Coupled thermomechanical waves in hyperbolic thermoelasticity
Article
Strunin, D. V., Melnik, R. V. N. and Roberts, A. J.. 2001. "Coupled thermomechanical waves in hyperbolic thermoelasticity." Journal of Thermal Stresses. 24 (2), pp. 121-140. https://doi.org/10.1080/01495730150500433
| Article Title | Coupled thermomechanical waves in hyperbolic thermoelasticity |
|---|---|
| ERA Journal ID | 3788 |
| Article Category | Article |
| Authors | Strunin, D. V. (Author), Melnik, R. V. N. (Author) and Roberts, A. J. (Author) |
| Journal Title | Journal of Thermal Stresses |
| Journal Citation | 24 (2), pp. 121-140 |
| Number of Pages | 20 |
| Year | 2001 |
| Place of Publication | Philadelphia, PA. United States |
| ISSN | 0149-5739 |
| 1521-074X | |
| Digital Object Identifier (DOI) | https://doi.org/10.1080/01495730150500433 |
| Web Address (URL) | http://pdfserve.informaworld.com/925998_751304989_713855301.pdf |
| Abstract | Using models incorporating a thermal relaxation time (hyperbolic models), we study the properties of spatially periodic thermoelastic waves propagating in an infinite rod. Analyzing the Lord-Schulman and Green-Lindsay linear models, we reveal dependencies of decay rates and frequency shifts of temperature and displacement upon the wave number for the case of weak thermoelastic coupling. We explore numerically a general nonlinear hyperbolic model, describing the time evolution of initially sinusoidal distributions of displacement and temperature. Mechanisms of nonlinear interaction between thermal and mechanical fields are qualitatively analyzed. It is demonstrated that larger relaxation times may provide smoother temperature profiles at an intermediate stage of the dynamics. |
| Keywords | coupled thermomechanical fields; hyperbolic thermoelasticity; thermal relaxation time |
| ANZSRC Field of Research 2020 | 510304. Thermodynamics and statistical physics |
| 490410. Partial differential equations | |
| 401205. Experimental methods in fluid flow, heat and mass transfer | |
| Public Notes | Files associated with this item cannot be displayed due to copyright restrictions. |
| Byline Affiliations | Department of Mathematics and Computing |
| Commonwealth Scientific and Industrial Research Organisation (CSIRO), Australia |
Permalink -
https://research.usq.edu.au/item/9y53y/coupled-thermomechanical-waves-in-hyperbolic-thermoelasticity
2094
total views72
total downloads4
views this month0
downloads this month
Export as
Related outputs
Finding exact solutions for selected nonlinear evolution differential equations
Bhanot, Rajeev P., Mohammed, Mayada G.. and Strunin, Dmitry V.. 2023. "Finding exact solutions for selected nonlinear evolution differential equations." Journal of Interdisciplinary Mathematics. 26 (7), pp. 1461-1470. https://doi.org/10.47974/JIM-1566Symmetry-breaking transitions in quiescent and moving solitons in fractional couplers
Strunin, Dmitry V. and Malomed, Boris A.. 2023. "Symmetry-breaking transitions in quiescent and moving solitons in fractional couplers." Physical Review E. 107 (6). https://doi.org/10.1103/PhysRevE.107.064203An effective high-order five-point stencil, based on integrated-RBF approximations, for the first biharmonic equation and its applications in fluid dynamics
Mai-Duy, Nam, Tien, Cam Minh Tri, Strunin, Dmitry and Karunasena, Karu. 2023. "An effective high-order five-point stencil, based on integrated-RBF approximations, for the first biharmonic equation and its applications in fluid dynamics." International Journal of Numerical Methods for Heat and Fluid Flow. 33 (7), pp. 2593-2616. https://doi.org/10.1108/HFF-11-2022-0673A new high-order nine-point stencil, based on integrated-RBF approximations, for the first biharmonic equation
Mai-Duy, N., Strunin, D. and Karunasena, W.. 2022. "A new high-order nine-point stencil, based on integrated-RBF approximations, for the first biharmonic equation." Engineering Analysis with Boundary Elements. 143, pp. 687-699. https://doi.org/10.1016/j.enganabound.2022.07.014Computing high-order derivatives in compact integrated-RBF stencils
