ORCID Profile
0000-0001-5355-2288
Current Organisation
University of South Australia
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Research Topics
In Research Link Australia (RLA), "Research Topics" refer to ANZSRC FOR and SEO codes. These topics are either sourced from ANZSRC FOR and SEO codes listed in researchers' related grants or generated by a large language model (LLM) based on their publications.
Top 5 Research Topics
ANZSRC Field of Research (FoR)
Numerical Solution of Differential and Integral Equations | Numerical Analysis | Dynamical Systems in Applications | Applied Mathematics |
ANZSRC Socio-Economic Objective (SEO)
Expanding Knowledge in Engineering | Expanding Knowledge in the Mathematical Sciences
Related Links
Publications
Good coupling for the multiscale patch scheme on systems with microscale heterogeneity
Publisher: Elsevier BV
Date: 05-2017
Diffusive growth of fullerenes and carbon nanotubes
Publisher: AIP Publishing
Date: 22-12-2009
DOI: 10.1063/1.3277673
Abstract: The video of a growing fullerene within a carbon nanotube, initiated by a tungsten catalyst, provides a dramatic realization of a complex nanoscale process. While there may be many detailed models which can account for this growth, we propose one of the simplest possible models which is consistent with the major observed features of the growth process. In particular, we assume that the fullerene is immersed in a carbon vapor environment, and that the growth occurs as a consequence of the diffusion of the carbon vapor into the fullerene. Moreover, we assume that the classical diffusion equation applies in the region exterior to the fullerene and that a standard Stefan condition applies at the moving fullerene surface. We assume that the gaseous medium through which the carbon atoms diffuse is represented through the value of the diffusion coefficient D appearing in the classical diffusion equation. We also assume that the influence of the catalyst is felt through the value of the constant α appearing in the Stefan condition. Based on these assumptions, we derive simple similarity solutions for both spherical and ellipsoidal fullerenes which are entirely consistent with the observations. A corresponding analysis is provided for the longitudinal growth of a carbon nanotube.
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
An Equation Free Algorithm Accurately Simulates Macroscale Shocks Arising From Heterogeneous Microscale Systems
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Date: 2021
High-order homogenisation by learning spatial discretisations of PDEs that provably preserve self-adjointness
Publisher: Elsevier BV
Date: 12-2022
A dynamical systems approach to simulating macroscale spatial dynamics in multiple dimensions
Publisher: Springer Science and Business Media LLC
Date: 10-2013
Slowly varying, macroscale models emerge from microscale dynamics over multiscale domains
Publisher: Oxford University Press (OUP)
Date: 05-07-2017
Nonlinearσ
Publisher: American Physical Society (APS)
Date: 29-10-2004
Accuracy of Patch Dynamics with Mesoscale Temporal Coupling for Efficient Massively Parallel Simulations
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2016
DOI: 10.1137/15M1015005
Proceedings of the 16th Computational Techniques and Applications Conference
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 08-03-2013
Resolution of subgrid microscale interactions enhances the discretisation of nonautonomous partial differential equations
Publisher: Elsevier BV
Date: 07-2017
Geometric influence on Ruderman-Kittel-Kasuya-Yosida interactions in zigzag carbon nanotubes
Publisher: AIP Publishing
Date: 18-04-2012
DOI: 10.1063/1.4704677
Abstract: We derive an analytic description of the spin susceptibility in finite length zigzag carbon nanotubes (CNT) with chirality (n, 0). The spin susceptibility is proportional to the Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions which describes indirect carrier mediated exchange coupling between localized magnetic moments. We show that the strongest RKKY interactions are along the edges of the nanotube and in the thermodynamic limit at half filling with spin symmetry the shape of the susceptibility curve about the edge of the CNT can be determined solely by the lattice geometry represented by the parameter n and a parameter L which describes the nanotube length. We also show that the introduction of Zeeman splitting or doping may have no effect on the spin susceptibility, provided n is small. A detailed knowledge of magnetic interactions, such as RKKY interactions, in CNT is of vital importance to the development of nanotechnology applications.
