ioannis~G. Kevrekidis. Computer Methods in Applied Mechanics and Engineering, 413(116133):1--21, August 2023.

  • Ngamta Thamwattana, Mike Meylan, and A.~J. Roberts, editors. Proceedings of the 2020 Mathematics in Industry Study Group, volume 62 of ANZIAM J., December 2022. http://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/17406 [2022-12-06].

  • Ngamta Thamwattana, Mike Meylan, and A.~J. Roberts, editors. Proceedings of the 2022 Mathematics in Industry Study Group, volume 64 of ANZIAM J., December 2022. http://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/17494 [2022-12-06].

  • High-order homogenisation by learning spatial discretisations of {PDEs} that provably preserve self-adjointness. J.~E. Bunder and A.~J. Roberts. Partial Differential Equations in Applied Mathematics, 6(100449):1--16, September 2022.

  • Backwards theory supports modelling via invariant manifolds for non-autonomous dynamical systems. A.~J. Roberts. Technical report, [http://arxiv.org/abs/1804.06998v5], May 2022.

  • Learning high-order spatial discretisations of pdes with symmetry-preserving iterative algorithms. J.~E. Bunder and A.~J. Roberts. Technical report, https://arxiv.org/abs/2204.06743, April 2022.

  • Adaptively detect and accurately resolve macro-scale shocks in an efficient {Equation}-{Free} multiscale simulation. John Maclean, J.~E. Bunder, I.~G. Kevrekidis, and A.~J. Roberts. SIAM Journal on Scientific Computing, 44(4):A2557--A2581, 2022.

  • A toolbox of equation-free functions in matlab/octave for efficient system level simulation. John Maclean, J.~E. Bunder, and A.~J. Roberts. Numerical Algorithms, 87:1729--1748, oct 2021.

  • Equation-free patch scheme for efficient computational homogenisation via self-adjoint coupling. J.~E. Bunder, I.~G. Kevrekidis, and A.~J. Roberts. Numerische Mathematik, 149(2):229--272, July 2021.

  • Large-scale simulation of shallow water waves with computation only on small staggered patches. J.E. Bunder, J. Divahar, Ioannis~G. Kevrekidis, Trent~W. Mattner, and A.J. Roberts. International Journal for Numerical Methods in Fluids, 93(4):953--977, apr 2021.

  • An equation free algorithm accurately simulates macroscale shocks arising from heterogeneous microscale systems. John Maclean, J.~E. Bunder, A.~J. Roberts, and I.~G. Kevrekidis. IEEE Journal on Multiscale and Multiphysics Computational Techniques, 6:8--15, February 2021.

  • Rigorous modelling of nonlocal interactions determines a macroscale advection-diffusion {PDE}. A.~J. Roberts. In David~R. Wood, Jan~de Gier, Cheryl~E. Praeger, and Terence Tao, editors, 2019-20 MATRIX Annals, MATRIX Book Series, pages 423--437. Springer International Publishing, February 2021.

  • Nonlinear emergent macroscale {PDEs}, with error bound, for nonlinear microscale systems. J.~E. Bunder and A.~J. Roberts. Springer Nature Applied Sciences, 3(703):1--28, 2021.

  • Linear Algebra for the 21st Century. A.~J. Roberts. Oxford University Press, oct 2020 Download (draft) article.

  • High-order homogenisation via holistic discretisation that preserves self-adjointness of pdes, learning?? A.J. Roberts and J.E. Bunder. Technical report, University of Adelaide, may 2020.

  • Linking machine learning with multiscale numerics: Data-driven discovery of homogenized equations. Hassan Arbabi, Judith~E. Bunder, Giovanni Samaey, Anthony~J. Roberts, and Ioannis~G. Kevrekidis. Journal of The Minerals, Metals & Materials Society, 72:4444--4457, 2020.

  • Snezhana~I. Abarzhi, Alexander Nepomnyashchy, Anthony~J. Roberts, and Joseph Klewicki, editors. 2019-20 MATRIX Annals: Conservation Laws, Interfaces and Mixing, 2020 Download (draft) article.

  • Lyapunov exponents of the {Kuramoto--Sivashinsky PDE}. Russell~A. Edson, J.~E. Bunder, Trent~W. Mattner, and A.~J. Roberts. ANZIAM Journal, 61(3):270--285, jul 2019.

  • Multiscale modelling of microscale heterogeneous systems: analysis supports systematic and efficient macroscale modelling and simulation. A.J. Roberts. Technical report, AMSI Winter School on Computational Modeling of Heterogeneous Media [https://arxiv.org/abs/1907.09685], jul 2019.

  • Multiscale modelling couples patches of two-layer thin fluid flow. Meng Cao and A.~J. Roberts. In Xiaopeng Chen, Yan Lv, and Wei Wang, editors, Stochastic PDEs and Modelling of Multiscale Complex System, volume 20 of Interdisciplinary Mathematical Sciences, chapter 7, pages 111--137. World Sci, jan 2019.

  • Normal forms and invariant manifolds for nonlinear, non-autonomous {PDEs}, viewed as {ODEs} in infinite dimensions. Peter Hochs and A.~J. Roberts. J. Differential Equations, 267(12):7263--7312, 2019.

  • Equation-free function toolbox for matlab/octave. A.~J. Roberts, John Maclean, and J.~E. Bunder. Technical report, [https://github.com/uoa1184615/EquationFreeGit], 2019--2025.

  • Error {Estimation} on {Projective} {Integration} of {Expensive} {Multiscale} {Stochastic} {Simulation}. Xiaopeng Chen and A.~J. Roberts. In Xiaopeng Chen, Yan Lv, and Wei Wang, editors, Stochastic {PDEs} and {Modelling} of {Multiscale} {Complex} {System}, volume 20 of Interdisciplinary {Mathematical} {Sciences}, chapter 11, pages 177--193. World Sci., December 2018.

  • Boundary conditions for macroscale waves in an elastic system with microscale heterogeneity. Chen Chen, A.~J. Roberts, and J.~E. Bunder. IMA Journal of Applied Mathematics, 83(3):1--33, jun 2018 Download (draft) article.

  • Couple microscale periodic patches to simulate macroscale emergent dynamics. Hammad Alotaibi, Barry Cox, and A.~J. Roberts. ANZIAM~J., 59(3):313--334, 2018.

  • Center manifolds for infinite dimensional random dynamical systems. Xiaopeng Chen, A.~J. Roberts, and Jinqiao Duan. Dynamical Systems (CDSS), 34(2):334--355, 2018.

  • Smooth subgrid fields underpin rigorous closure in spatial discretisation of reaction-advection-diffusion {PDE}s. G.~A. Jarrad and A.~J. Roberts. Applied Numerical Mathematics, 132:91--110, 2018.

  • Good coupling for the multiscale patch scheme on systems with microscale heterogeneity. J.~E. Bunder, A.~J. Roberts, and I.~G. Kevrekidis. J.~Computational Physics, 337:154--174, may 2017.

  • Resolution of subgrid microscale interactions enhances the discretisation of nonautonomous partial differential equations. J.~E. Bunder and A.~J. Roberts. Applied Mathematics and Computation, 304:164--179, 2017.

  • Slowly varying, macroscale models emerge from microscale dynamics over multiscale domains. A.~J. Roberts and J.~E. Bunder. IMA Journal of Applied Mathematics, 82:971--1012, 2017 Download (draft) article.

  • Dynamics of suspended rigid aggregating particles in flowing medium: theory, analysis and scientific computing. Sarthok Sircar and Anthony~J. Roberts. Technical report, [http://arxiv.org/abs/1610.02100], October 2016.

