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Resolve the multitude of microscale interactions to holistically discretise
the stochastically forced {Burgers'} partial differential equation.
A.~J. Roberts.
Technical report, http://arxiv.org/abs/math.DS/0601702, January 2006 Download (draft) article.
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Computer algebra derives discretisations of the stochastically forced
{Burgers'} partial differential equation.
A.~J. Roberts.
Technical report,
[http://www.sci.usq.edu.au/staff/robertsa/CA/caddsfbpde.pdf], January
2006.
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Create useful low-dimensional models of complex dynamical systems.
A.~J. Roberts.
Technical report, http://www.sci.usq.edu.au/staff/robertsa/Modelling/,
2005.
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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.
Technical report, submitted to the Proceedings of the 2005 Mathematics in
Industry Study Group, July 2005.
-
Rob May and A.~J. Roberts, editors.
Proc. of 12th Computational Techniques and Applications Conference
CTAC-2004, volume 46(E) of ANZIAM~J., 2005.
http://anziamj.austms.org.au/V46/CTAC2004.
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Computer algebra resolves a multitude of microscale interactions to model
stochastic partial differential equations.
A.~J. Roberts.
Technical report,
[http://www.sci.usq.edu.au/staff/robertsa/CA/multinoise.pdf], December
2005.
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Resolve the multitude of microscale interactions to model stochastic partial
differential equations.
A.~J. Roberts.
Technical report, http://arxiv.org/abs/math.DS/0506533, June 2005.
Submitted to LMS Journal of Computation and Mathematics Download (draft) article.
-
Teach fundamental abstract linear algebra starting from singular value
decomposition.
A.~J. Roberts.
Technical report, University of Southern Queensland, 2005.
Submitted to Delta'05 Conference Proccedings.
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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.
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Jagoda Crawford and A.~J. Roberts, editors.
Proc. of 11th Computational Techniques and Applications Conference
CTAC-2003, volume 45(E) of ANZIAM~J., 2004.
[Online] http://anziamj.austms.org.au/V45/CTAC2003.
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Accurately model the {Kuramoto--Sivashinsky} dynamics with holistic
discretisation.
T. MacKenzie and A.~J. Roberts.
Technical report, http://arxiv.org/abs/math.DS/0506562, March 2005 Download (draft) article.
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Computations of short-crested deep-water waves.
M. Ioualalen, M. Okamura, S. Cornier, C. Kharif, and A.~J. Roberts.
J.~Waterwy, Port, Coast and Ocean Enginrg, to appear.
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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.
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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.
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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.
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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.
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A normal form of thin fluid film equations solves the transient paradox.
A.~J. Roberts.
Technical report, http://arxiv.org/abs/nlin.CD/0408059, July 2005 Download (draft) article.
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Check the slowly-varying normal form of thin film fluids.
A.~J. Roberts.
Technical report, http://www.sci.usq.edu.au/staff/aroberts/nff.red, 2004.
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The prisoners may be in two minds.
A.~J. Roberts.
Aust. Maths. Soc. Gazette, 31:30--33, 2004 Download (draft) article.
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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].
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An accurate and comprehensive model of thin fluid flows with inertia on
curved substrates.
A.~J. Roberts and Zhenquan Li.
J.~Fluid Mech., page to appear, 2006.
http://arXiv.org/abs/chao-dyn/9906011 Download (draft) article.
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Two-zone model of shear dispersion in a channel using centre manifolds.
A.~J. Roberts and D.~V. Strunin.
Q.~J. Mech. Appl. Maths., 57:363--378, 2004.
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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].
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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.
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Low-dimensional modelling of a generalized {Burgers'} equation.
Zhenquan Li and A.~J. Roberts.
Technical report, http://arXiv.org/abs/math-ph/0307064, 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/V44/CTAC2001/Mack Download (draft)
article.
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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.
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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.
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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.
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Holistic discretisation of dynamical partial differential equations.
A.~J. Roberts.
Technical report, http://www.sci.usq.edu.au/staff/aroberts/holistic.html,
April 2003.
version 1.1 Download (draft)
article.
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Holistic discretise three coupled dynamical partial differential
equations.
A.~J. Roberts.
Technical report, http://www.sci.usq.edu.au/staff/aroberts/holisti3.html,
April 2003.
version $\beta$.2 Download (draft)
article.
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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/V45/CTAC2003/Robe [December 14,
2003].
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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/V44/CTAC2001/Robe 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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
http://dx.doi.org/10.1017/S0022112001007133.
