• 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. http://anziamj.austms.org.au/ojs/index.php/ANZIAMJ/article/view/1466 [September 3, 2009] Do wnload (draft) article.

  • 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.

  • Holistic discretise three coupled dynamical partial differential equations. A.~J. Roberts. Technical report, http://www.maths.adelaide.edu.au/anthony.roberts/holistic3.html, April 2009. version $\beta $.2 Download (draft) article.

  • Holistic discretisation of dynamical partial differential equations. A.~J. Roberts. Technical report, http://www.maths.adelaide.edu.au/anthony.roberts/holistic1.html, April 2009 Download (draft) article.

  • Slow manifold and averaging for slow-fast stochastic differential system. Wei Wang and A.~J. Roberts. Technical report, http://arxiv.org/abs/0903.1375, 2009.

  • 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.

  • 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://anziamj.austms.org.au/ojs/index.php/ANZIAMJ/issue/view/37 Downlo ad (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.

  • Normal form of stochastic or deterministic multiscale differential equations. A.~J. Roberts. Technical report, http://www.maths.adelaide.edu.au/anthony.roberts/sdenf.html, 2009 Download (draft) article.

  • Maximum likelihood multifractal analyser of 2d data. A.~J. Roberts. Technical report, http://www.maths.adelaide.edu.au/anthony.roberts/multifractal.html, January 2009 Down load (draft) article.

  • Model emergent dynamics in complex systems. A.~J. Roberts. Technical report, http://www.maths.adelaide.edu.au/anthony.roberts/Modelling, 2009 Download (draft) article.

  • 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.

  • 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, 2009. http://hdl.handle.net/2440/49292 Download (draft) article.

  • Elementary calculus of financial mathematics. A.~J. Roberts, volume 15 of Mathematical Modeling and Computation. SIAM, Philadelphia, December 2008 Download (draft) article.

  • 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. http://anziamj.austms.org.au/ojs/index.php/ANZIAMJ/article/view/1391 [November 11, 2008] Do wnload (draft) article.

  • 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.

  • Macroscopic reduction for stochastic reaction-diffusion equations. Wei Wang and A.~J. Roberts. Technical report, http://arxiv.org/abs/0812.1837, 2008.

  • Equation-free computation: an overview of patch dynamics. G. Samaey, A.~J. Roberts, and I.~G. Kevrekidis. Oxford University Press, 2008.

  • Choose interelement coupling to preserve self-adjoint dynamics in multiscale modelling and computation. A.~J. Roberts. Technical report, http://arxiv.org/abs/0811.0688, 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.

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

  • 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.

  • 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://anziamj.austms.org.au/ojs/index.php/ANZIAMJ/issue/view/13.

  • 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.

  • Resolve subgrid microscale interactions to discretise stochastic partial differential equations. A.~J. Roberts. preprint, January 2008.

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

  • 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 Dow nload (draft) article.

  • 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 Download (draft) article.

  • The style files: Use the most informative synonym. A.~J. Roberts. The Australian Mathematical Society Gazette, 34(4):208--209, September 2007. Unrefereed. Down load (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. http://anziamj.austms.org.au/ojs/index.php/ANZIAMJ/article/view/36, June 2007 Down load (draft) article.

  • 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. Down load (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/ 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.

  • 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. http://arXiv.org/abs/math.DS/0002138 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, to appear, 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://anziamj.austms.org.au/ojs/index.php/ANZIAMJ/issue/view/9 Download (draft) article.

  • The inertial dynamics of thin film flow of non-newtonian fluids. A.~J. Roberts. Physics Letters~A, 372:1607--1611, 2007. doi:10.1016/j.physleta.2007.10.014.

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

  • General tooth boundary conditions for equation free modelling. A.~J. Roberts and I.~G. Kevrekidis. SIAM J.~Scientific Computing, 29(4):1495--1510, 2007. doi:10.1137/060654554 Download (draft) article.

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

  • 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.

  • 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. doi:10.1017/S0022112006008640.

  • 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.

  • 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. http://anziamj.austms.org.au/V47EMAC2005.

  • 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.

  • Resolving the multitude of microscale interactions accurately models stochastic partial differential equations. A.~J. Roberts. LMS J.~Computation and Maths, 9:193--221, 2006. http://www.lms.ac.uk/jcm/9/lms2005-032 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. doi:10.1016/j.physd.2006.08.018 Download (draft) article.

  • 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.

  • 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.

  • 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 Download (draft) article.

  • 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.

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

  • 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. \protect http://anziamj.austms.org.au/V46/CTAC2004/Robe [July 20, 2005].

  • Linear algebra: a draft proposal. A.~J. Roberts. Technical report, University of Southern Queensland, http://www.sci.usq.edu.au/staff/robertsa/propose.pdf, April 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. http://anziamj.austms.org.au/V46/CTAC2004.

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

  • 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. [Online] http://anziamj.austms.org.au/V45/E051 [February 17, 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.

  • Zero-sum games theory. A.~J. Roberts. Technical report, University of Southern Queensland, 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. [Online] http://anziamj.austms.org.au/V45/CTAC2003.

  • 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.

  • 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. http://epubs.siam.org/sam-bin/dbq/article/60088 Download (draft) article.

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

  • 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.