Mai-Duy, N., Strunin, D. and Karunasena, W.. 2022. "Computing high-order derivatives in compact integrated-RBF stencils." Engineering Analysis with Boundary Elements. 135, pp. 369-381. https://doi.org/10.1016/j.enganabound.2021.11.025New approximations for one-dimensional 3-point and two-dimensional 5-point compact integrated RBF stencils
Mai-Duy, Nam and Strunin, Dmitry. 2021. "New approximations for one-dimensional 3-point and two-dimensional 5-point compact integrated RBF stencils." Engineering Analysis with Boundary Elements. 125, pp. 12-22. https://doi.org/10.1016/j.enganabound.2021.01.001Parametric Space for Elastic Waves in Porous Media with Complex Rheology
Ali, Adham A. and Strunin, Dmitry V.. 2020. "Parametric Space for Elastic Waves in Porous Media with Complex Rheology." International Journal of Mechanical Engineering and Robotics Research. 9 (6), pp. 825-829. https://doi.org/10.18178/ijmerr.9.6.825-829Numerical solution of a highly nonlinear and non-integrable equation using integrated radial basis function network method
Bhanot, Rajeev P., Strunin, Dmitry V. and Ngo-Cong, Duc. 2020. "Numerical solution of a highly nonlinear and non-integrable equation using integrated radial basis function network method." Chaos: an interdisciplinary journal of nonlinear science. 30 (8). https://doi.org/10.1063/5.0009215Rheology and decay rate for Frenkel-Biot P1 waves in porous media with gas bubbles
Strunin, Dmitry V. and Ali, Adham A.. 2019. "Rheology and decay rate for Frenkel-Biot P1 waves in porous media with gas bubbles." International Journal of Mechanics. 13, pp. 156-163.The role of rheology in modelling elastic waves with gas bubbles in granular fluid-saturated media
Ali, Adham A. and Strunin, Dmitry V.. 2019. "The role of rheology in modelling elastic waves with gas bubbles in granular fluid-saturated media." Journal of Mechanics of Materials and Structures. 14 (1), pp. 1-24. https://doi.org/10.2140/jomms.2019.14.1Parameters and branching auto-pulses in a fluid channel with active walls
Strunin, Dmitry and Ahmed, Fatima. 2019. "Parameters and branching auto-pulses in a fluid channel with active walls." Fluids. 4 (3). https://doi.org/10.3390/fluids4030160Nonlinear stability in seismic waves
Ali, Adham A. and Strunin, Dmitry V.. 2017. "Nonlinear stability in seismic waves." Australian and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal. 57, pp. C382-C397. https://doi.org/10.21914/anziamj.v57i0.10441Dynamics of curved reaction fronts under a single-equation model
Bhanot, R. P. and Strunin, D.V.. 2018. "Dynamics of curved reaction fronts under a single-equation model." Australian and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal. 57, pp. C398-C412. https://doi.org/10.21914/anziamj.v57i0.10446The effect of rheology with gas bubbles on linear elastic waves in fluid-saturated granular media
Ali, A. A. and Strunin, D. V.. 2018. "The effect of rheology with gas bubbles on linear elastic waves in fluid-saturated granular media." International Journal of Applied Mechanics and Engineering. 23 (3), pp. 575-594. https://doi.org/10.2478/ijame-2018-0031Simulations of autonomous fluid pulses between active elastic walls using the 1D-IRBFN Method
Ahmed, Fatima Z., Mohammed, Mayada G., Strunin, Dmitry V. and Ngo-Cong, Duc. 2018. "Simulations of autonomous fluid pulses between active elastic walls using the 1D-IRBFN Method ." Mathematical Modelling of Natural Phenomena (MMNP). 13 (5), pp. 1-25. https://doi.org/10.1051/mmnp/2018058Co-ordinate transforms underpin multiscale modelling and reduction in deterministic and stochastic systems
Roberts, A. J.. 2008. "Co-ordinate transforms underpin multiscale modelling and reduction in deterministic and stochastic systems." Abbott, Derek, Aste, Tomaso, Batchelor, Murray and Dewar, Robert (ed.) Complex Systems II: SPIE Symposium on Microelectronics, MEMS, and Nanotechnology 2007. Canberra, Australia 05 - 07 Dec 2007 United States. SPIE. https://doi.org/10.1117/12.767596A generalised finite difference scheme based on compact integrated radial basis function for flow in heterogeneous soils
Ngo-Cong, D., Tien, C.M.T., Nguyen-Ky, T., An-Vo, D.-A., Mai-Duy, N., Strunin, D. V. and Tran-Cong, T.. 2017. "A generalised finite difference scheme based on compact integrated radial basis function for flow in heterogeneous soils." International Journal for Numerical Methods in Fluids. 85 (7), pp. 404-429. https://doi.org/10.1002/fld.4386A dynamical systems approach to simulating macroscale spatial dynamics in multiple dimensions