  • Splitting in systems of {PDE}s for two-phase multicomponent flow in porous media. Sara Borazjani, A.~J. Roberts, and Pavel Bedrikovetsky. Applied Mathematics Letters, 53:25--32, 2016 Download (draft) article.

  • Accuracy of patch dynamics with mesoscale temporal coupling for efficient massively parallel simulations. Judith Bunder, A.~J. Roberts, and Ioannis~G. Kevrekidis. SIAM Journal on Scientific Computing, 38(4):C335--C371, 2016.

  • Multiscale modelling couples patches of nonlinear wave-like simulations. Meng Cao and A.~J. Roberts. IMA J.~Applied Maths., 81(2):228--254, 2016.

  • Modelling suspended sediment in environmental turbulent fluids. Meng Cao and A.~J. Roberts. J.~Engrg. Maths, 98(1):187--204, 2016.

  • Troy Farrell and A.~J. Roberts, editors. Proceedings of the Mathematics and Statistics in Industry Study Group 2014, volume 56(E) of ANZIAM Journal, 2016.

  • Troy Farrell and A.~J. Roberts, editors. Proceedings of the Mathematics and Statistics in Industry Study Group 2015, volume 57(E) of ANZIAM Journal, 2016.

  • Ion mediated crosslink driven mucous swelling kinetics. Sarthok Sircar and A.~J. Roberts. J. Discrete and Continuous Dynamical System~B, 21(6):1937--1951, 2016.

  • Surface deformation and shear flow in ligand mediated cell adhesion. Sarthok Sircar and A.~J. Roberts. Journal of Mathematical Biology, pages 1--18, 2016.

  • Ligand mediated adhesive mechanics of two deformed spheres. Sarthok Sircar, Andrei Kotousov, Giang Nguyen, and A.~J. Roberts. European Physical Journal E, 39(95), 2016.

  • Graeme Wake and Anthony Roberts, editors. Proceedings of the Mathematics for Industry {NZ} Study Group 2015, volume 57(E) of ANZIAM Journal, 2016.

  • Macroscale boundary conditions for a non-linear heat exchanger. Chen Chen, A.~J. Roberts, and J.~E. Bunder. In Jason Sharples and Judith Bunder, editors, Proceedings of the 17th Biennial Computational Techniques and Applications Conference, CTAC-2014, volume 56 of ANZIAM J., pages C16--C31, September 2015.

  • Centre manifolds for stochastic evolution equations. Xiaopeng Chen, A.~J. Roberts, and Jinqiao Duan. Journal of Difference Equations and Applications, June 2015.

  • A.~J. Roberts. Effective multiscale computational modeling of spatio-temporal systems, May 2015. Video of talk at SIAM conference on Dynamical Systems Download (draft) article.

  • Numerical integration of ordinary differential equations with rapidly oscillatory factors. J.~E. Bunder and A.~J. Roberts. Journal of Computational and Applied Mathematics, 282:54--70, 2015 Download (draft) article.

  • Macroscale, slowly varying, models emerge from the microscale dynamics in long thin domains. A.~J. Roberts. IMA Journal of Applied Mathematics, 80(5):1492--1518, 2015.

  • Model emergent dynamics in complex systems. A.~J. Roberts. SIAM, Philadelphia, Jan 2015 Download (draft) article.

  • Diffusion approximation for self-similarity of stochastic advection in {B}urgers' equation. Wei Wang and A.~J. Roberts. Communications in Mathematical Physics, 333(3):1287--1316, 2015.

  • The macroscale boundary conditions for diffusion in a material with microscale varying diffusivities. Chen Chen, A.~J. Roberts, and J.~E. Bunder. In Mark Nelson, Tara Hamilton, Michael Jennings, and Judith Bunder, editors, Proceedings of the 11th Biennial Engineering Mathematics and Applications Conference, EMAC-2013, volume 55 of ANZIAM J., pages C218--C234, July 2014.

  • Troy Farrell and A.~J. Roberts, editors. Proceedings of the Mathematics in Industry Study Group 2013, volume 55(E) of ANZIAM Journal, 2014.

  • A dynamical systems approach to simulating macroscale spatial dynamics in multiple dimensions. A.~J. Roberts, Tony MacKenzie, and Judith Bunder. J.~Engineering Mathematics, 86(1):175--207, 2014.

  • Approximation of the random inertial manifold of singularly perturbed stochastic wave equations. Yan Lv, Wei Wang, and A.~J. Roberts. Stochastics and Dynamics, 14(2):1350018, 2014 Download (draft) article.

  • Large deviation principle for singularly perturbed stochastic damped wave equations. Yan Lv and A.~J. Roberts. Stochastic Analysis and Applications, 32(1):50--60, 2014. doi:10.1080/07362994.2013.838681
    .

  • Multiscale modelling couples patches of wave-like simulations. Meng Cao and A.~J. Roberts. In Scott McCue, Tim Moroney, Dann Mallet, and Judith Bunder, editors, Proceedings of the 16th Biennial Computational Techniques and Applications Conference, CTAC-2012, volume 54 of ANZIAM J., pages C153--C170, May 2013.

  • Simulating stochastic inertial manifolds by a backward-forward approach. Xingye Kan, Jinqiao Duan, Ioannis~G. Kevrekidis, and A.~J. Roberts. SIAM J.~Appl. Dyn. Systems, 12(1):487--514, 2013. http://arxiv.org/abs/1206.4954 Download (draft) article.

  • John Shephard, Andrew Stacey, and A.~J. Roberts, editors. Proceedings of the Mathematics in Industry Study Group 2012, volume 54(E) of ANZIAM Journal, 2013.

  • A survey of centre manifold and related theorems. A.J. Roberts. Technical report, University of Adelaide, 2013--9.

  • Macroscopic reduction for stochastic reaction-diffusion equations. Wei Wang and A.~J. Roberts. IMA Journal of Applied Mathematics, 78(6):1237--1264, 2013.

  • Self similarity and attraction in stochastic nonlinear reaction-diffusion systems. Wei Wang and A.~J. Roberts. SIAM J.~Applied Dynamical Systems, 12(1):450--486, 2013.

  • Modelling 3d turbulent floods based upon the smagorinski large eddy closure. Meng Cao and A.~J. Roberts. In P.~A. Brandner and B.~W. Pearce, editors, 18th Australasian Fluid Mechanics Conference, Dec 2012 .

  • Modify the improved euler scheme to integrate stochastic differential equations. A.~J. Roberts. Technical report, [http://arxiv.org/abs/1210.0933], Oct 2012.

  • Patch dynamics for macroscale modelling in one dimension. J.~E. Bunder and A.~J. Roberts. In Mark Nelson, Mary Coupland, Harvinder Sidhu, Tara Hamilton, and A.~J. Roberts, editors, Proceedings of the 10th Biennial Engineering Mathematics and Applications Conference, EMAC-2011, volume 53 of ANZIAM J., pages C280--C295, June 2012.

  • Construct invariant manifolds such as centre manifolds, spectral submanifolds, nonlinear normal modes, of ordinary, partial, or delay differential equations (autonomous or periodically forced). A.~J. Roberts. Technical report, https://tuck.adelaide.edu.au/gencm.html [November 10, 2025], 2012--2025.

  • Mark Nelson, Anthony~J. Roberts, Mary Coupland, Tara Hamilton, and Harvinder Sidhu, editors. Proceedings of the Engineering Mathematics and Applications Conference, volume 53 of ANZIAM Journal, 2012.

  • Slow manifold and averaging for slow-fast stochastic differential system. Wei Wang and A.~J. Roberts. Journal of Mathematical Analysis and Applications, 398:822--839, 2012. doi:10.1016/j.jmaa.2012.09.029
    Download (draft) article.