  • 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. [Online]

    {http://anziamj.austms.org.au/ojs/index.php/ANZIAMJ/article/view/869} [December 14, 2003] Dow nload (draft) article.

  • 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.

  • 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 Download (draft) article.

  • 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. http://anziamj.austms.org.au/ojs/index.php/ANZIAMJ/article/view/701 Dow nload (draft) article.

  • 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 Download (draft) article.

  • 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. http://anziamj.austms.org.au/ojs/index.php/ANZIAMJ/article/view/694 Dow nload (draft) article.

  • Modelling the dynamics of turbulent floods. Z. Mei, A.~J. Roberts, and Zhenquan Li. SIAM J.~Appl. Math., 63(2):423--458, 2003. http://epubs.siam.org/sam-bin/dbq/article/35886 Download (draft) article.

  • 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 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.

  • 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.

  • 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. doi:10.1017/S0022112001007133.

  • 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 holistic finite difference approach models linear dynamics consistently. A.~J. Roberts. Mathematics of Computation, 72:247--262, 2002. http://www.ams.org/mcom/2003-72-241/S0025-5718-02-01448-5 Download (draft) article.

  • 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.

  • 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.

  • 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.

  • 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.

  • Simple and fast multigrid solution of {Poisson's} equation using diagonally oriented grids. A.~J. Roberts. ANZIAM~J., 43(E):E1--E36, July 2001. http://anziamj.austms.org.au/ojs/index.php/ANZIAMJ/article/view/465 Download (draft) article.

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

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

  • 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.

  • 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.

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

  • Holistic discretisation ensures fidelity to {Burgers'} equation. A.~J. Roberts. Applied Numerical Modelling, 37:371--396, 2001. doi:10.1016/S0168-9274(00)00053-2 Download (draft) article.

  • 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.

  • 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.

  • 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.

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

  • 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.

  • 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.

  • 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.

  • 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.

  • 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.

  • 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.

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

  • 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.

  • Approximate models of dynamic thermoviscoelasticity describing shape memory alloy phase transitions. R.~V.~N. Melnik and A.~J. Roberts. In D.~Stewart &~S. Oliviera, editor, 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.

  • 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.

  • 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.

  • 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.

  • 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.

  • 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. http://anziamj.austms.org.au/V42/CTAC99/Mack Download (draft) article.

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

  • Advection-dispersion in symmetric field-flow fractionation channels. S.~A. Suslov and A.~J. Roberts. J.~Math. Chem., 26:27--46, 1999. doi:10.1023/A:1019169408365.

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

  • 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.

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

  • 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.

  • 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.

  • 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.

  • 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.

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

  • 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.

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

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

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

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

  • Low-dimensional modelling of dynamics via computer algebra. A.~J. Roberts. Computer Phys. Comm., 100:215--230, 1997. doi:10.1016/S0010-4655(96)00162-2.

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

  • 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.

  • 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.

  • Low-dimensional models of thin film fluid dynamics. A.~J. Roberts. Phys. Letts.~A, 212:63--72, 1996. doi:10.1016/0375-9601(96)00040-0.

  • 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.

  • On the low-dimensional modelling of {Stratonovich} stochastic differential equations. Xu Chao and A.~J. Roberts. Physica~A, 225:62--80, 1996. doi:10.1016/0378-4371(95)00387-8.

  • 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 accurate dynamic modelling of contaminant dispersion in channels. S.~D. Watt and A.~J. Roberts. SIAM J.~Appl. Math., 55(4):1016--1038, 1995. http://epubs.siam.org/sam-bin/dbq/article/25797.

  • 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 Download (draft) article.

  • Equations for turbulent flood waves. Z. Mei and A.~J. Roberts. In A. Mielke and K. Kirchg\unhbox \voidb@x \bgroup \let \unhbox \voidb@x \setbox \@tempboxa \hbox {a\global \mathchardef \accent@spacefactor \spacefactor }\accent 127 a\egroup \spacefactor \accent@spacefactor ssner, editors, Structure and dynamics of nonlinear waves in fluids, pages 342--352. World Sci, 1995.

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

  • Initial conditions for models of dynamical systems. S.~M. Cox and A.~J. Roberts. Physica~D, 85:126--141, 1995. doi:10.1016/0167-2789(94)00201-Z.

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

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

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

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

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

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

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

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

  • Slow methods for simple people. A.~J. Roberts. Technical Report WHOI-92-16, Woods Hole Oceanog. Inst., 1992. pp149--154.

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

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

  • 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.

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

  • Standing waves in deep water: their stability and extreme form. G.~N. Mercer and A.~J. Roberts. Phys. Fluids~A, 4:259--269, 1991.

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

  • 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.

  • 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. doi:10.2307/1427600.

  • 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. http://link.aip.org/link/?SMM/50/1547/1.

  • 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.

  • 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.

  • 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.

  • 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. http://locus.siam.org/SIMA/volume-20/art_0520094.html.

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

  • 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.

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

  • 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.

  • 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.

  • 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 introduction to the technique of reconstitution. A.~J. Roberts. SIAM J.~Math. Anal., 16:1243--1257, 1985. http://locus.siam.org/SIMA/volume-16/art_0516089.html.

  • 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.

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

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

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

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

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

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

  • 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.

    • Copyright Tony Roberts, School of Mathematical Sciences, University of Adelaide, South Australia; prepared December 21, 2009, from site.tex