Anthony Roberts-数学中心
Anthony Roberts

Overseas Guest Professors:Anthony Roberts

Name:Anthony Roberts
Title:Professor
Gender:male
Tel:
Email:anthony.roberts@adelaide.edu.au
HomePage:
http://www.maths.adelaide.edu.au/anthony.roberts/index.php
Basic:
Professor
School of Mathematical Sciences
The University of Adelaide, Australia
Educational background:
Work experience:
The University of Adelaide, School of Mathematical Sciences
North Terrace, South Australia
Research fields:
Selected Publications

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, accepted Aug 08, 2013, to appear Download (draft) article.
Model emergent dynamics in complex systems. A.~J. Roberts. Technical report, [http://www.maths.adelaide.edu.au/anthony.roberts/modelling.php], 2009--2014 Download (draft) article.
Better buffers for patches in macroscale simulation of systems with microscale randomness. J.~E. Bunder, A.~J. Roberts, and I.G. Kevrekidis. Technical report, [http://arxiv.org/abs/1312.1415], Dec 2013.
Macroscale, slowly varying, models emerge from the microscale dynamics in long thin domains. A.~J. Roberts. Technical report, [http://arxiv.org/abs/1310.1541], Dec 2013.
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. http://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/6137 [May 14, 2013] Download (draft) article.
Numerical integration of ordinary differential equations with rapidly oscillatory factors. J.~E. Bunder and A.~J. Roberts. Technical report, [http://arxiv.org/abs/1305.5022], 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 Download (draft) article.
Accurate macroscale modelling of spatial dynamics in multiple dimensions. A.~J. Roberts, Tony MacKenzie, and Judith Bunder. J.~Engineering Mathematics, Online 01-Oct, 2013 Download (draft) article.
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.
Center manifolds for stochastic evolution equations. Xiaopeng Chen, A.~J. Roberts, and Jinqiao Duan. Technical report, [http://arxiv.org/abs/1210.5924], October 2012 Download (draft) article.
Modify the improved euler scheme to integrate stochastic differential equations. A.~J. Roberts. Technical report, [http://arxiv.org/abs/1210.0933], Oct 2012.
Find centre manifolds of general ordinary differential equations (autonomous). A.~J. Roberts. Technical report, http://www.maths.adelaide.edu.au/anthony.roberts/gencm.php, July 2012 Download (draft) article.
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. http://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/5074 [June 21, 2012] Download (draft) article.
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 for slow-fast stochastic partial differential equations. Wei Wang, A.~J. Roberts, and Jinqiao Duan. J.~Differential Equations, 253(12):3501--3522, 2012.
Averaging 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.
Macroscopic reduction for stochastic reaction-diffusion equations. Wei Wang and A.~J. Roberts. IMA Journal of Applied Mathematics, published online 16 August, 2012.
Mark Nelson, Anthony~J. Roberts, Mary Coupland, Tara Hamilton, and Harvinder Sidhu, editors. Proceedings of the Engineering Mathematics and Applications Conference, volume 53 of ANZIAM Journal, 2012. http://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/5172 Download (draft) article.
Diffusion approximation for self-similarity of stochastic advection in {B}urgers' equation. Wei Wang and A.~J. Roberts. Technical report, [http://arxiv.org/abs/1203.0463v1], 2012.
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. http://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/3764 [August 10, 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.
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, 2011. http://arxiv.org/abs/1102.2037 Download (draft) article.
Scientific achievements:
Other: