Anthony Roberts

Rigorous modelling of nonlocal interactions determines a macroscale advection-diffusion PDE

Publisher: Springer International Publishing

Date: 2021

DOI: 10.1007/978-3-030-62497-2_25

Adaptively Detect and Accurately Resolve Macro-scale Shocks in an Efficient Equation-Free Multiscale Simulation

Publisher: Society for Industrial & Applied Mathematics (SIAM)

Date: 08-2022

DOI: 10.1137/21M1437172

Proceedings of the Mathematics for Industry NZ Study Group 2017

Publisher: Australian Mathematical Publishing Association, Inc.

Date: 15-08-2019

DOI: 10.21914/ANZIAMJ.V59I0.14540

Abstract: This Special Section of the ANZIAM Journal (Electronic Supplement) contains the refereed papers from the 2017 Mathematics for Industry NZ Study Group (MINZ 2017) held at Victoria University, Wellington, New Zealand from 26--30 June, 2017. The MINZ is a special interest meeting of ANZIAM, the Australia and New Zealand Industrial and Applied Mathematics ision of the Australian Mathematics Society. MINZ was formed to provide a national entity to host workshops where companies pitch their problems to New Zealand’s mathematical scientists. They then work collaboratively to generate practical solutions through modelling, statistical analysis or computation.

Proceedings of the 2022 Mathematics in Industry Study Group

Publisher: Australian Mathematical Publishing Association, Inc.

Date: 06-12-2022

DOI: 10.21914/ANZIAMJ.V64.17494

Abstract: This special Section of the ANZIAM Journal (Electronic Supplement) contains the refereed papers from the 2022 Mathematics in Industry Study Group (MISG2022) held at the University of Newcastle from 14--18 February 2022. This report provides the equation-free outcomes.

High-order homogenisation by learning spatial discretisations of PDEs that provably preserve self-adjointness

Publisher: Elsevier BV

Date: 12-2022

DOI: 10.1016/J.PADIFF.2022.100449

Equation-free patch scheme for efficient computational homogenisation via self-adjoint coupling

Publisher: Springer Science and Business Media LLC

Date: 10-2021

DOI: 10.1007/S00211-021-01232-5

Proceedings of the 2021 Mathematics in Industry Study Group

Publisher: Australian Mathematical Publishing Association, Inc.

Date: 16-02-2023

DOI: 10.21914/ANZIAMJ.V63.17984

Abstract: This special Section of the ANZIAM Journal (Electronic Supplement) contains the refereed papers from the 2021 Mathematics in Industry Study Group (MISG-2021) held at the University of Newcastle from 27 to 30 January 2021. This report provides the equation-free outcomes.

Smooth subgrid fields underpin rigorous closure in spatial discretisation of reaction–advection–diffusion PDEs

Publisher: Elsevier BV

Date: 10-2018

DOI: 10.1016/J.APNUM.2018.05.011

A toolbox of equation-free functions in Matlab/Octave for efficient system level simulation

Publisher: Springer Science and Business Media LLC

Date: 30-10-2021

DOI: 10.1007/S11075-020-01027-Z

Nonlinear emergent macroscale PDEs, with error bound, for nonlinear microscale systems

Publisher: Springer Science and Business Media LLC

Date: 19-06-2021

DOI: 10.1007/S42452-021-04229-9

Abstract: Many multiscale physical scenarios have a spatial domain which is large in some dimensions but relatively thin in other dimensions. These scenarios includes homogenization problems where microscale heterogeneity is effectively a ‘thin dimension’. In such scenarios, slowly varying, pattern forming, emergent structures typically dominate the large dimensions. Common modelling approximations of the emergent dynamics usually rely on self-consistency arguments or on a nonphysical mathematical limit of an infinite aspect ratio of the large and thin dimensions. Instead, here we extend to nonlinear dynamics a new modelling approach which analyses the dynamics at each cross-section of the domain via a multivariate Taylor series (Roberts and Bunder in IMA J Appl Math 82(5):971–1012, 2017. 10.1093/imamat/hxx021 ). Centre manifold theory extends the analysis at in idual cross-sections to a rigorous global model of the system’s emergent dynamics in the large but finite domain. A new remainder term quantifies the error of the nonlinear modelling and is expressed in terms of the interaction between cross-sections and the fast and slow dynamics. We illustrate the rigorous approach by deriving the large-scale nonlinear dynamics of a thin liquid film on a rotating substrate. The approach developed here empowers new mathematical and physical insight and new computational simulations of previously intractable nonlinear multiscale problems.

Proceedings of the Mathematics for Industry NZ Study Group 2016

Publisher: Australian Mathematical Publishing Association, Inc.

