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EDITORIAL: SPECIAL ISSUE IN HONOUR OF PROFESSOR ANTHONY ROBERTS

Published online by Cambridge University Press:  29 October 2025

JUDITH E. BUNDER Open the ORCID record for JUDITH E. BUNDER [Opens in a new window]
JUDITH E. BUNDER*
Affiliation:
UniSA STEM, University of South Australia , Adelaide SA 5000, Australia
*
e-mail: judy.bunder@unisa.edu.au
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Editorial
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The ANZIAM Journal , Volume 67 , 2025 , e36
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© The Author(s), 2025. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc

This issue of the ANZIAM Journal is dedicated to Emeritus Professor Anthony Roberts of the University of Adelaide. Anthony (or Tony, as most of us know him) has made a significant contribution to the ANZIAM Journal, both as a long-time editor and a prolific author. In 1997, he was the founding editor of the Electronic Supplement of the ANZIAM Journal, at a time when there were very few online journals, and he remained in this position until 2022. In this role, he oversaw the publication of the Proceedings of the Mathematics in Industry Study Group (MISG), the Proceedings of the biannual Engineering Mathematics and Applications Conferences (EMAC), and Computational Techniques and Applications Conferences (CTAC). He also pioneered the free publication of all back issues of all AustMS journals, and this service continues today under contract with Cambridge University Press. In 2023, Tony was awarded the prestigious ANZIAM medal, the highest honour for an applied mathematician in our society, in recognition of his many contributions to ANZIAM and his remarkable research achievements.

Tony completed his PhD at the University of Cambridge on nonlinear buoyancy effects in fluids, under the supervision of Herbert Huppert. He is now a leading expert in dynamical systems theory where he develops and applies both theoretical and numeric techniques, including novel computer algebra algorithms, with a focus on the application and principles of modelling the emergent dynamics of complex multiscale system. Tony’s research contributions cover a broad range of applications, such as dispersion through rivers and pipes; turbulent dynamics of rivers and floods; elastic deformations; shape-memory alloy probability distributions; discrete models of partial differential equations for numerical analysis; and error bounds of numerical methods. This special issue, consisting of articles from a few of Tony’s collaborators, highlights the diversity of his interests and his wide-spread influence on applied mathematics research.

During Tony’s Professorship of Applied Mathematics at the University of Southern Queensland (1993–2008), he began collaborating with Dmitry Strunin, Sergey Suslov, Mansour Ioualalen and Zhenquan Li, on a variety of topics, including nonlinear theories, turbulence, flow in thin film and channels, and wave stability in deep water. Here, Strunin, Malomed and McKeiver [Reference Strunin, Malomed and McKeiver8] present numerical results for symmetries in soliton collisions, Pototsky and Suslov [Reference Pototsky and Suslov6] study the influence of harmonic vibrations on the formation of solitary waves in liquid films, Colón Useche, Paul and Ioualalen [Reference Colón Useche, Paul and Ioualalen3] discuss the persistency of resonance in deep water waves, and Lal and Li [Reference Lal and Li5] verify the accuracy of a mesh refinement for flow about a square cylinder.

One of Tony’s major research interests is the low-dimensional modelling of multiscale dynamical and stochastic systems, and their emergent behaviours, and this led to collaborations with Wei Wang, Giovanni Samaey and Jinqiao Duan. Here, Bossuyt, Vandewalle and Samaey [Reference Bossuyt, Vandewalle and Samaey1] study the convergence of the Parareal algorithm for multiscale initial-value problems, and Zhang, Gao, Guo, Duan and Nikolenko [Reference Zhang, Gao, Guo, Duan and Nikolenko9] propose an early warning system for epilepsy patients based on eeg data; thus illustrating the broad applicability of data-driven models and numerical algorithms. At the University of Adelaide (2008–2020 as Professor, 2020–present as Emeritus Professor), Tony continued his work on emergent dynamics in collaboration with Wei Wang, Xiaolong Chen and myself, and applied his methodologies to applications, such as biological processes in collaboration with Sarthok Sircar. Here, Shi and Wang [Reference Shi and Wang7] conduct a stability analysis for the stochastic McKean–Vlasov equation, and Chen and Gao [Reference Chen and Gao2] study the stochastic Kuramoto–Sivashinsky equation and the existence and uniqueness of its solutions. Also, Ghosh, Chauhan and Sircar [Reference Ghosh, Chauhan and Sircar4] propose a time integration method for the fractional advection–diffusion-reaction equations.

It has been a pleasure to compile this special issue of the ANZIAM Journal and to present a small sample of the diverse interests of Tony and his collaborators. Long may Tony continue in his role as researcher, collaborator and mentor at the Adelaide University (from 2026)!

References

Bossuyt, I., Vandewalle, S. and Samaey, G., “Micro-macro Parareal, from ordinary differential equations to stochastic differential equations and back again”, ANZIAM J. 67 (2025) Article ID e13; doi:10.1017/S1446181124000270.CrossRefGoogle Scholar
Chen, X. and Gao, H., “Dynamics of nonlocal Kuramoto–Sivashinsky equations with multiplicative white noise”, ANZIAM J. 67 (2025) Article ID e34; doi:10.1017/S1446181125100187.CrossRefGoogle Scholar
Colón Useche, S. C., Paul, S. and Ioualalen, M., “Harmonic resonance of short-crested gravity waves on deep water: On their persistency”, ANZIAM J. 67 (2025) Article ID e1; doi:10.1017/S1446181124000129.CrossRefGoogle Scholar
Ghosh, D., Chauhan, T. and Sircar, S., “Implicit-explicit time integration method for fractional advection-diffusion-reaction equations”, ANZIAM J. 67 (2025) Article ID e2; doi:10.1017/S1446181124000154.CrossRefGoogle Scholar
Lal, R. and Li, Z., “Further accuracy verification of a 2D adaptive mesh refinement method using steady flow past a square cylinder”, ANZIAM J. 67 (2025) Article ID e3; doi:10.1017/S1446181124000166.CrossRefGoogle Scholar
Pototsky, A. and Suslov, S. A., “Effect of external harmonic vibrations on the formation of solitary waves in falling two-layer liquid films”, ANZIAM J. 67 (2025) Article ID e5; doi:10.1017/S144618112400018X.CrossRefGoogle Scholar
Shi, C. and Wang, W., “Stability analysis for stochastic McKean–Vlasov equation”, ANZIAM J. 67 (2025) Article ID e6; doi:10.1017/S1446181124000208.CrossRefGoogle Scholar
Strunin, D. V., Malomed, B. A. and McKeiver, J. L., “Symmetry restoration in collisions of solitons in fractional couplers”, ANZIAM J. 67 (2025) Article ID e7; doi:10.1017/S1446181124000245.CrossRefGoogle Scholar
Zhang, P., Gao, T., Guo, J., Duan, J. and Nikolenko, S., “Early warning prediction with automatic labelling in epilepsy patients”, ANZIAM J. 67 (2025) Article ID e4; doi:10.1017/S1446181124000178.CrossRefGoogle Scholar