  • Average and deviation for slow-fast stochastic partial differential equations. Wei Wang and A.~J. Roberts. J. Differential Equations, 253:1265--1286, 2012.

  • Large deviations and approximations for slow-fast stochastic reaction-diffusion equations. Wei Wang, A.~J. Roberts, and Jinqiao Duan. J.~Differential Equations, 253(12):3501--3522, 2012.

  • Averaging approximation to singularly perturbed nonlinear stochastic wave equations. {Yan Lv} and A.~J. Roberts. J.~Math. Phys., 53(6):062702, 2012 Download (draft) article.

  • Projective integration of expensive multiscale stochastic simulation. Xiaopeng Chen, A.~J. Roberts, and Ioannis~G. Kevrekidis. In W. McLean and A.~J. Roberts, editors, Proceedings of the 15th Biennial Computational Techniques and Applications Conference, CTAC-2010, volume 52 of ANZIAM J., pages C661--C677, August 2011.

  • Averaging, homogenization and slow manifolds for stochastic partial differential equations. Jinqiao~Q. Duan, A.~J. Roberts, and Wei Wang. In Huaizhong Zhao and Aubrey Truman, editors, New Trends in Stochastic Analysis and Related Topics, volume 12 of Interdisciplinary Mathematical Sciences, chapter 3, pages 95--131. World Scientific, 2011.

  • Computer algebra derives the slow manifold of patch or element dynamics on lattices in two dimensions. Tony MacKenzie and A.~J. Roberts. Technical report, The University of Adelaide, http://arxiv.org/abs/1102.2037, 2011.

  • John~J. Shepherd, Andrew Stacey, and Anthony~J. Roberts, editors. Proceedings of the Mathematics in Industry Study Group 2011, volume 53(E) of ANZIAM~J., 2011.

  • Macroscopic discrete modelling of stochastic reaction-diffusion equations on a periodic domain. Wei Wang and A.~J. Roberts. Discrete and Continuous Dynamical System~A, 31(1):253--273, 2011.

  • On the approximation for singularly perturbed stochastic wave equations. Wei Wang, Yan Lv, and A.~J. Roberts. Technical report, http://arxiv.org/abs/1109.3000, 2011 Download (draft) article.

  • The harmonic mean renormalises random diffusion across a spatial multigrid. A.~J. Roberts. In P. Howlett, M. Nelson, and A.~J. Roberts, editors, Proceedings of the 9th Biennial Engineering Mathematics and Applications Conference, EMAC-2009, volume 51 of ANZIAM J., pages C83--C96, April 2010.

  • Resolve subgrid microscale interactions to discretise stochastic partial differential equations. A.~J. Roberts. preprint, January 2010.

  • Choose interelement coupling to preserve self-adjoint dynamics in multiscale modelling and computation. A.~J. Roberts. Applied Numerical Modelling, 60:949--973, 2010.

  • Computer algebra compares the stochastic superslow manifold of an averaged spde with that of the original slow-fast spde. A.~J. Roberts. Technical report, University of Adelaide, 2010.

  • Effectively model dynamics, deterministic and stochastic, across multiple space and time scales. A.~J. Roberts. In J.~G. Hartnett and P.~C. Abbott, editors, Frontiers of Fundamental and Computational Physics: 10th International Symposium, volume 1246, pages 75--87. AIP, 2010.

  • Andrew Metcalfe, Phil Howlett, Mark Nelson, and A.~J. Roberts, editors. Proceedings of the 9th Biennial Engineering Mathematics and Applications Conference, EMAC-2009, volume 51(E) of ANZIAM~J., 2010.

  • John~J. Shepherd, Andrew Stacey, and Anthony~J. Roberts, editors. Proceedings of the Mathematics in Industry Study Group 2010, volume 52(E) of ANZIAM~J., 2010.

  • William McLean and A.~J. Roberts, editors. Proceedings of 15th Computational Techniques and Applications Conference CTAC-2010, volume 52(E) of ANZIAM~J., 2010.

  • A.~J. Roberts. Stochastically forced, cubic reaction-diffusion equation, 2010 Download (draft) article.

  • Equation-free computation: an overview of patch dynamics. G. Samaey, A.~J. Roberts, and I.~G. Kevrekidis. In Jacob Fish, editor, Multiscale methods: bridging the scales in science and engineering, chapter 8, pages 216--246. Oxford University Press, 2010.

  • Modelling turbulent flow from dam break using slow manifolds. D.~J. Georgiev, A.~J. Roberts, and D.~V. Strunin. In Geoffry~N. Mercer and A.~J. Roberts, editors, Proceedings of the 14th Biennial Computational Techniques and Applications Conference, CTAC-2008, volume 50 of ANZIAM J., pages C1033--C1051, September 2009.

  • Low-dimensional boundary-layer model of turbulent dispersion in a channel. D.~V. Strunin and A.~J. Roberts. In S.~I. Ao, Len Gelman, David W.~L. Hukins, Andrew Hunter, and A.~M. Korsunsky, editors, Proc. of the World Congress on Engineering, International Conference of Applied and Engineering Mathematics ICAEM-2009, volume II of Lecture Notes in Engineering and Computer Science, pages 1230--1234, Imperial College London, UK, July 2009. Newswood Limited, International Association of Engineers.

  • Computer algebra derives the slow manifold of macroscale holistic discretisations in two dimensions. Tony MacKenzie and A.~J. Roberts. Technical report, The University of Adelaide, http://hdl.handle.net/2440/49292, 2009.

  • Holistic discretisation ensures fidelity to dynamics in two spatial dimensions. Tony MacKenzie and A.~J. Roberts. Technical report, http://arxiv.org/abs/0904.0855v1, 2009.

  • Model emergent dynamics in complex systems. A.~J. Roberts. Technical Report 2nd edition, http://tuck.adelaide.edu.au/modelling.php [November 10, 2025], 2009--2025.

  • Maximum likelihood multifractal analyser of point data. A.~J. Roberts. Technical report, http://www.maths.adelaide.edu.au/anthony.roberts/multifractal.html, January 2009 Download (draft) article.

  • Model dynamics across multiple length and time scales on a spatial multigrid. A.~J. Roberts. Multiscale Modeling and Simulation, 7(4):1525--1548, 2009 Download (draft) article.

  • Elementary calculus of financial mathematics. A.~J. Roberts, volume 15 of Mathematical Modeling and Computation. SIAM, Philadelphia, 2009. Appeared twice (two printings) in SIAM's top-25 best sellers for the year ending April, 2010. Download (draft) article.

  • Geoffry~N. Mercer and A.~J. Roberts, editors. Proceedings of 14th Computational Techniques and Applications Conference CTAC-2008, volume 50(E) of ANZIAM~J., 2009. http://journal.austms.org.au/ojs/index.php/ANZIAMJ/issue/view/37 Download (draft) article.

  • Derive invariant manifolds and/or normal forms of general stochastic or non-autonomous, multiscale, differential equations. A.~J. Roberts. Technical report, http://tuck.adelaide.edu.au/sdenf.php [November 10, 2025], 2009--2025.

  • A mathematical model for the iterative effects of tnf-alpha positive feedback mechanisms on inflammatory cascades in tlr-4 mediated signalling pathways. Bryan Essien, Michael Kotiw, Harry Butler, Dmitry Strunin, and A.J. Roberts. Technical report, University of Southern Queensland, 2009.

  • Average and deviation for the stochastic fitzhugh--nagumo system. W. Wang and A.~J. Roberts. In Geoffry~N. Mercer and A.~J. Roberts, editors, Proceedings of the 14th Biennial Computational Techniques and Applications Conference, CTAC-2008, volume 50 of ANZIAM J., pages C292--C307, November 2008.