Roberts, A. J., MacKenzie, T. and Bunder, J. E.. 2014. "A dynamical systems approach to simulating macroscale spatial dynamics in multiple dimensions." Journal of Engineering Mathematics. 86 (1), pp. 175-207. https://doi.org/10.1007/s10665-013-9653-6On nonlinear dynamics of neutral modes in elastic waves in granular media
Strunin, D. V. and Ali, A. A.. 2016. "On nonlinear dynamics of neutral modes in elastic waves in granular media." Journal of Coupled Systems and Multiscale Dynamics. 4 (3). https://doi.org/10.1166/jcsmd.2016.1105Numerical solution for the fluid flow between active elastic walls
Ahmed, F. Z., Strunin, D. V., Mohammed, M. G. and Bhanot, R. P.. 2016. "Numerical solution for the fluid flow between active elastic walls." Australian and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal. 57, pp. C221-C234. https://doi.org/10.21914/anziamj.v57i0.10453Using 1D-IRBFN method for solving high-order nonlinear differential equations arising in models of active-dissipative systems
Strunin, Dmitry V., Ngo-Cong, Duc and Bhanot, Rajeev. 2015. "Using 1D-IRBFN method for solving high-order nonlinear differential equations arising in models of active-dissipative systems." Idelsohn, Sergio R., Sonzogni, Victorio, Coutinho, Alvaro, Cruchaga, Marcela, Lew, Adrian and Cerrolaza, Miguel (ed.) 1st Pan-American Congress on Computational Mechanics, (PANACM 2015) in conjunction with the XI Argentine Congress on Computational Mechanics (MECOM 2015). Buenos Aires, Argentina 27 - 29 Apr 2015 Barcelona, Spain.Range of validity and intermittent dynamics of the phase of oscillators with nonlinear self-excitation
Strunin, D. V. and Mohammed, M. G.. 2015. "Range of validity and intermittent dynamics of the phase of oscillators with nonlinear self-excitation." Communications in Nonlinear Science and Numerical Simulation. 29 (1-3), pp. 128-147. https://doi.org/10.1016/j.cnsns.2015.04.024On dissipative nature of elastic waves
Strunin, D. V.. 2014. "On dissipative nature of elastic waves." Journal of Coupled Systems and Multiscale Dynamics. 2 (2), pp. 70-73. https://doi.org/10.1166/jcsmd.2014.1045Higher-order approximation of contaminant transport equation for turbulent channel flows based on centre manifolds and its numerical solution
Ngo-Cong, D., Mohammed, F. J., Strunin, D. V., Skvortsov, A. T., Mai-Duy, N. and Tran-Cong, T.. 2015. "Higher-order approximation of contaminant transport equation for turbulent channel flows based on centre manifolds and its numerical solution." Journal of Hydrology. 525, pp. 87-101. https://doi.org/10.1016/j.jhydrol.2015.03.038Soliton-like thermoelastic waves
Strunin, Dmitry and Melnik, Roderick. 2014. "Soliton-like thermoelastic waves ." Hetnarski, Richard B. (ed.) Encyclopedia of thermal stresses. Dordrecht, Netherlands. Springer. pp. 4433-4438Finite-difference approach for a 6th-order nonlinear phase equation with self-excitation
Mohammed, Mayada and Strunin, Dmitry. 2014. "Finite-difference approach for a 6th-order nonlinear phase equation with self-excitation." Nagamiya, Shoji and Motobayashi, Tohru (ed.) 12th Asia Pacific Physics Conference 2013. Makuhari, Japan 14 - 19 Jul 2013 Makuhari, Japan.Computer algebra derives the slow manifold of patch or element dynamics on lattices in two dimensions
MacKenzie, Tony and Roberts, A. J.. 2014. Computer algebra derives the slow manifold of patch or element dynamics on lattices in two dimensions. Adelaide, Australia. University of Adelaide.Accurate macroscale modelling of spatial dynamics in multiple dimensions
Roberts, A. J., MacKenzie, Tony and Bunder, J. E.. 2012. Accurate macroscale modelling of spatial dynamics in multiple dimensions. Adelaide, Australia. University of Adelaide.Asymptotics of averaged turbulent transfer in canopy flows
Mohammed, F. J., Strunin, D. V., Ngo-Cong, D. and Tran-Cong, T.. 2015. "Asymptotics of averaged turbulent transfer in canopy flows." Journal of Engineering Mathematics. 91 (1), pp. 81-104. https://doi.org/10.1007/s10665-014-9737-yModelling dispersion in laminar and turbulent flows in an open channel based on centre manifolds using 1D-IRBFN method
