**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.

**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. Technical report,

`http://arxiv.org/abs/2108.11568`, August 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.

**Equation-free function toolbox for matlab/octave**. A.~J. Roberts, John Maclean, and J.~E. Bunder. Technical report, [

`https://github.com/uoa1184615/EquationFreeGit`], 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*, accepted 21 Sept 2020, 2020.

*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.

**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.

**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.

**Backwards theory supports modelling via invariant manifolds for non-autonomous dynamical systems**. A.~J. Roberts. Technical report, [

`http://arxiv.org/abs/1804.06998`], January 2019.

**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.

**Center manifolds for infinite dimensional random dynamical systems**. Xiaopeng Chen, A.~J. Roberts, and Jinqiao Duan.

*Dynamical Systems (CDSS)*, 34(2):334--355, 2018.

**Couple microscale periodic patches to simulate macroscale emergent dynamics**. Hammad Alotaibi, Barry Cox, and A.~J. Roberts.

*ANZIAM~J.*, 59(3):313--334, 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.

**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.

**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.

**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.

**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.

**Surface deformation and shear flow in ligand mediated cell adhesion**. Sarthok Sircar and A.~J. Roberts.

*Journal of Mathematical Biology*, pages 1--18, 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.

**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.

**Modelling suspended sediment in environmental turbulent fluids**. Meng Cao and A.~J. Roberts.

*J.~Engrg. Maths*, 98(1):187--204, 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.

*Proceedings of the Mathematics and Statistics in Industry Study Group 2015*, volume 57(E) of

*ANZIAM Journal*, 2016.

*Proceedings of the Mathematics and Statistics in Industry Study Group 2014*, volume 56(E) of

*ANZIAM Journal*, 2016.

*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.

**Effective multiscale computational modeling of spatio-temporal systems**, May 2015. Video of talk at SIAM conference on Dynamical Systems 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.

**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.

**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.

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

**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.

**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 .

**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.

**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 Download (draft) article.

*Proceedings of the Mathematics in Industry Study Group 2013*, volume 55(E) of

*ANZIAM Journal*, 2014.

**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.

**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.

**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.

**Macroscopic reduction for stochastic reaction-diffusion equations**. Wei Wang and A.~J. Roberts.

*IMA Journal of Applied Mathematics*, 78(6):1237--1264, 2013.

*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.

**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.

**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.

**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.

**Average and deviation for slow-fast stochastic partial differential equations**. Wei Wang and A.~J. Roberts.

*J. Differential Equations*, 253:1265--1286, 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.

*Proceedings of the Engineering Mathematics and Applications Conference*, volume 53 of

*ANZIAM Journal*, 2012.

**Construct invariant manifolds of ordinary or delay differential equations (autonomous)**. A.~J. Roberts. Technical report,

`https://tuck.adelaide.edu.au/gencm.html`, 2012--2021.

**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.

**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.

**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.

*Proceedings of the Mathematics in Industry Study Group 2011*, volume 53(E) of

*ANZIAM~J.*, 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.

**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.

**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.

**Choose interelement coupling to preserve self-adjoint dynamics in multiscale modelling and computation**. A.~J. Roberts.

*Applied Numerical Modelling*, 60:949--973, 2010.

**Stochastically forced, cubic reaction-diffusion equation,**, 2010 Download (draft) article.

`http://math.iit.edu/~spde2010/TonyRobertsMovieSPDE2010.mpg`

**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.

**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.

*Proceedings of 15th Computational Techniques and Applications Conference CTAC-2010*, volume 52(E) of

*ANZIAM~J.*, 2010.

*Proceedings of the Mathematics in Industry Study Group 2010*, volume 52(E) of

*ANZIAM~J.*, 2010.

*Proceedings of the 9th Biennial Engineering Mathematics and Applications Conference, EMAC-2009*, volume 51(E) of

*ANZIAM~J.*, 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.

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

**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.

*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.

**Slow manifold of stochastic or deterministic multiscale differential equations**. A.~J. Roberts. Technical report,

`http://tuck.adelaide.edu.au/sdenf.php`, 2009--2021.

**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.

**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,

`http://hdl.handle.net/2440/49292`, 2009.

**Normal form of stochastic or deterministic multiscale differential equations**. A.~J. Roberts. Technical report,

`http://tuck.adelaide.edu.au/sdenf.php`, 2009--2021.

**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 emergent dynamics in complex systems**. A.~J. Roberts. Technical Report 2nd edition,

`http://tuck.adelaide.edu.au/modelling.php`, 2009--2021.

**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.

**Combined instructions and template for articles submitted to the anziam journal**. A.~J. Roberts.

*ANZIAM~J. (Electronic supplement)*, 50, 2008.

**Normal form transforms separate slow and fast modes in stochastic dynamical systems**. A.~J. Roberts.

*Physica~A*, 387:12--38, 2008.