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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.
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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.
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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.
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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.
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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.
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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 Physics Communications, 142:316--321, 2001 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 Download (draft) article.
-
Holistic discretisation ensures fidelity to {Burgers'} equation.
A.~J. Roberts.
Applied Numerical Modelling, 37:371--396, 2001 Download (draft) article.
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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.
submitted to J.~Eng. Maths. Download (draft) article.
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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.
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An accurate lubrication model of contaminated coating flows.
M.~E. Simpson and A.~J. Roberts.
Computer Phys. Commun., 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.
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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, submitted to Journal of Engineering Mechanics, 2001.
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Reproductive pair correlations, {B}rownian bugs and plankton patches.
W.~R. Young, A.~J. Roberts, and G. Stuhne.
Nature, 412:328--331, 2001.
19th July.
-
A flexible error estimate for the application of centre manifold theory.
Zhenquan Li and A.~J. Roberts.
Technical report, http://arXiv.org/abs/math.DS/0002138, February 2000 Download (draft) article.
-
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.
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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.
-
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.
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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.
-
Dynamics of rubber-like polymers with hyperbolic models of coupled
thermoelasticity.
R.~V.~N. Melnik, D.~V. Strunin, and A.~J. Roberts.
submitted Euro. J.~Mech. A/Solids, March 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.
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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.
-
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.
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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.
-
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.
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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.
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Stability regimes of finite depth short-crested waves.
M. Ioualalen, C. Kharif, and A.~J. Roberts.
J.~Phys. Oceanogr., 29(9):2318--2331, 1999.
-
Modelling dynamics of shape-memory-alloys via computer algebra.
R.~V.~N. Melnik, A.~J. Roberts, and K. A.Thomas.
In V.~V. Varadan, editor, Mathematics and Control in Smart Structures,
Proc. of SPIE, volume 3667, pages 290--301, 1999.
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Dynamics of shape-memory-alloys: A reduction procedure for 3d models.
R.~V.~N. Melnik, A.~J. Roberts, and K.~A. Thomas.
In W. Wunderlich, editor, Proceedings of the European Conference on
Computational Mechanics: Solids, Structures and Coupled Problems in
Engineering, page 328, 1999.
-
Differential-algebraic equations deserve more attention.
A.~J. Roberts.
Aust. Maths. Soc. Gazette, 26:75--79, 1999.
-
Branching behaviour of standing waves---the signatures of resonance.
D. Smith and A.~J. Roberts.
Phys. Fluids, 11(5):1051--1064, May 1999.
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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.
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Advection-dispersion in symmetric field-flow fractionation channels.
S.~A. Suslov and A.~J. Roberts.
J.~Math. Chem., 26:27--46, 1999.
-
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.
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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.
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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.
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{LaTeX}: from quick and dirty to style and finesse.
A.~J. Roberts.
Technical report, http://www.sci.usq.edu.au/staff/aroberts/LaTeX, 1998 Download (draft)
article.
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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.
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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.
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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 Download (draft) article.
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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.
-
Low-dimensional modelling of dynamics via computer algebra.
A.~J. Roberts.
Computer Phys. Comm., 100:215--230, 1997.
-
Low-dimensional modelling of dynamical systems.
A.~J. Roberts.
Technical report, http://arXiv.org/abs/chao-dyn/9705010, 1997 Download (draft) article.
-
Solution to problem 96-14: An integral.
A.~J. Roberts.
SIAM Review, 39:pp526--7, 1997.
-
Modelling and simulation.
A.~J. Roberts.
Australasian Science, 18(3):5--6, sept 1997.
-
Bow-like free surfaces under gravity.
E.~O. Tuck and A.~J. Roberts.
Phil. Trans. R.~Soc. Lond.~A, 355:665--677, 1997.
-
Parallel algorithms for spatial data partition and join processing.
Yanchun Zhang, Jitian Xiao, and A.~J. Roberts.
In A. Goscinski, M. Hobbs, and Wanlei Zhou, editors, Algorithms and
architectures for parallel processing, pages 703--716, 1997.
-
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.
-
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.
-
Unbiased estimation of multi-fractal dimensions of finite data sets.
A.~J. Roberts and A. Cronin.
Physica~A, 233:867--878, 1996.
-
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. Maths. Soc.~B, 38:101--125, 1996.
-
Initial conditions for models of dynamical systems.
S.~M. Cox and A.~J. Roberts.
Physica~D, 85:126--141, 1995.