Mohammed, F. J., Ngo-Cong, D., Strunin, D. V., Mai-Duy, N. and Tran-Cong, T.. 2014. "Modelling dispersion in laminar and turbulent flows in an open channel based on centre manifolds using 1D-IRBFN method." Applied Mathematical Modelling: simulation and computation for engineering and environmental systems. 38 (14), pp. 3672-3691. https://doi.org/10.1016/j.apm.2013.12.007Validity and dynamics in the nonlinearly excited 6th-order phase equation
Strunin, Dimitry and Mohammed, Mayada. 2013. "Validity and dynamics in the nonlinearly excited 6th-order phase equation." Costa, David, Feng, Wei and Feng, Zhaosheng (ed.) 9th American Institute of Mathematical Sciences International Conference on Dynamical Systems, Differential Equations and Applications (AIMS 2013). Orlando, United States 01 - 05 Jul 2012 Springfield, MO. United States.Numerical analysis of an averaged model of turbulent transport near a roughness layer
Strunin, D. V. and Mohammed, F. J.. 2012. "Numerical analysis of an averaged model of turbulent transport near a roughness layer." Australian and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal. 53 (S), pp. C142-C154.Parametric space for nonlinearly excited phase equation
Strunin, D. V. and Mohammed, M. G.. 2012. "Parametric space for nonlinearly excited phase equation." Australian and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal. 53 (S), pp. C236-C248.The role of natural gases in seismics of hydrocarbon reservoirs
Nikolaevskiy, Victor and Strunin, Dmitry. 2012. "The role of natural gases in seismics of hydrocarbon reservoirs." Laverov, N. P., Beresnev, Igor and Gray, Rob (ed.) 3rd International Conference Elastic Wave Effect on Fluid in Porous Media (EWEF 2012). Moscow, Russia 24 - 28 Sep 2012 Moscow, Russia.Branching behavior of standing waves - the signatures of resonance
Smith, D. H. and Roberts, A. J.. 1999. "Branching behavior of standing waves - the signatures of resonance." Physics of Fluids. 11 (5), pp. 1051-1064. https://doi.org/10.1063/1.869976The style files: use the most informative synonym
Roberts, Tony. 2007. "The style files: use the most informative synonym." Gazette of the Australian Mathematical Society. 34 (4), pp. 208-209.Transition to self-similarity of diffusion of tracer in turbulent patch
Strunin, Dmitry V.. 2001. "Transition to self-similarity of diffusion of tracer in turbulent patch." Journal of Engineering Mechanics. 127 (11), pp. 1089-1095. https://doi.org/10.1061/(ASCE)0733-9399(2001)127:11(1089)Modelling the dynamics of turbulent floods
Mei, Z., Roberts, A. J. and Li, Zhenquan. 2002. "Modelling the dynamics of turbulent floods." SIAM Journal on Applied Mathematics. 63 (2), pp. 423-458. https://doi.org/10.1137/S0036139999358866Reproductive pair correlations and the clustering of organisms
Young, W. R., Roberts, A. J. and Stuhne, Gordan. 2001. "Reproductive pair correlations and the clustering of organisms." Nature. 412 (6844), pp. 328-331. https://doi.org/10.1038/35085561The style files: write what you mean
Roberts, Tony. 2007. "The style files: write what you mean." Gazette of the Australian Mathematical Society. 34 (3), pp. 156-157.General tooth boundary conditions for equation free modeling
Roberts, A. J. and Kevrekidis, I. G.. 2007. "General tooth boundary conditions for equation free modeling." SIAM Journal on Scientific Computing. 29 (4), pp. 1495-1510. https://doi.org/10.1137/060654554The style files: appearance affects communication; but not necessarily as you like
Roberts, Tony. 2007. "The style files: appearance affects communication; but not necessarily as you like." Gazette of the Australian Mathematical Society. 34 (2), pp. 78-80.Similarity without diffusion: shear turbulent layer damped by buoyancy
Strunin, D. V.. 2006. "Similarity without diffusion: shear turbulent layer damped by buoyancy." Journal of Engineering Mathematics. 54 (3), pp. 211-224. https://doi.org/10.1007/s10665-005-9010-5On characteristic times in generalized thermoelasticity
Strunin, Dmitry V.. 2001. "On characteristic times in generalized thermoelasticity." Journal of Applied Mechanics. 68 (5), pp. 816-817. https://doi.org/10.1115/1.1386696Two-zone model of shear dispersion in a channel using centre manifolds