  • The style files: Teach explicit skills with feedback. A.~J. Roberts. The Australian Mathematical Society Gazette, 35(3):156--157, July 2008. Unrefereed Download (draft) article.

  • The style files: Write to read breadth first, not depth first. A.~J. Roberts. The Australian Mathematical Society Gazette, 35(1):17--19, March 2008. Unrefereed Download (draft) article.

  • Normal form transforms separate slow and fast modes in stochastic dynamical systems. A.~J. Roberts. Physica~A, 387:12--38, 2008.

  • Co-ordinate transforms underpin multiscale modelling and reduction in deterministic and stochastic systems. A.~J. Roberts. In Derek Abbott, Tomaso Aste, Murray Batchelor, Robert Dewar, Tiziana~Di Matteo, and Tony Guttmann, editors, Complex Systems II: SPIE Symposium on Microelectronics, MEMS, and Nanotechnology, 5--7 December 2007 at The Australian National Univ, volume 6802, page 68021F, 2008.

  • Geoff Mercer and A.~J. Roberts, editors. Proceedings of the 8th Biennial Engineering Mathematics and Applications Conference, EMAC-2007, volume 49(E) of ANZIAM~J., 2008. http://journal.austms.org.au/ojs/index.php/ANZIAMJ/issue/view/13.

  • Computer algebra describes flow of turbulent floods via the {Smagorinski} large eddy closure. A.~J. Roberts. Technical report, http://eprints.usq.edu.au/4008/, 2008.

  • Model turbulent floods with the {Smagorinski} large eddy closure. A.~J. Roberts, D.~J. Georgiev, and D.~V. Strunin. Technical report, http://arxiv.org/abs/0805.3192, 2008.

  • Conserving self-adjoint rules for coupling in multiscale modelling. A.~J. Roberts. Technical report, University of Southern Queensland, 2008.

  • Computer algebra derives discretisations via self-adjoint multiscale modelling. A.~J. Roberts. Technical report, http://eprints.usq.edu.au/4275/, 2008 Download (draft) article.

  • A.~J. Roberts. Nash equilibria: strategies in the prisoner's dilemma, 2008. http://www.youtube.com/watch?v=5Ug2EVjdS4E Download (draft) article.

  • A.~J. Roberts. Nash equilibria: Nash's solution of the prisoner's dilemma, 2008. http://www.youtube.com/watch?v=J4n-Eg6UAw8 Download (draft) article.

  • Combined instructions and template for articles submitted to the anziam journal. A.~J. Roberts. ANZIAM~J. (Electronic supplement), 50, 2008.

  • Combined instructions and template for articles submitted to the {ANZIAM} {Journal}. Anthony~John Roberts. Technical report, ANZIAM Journal, 2008--2016.

  • The dynamics of the vertical structure of turbulence in flood flows. D.~J. Georgiev, A.~J. Roberts, and D.~V. Strunin. In Wayne Read, Jay~W. Larson, and A.~J. Roberts, editors, Proceedings of the 13th Biennial Computational Techniques and Applications Conference, CTAC-2006, volume 48, pages C573--C590, December 2007.

  • Computer algebra models dynamics on a multigrid across multiple length and time scales. A.~J. Roberts. Technical report, University of Southern Queensland, http://eprints.usq.edu.au/3373/, November 2007.

  • The style files: Use the most informative synonym. A.~J. Roberts. The Australian Mathematical Society Gazette, 34(4):208--209, September 2007. Unrefereed. Download (draft) article.

  • The style files: Write what you mean. A.~J. Roberts. The Australian Mathematical Society Gazette, 34(3):156--157, July 2007. Unrefereed. Download (draft) article.

  • Subgrid and interelement interactions affect discretisations of stochastically forced diffusion. A.~J. Roberts. In Wayne Read, Jay~W. Larson, and A.~J. Roberts, editors, Proceedings of the 13th Biennial Computational Techniques and Applications Conference, CTAC-2006, volume 48 of ANZIAM~J., pages C168--C187, June 2007.

  • The style files: Appearance affects communication; but not necessarily as you like. A.~J. Roberts. The Australian Mathematical Society Gazette, 34(2):78--80, May 2007. Unrefereed. Download (draft) article.

  • The style files: Omit redundant words. A.~J. Roberts. The Australian Mathematical Society Gazette, 34(1):20--21, March 2007. Unrefereed. Download (draft) article.

  • Computer algebra models the inertial dynamics of a thin film flow of power law fluids and other generalised newtonian fluids. A.~J. Roberts. Technical report, University of Southern Queensland, February 2007. http://eprints.usq.edu.au/archive/00002010/.

  • Nonlinear dynamics on centre manifolds describing turbulent floods: k-omega model. D.~J. Georgiev, A.~J. Roberts, and D.~V. Strunin. In Boris Belinskiy, Kunquan Lan, Xin Lu, Alain Miranville, and R. Shivaji, editors, Proceedings of the 6th AIMS International Conference ( Poitiers, France), pages 419--428, 2007 Download (draft) article.

  • Numerical methods for coupled nonlinear problems of dynamic thermoelasticity and shape memory alloys modeling. R. Melnik, D.~Roy Mahapatra, L. Wang, and A.~J. Roberts. In E. Onate, M. Papadrakis, and B. Schefler, editors, Computational Methods for Coupled Problems in Science and Engineering (Coupled Problems 2007), pages 461--464. CIMNE, Barcelona, 2007.

  • Resolve subgrid microscale interactions to discretise stochastic partial differential equations. A.~J. Roberts. Technical report, http://arxiv.org/abs/math.DS/0601702, January 2007.

  • General tooth boundary conditions for equation free modelling. A.~J. Roberts and I.~G. Kevrekidis. SIAM J.~Scientific Computing, 29(4):1495--1510, 2007.

  • Computer algebra derives normal forms of stochastic differential equations. A.~J. Roberts. Technical report, http://eprints.usq.edu.au/archive/00001873, 2007.

  • The inertial dynamics of thin film flow of non-newtonian fluids. A.~J. Roberts. Physics Letters~A, 372:1607--1611, 2007.

  • Wayne Read, Jay~W. Larson, and A.~J. Roberts, editors. Proceedings of 13th Computational Techniques and Applications Conference CTAC-2006, volume 48(E) of ANZIAM~J., 2007. http://journal.austms.org.au/ojs/index.php/ANZIAMJ/issue/view/9 Download (draft) article.

  • Fractal landscape method: an alternative approach to measuring area-restricted searching behavior. Yann Tremblay, A.~J. Roberts, and Daniel~P. Costa. Journal of Experimental Biology, 210:935--945, 2007 Download (draft) article.

  • A flexible error estimate for the application of centre manifold theory. Zhenquan Li and A.~J. Roberts. Global Journal of Pure and Applied Mathematics, 3(3):241--249, 2007 Download (draft) article.

  • Low-dimensional modelling of a generalized {Burgers'} equation. Zhenquan Li and A.~J. Roberts. Global Journal of Pure and Applied Mathematics, 3(3):203--218, 2007. http://arXiv.org/abs/math-ph/0307064 Download (draft) article.

  • The style files: Favour the present tense. A.~J. Roberts. The Australian Mathematical Society Gazette, 33(5):313--314, November 2006. Unrefereed. Download (draft) article.

  • The style files: Explicitly avoid false conditionals. A.~J. Roberts. The Australian Mathematical Society Gazette, 33(4):241--242, September 2006. Unrefereed. Download (draft) article.