**Nash equilibria: strategies in the prisoner's dilemma**, 2008.

`http://www.youtube.com/watch?v=5Ug2EVjdS4E`Download (draft) article.

**Nash equilibria: Nash's solution of the prisoner's dilemma**, 2008.

`http://www.youtube.com/watch?v=J4n-Eg6UAw8`Download (draft) article.

**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.

*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`.

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

**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.

**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.

**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/`.

**The inertial dynamics of thin film flow of non-newtonian fluids**. A.~J. Roberts.

*Physics Letters~A*, 372:1607--1611, 2007.

**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.

**General tooth boundary conditions for equation free modelling**. A.~J. Roberts and I.~G. Kevrekidis.

*SIAM J.~Scientific Computing*, 29(4):1495--1510, 2007.

**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 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.

*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.

**Computer algebra derives normal forms of stochastic differential equations**. A.~J. Roberts. Technical report,

`http://eprints.usq.edu.au/archive/00001873`, 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.

**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.

**Resolving the multitude of microscale interactions accurately models stochastic partial differential equations**. A.~J. Roberts.

*LMS J.~Computation and Maths*, 9:193--221, 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.

**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.

**A normal form of thin fluid film equations solves the transient paradox**. A.~J. Roberts.

*Physica~D*, 223(1):69--81, 2006.

*Proceedings of the 7th Biennial Engineering Mathematics and Applications Conference, EMAC-2005*, volume 47(E) of

*ANZIAM~J.*, 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.

**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`.

*Proceedings of 12th Computational Techniques and Applications Conference CTAC-2004*, volume 46(E) of

*ANZIAM~J.*, 2005.

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

**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.

**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.

**The prisoners may be in two minds**. A.~J. Roberts.

*Austral. Math. Soc. Gazette*, 31:30--33, 2004 Download (draft) article.

**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.

**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.

*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.

**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.

**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 the dynamics of turbulent floods**. Z. Mei, A.~J. Roberts, and Zhenquan Li.

*SIAM J.~Appl. Math.*, 63(2):423--458, 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 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.

**Holistic discretisation of dynamical partial differential equations**. A.~J. Roberts. Technical report,

`https://tuck.adelaide.edu.au/holistic1.html`, 2003--2021.

**Holistic discretise three coupled dynamical partial differential equations**. A.~J. Roberts. Technical report,

`http://tuck.adelaide.edu.au/holistic3.php`, 2003--2021.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**Holistic projection of initial conditions onto a finite difference approximation**. A.~J. Roberts.

*Computer Phys. Comm.*, 142:316--321, 2001 Download (draft) article.

**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.

**Reproductive pair correlations and the clustering of organisms**. W.~R. Young, A.~J. Roberts, and G. Stuhne.

*Nature*, 412:328--331, 2001. 19th July.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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.

**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. doi:10.1023/A:1019169408365 .

**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.

**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.

**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.

**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.

**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/index.php`, 1998 Download (draft) article.

**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.

**Modelling and simulation**. A.~J. Roberts.

*Australasian Science*, 18(3):5--6, sept 1997.

**Low-dimensional modelling of dynamics via computer algebra**. A.~J. Roberts.

*Computer Phys. Comm.*, 100:215--230, 1997.

**Solution to problem 96-14: An integral**. A.~J. Roberts.

*SIAM Review*, 39:pp526--7, 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.

**Low-dimensional modelling of dynamical systems**. A.~J. Roberts. Technical report,

`http://arXiv.org/abs/chao-dyn/9705010`, 1997 Download (draft) article.

**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.

**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`.

**Dimensional reduction of a bushfire model**. S.~D. Watt, A.~J. Roberts, and R.~O. Weber.

*Mathl. Computer Modelling*, 21(9):79--83, 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 Download (draft) article.

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

**The importance of beings fractal**. A.~J. Roberts.

*Australasian Science*, page 23, April 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.

**Initialisation and the quasi-geostrophic slow manifold**. S.~M. Cox and A.~J. Roberts. Technical report,

`http://arXiv.org/abs/nlin.CD/0303011`, 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.

**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.

**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.

**A virtual supercomputer from a network of workstations**. A.~J. Roberts.

*Austral. Adv. Comp. Newslet.*, 2(2), 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.

**The quasi-geostrophic slow manifold**. S.~M. Cox and A.~J. Roberts. In

*Proc 11th Austral. Fluid Mech Conf*, 1992 Download (draft) article.

**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.

**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.

**Centre manifolds of forced dynamical systems**. S.~M. Cox and A.~J. Roberts.

*J.~Austral. Math. Soc.~B*, 32:401--436, 1991.

**Standing waves in deep water: their stability and extreme form**. G.~N. Mercer and A.~J. Roberts.

*Phys. Fluids~A*, 4:259--269, 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. (Downloaded 467 times in the period 2018--2020, the 16th highest for the journal.).

**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.

**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.

**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.

*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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