Date: 29-11-2016

DOI: 10.21914/ANZIAMJ.V58I0.11555

Normal forms and invariant manifolds for nonlinear, non-autonomous PDEs, viewed as ODEs in infinite dimensions

Publisher: Elsevier BV

Date: 12-2019

DOI: 10.1016/J.JDE.2019.07.021

COUPLE MICROSCALE PERIODIC PATCHES TO SIMULATE MACROSCALE EMERGENT DYNAMICS

Publisher: Cambridge University Press (CUP)

Date: 2018

DOI: 10.1017/S1446181117000396

Abstract: Macroscale “continuum” level predictions are made by a new way to construct computationally efficient “wrappers” around fine-scale, microscopic, detailed descriptions of dynamical systems, such as molecular dynamics. It is often significantly easier to code a microscale simulator with periodicity: so the challenge addressed here is to develop a scheme that uses only a given periodic microscale simulator specifically, one for atomistic dynamics. Numerical simulations show that applying a suitable proportional controller within “action regions” of a patch of atomistic simulation effectively predicts the macroscale transport of heat. Theoretical analysis establishes that such an approach will generally be effective and efficient, and also determines good values for the strength of the proportional controller. This work has the potential to empower systematic analysis and understanding at a macroscopic system level when only a given microscale simulator is available.

A Model for Coating Steel—Draining Under Gravity

Publisher: Springer Nature Singapore

Date: 2022

DOI: 10.1007/978-981-19-1154-5_1

Proceedings of the 2020 Mathematics in Industry Study Group

Publisher: Australian Mathematical Publishing Association, Inc.

Date: 06-12-2022

DOI: 10.21914/ANZIAMJ.V62.17406

Abstract: MISG 2020 University of Newcastle, Australia 28 January -- 1 February, 2020 This special Section of the ANZIAM Journal (Electronic Supplement) contains the refereed papers from the 2020 Mathematics and Statistics in Industry Study Group (MISG 2020) held at the University of Newcastle from 28 January -- 1 February 2020. The MISG is a special interest meeting of ANZIAM, the Australia and New Zealand Industrial and Applied Mathematics (ANZIAM) ision of the Australian Mathematics Society. The MISG meetings take place annually and provide a forum where projects proposed by industry can be worked on intensively, by high profile scientists in the fields of Applied Mathematics, Statistics and Operations Research, from Australia, New Zealand and the world beyond, along with representatives from the industries proposing the projects. The writing of these papers was coordinated by the project moderators in consultation with the coauthors and company representatives. The manuscripts were submitted to the editors, Associate Professor Mike Meylan, Professor Ngamta Thamwattana and Professor Tony Roberts, and were subsequently refereed by two expert referees. On the advice of the referees, manuscripts were accepted for publication, subject to the recommended revisions, and formally approved by the editorial committee. At MISG 2020, six projects were presented from erse industries, with 78 delegates participating. Industry Partners We gratefully acknowledge the support of our industry partners: Lovells Springs Safearth Concrush Hyper Q Aerospace. Acknowledgements In addition to our industry partners, we gratefully acknowledge support from the following organisations: ANZIAM Office of the NSW Chief Scientist \\& Engineer, Department of Industry, NSW Government Priority Research Centre: Computer Assisted Research Mathematics and its Applications, The University of Newcastle Faculty of Science, The University of Newcastle. We are also grateful to Professor Ryan Loxton from the Centre for Optimisation and Decision Science, Curtin University, for giving a public lecture on power of optimisation research in mining, energy, and agriculture industries, as part of the MISG's outreach event and acknowledge the support from the Hunter Branch of the Royal Society of NSW in promoting the public lecture. We are also grateful to Professor Mark McGuinness (Victoria University of Wellington), Professor Troy Farrell (Queensland University of Technology), Associate Professor Amie Albrecht (University of South Australia) and Dr Neville Fowkes (University of Western Australia) for their helpful advice and comments in organising the MISG 2020. MISG2020 Organising Committee Professor Ngamta Thamwattana (Co-Director) Associate Professor Mike Meylan (Co-Director) Mrs Juliane Turner (Administrative Support) Dr David Allingham (Technical Support)

Two novel families of multiscale staggered patch schemes efficiently simulate large-scale, weakly damped, linear waves

Publisher: Elsevier BV

Date: 08-2023

DOI: 10.1016/J.CMA.2023.116133

Proceedings of the Mathematics in Industry Study Group 2012

Publisher: Australian Mathematical Publishing Association, Inc.

Date: 16-06-2015

DOI: 10.21914/ANZIAMJ.V54I0.9753

Large-scale simulation of shallow water waves via computation only on small staggered patches

Publisher: Wiley

Date: 03-11-2020

DOI: 10.1002/FLD.4915

LYAPUNOV EXPONENTS OF THE KURAMOTO–SIVASHINSKY PDE

Publisher: Cambridge University Press (CUP)

Date: 07-2019

DOI: 10.1017/S1446181119000105

Abstract: The Kuramoto–Sivashinsky equation is a prototypical chaotic nonlinear partial differential equation (PDE) in which the size of the spatial domain plays the role of a bifurcation parameter. We investigate the changing dynamics of the Kuramoto–Sivashinsky PDE by calculating the Lyapunov spectra over a large range of domain sizes. Our comprehensive computation and analysis of the Lyapunov exponents and the associated Kaplan–Yorke dimension provides new insights into the chaotic dynamics of the Kuramoto–Sivashinsky PDE, and the transition to its one-dimensional turbulence.