  • The style files: Inform with titles, abstracts and introductions. A.~J. Roberts. The Australian Mathematical Society Gazette, 33(3):169--170, July 2006. Unrefereed. Download (draft) article.

  • The style files: Clarify this. A.~J. Roberts. The Australian Mathematical Society Gazette, 33(2):104--105, May 2006. Unrefereed. Download (draft) article.

  • An accurate and comprehensive model of thin fluid flows with inertia on curved substrates. A.~J. Roberts and Zhenquan Li. J.~Fluid Mech., 553:33--73, April 2006.

  • The style files: Prefer active writing to passive. A.~J. Roberts. The Australian Mathematical Society Gazette, 33(1):22--23, March 2006. Unrefereed. Download (draft) article.

  • Computation of short-crested deep-water waves. M. Ioualalen, M. Okamura, S. Cornier, C. Kharif, and A.~J. Roberts. J.~Waterway, Port, Coast and Ocean Engrg, 132(3):157--165, 2006.

  • Accurately model the {Kuramoto--Sivashinsky} dynamics with holistic discretisation. T. MacKenzie and A.~J. Roberts. SIAM J.~Applied Dynamical Systems, 5(3):365--402, 2006 Download (draft) article.

  • A normal form of thin fluid film equations solves the transient paradox. A.~J. Roberts. Physica~D, 223(1):69--81, 2006.

  • Resolving the multitude of microscale interactions accurately models stochastic partial differential equations. A.~J. Roberts. LMS J.~Computation and Maths, 9:193--221, 2006.

  • Computer algebra derives discretisations of the stochastically forced {Burgers'} partial differential equation. A.~J. Roberts. Technical report, [http://eprints.usq.edu.au/1322/], January 2006 Download (draft) article.

  • Andrew Stacey, Bill Blyth, John Shepherd, and A.~J. Roberts, editors. Proceedings of the 7th Biennial Engineering Mathematics and Applications Conference, EMAC-2005, volume 47(E) of ANZIAM~J., 2006.

  • Predicting the off-site deposition of spray drift from horticultural spraying through porous barriers on soil and plant surfaces. G.~N. Mercer and A.~J. Roberts. In Graeme Wake, editor, Proceedings of the 2005 Mathematics in Industry Study Group, pages 27--52. MISG, Centre for Mathematics in Industry, Massey University, December 2005.

  • Computer algebra resolves a multitude of microscale interactions to model stochastic partial differential equations. A.~J. Roberts. Technical report, [http://eprints.usq.edu.au/archive/00001242/], December 2005.

  • Higher order accuracy in the gap-tooth scheme for large-scale dynamics using microscopic simulators. A.~J. Roberts and I.~G. Kevrekidis. In Rob May and A.~J. Roberts, editors, Proc. of 12th Computational Techniques and Applications Conference CTAC-2004, volume 46 of ANZIAM~J., pages C637--C657, July 2005.

  • Use the information dimension, not the hausdorff. A.~J. Roberts. Technical report, http://arxiv.org/abs/nlin.PS/0512014, July 2005 Download (draft) article.

  • Linear algebra: a draft proposal. A.~J. Roberts. Technical report, University of Southern Queensland, April 2005.

  • Nonlinear analysis of rubber-based polymeric materials with thermal relaxation models. R.~V.~N. Melnik, D.~V. Strunin, and A.~J. Roberts. Numerical Heat Transfer: Part~A: Applications, 47:549--569, 2005. http://taylorandfrancis.metapress.com/link.asp?id=y7hnhm6m0yv76taa.

  • Teach fundamental abstract linear algebra starting from singular value decomposition. A.~J. Roberts. Technical report, University of Southern Queensland, 2005.

  • Rob May and A.~J. Roberts, editors. Proceedings of 12th Computational Techniques and Applications Conference CTAC-2004, volume 46(E) of ANZIAM~J., 2005.

  • Analyse gap-tooth patch boundary conditions with {Reduce}. A.~J. Roberts. Technical report, http://www.sci.usq.edu.au/staff/aroberts/linpbc.red, September 2004.

  • A corrected quadrature formula and applications. Nenad Ujevic and A.~J. Roberts. ANZIAM~J., 45(E):E41--E56, February 2004.

  • Image processing of finite size rat retinal ganglion cells using multifractal and local connected fractal analysis. H.~F. Jelinek, D.~J. Cornforth, A.~J. Roberts, G. Landini, P. Bourke, and A. Iorio. In 17th Australian Joint Conference on Artificial Intelligence, volume 3339 of Lecture Notes in Computer Science, pages 961--966. Springer--Verlag Heidelberg, 2004 Download (draft) article.

  • Computational models for multi-scale coupled dynamic problems. R.~V.~N. Melnik and A.~J. Roberts. Future Generation Computer Systems, 20(3):453--464, 2004 Download (draft) article.

  • The prisoners may be in two minds. A.~J. Roberts. Austral. Math. Soc. Gazette, 31:30--33, 2004 Download (draft) article.

  • Shear dispersion along circular pipes is affected by bends, but the torsion of the pipe is negligible. A.~J. Roberts. SIAM J.~Applied Dynamical Systems, 3:433--462, 2004.

  • Check the slowly-varying normal form of thin film fluids. A.~J. Roberts. Technical report, http://www.sci.usq.edu.au/staff/aroberts/CA/nff.red, 2004.

  • Jagoda Crawford and A.~J. Roberts, editors. Proceedings of 11th Computational Techniques and Applications Conference CTAC-2003, volume 45(E) of ANZIAM~J., 2004.

  • Zero-sum games theory. A.~J. Roberts. Technical report, University of Southern Queensland, 2004.

  • Two-zone model of shear dispersion in a channel using centre manifolds. A.~J. Roberts and D.~V. Strunin. Quart. J.~Mech. Appl. Math., 57:363--378, 2004.

  • A step towards holistic discretisation of stochastic partial differential equations. A.~J. Roberts. In Jagoda Crawford and A.~J. Roberts, editors, Proc. of 11th Computational Techniques and Applications Conference CTAC-2003, volume 45, pages C1--C15, December 2003.

  • Engineering mathematics: time for a core curriculum? Particia Cretchley, A.~J. Roberts, and Chris Harman. In R.~L. May and W.~F. Blyth, editors, Proceedings of the Sixth Engineering Mathematics and Applications Conference, pages 25--30, July 2003.

  • Holistic discretisation of shear dispersion in a two-dimensional channel. T. MacKenzie and A.~J. Roberts. In K. Burrage and Roger~B. Sidje, editors, Proc. of 10th Computational Techniques and Applications Conference CTAC-2001, volume 44, pages C512--C530, March 2003.

  • Low {P}randtl number fluid convection modelled using symbolic algebra ({REDUCE}) and {M}atlab. Tim Passmore and A.~J. Roberts. In K. Burrage and Roger~B. Sidje, editors, Proc. of 10th Computational Techniques and Applications Conference CTAC-2001, volume 44, pages C590--C626, March 2003.

  • Derive boundary conditions for holistic discretisations of {Burgers'} equation. A.~J. Roberts. In K. Burrage and Roger~B. Sidje, editors, Proc. of 10th Computational Techniques and Applications Conference CTAC-2001, volume 44, pages C664--C686, March 2003.

  • Dynamics of a turbulent layer generated by velocity jump. D.~V. Strunin and A.~J. Roberts. In K. Burrage and Roger~B. Sidje, editors, Proc. of 10th Computational Techniques and Applications Conference CTAC-2001, volume 44, pages C723--C738, March 2003.

  • Modelling nonlinear dynamics of shape-memory-alloys with approximate models of coupled thermoelasticity. R.~V.~N. Melnik and A.~J. Roberts. Z.~Angew. Math. Mech., 83:93--104, 2003.