Superbosonization Formula and its Application to Random Matrix Theory
Publisher: Springer Science and Business Media LLC
Date: 15-09-2027
Electronic properties of carbon nanotubes with distinct bond lengths
Publisher: AIP Publishing
Date: 15-01-2010
DOI: 10.1063/1.3289320
Abstract: In band structure calculations commonly used to derive the electronic properties of carbon nanotubes, it is generally assumed that all bond lengths are equal. However, hexagonal carbon lattices are often irregular and may contain as many as three distinct bond lengths. A regular (n,m) carbon nanotube will be metallic if p=(n−m)/3 for integer p. Here we analytically derive the generalized condition for metallic irregular carbon nanotubes. This condition is particularly relevant to small radius nanotubes and nanotubes experiencing small applied strains.
Physical, cognitive, and mental health impacts of COVID-19 after hospitalisation (PHOSP-COVID): a UK multicentre, prospective cohort study
Publisher: Elsevier BV
Date: 11-2021
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.
Numerical integration of ordinary differential equations with rapidly oscillatory factors
Publisher: Elsevier BV
Date: 07-2015
The macroscale boundary conditions for diffusion in a material with microscale varying diffusivities
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 10-07-2014
Concurrent magnetic and metal-insulator transitions in Eu1−xSmxB6 single crystals
Publisher: AIP Publishing
Date: 26-01-2009
DOI: 10.1063/1.3077023
Abstract: The effects of magnetic doping on a EuB6 single crystal were investigated based on magnetic and transport measurements. A modest 5% Sm substitution for Eu changes the magnetic and transport properties dramatically and gives rise to concurrent antiferromagnetic and metal-insulator transitions (MITs) from ferromagnetic MIT for EuB6. Magnetic doping simultaneously changes the itinerant carrier density and the magnetic interactions. We discuss the origin of the concurrent magnetic MIT in Eu1−xSmxB6.
Proceedings of the 17th Computational Techniques and Applications Conference
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 13-10-2015
Generic short-range interactions in two-leg ladders
Publisher: American Physical Society (APS)
Date: 30-01-2009
Patch dynamics for macroscale modelling in one dimension
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 21-06-2012
Spin-polarized transport in dilute magnetic semiconductor tunnel junctions
Publisher: AIP Publishing
Date: 27-08-2007
DOI: 10.1063/1.2775032
Abstract: The author considers transport properties of a trilayer junction consisting of an insulator sandwiched between two dilute magnetic semiconductors (DMSs). The magnetization directions of the two DMSs are not parallel but at a relative angle of θ. After calculating the transmission probabilities, the author calculates the conductance using the Landauer formula. The author defines a ratio R(θ,T), related to the tunneling magnetoresistance, which compares the θ=0 to the θ≠0 conductance at temperature T. The author also calculates R(θ,T) semiclassically using the well-known Julliere formula. The author shows that, in general, R(θ,T) obtained from the Julliere formula poorly approximates R(θ,T) obtained from the Landauer formula.
Electronic properties of silicon nanotubes with distinct bond lengths
Publisher: American Physical Society (APS)
Date: 03-06-2009
Dynamical symmetry enlargement in metallic zigzag carbon nanotubes
Publisher: American Physical Society (APS)
Date: 16-02-2007
Equation-free patch scheme for efficient computational homogenisation via self-adjoint coupling
Publisher: Springer Science and Business Media LLC
Date: 10-2021
Linking Machine Learning with Multiscale Numerics: Data-Driven Discovery of Homogenized Equations
Publisher: Springer Science and Business Media LLC
Date: 29-10-2020
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
Derivation of the probability distribution function for the local density of states of a disordered quantum wire via the replica trick and supersymmetry
Publisher: Elsevier BV
Date: 2001
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.