Proceedings of the Mathematics for Industry NZ Study Group 2015

Publisher: Australian Mathematical Publishing Association, Inc.

Date: 02-03-2016

DOI: 10.21914/ANZIAMJ.V57I0.10620

Couple microscale periodic patches to simulate macroscale emergent dynamics

Publisher: Australian Mathematical Publishing Association, Inc.

Date: 04-04-2018

DOI: 10.21914/ANZIAMJ.V59I0.11859

Proceedings of the 2015 Mathematics and Statistics in Industry Study Group

Publisher: Australian Mathematical Publishing Association, Inc.

Date: 02-07-2016

DOI: 10.21914/ANZIAMJ.V57I0.11056

Slow-burning instabilities of Dufort-Frankel finite differencing

Publisher: Australian Mathematical Publishing Association, Inc.

Date: 30-07-2021

DOI: 10.21914/ANZIAMJ.V63.15640

Abstract: DuFort–Frankel averaging is a tactic to stabilize Richardson’s unstable three-level leapfrog timestepping scheme. By including the next time level in the right-hand-side evaluation, it is implicit, but it can be rearranged to give an explicit updating formula, thus apparently giving the best of both worlds. Textbooks prove unconditional stability for the heat equation, and extensive use on a variety of advection–diffusion equations has produced many useful results. Nonetheless, for some problems the scheme can fail in an interesting and surprising way, leading to instability at very long times. An analysis for a simple problem involving a pair of evolution equations that describe the spread of a rabies epidemic gives insight into how this occurs. An even simpler modified diffusion equation suffers from the same instability. Finally, the rabies problem is revisited and a stable method is found for a restricted range of parameter values, although no prescriptive recipe is known which selects this particular choice. doi:10.1017/S1446181121000043

Proceedings of the 2014 Mathematics and Statistics in Industry Study Group

Publisher: Australian Mathematical Publishing Association, Inc.

Date: 02-07-2016

DOI: 10.21914/ANZIAMJ.V56I0.11055

Trinity College, University Of Cambridge

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Trinity College, University Of Cambridge

Location: United Kingdom of Great Britain and Northern Ireland

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University Of Adelaide

Location: Australia

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University Of Cambridge

Location: United Kingdom of Great Britain and Northern Ireland

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University Of Southern Queensland

Location: Australia

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ARC Complex Open Systems Research Network

Start Date: 2004

End Date: 2009

Funder: Australian Research Council

Modeling, Mathematical Analysis, And Computation Of Multiscale Systems

Start Date: 2020

End Date: 2022

Funder: Australian Research Council

Multiscale Modelling Of Systems With Complex Microscale Detail

Start Date: 2018

End Date: 2020

Funder: Australian Research Council

Energetically Open Systems Research Network Study

Start Date: 2003

End Date: 2003

Funder: Australian Research Council

Discovery Projects - Grant ID: DP0774311

Start Date: 2007

End Date: 12-2012

Amount: $392,141.00

Funder: Australian Research Council

Discovery Projects - Grant ID: DP0560040

Start Date: 06-2005

End Date: 12-2007

Amount: $118,000.00

Funder: Australian Research Council

Discovery Projects - Grant ID: DP150102385

Start Date: 02-2015

End Date: 12-2019

Amount: $530,700.00

Funder: Australian Research Council

Discovery Projects - Grant ID: DP200103097

Start Date: 02-2020

End Date: 12-2024

Amount: $510,000.00

Funder: Australian Research Council

Linkage Projects - Grant ID: LP100100613

Start Date: 01-2011

End Date: 01-2014

Amount: $448,000.00

Funder: Australian Research Council

Discovery Projects - Grant ID: DP0988738

Start Date: 2009

End Date: 12-2012

Amount: $315,000.00

Funder: Australian Research Council

Special Research Initiatives - Grant ID: SR0354716

Start Date: 12-2003

End Date: 12-2004

Amount: $10,000.00

Funder: Australian Research Council

Discovery Projects - Grant ID: DP120104260

Start Date: 2012

End Date: 06-2015

Amount: $330,000.00

Funder: Australian Research Council

Linkage Projects - Grant ID: LP110200799

Start Date: 03-2012

End Date: 08-2014

Amount: $360,000.00

Funder: Australian Research Council

Research Networks - Grant ID: RN0460006

Start Date: 07-2004

End Date: 06-2009

Amount: $1,500,000.00

Funder: Australian Research Council

Discovery Projects - Grant ID: DP180100050

Start Date: 2018

End Date: 12-2021

Amount: $327,234.00

Funder: Australian Research Council

Discovery Projects - Grant ID: DP220103156

Start Date: 06-2023

End Date: 05-2026

Amount: $375,000.00

Funder: Australian Research Council