  • A holistic finite difference approach models linear dynamics consistently. A.~J. Roberts. Mathematics of Computation, 72:247--262, 2003.

  • Holistic discretisation of dynamical partial differential equations. A.~J. Roberts. Technical report, https://tuck.adelaide.edu.au/holistic1.html [November 10, 2025], 2003--2025.

  • Holistic discretise three coupled dynamical partial differential equations. A.~J. Roberts. Technical report, http://tuck.adelaide.edu.au/holistic3.php [November 10, 2025], 2003--2025.

  • Low-dimensional modelling of dynamical systems applied to some dissipative fluid mechanics. A.~J. Roberts. In Rowena Ball and Nail Akhmediev, editors, Nonlinear dynamics from lasers to butterflies, volume 1 of Lecture Notes in Complex Systems, chapter 7, pages 257--313. World Scientific, 2003.

  • Modelling the dynamics of turbulent floods. Z. Mei, A.~J. Roberts, and Zhenquan Li. SIAM J.~Appl. Math., 63(2):423--458, 2003.

  • Multifractal analysis: a pilot study using rat ganglion cells. H.~F. Jelinek, A.~J. Roberts, and L. Peichl. Proc. Austr. Neurosci. Soc., 13:152, 2002.

  • Coupled thermomechanical dynamics of phase transitions in shape memory alloys and related hysteresis phenomena. R.~V.~N. Melnik, A.~J. Roberts, and K.~A. Thomas. Mechanics Research Communications, 28:637--651, 2002.

  • Computational models for materials with shape memory: towards a systematic description of coupled phenomena. R.~V.~N. Melnik and A.~J. Roberts. In P.~M.~A. Sloot, C.~J.~K. Tan, J.~J. Dongarra, and A.~G. Hoekstra, editors, Computational Science-ICCS2002, Lecture Notes in Computer Science, pages 490--499. Springer, 2002.

  • Phase transitions in shape memory alloys with hyperbolic heat conduction and differential-algebraic models. R.~V.~N. Melnik, A.~J. Roberts, and K.~A. Thomas. Computational Mechanics, 29:16--26, 2002 Download (draft) article.

  • Holistic discretisation illuminates and enhances the numerical modelling of differential equations. A.~J. Roberts. Technical report, http://www.sci.usq.edu.au/research/workingpapers/sc-mc-0111.ps, 2002 Download (draft) article.

  • A lubrication model of coating flows over a curved substrate in space. R.~Valery Roy, A.~J. Roberts, and M.~E. Simpson. J.~Fluid Mech., 454:235--261, 2002.

  • Self-similarity of decaying turbulent jet. D.~V. Strunin and A.~J. Roberts. In Proceedings of the fifth biennial engineering mathematics and applications conference, EMAC 2002, pages 205--210, 2002.

  • Simple and fast multigrid solution of {Poisson's} equation using diagonally oriented grids. A.~J. Roberts. ANZIAM~J., 43(E):E1--E36, July 2001.

  • A model of weakly vortical interfacial flow. G.~A. Jarrad and A.~J. Roberts. ANZIAM~J., 42(E):E69--E101, March 2001.

  • Efficient design of tall tapered feeders. M.~J. McGuinness and A.~J. Roberts. In J. Hewitt, editor, Proceedings of the 2001 Mathematics in Industry Study Group, pages 60--77. 2001.

  • Modeling dynamics of multilayered {SMA} actuators. R.~V. Melnik and A.~J. Roberts. In Ronald A.~Lawes Dinesh K.~Sood and Vasundara~V. Varadan, editors, Smart Structures and Devices, volume 4235 of {SPIE} proceedings, pages 117--125, 2001.

  • An accurate lubrication model of contaminated coating flows. A.~J. Roberts and M.~E. Simpson. Technical report, http://arXiv.org/abs/math.DS/0102207, 2001 Download (draft) article.

  • Holistic projection of initial conditions onto a finite difference approximation. A.~J. Roberts. Computer Phys. Comm., 142:316--321, 2001 Download (draft) article.

  • Holistically discretise the {Swift-Hohenberg} equation on a scale larger than its spatial pattern. A.~J. Roberts. Technical report, http://arXiv.org/abs/math.NA/0110153, 2001 Download (draft) article.

  • Models encompassing hydraulic jumps in radial flows over a horizontal plate. A.~J. Roberts and D.~V. Strunin. In V.~V. Kluev and N.~E. Mastorakis, editors, Topics in Applied and Theoretical Mathematics and Computer Science, pages 31--36. WSES Press, 2001.

  • Holistic discretisation illuminates and enhances the numerical modelling of differential equations. A.~J. Roberts. In V.~V. Kluev and N.~E. Mastorakis, editors, Topics in Applied and Theoretical Mathematics and Computer Science, pages 81--89. WSES Press, 2001.

  • Holistic discretisation ensures fidelity to {Burgers'} equation. A.~J. Roberts. Applied Numerical Modelling, 37:371--396, 2001 Download (draft) article.

  • An accurate lubrication model of contaminated coating flows. M.~E. Simpson and A.~J. Roberts. Computer Phys. Comm., 142:330--332, 2001.

  • Coupled thermomechanical waves in hyperbolic thermoelasticity. D.~V. Strunin, R.~V.~N. Melnik, and A.~J. Roberts. J.~Thermal Stresses, 24(2):121--140, 2001.

  • Complete self-similarity in $k$-$l$ models of turbulence induced by step-wise profiles of velocity or buoyancy. D.~V. Strunin and A.~J. Roberts. Technical report, University of Southern Queensland, 2001.

  • Reproductive pair correlations and the clustering of organisms. W.~R. Young, A.~J. Roberts, and G. Stuhne. Nature, 412:328--331, 2001. 19th July.

  • Solve differential-algebraic equations in matlab. A.~J. Roberts. Technical report, http://www.sci.usq.edu.au/staff/robertsa/dae.dtx, May 2000 Download (draft) article.

  • Dynamics of rubber-like polymers with hyperbolic models of coupled thermoelasticity. R.~V.~N. Melnik, D.~V. Strunin, and A.~J. Roberts. Technical report, University of Southern Queensland, March 2000.

  • Holistic finite differences accurately model the dynamics of the {Kuramoto--Sivashinsky} equation. T. Mackenzie and A.~J. Roberts. ANZIAM~J., 42(E):C918--C935, 2000.

  • The dynamics of reaction diffusion equations lead to a holistic discretisation. T. MacKenzie and A.~J. Roberts. In R.~L. May, G.~F. Fitz-Gerald, and I.~H. Grundy, editors, EMAC 2000 Proceedings. Proceedings of the fourth biennial Engineering Mathematics and Applications Conference, pages 199--202, 2000.

  • Dip coating process for hot metal castings. M.~J. McGuinness and A.~J. Roberts. In J. Hewitt, editor, Proceedings of the 1999 Mathematics in Industry Study Group, pages 20--48. 2000.

  • Numerical analysis of the behaviour of rubber-like polymers with hyperbolic models of nonlinear thermoelasticity. R.~V.~N. Melnik, D.~V. Strunin, and A.~J. Roberts. In M. Deville and R. Owens, editors, Proc. of the 16th IMACS World Congress on Scientific Computation, Applied Mathematics and Simulation, pages 1--6, 2000.

  • Mathematical and numerical analysis of {Falk-Konopka-type} models for shape-memory alloys. R.~V.~N. Melnik, A.~J. Roberts, and K.~A. Thomas. International J.~Differential Equations and Applications, 1A:291--300, 2000.