Roberts, A. J. and Strunin, Dmitry V.. 2004. "Two-zone model of shear dispersion in a channel using centre manifolds." The Quarterly Journal of Mechanics and Applied Mathematics. 57 (3), pp. 363-378. https://doi.org/10.1093/qjmam/57.3.363Modelling the confinement of spilled oil with floating booms
Zhu, Song Ping and Strunin, Dmitry V.. 2001. "Modelling the confinement of spilled oil with floating booms." Applied Mathematical Modelling: simulation and computation for engineering and environmental systems. 25 (9), pp. 713-729. https://doi.org/10.1016/S0307-904X(01)00008-7The style files: omit redundant words
Roberts, Tony. 2007. "The style files: omit redundant words." Gazette of the Australian Mathematical Society. 34 (1), pp. 20-21.Accurately model the Kuramoto-Sivashinsky dynamics with holistic discretisation
MacKenzie, T. and Roberts, A. J.. 2006. "Accurately model the Kuramoto-Sivashinsky dynamics with holistic discretisation." SIAM Journal on Applied Dynamical Systems. 5 (3), pp. 365-402. https://doi.org/10.1137/050627733A model of turbulent dispersion through roughness layer using centre manifolds
Strunin, Dmitry V.. 2011. "A model of turbulent dispersion through roughness layer using centre manifolds." Massengill, H. P. (ed.) 6th AIAA Theoretical Fluid Mechanics Conference. Honolulu, United States 27 - 30 Jun 2011 Red Hook, NY. United States.Universality of turbulent dispersion in a steady flow in an open channel
Strunin, D. V.. 2011. "Universality of turbulent dispersion in a steady flow in an open channel." The Quarterly Journal of Mechanics and Applied Mathematics. 64 (2), pp. 197-214. https://doi.org/10.1093/qjmam/hbr002Dynamics of two charged particles in viscous fluid at small Reynolds numbers
Stepanyants, Y. A. and Strunin, D. V.. 2011. "Dynamics of two charged particles in viscous fluid at small Reynolds numbers." de Oliveira, Cassiano (ed.) 2011 International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Enginnering (MC 2011). Rio de Janeiro, Brazil 08 - 12 May 2011 Rio de Janeiro.An averaged model of dispersion of pollutant in a channel: logarithmic flow
Strunin, Dmitry V.. 2010. "An averaged model of dispersion of pollutant in a channel: logarithmic flow." Hangos, K. (ed.) 29th IASTED International Conference on Modelling, Identification and Control (MIC 2010). Innsbruck, Austria 15 - 17 Feb 2010 Calgary, Canada.Low-dimensional modelling of a generalised Burgers equation
Li, Zhenquan and Roberts, A. J.. 2007. "Low-dimensional modelling of a generalised Burgers equation." Global Journal of Pure and Applied Mathematics. 3 (3), pp. 203-218.A flexible error estimate for the application of centre manifold theory
Li, Zhenquan and Roberts, A. J.. 2007. "A flexible error estimate for the application of centre manifold theory." Global Journal of Pure and Applied Mathematics. 3 (3), pp. 241-249.Fractal landscape method: an alternative approach to measuring area-restricted searching behavior
Tremblay, Yann, Roberts, Antony J. and Costa, Daniel P.. 2007. "Fractal landscape method: an alternative approach to measuring area-restricted searching behavior." The Journal of Experimental Biology. 210 (6), pp. 935-945. https://doi.org/10.1242/jeb.02710A normal form of thin fluid film equations solves the transient paradox
Roberts, A. J.. 2006. "A normal form of thin fluid film equations solves the transient paradox." Physica D: Nonlinear Phenomena. 223 (1), pp. 69-81. https://doi.org/10.1016/j.physd.2006.08.018Low-dimensional modelling of dynamical systems applied to some dissipative fluid mechanics
Roberts, A. J.. 2003. "Low-dimensional modelling of dynamical systems applied to some dissipative fluid mechanics." Ball, Rowena and Akhmediev, Nial (ed.) Nonlinear dynamics from lasers to butterflies: selected lectures from the 15th Canberra International Physics Summer School. World Scientific Publishing. pp. 257-313Modelling nonlinear dynamics of shape-memory-alloys with approximate models of coupled thermoelasticity
Melnik, Roderick V. N. and Roberts, A. J.. 2003. "Modelling nonlinear dynamics of shape-memory-alloys with approximate models of coupled thermoelasticity." Journal of Applied Mathematics and Mechanics (ZAMM). 83 (2), pp. 93-104. https://doi.org/10.1002/zamm.200310009A new case of truncated phase equation for coupled oscillators