Ruderman-Kittel-Kasuya-Yosida interactions on a bipartite lattice
Publisher: American Physical Society (APS)
Date: 29-10-2009
Zigzag carbon nanotubes with generic electron-electron interactions
Publisher: American Physical Society (APS)
Date: 06-10-2009
Proceedings of the 14th Engineering Mathematics and Applications Conference
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 30-08-2020
DOI: 10.21914/ANZIAMJ.V61I0.15015
Abstract: EMAC 2019 UNSW Canberra, Australia 26th Nov–29th Nov 2019 This Special Section of the ANZIAM Journal (Electronic Supplement) contains the refereed papers from the 14th Engineering Mathematics and Applications Conference (EMAC2019), which was held at the UNSW Canberra, Australia from 26th November to 29th November 2019. EMAC is held under the auspices of the Engineering Mathematics Group (EMG), which is a special interest group of the Australian and New Zealand Industrial and Applied Mathematics ision of the Australian Mathematics Society. This conference provides a forum for researchers interested in the development and use of mathematical methods in engineering and applied mathematics, and aims to foster interactions between mathematicians and engineers, from both academia and industry. A further theme of the conference is the mathematical education of applied mathematicians and engineers. The event attracted participants from around the globe, including: New Zealand, Saudi Arabia, United Kingdom, Japan and Australia. The invited speakers at the 2019 meeting crossed the spectrum of specialities in engineering, mathematics, education and industry. They were: Alexander Kalloniatis (Defence Science and Technology Group), Robert K. Niven (UNSW Canberra), Katherine Seaton (La Trobe University) and Antoinette Tordesillas (University of Melbourne). All of the articles included in the EMAC 2019 Proceedings have been critically peer reviewed to the usual standards of the ANZIAM Journal. EMAC 2019 Organising Committee The conference organising committee were Fiona Richmond, Zlatko Jovanoski (Director), Leesa Sidhu, Duncan Sutherland, Fangbao Tian, Isaac Towers, Timothy Trudgian and Simon Watt. The invited speakers were chosen by a committee of experts including Alys Clark, Jennifer Flegg, Bronwyn Hajek (EMG Chair), Zlatko Jovanoski, Dann Mallet, Robert Niven, Brandon Pincombe, Melanie Roberts (Chair) and Harvinder Sidhu.
General model for diffusive growth of nanostructures
Publisher: Oxford University Press (OUP)
Date: 08-08-2013
Two novel families of multiscale staggered patch schemes efficiently simulate large-scale, weakly damped, linear waves
Publisher: Elsevier BV
Date: 08-2023
Macroscale boundary conditions for a non-linear heat exchanger
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 23-09-2020
Boundary conditions for macroscale waves in an elastic system with microscale heterogeneity
Publisher: Oxford University Press (OUP)
Date: 19-03-2018
Phase diagrams of the metallic zigzag carbon nanotube
Publisher: American Physical Society (APS)
Date: 07-2008
Modelling the Diffusive Growth of Carbon Fullerenes
Publisher: Trans Tech Publications, Ltd.
Date: 09-2011
DOI: 10.4028/WWW.SCIENTIFIC.NET/MSF.700.100
Abstract: Recently, the present authors proposed a model describing fullerene growth in carbonvapor for which the di usion equation is assumed outside the fullerene and a family of possibleStefan conditions describe the growing fullerene surface. Here we consider a related model, butwith the additional assumption that the fullerene surface atomic density is constant throughoutthe growth process, which is justi ed by experimental data. We show that this constraint onthe fullerene lattice structure limits the solution to one possible Stefan condition. The proposedmodel may be extended to any nanostructure with constant atomic surface density.
Proceedings of the 11th Engineering Mathematics and Applications Conference
Publisher: Australian Mathematical Publishing Association, Inc.
Date: 17-06-2014
Spin-wave relaxation in diluted magnetic semiconductors within the self-consistent Green’s function approach
Publisher: AIP Publishing
Date: 14-08-2006
DOI: 10.1063/1.2335666
Abstract: The authors employ a self-consistent Green’s function approach to investigate the spin-wave relaxation Γ(p) in diluted magnetic semiconductors. They find that the trend of the spin-wave relaxation strongly depends on the ratio of the itinerant and impurity spin densities. For density ratios in the Ruderman-Kittel-Kasuya-Yosida phase, Γ(p) decreases even though thermal fluctuations increase. On the other hand, in the strong coupling phase, an interesting peak structure appears. They discuss the implications of their numerical results for experiments.
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Multiscale Modelling Of Systems With Complex Microscale Detail
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End Date: 2021
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End Date: 2024
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