  • Computing dynamics of copper-based {SMA} via centre manifold reduction of {3D} models. R.~V.~N. Melnik, A.~J. Roberts, and K.~A. Thomas. Computational Materials Science, 18:255--268, 2000.

  • Approximate models of dynamic thermoviscoelasticity describing shape memory alloy phase transitions. R.~V.~N. Melnik and A.~J. Roberts. In D. Stewart and S. Oliviera, editors, New methods in Applied and computational mathematics (NEMACOM 98), volume 38 of Proceedings of the Centre for Mathematics and its Applications, ANU, pages 17--32, 2000.

  • Rigorous zonal modelling of contaminant dispersion in shear flows. A.~J. Roberts and D.~V. Strunin. In N. Mastorakis, editor, Recent Advances in Applied and Theoretical Mechanics, pages 64--70. WSES Press, 2000.

  • Rigorous zonal modelling of contaminant dispersion in shear flows. A.~J. Roberts and D.~V. Strunin. In N. Mastorakis, editor, Proc. of the WSES Int. Conf. on Applied and Theoretical Mechanics, pages 2011--2017, 2000. CD-ROM.

  • Computer algebra derives correct initial conditions for low-dimensional dynamical models. A.~J. Roberts. Computer Phys. Comm., 126(3):187--206, 2000.

  • Numerical modelling of thermoelastic processes using nonlinear theories with thermal relaxation times. D.~V. Strunin, R.~V.~N. Melnik, and A.~J. Roberts. ANZIAM~J., 42(E):C1356--C1378, 2000.

  • Modelling of sample dynamics in rectangular asymmetrical flow field-flow fractionation channels. S.~A. Suslov and A.~J. Roberts. Analytical Chemistry, 72(18):4331--4345, 2000.

  • Branching behaviour of standing waves---the signatures of resonance. D. Smith and A.~J. Roberts. Phys. Fluids, 11(5):1051--1064, May 1999.

  • Stability regimes of finite depth short-crested waves. M. Ioualalen, C. Kharif, and A.~J. Roberts. J.~Phys. Oceanogr., 29(9):2318--2331, 1999.

  • Modelling dynamics of shape-memory-alloys via computer algebra. R.~V.~N. Melnik, A.~J. Roberts, and K. A.Thomas. In V.~V. Varadan, editor, Mathematics and Control in Smart Structures, Proc. of SPIE, volume 3667, pages 290--301, 1999.

  • Dynamics of shape-memory-alloys: A reduction procedure for 3d models. R.~V.~N. Melnik, A.~J. Roberts, and K.~A. Thomas. In W. Wunderlich, editor, Proceedings of the European Conference on Computational Mechanics: Solids, Structures and Coupled Problems in Engineering, page 328, 1999.

  • Differential-algebraic equations deserve more attention. A.~J. Roberts. Austral. Math. Soc. Gazette, 26:75--79, 1999.

  • Advection-dispersion in symmetric field-flow fractionation channels. S.~A. Suslov and A.~J. Roberts. J.~Math. Chem., 26:27--46, 1999.

  • Projection of initial conditions for thin film flow models. S.~A. Suslov and A.~J. Roberts. In IUTAM Symposium on Nonlinear Wave Behavior in Multi-Phase Flow, 1999.

  • Similarity, attraction and initial conditions in an example of nonlinear diffusion. S.~A. Suslov and A.~J. Roberts. J.~Austral. Math. Soc.~B, 40(E):E1--E26, October 1998.

  • An accurate model of thin 2d fluid flows with inertia on curved surfaces. A.~J. Roberts. In P.~A. Tyvand, editor, Free-surface flows with viscosity, volume 16 of Advances in Fluid Mechanics Series, chapter 3, pages 69--88. Comput Mech Pub, 1998.

  • {LaTeX}: from quick and dirty to style and finesse. A.~J. Roberts. Technical report, http://www.maths.adelaide.edu.au/anthony.roberts/LaTeX/index.php, 1998 Download (draft) article.

  • First-order accurate scheme to integrate the ito sde. A.~J. Roberts. Technical report, http://www.sci.usq.edu.au/staff/aroberts/sde1.m, 1998 Download (draft) article.

  • Numerical thin film dynamics. M. Simpson and A.~J. Roberts. In B.~J. Noye, M.~D. Teubner, and A.~W. Gill, editors, {Computational Techniques and Applications: CTAC-97}, pages 623--630. World Sci. Pub. Co., 1998.

  • Level set methods in free-surface hydrodynamics. D. Smith and A.~J. Roberts. In B.~J. Noye, M.~D. Teubner, and A.~W. Gill, editors, {Computational Techniques and Applications: CTAC-97}, pages 639--646. World Sci. Pub. Co., 1998.

  • Proper initial conditions for the lubrication model of thin film fluid flow. S.~A. Suslov and A.~J. Roberts. Technical report, http://arXiv.org/abs/chao-dyn/9804018, 1998 Download (draft) article.

  • The accurate modelling of thin {3D} fluid flows with inertia on curved substrates. Zhenquan Li and A.~J. Roberts. In {Proceedings of Engineering Mathematics Applications Conference: EMAC98}, pages 315--318, 1998.

  • Low-dimensional modelling of dynamics via computer algebra. A.~J. Roberts. Computer Phys. Comm., 100:215--230, 1997.

  • Low-dimensional modelling of dynamical systems. A.~J. Roberts. Technical report, http://arXiv.org/abs/chao-dyn/9705010, 1997 Download (draft) article.

  • Solution to problem 96-14: An integral. A.~J. Roberts. SIAM Review, 39:pp526--7, 1997.

  • Modelling and simulation. A.~J. Roberts. Australasian Science, 18(3):5--6, sept 1997.

  • Bow-like free surfaces under gravity. E.~O. Tuck and A.~J. Roberts. Phil. Trans. R.~Soc. Lond.~A, 355:665--677, 1997.

  • Parallel algorithms for spatial data partition and join processing. Yanchun Zhang, Jitian Xiao, and A.~J. Roberts. In A. Goscinski, M. Hobbs, and Wanlei Zhou, editors, Algorithms and architectures for parallel processing, pages 703--716, 1997.

  • Internal structure of extreme standing waves in deep water. D. Smith and A.~J. Roberts. Phys. Fluids, 8(3):697--703, March 1996.

  • On the low-dimensional modelling of {Stratonovich} stochastic differential equations. Xu Chao and A.~J. Roberts. Physica~A, 225:62--80, 1996.

  • On the observability of finite depth short-crested water waves. M. Ioualalen, C. Kharif, and A.~J. Roberts. J.~Fluid Mech., 322:1--19, 1996.

  • Low-dimensional models of thin film fluid dynamics. A.~J. Roberts. Phys. Letts.~A, 212:63--72, 1996.

  • Unbiased estimation of multi-fractal dimensions of finite data sets. A.~J. Roberts and A. Cronin. Physica~A, 233:867--878, 1996. doi:10.1016/S0378-4371(96)00165-3
    .

  • The construction of zonal models of dispersion in channels via matching centre manifolds. S.~D. Watt and A.~J. Roberts. J.~Austral. Math. Soc.~B, 38:101--125, 1996.

  • Initial conditions for models of dynamical systems. S.~M. Cox and A.~J. Roberts. Physica~D, 85:126--141, 1995.

  • Fractal and multi-fractal patterns of seaweed settlement. L.~M. Emmerson and A.~J. Roberts. preprint, 1995.

  • Equations for turbulent flood waves. Z. Mei and A.~J. Roberts. In A. Mielke and K. Kirchgassner, editors, Structure and dynamics of nonlinear waves in fluids, pages 342--352. World Sci, 1995.