Strunin, Dmitry V.. 2009. "A new case of truncated phase equation for coupled oscillators ." Yahya, Abu Hasan (ed.) 5th Asian Mathematical Conference (AMC2009). Kuala Lumpur, Malaysia 22 - 26 Jun 2009 Kuala-Lumpur, Malaysia.Modelling turbulent flow from dam break using slow manifolds
Georgiev, D. J., Roberts, A. J. and Strunin, D. V.. 2009. "Modelling turbulent flow from dam break using slow manifolds ." Australian and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal. 50 (S), pp. C1033-C1051.Effect of canine hyperimmune plasma on TNFa and inflammatory cell levels in a lipopolysaccharide-mediated rat air pouch model of inflammation
Strunin, Dmitry, Essien, Bryan, Kotiw, Michael and Butler, Harry. 2009. "Effect of canine hyperimmune plasma on TNFa and inflammatory cell levels in a lipopolysaccharide-mediated rat air pouch model of inflammation." Reinhart, Konrad (ed.) Sepsis 2009: Critical Care Conference. Amsterdam, Netherlands 11 - 14 Nov 2009 https://doi.org/10.1186/cc8064Low Prandtl number fluid convection modelled using symbolic algebra (REDUCE) and Matlab
Passmore, Tim and Roberts, A. J.. 2003. "Low Prandtl number fluid convection modelled using symbolic algebra (REDUCE) and Matlab." ANZIAM 2003: Computational Techniques and Applications. Toowoomba, Australia 16 - 18 Jul 2003 Cambridge, United Kingdom .Phase equation with nonlinear excitation for nonlocally coupled oscillators
Strunin, D. V.. 2009. "Phase equation with nonlinear excitation for nonlocally coupled oscillators." Physica D: Nonlinear Phenomena. 238 (18), pp. 1909-1916. https://doi.org/10.1016/j.physd.2009.06.022Low-dimensional boundary-layer model of turbulent dispersion in a channel
Strunin, Dmitry V. and Roberts, Anthony J.. 2009. "Low-dimensional boundary-layer model of turbulent dispersion in a channel." Ao, S. I., Gelman, Len, Hukins, David W. L., Hunter, Andrew and Korsunsky, A. M. (ed.) WCE 2009: World Congress of Engineering . London, United Kingdom 01 - 03 Jul 2009 London, UK.Fluid flow between active elastic plates
Strunin, D. V.. 2009. "Fluid flow between active elastic plates." Australian and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal. 50 (S), pp. C871-C883.Two-dimensional particle solution of the extended Hamilton-Jacobi equation
Strunin, D. V.. 2008. "Two-dimensional particle solution of the extended Hamilton-Jacobi equation." Australian and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal. 50 (August), pp. C282-C291.A mathematical model to account for quantitative iterative effect of TNF-α positive feedback mechanism on inflammatory cascade in TLR-4 mediated TNF-α signaling pathway
Roberts, Tony, Essien, Bryan, Kotiw, Michael, Butler, Harry and Strunin, Dmitry. 2008. "A mathematical model to account for quantitative iterative effect of TNF-α positive feedback mechanism on inflammatory cascade in TLR-4 mediated TNF-α signaling pathway." Ragan, Mark (ed.) 19th International Conference on Genome Informatics (GIW 2008). Gold Coast, Australia 01 - 03 Dec 2008 London, United Kingdom.Dynamical system approach and attracting manifolds in K-epsilon model of turbulent jet
Strunin, D. V.. 2008. "Dynamical system approach and attracting manifolds in K-epsilon model of turbulent jet." Bulletin of the Belgian Mathematical Society: Simon Stevin. 15 (5), pp. 935-946.Advection-dispersion in symmetric field-flow fractionation channels
Suslov, Sergey A. and Roberts, A. J.. 1998. Advection-dispersion in symmetric field-flow fractionation channels. Toowoomba, Australia. University of Southern Queensland.Phenomenological approach to 3D spinning combustion waves: numerical experiments with a rectangular rod
Strunin, Dmitry V. and Suslov, Sergey A.. 2005. "Phenomenological approach to 3D spinning combustion waves: numerical experiments with a rectangular rod." International Journal of Self Propagating High Temperature Synthesis. 14 (1), pp. 33-39.The style files: teach explicit skills with feedback
Roberts, Tony. 2008. "The style files: teach explicit skills with feedback." Gazette of the Australian Mathematical Society. 35 (3), pp. 156-157.The style files: write to read breadth first, not depth first