-
Fractal and multi-fractal patterns of seaweed settlement.
L.~M. Emmerson and A.~J. Roberts.
preprint, 1995.
-
Equations for turbulent flood waves.
Z. Mei and A.~J. Roberts.
In A. Mielke and K. Kirchg\"assner, 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.
-
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.
-
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.
-
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.
-
The importance of beings fractal.
A.~J. Roberts.
Australasian Science, page 23, April 1994.
-
A one-dimensional introduction to continuum mechanics.
A.~J. Roberts.
World Sci, 1994.
-
Estimate generalised fractal dimensions of a set of points.
A.~J. Roberts.
Technical report, http://www.sci.usq.edu.au/staff/aroberts/fdim.sh, 1994
Download (draft)
article.
-
An invariant manifold approach to modelling the dynamics of the
kuramoto-sivashinsky equation.
D.~I. Oats and A.~J. Roberts.
Preprint, 1993.
-
The invariant manifold of beam deformations. part 1: the simple circular
rod.
A.~J. Roberts.
J.~Elas., 30:1--54, 1993.
-
The quasi-geostrophic slow manifold.
S.~M. Cox and A.~J. Roberts.
In Proc 11th Aust. Fluid Mech Conf, 1992.
-
Extreme standing waves and their stability.
G.~N. Mercer and A.~J. Roberts.
In M.~L. Banner and R.~H.~J. Grimshaw, editors, Proc IUTAM Sym on breaking
waves, pages 383--387. Springer-Verlag, 1992.
-
A sub-centre manifold description of the evolution and interaction of
nonlinear dispersive waves.
A.~J. Roberts.
In L. Debnath, editor, Nonlinear waves, chapter 9, pages 127--156.
World Sci, 1992.
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Planform evolution in convection---an embedded centre manifold.
A.~J. Roberts.
J.~Austral. Math. Soc.~B, 34:174--198, 1992.
-
Boundary conditions for approximate differential equations.
A.~J. Roberts.
J.~Austral. Math. Soc.~B, 34:54--80, 1992.
-
Slow methods for simple people.
A.~J. Roberts.
Technical Report WHOI-92-16, Woods Hole Oceanog. Inst., 1992.
pp149--154.
-
Rational mathematical modelling---shear dispersion and planform
selection.
A.~J. Roberts.
Technical Report WHOI-92-16, Woods Hole Oceanog. Inst., 1992.
pp155--166.
-
A virtual supercomputer from a network of workstations.
A.~J. Roberts.
Aust. Adv. Comp. Newslet., 2(2), 1992.
-
Centre manifolds of forced dynamical systems.
S.~M. Cox and A.~J. Roberts.
J.~Austral. Math. Soc.~B, 32:401--436, 1991.
-
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.~Aust. Maths. 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.
http://locus.siam.org/SIAP/volume-50/art_0150091.html.
-
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.
http://locus.siam.org/SIMA/volume-20/art_0520094.html.
-
Appropriate initial conditions for asymptotic descriptions of the long term
evolution of dynamical systems.
A.~J. Roberts.
J.~Austral. Math. Soc.~B, 31:48--75, 1989.
-
Use of implicit and explicit flux-corrected transport algorithms in gas
discharge problems involving a non-uniform velocity fields.
P. Stienle, R. Morrow, and A.~J. Roberts.
J.~Comput Phys., 85, 1989.
-
A variational approach to the problem of deep water waves forming a circular
caustic.
T.~R. Marchant and A.~J. Roberts.
J.~Fluid Mech., 194:581--597, 1988.
-
The application of centre manifold theory to the evolution of systems which
vary slowly in space.
A.~J. Roberts.
J.~Austral. Math. Soc.~B, 29:480--500, 1988.
-
The initial flow of liquid in an accelerating tank.
A.~J. Roberts.
J.~Eng. Mech., 114:175--180, 1988.
-
Properties of short-crested waves in water of finite depth.
T.~R. Marchant and A.~J. Roberts.
J.~Austral. Math. Soc.~B, 29:103--125, 1987.
-
Transient free-surface flows generated by a moving vertical plate.
A.~J. Roberts.
Quart. J.~Mech. Appl. Math., 30:129--158, 1987.
-
An introduction to the technique of reconstitution.
A.~J. Roberts.
SIAM J.~Math. Anal., 16:1243--1257, 1985.
http://locus.siam.org/SIMA/volume-16/art_0516089.html.
-
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 wave.
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.
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