  • The {Swift--Hohenberg} equation requires non-local modifications to model spatial pattern evolution of physical problems. A.~J. Roberts. Technical report, http://arXiv.org/abs/patt-sol/9412002, 1995.

  • The accurate dynamic modelling of contaminant dispersion in channels. S.~D. Watt and A.~J. Roberts. SIAM J.~Appl. Math., 55(4):1016--1038, 1995.

  • Dimensional reduction of a bushfire model. S.~D. Watt, A.~J. Roberts, and R.~O. Weber. Mathl. Computer Modelling, 21(9):79--83, 1995.

  • The importance of beings fractal. A.~J. Roberts. Australasian Science, page 23, April 1994.

  • Initialisation and the quasi-geostrophic slow manifold. S.~M. Cox and A.~J. Roberts. Technical report, http://arXiv.org/abs/nlin.CD/0303011, 1994.

  • A complete model of shear dispersion in pipes. G.~N. Mercer and A.~J. Roberts. Jap. J.~Indust. Appl. Math., 11:499--521, 1994.

  • The form of standing waves on finite depth water. G.~N. Mercer and A.~J. Roberts. Wave Motion, 19:233--244, 1994.

  • A one-dimensional introduction to continuum mechanics. A.~J. Roberts. World Sci, 1994.

  • Estimate generalised fractal dimensions of a set of points. A.~J. Roberts. Technical report, http://www.sci.usq.edu.au/staff/aroberts/fdim.sh, 1994 Download (draft) article.

  • An invariant manifold approach to modelling the dynamics of the kuramoto-sivashinsky equation. D.~I. Oats and A.~J. Roberts. Preprint, 1993.

  • The invariant manifold of beam deformations. part 1: the simple circular rod. A.~J. Roberts. J.~Elas., 30:1--54, 1993.

  • The quasi-geostrophic slow manifold. S.~M. Cox and A.~J. Roberts. In Proc 11th Austral. Fluid Mech Conf, 1992 Download (draft) article.

  • Standing waves in deep water: their stability and extreme form. G.~N. Mercer and A.~J. Roberts. Phys. Fluids~A, 4:259--269, 1992.

  • Extreme standing waves and their stability. G.~N. Mercer and A.~J. Roberts. In M.~L. Banner and R.~H.~J. Grimshaw, editors, Proc IUTAM Sym on breaking waves, pages 383--387. Springer-Verlag, 1992.

  • A sub-centre manifold description of the evolution and interaction of nonlinear dispersive waves. A.~J. Roberts. In L. Debnath, editor, Nonlinear waves, chapter 9, pages 127--156. World Sci, 1992.

  • Planform evolution in convection---an embedded centre manifold. A.~J. Roberts. J.~Austral. Math. Soc.~B, 34:174--198, 1992.

  • Boundary conditions for approximate differential equations. A.~J. Roberts. J.~Austral. Math. Soc.~B, 34:54--80, 1992.

  • Slow methods for simple people. A.~J. Roberts. Technical Report WHOI-92-16, Woods Hole Oceanog. Inst., 1992. pp.149--154.

  • Rational mathematical modelling---shear dispersion and planform selection. A.~J. Roberts. Technical Report WHOI-92-16, Woods Hole Oceanog. Inst., 1992. pp155--166.

  • A virtual supercomputer from a network of workstations. A.~J. Roberts. Austral. Adv. Comp. Newslet., 2(2), 1992.

  • Centre manifolds of forced dynamical systems. S.~M. Cox and A.~J. Roberts. J.~Austral. Math. Soc.~B, 32:401--436, 1991.

  • Reflection of nonlinear deep-water waves incident onto a wedge of arbitrary angle. T.~R. Marchant and A.~J. Roberts. J.~Austral. Math. Soc.~B, 32:61--96, 1990.

  • A centre manifold description of contaminant dispersion in channels with varying flow properties. G.~N. Mercer and A.~J. Roberts. SIAM J.~Appl. Math., 50:1547--1565, 1990.

  • A description of the long-term behaviour of absorbing continuous time {Markov} chains using a centre manifold. P.~K. Pollett and A.~J. Roberts. Advances Applied Probability, 22:111--128, 1990.

  • Low-dimensionality---approximations in mechanics. A.~J. Roberts. In J. Noye and W. Hogarth, editors, {Computational Techniques and Applications: CTAC--89}, pages 715--722. Hemisphere, 1990.

  • The utility of an invariant manifold description of the evolution of a dynamical system. A.~J. Roberts. SIAM J.~Math. Anal., 20:1447--1458, 1989.

  • Appropriate initial conditions for asymptotic descriptions of the long term evolution of dynamical systems. A.~J. Roberts. J.~Austral. Math. Soc.~B, 31:48--75, 1989.

  • Use of implicit and explicit flux-corrected transport algorithms in gas discharge problems involving a non-uniform velocity fields. P. Stienle, R. Morrow, and A.~J. Roberts. J.~Comput Phys., 85, 1989.

  • A variational approach to the problem of deep water waves forming a circular caustic. T.~R. Marchant and A.~J. Roberts. J.~Fluid Mech., 194:581--597, 1988.

  • The application of centre manifold theory to the evolution of systems which vary slowly in space. A.~J. Roberts. J.~Austral. Math. Soc.~B, 29:480--500, 1988.

  • The initial flow of liquid in an accelerating tank. A.~J. Roberts. J.~Eng. Mech., 114:175--180, 1988.

  • Properties of short-crested waves in water of finite depth. T.~R. Marchant and A.~J. Roberts. J.~Austral. Math. Soc.~B, 29:103--125, 1987.

  • Transient free-surface flows generated by a moving vertical plate. A.~J. Roberts. Quart. J.~Mech. Appl. Math., 30:129--158, 1987.

  • An introduction to the technique of reconstitution. A.~J. Roberts. SIAM J.~Math. Anal., 16:1243--1257, 1985.

  • Simple examples of the derivation of amplitude equations for systems of equations possessing bifurcations. A.~J. Roberts. J.~Austral. Math. Soc.~B, 27:48--65, 1985.

  • An analysis of near marginal, mildly penetrative convection with heat flux prescribed on the boundaries. A.~J. Roberts. J.~Fluid Mech., 158:71--93, 1985.

  • Highly nonlinear short-crested water waves. A.~J. Roberts. J.~Fluid Mech., 135:301--321, 1983.

  • Notes on long-crested water wave. A.~J. Roberts and D.~H. Peregrine. J.~Fluid Mech., 135:323--335, 1983.

  • The calculation of nonlinear short-crested wave. A.~J. Roberts and L.~W. Schwartz. Phys. Fluids, 26:2388, 1983.

  • A stable and accurate numerical method to calculate the motion of a sharp interface between fluids. A.~J. Roberts. IMA J.~Appl. Math., 31:13--35, 1983.

  • Nonlinear buoyancy effects in fluids. A.~J. Roberts. PhD thesis, University of Cambridge, July 1982.

  • The behaviour of harmonic resonant steady solutions to a model differential equation. A.~J. Roberts. Quart. J.~Mech. Appl. Math., 34:287--310, 1981.

  • Fixed flux penetrative convection. A.~J. Roberts. Technical Report WHOI-81-102, Woods Hole Oceanog. Inst., 1981. pp177--188 Download (draft) article.

  • Inverse solutions in free-surface hydrodynamics via solution of a complex differential equation. A.~J. Roberts. Honours project, University of Adelaide, 1977 Download (draft) article.

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    Copyright Tony Roberts, School of Mathematical Sciences, University of Adelaide, South Australia. ORCID=0000-0001-8930-1552 01-January-1970 00:00