Roberts, Tony. 2008. "The style files: write to read breadth first, not depth first." Gazette of the Australian Mathematical Society. 35 (1), pp. 17-19.Computer algebra derives discretisations via self-adjoint multiscale modelling
Roberts, A. J.. 2008. "Computer algebra derives discretisations via self-adjoint multiscale modelling." Unpublihsed.Universal regimes of a free turbulent jet
Strunin, D. V.. 2007. "Universal regimes of a free turbulent jet." Jacobs, Peter A., McIntyre, Tim, Cleary, Matthew J., Buttsworth, David R., Mee, David, Clements, Rose, Morgan, Richard and Lemckert, Charles (ed.) 16th Australasian Fluid Mechanics Conference (AFMC 2007). Gold Coast, Australia 03 - 07 Dec 2007 Brisbane, Australia.Attractors in confined source problems for coupled nonlinear diffusion
Strunin, Dmitry V.. 2007. "Attractors in confined source problems for coupled nonlinear diffusion." SIAM Journal on Applied Mathematics. 67 (6), pp. 1654-1674. https://doi.org/10.1137/060657923A numerical model for the confinement of oil spill with floating booms
Zhu, SongPing and Strunin, Dmitry V.. 2002. "A numerical model for the confinement of oil spill with floating booms." Spill Science and Technology Bulletin. 7 (5-6), pp. 249-255. https://doi.org/10.1016/S1353-2561(02)00042-7Computer algebra describes flow of turbulent floods via the Smagorinski large eddy closure
Roberts, A. J.. 2008. Computer algebra describes flow of turbulent floods via the Smagorinski large eddy closure. Toowoomba, Australia. University of Southern Queensland.The inertial dynamics of thin film flow of non-Newtonian fluids
Roberts, A. J.. 2008. "The inertial dynamics of thin film flow of non-Newtonian fluids." Physics Letters A. 372 (10), pp. 1607-1611. https://doi.org/10.1016/j.physleta.2007.10.014Normal form transforms separate slow and fast modes in stochastic dynamical systems
Roberts, A. J.. 2008. "Normal form transforms separate slow and fast modes in stochastic dynamical systems." Physica A: Statistical Mechanics and its Applications. 387 (1), pp. 12-38. https://doi.org/10.1016/j.physa.2007.08.023Computer algebra models dynamics on a multigrid across multiple length and time scales
Roberts, A. J.. 2007. Computer algebra models dynamics on a multigrid across multiple length and time scales.Nonlinear dynamics on centre manifolds describing turbulent floods: k-\omega model
Georgiev, Dian J., Roberts, A. J. and Strunin, Dmitry V.. 2007. "Nonlinear dynamics on centre manifolds describing turbulent floods: k-\omega model." Discrete and Continuous Dynamical Systems Series A.The dynamics of the vertical structure of turbulence in flood flows
Georgiev, D. J., Roberts, A. J. and Strunin, D. V.. 2007. "The dynamics of the vertical structure of turbulence in flood flows." Australian and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal. 48, pp. C573-C590. https://doi.org/10.0000/anziamj.v48i0.124Mathematical and numerical analysis of Falk-Konopka-type models for shape-memory alloys
Melnik, R. V. N., Roberts, A. J. and Thomas, K. A.. 2000. "Mathematical and numerical analysis of Falk-Konopka-type models for shape-memory alloys." International Journal of Differential Equations and Applications. 1A (3), pp. 291-300.Computing dynamics of copper-based SMA via center manifold reduction of 3D models
Melnik, R. V. N., Roberts, A. J. and Thomas, K. A.. 2000. "Computing dynamics of copper-based SMA via center manifold reduction of 3D models." Computational Materials Science. 18 (3/4), pp. 255-268.Models encompassing hydraulic jumps in radial flows over a horizontal plate
Strunin, Dmitry and Roberts, Tony. 2001. "Models encompassing hydraulic jumps in radial flows over a horizontal plate." Kluev, Vitaly and Mastorakis, Nikos (ed.) 2nd WSEAS Multiconference on Applied and Theoretical Mathematics (WSEAS 2001). Cairns, Australia 17 - 23 Dec 2001 Greece.New methods in applied and computational mathematics workshop
Melnik, Roderick. 2000. "New methods in applied and computational mathematics workshop ." Stewart, David , Melnik, Roderick and Oliveira, Suely (ed.) New Methods in Applied and Computational Mathematics Workshop (NEMACOM98). Hervey Bay, Australia 09 Jul 1998 Canberra, Australia.Dip coating process for hot metal castings
McGuinness, M. and Roberts, Anthony. 2000. "Dip coating process for hot metal castings." Hewitt, John (ed.) 16th Australian and New Zealand Mathematics In Industry Study Group (MISG 1999). Brisbane, Australia 01 - 05 Feb 1999 Adelaide, Australia.A corrected quadrature formula and applications
Ujevic, Nenad and Roberts, A. J.. 2004. "A corrected quadrature formula and applications." Australian and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal. 45 (E), pp. E41-E56.Phase transitions in shape memory alloys with hyperbolic heat conduction and differential-algebraic models
Melnik, R. V. N., Roberts, A. J. and Thomas, K. A.. 2002. "Phase transitions in shape memory alloys with hyperbolic heat conduction and differential-algebraic models." Computational Mechanics. 29 (1), pp. 16-26. https://doi.org/10.1007/s00466-002-0311-5Coupled thermomechanical dynamics of phase transitions in shape memory alloys and related hysteresis phenomena
Melnik, R. V. N., Roberts, A. J. and Thomas, K. A.. 2001. "Coupled thermomechanical dynamics of phase transitions in shape memory alloys and related hysteresis phenomena." Mechanics Research Communications. 28 (6), pp. 637-651. https://doi.org/10.1016/S0093-6413(02)00216-1A holistic finite difference approach models linear dynamics consistently
Roberts, A. J.. 2003. "A holistic finite difference approach models linear dynamics consistently." Mathematics of Computation. 72 (241), pp. 247-262. https://doi.org/10.1090/S0025-5718-02-01448-5Holistic discretisation ensures fidelity to Burger's equation
Roberts, A. J.. 2001. "Holistic discretisation ensures fidelity to Burger's equation." Applied Numerical Mathematics. 37 (3), pp. 371-396. https://doi.org/10.1016/S0168-9274(00)00053-2A lubrication model of coating flows over a curved substrate in space
Roy, R. Valery, Roberts, A. J. and Simpson, M. E.. 2002. "A lubrication model of coating flows over a curved substrate in space." Journal of Fluid Mechanics. 454 (1), pp. 235-261. https://doi.org/10.1017/S0022112001007133Nonlinear instability in generalized nonlinear phase diffusion equation
Strunin, Dmitry V.. 2003. "Nonlinear instability in generalized nonlinear phase diffusion equation." Progress of Theoretical Physics Supplement.Computer algebra models the inertial dynamics of a thin film flow of power law fluids and other non-Newtonian fluids
Roberts, A. J.. 2007. Computer algebra models the inertial dynamics of a thin film flow of power law fluids and other non-Newtonian fluids . University of Southern Queensland.Computer algebra derives normal forms of stochastic differential equations
Roberts, A. J.. 2007. Computer algebra derives normal forms of stochastic differential equations . Toowoomba, Australia. University of Southern Queensland.Computer algebra derives discretisations of the stochastically forced Burgers' partial differential equation
Roberts, A. J.. 2006. Computer algebra derives discretisations of the stochastically forced Burgers' partial differential equation. Toowoomba, Australia. University of Southern Queensland.The style files: favour the present tense
Roberts, Tony. 2006. "The style files: favour the present tense." Gazette of the Australian Mathematical Society. 33 (5), pp. 313-314.The style files: explicitly avoid false conditionals
Roberts, Tony. 2006. "The style files: explicitly avoid false conditionals." Gazette of the Australian Mathematical Society. 33 (4), pp. 241-242.The style files: inform with titles, abstracts and introductions
Roberts, Tony. 2006. "The style files: inform with titles, abstracts and introductions." Gazette of the Australian Mathematical Society. 33 (3), pp. 169-170.The style files: clarify this
Roberts, Tony. 2006. "The style files: clarify this." Gazette of the Australian Mathematical Society. 33 (2), pp. 104-105.The style files: prefer active writing to passive
Roberts, Tony. 2006. "The style files: prefer active writing to passive." Gazette of the Australian Mathematical Society. 33 (1), pp. 22-23.Computer algebra resolves a multitude of microscale interactions to model stochastic partial differential equations
Roberts, A. J.. 2005. Computer algebra resolves a multitude of microscale interactions to model stochastic partial differential equations. Toowoomba, Australia. University of Southern Queensland.