ORCID Profile
0000-0002-6688-9346
Current Organisation
UNSW Sydney
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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)
Mathematical Physics not elsewhere classified | Biological Mathematics | Dynamical Systems in Applications | Applied Mathematics |
ANZSRC Socio-Economic Objective (SEO)
Expanding Knowledge in the Physical Sciences | Expanding Knowledge in the Mathematical Sciences
Related Links
Publications
A fractional-order infectivity SIR model
Publisher: Elsevier BV
Date: 06-2016
Time-fractional geometric Brownian motion from continuous time random walks
Publisher: Elsevier BV
Date: 07-2019
Accurate Particle-Based Reaction Algorithms for Fixed Timestep Simulators
Publisher: Springer International Publishing
Date: 2020
Integrablization of time fractional PDEs
Publisher: Elsevier BV
Date: 03-2017
A discrete time random walk model for anomalous diffusion
Publisher: Elsevier BV
Date: 07-2015
Motor properties from persistence: a linear molecular walker lacking spatial and temporal asymmetry
Publisher: IOP Publishing
Date: 15-05-2015
Numeric solution of advection–diffusion equations by a discrete time random walk scheme
Publisher: Wiley
Date: 21-11-2019
DOI: 10.1002/NUM.22448
Transmembrane Extension and Oligomerization of the CLIC1 Chloride Intracellular Channel Protein upon Membrane Interaction
Publisher: American Chemical Society (ACS)
Date: 18-11-2011
DOI: 10.1021/BI2012564
Abstract: Chloride intracellular channel proteins (CLICs) differ from most ion channels as they can exist in both soluble and integral membrane forms. The CLICs are expressed as soluble proteins but can reversibly autoinsert into the membrane to form active ion channels. For CLIC1, the interaction with the lipid bilayer is enhanced under oxidative conditions. At present, little evidence is available characterizing the structure of the putative oligomeric CLIC integral membrane form. Previously, fluorescence resonance energy transfer (FRET) was used to monitor and model the conformational transition within CLIC1 as it interacts with the membrane bilayer. These results revealed a large-scale unfolding between the C- and N-domains of CLIC1 as it interacts with the membrane. In the present study, FRET was used to probe lipid-induced structural changes arising in the vicinity of the putative transmembrane region of CLIC1 (residues 24-46) under oxidative conditions. Intramolecular FRET distances are consistent with the model in which the N-terminal domain inserts into the bilayer as an extended α-helix. Further, intermolecular FRET was performed between fluorescently labeled CLIC1 monomers within membranes. The intermolecular FRET shows that CLIC1 forms oligomers upon oxidation in the presence of the membranes. Fitting the data to symmetric oligomer models of the CLIC1 transmembrane form indicates that the structure is large and most consistent with a model comprising approximately six to eight subunits.
Reaction-diffusion and reaction-subdiffusion equations on arbitrarily evolving domains
Publisher: American Physical Society (APS)
Date: 08-09-2020
Subdiffusive discrete time random walks via Monte Carlo and subordination
Publisher: Elsevier BV
Date: 11-2018
Discretization of fractional differential equations by a piecewise constant approximation
Publisher: EDP Sciences
Date: 2017
DOI: 10.1051/MMNP/2017063
Patterning of the MinD cell division protein in cells of arbitrary shape can be predicted using a heuristic dispersion relation
Publisher: American Institute of Mathematical Sciences (AIMS)
Date: 2016
Continuous-time random walks on networks with vertex- and time-dependent forcing
Publisher: American Physical Society (APS)
Date: 20-08-2013
An explicit numerical scheme for solving fractional order compartment models from the master equations of a stochastic process
Publisher: Elsevier BV
Date: 03-2019
Generalized master equations and fractional Fokker–Planck equations from continuous time random walks with arbitrary initial conditions
Publisher: Elsevier BV
Date: 03-2017
A Fractional Order Recovery SIR Model from a Stochastic Process
Publisher: Springer Science and Business Media LLC
Date: 03-2016
DOI: 10.1007/S11538-016-0151-7
Abstract: Over the past several decades, there has been a proliferation of epidemiological models with ordinary derivatives replaced by fractional derivatives in an ad hoc manner. These models may be mathematically interesting, but their relevance is uncertain. Here we develop an SIR model for an epidemic, including vital dynamics, from an underlying stochastic process. We show how fractional differential operators arise naturally in these models whenever the recovery time from the disease is power-law distributed. This can provide a model for a chronic disease process where in iduals who are infected for a long time are unlikely to recover. The fractional order recovery model is shown to be consistent with the Kermack-McKendrick age-structured SIR model, and it reduces to the Hethcote-Tudor integral equation SIR model. The derivation from a stochastic process is extended to discrete time, providing a stable numerical method for solving the model equations. We have carried out simulations of the fractional order recovery model showing convergence to equilibrium states. The number of infecteds in the endemic equilibrium state increases as the fractional order of the derivative tends to zero.
Molecular Interactions of the Min Protein System Reproduce Spatiotemporal Patterning in Growing and Dividing Escherichia coli Cells
Publisher: Public Library of Science (PLoS)
Date: 27-05-2015
Predicting First Traversal Times for Virions and Nanoparticles in Mucus with Slowed Diffusion
Publisher: Elsevier BV
Date: 07-2015
Nonconservative dynamics of optically trapped high-aspect-ratio nanowires
Publisher: American Physical Society (APS)
Date: 24-02-2016
A Mathematical Model for the Proliferation, Accumulation and Spread of Pathogenic Proteins Along Neuronal Pathways with Locally Anomalous Trapping
Publisher: EDP Sciences
Date: 2016
Non-linear Min protein interactions generate harmonics that signal mid-cell division in Escherichia coli
Publisher: Public Library of Science (PLoS)
Date: 17-10-2017
Fractional order compartment models
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2017
DOI: 10.1137/16M1069249
Continuous-time random walks that alter environmental transport properties
Publisher: American Physical Society (APS)
Date: 27-12-2011
Generalized Continuous Time Random Walks, Master Equations, and Fractional Fokker--Planck Equations
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2015
DOI: 10.1137/15M1011299
Precision Isotope Shift Measurements in Calcium Ions Using Quantum Logic Detection Schemes
Publisher: American Physical Society (APS)
Date: 29-07-2015
Turing Patterns from Dynamics of Early HIV Infection
Publisher: Springer Science and Business Media LLC
Date: 02-04-2013
DOI: 10.1007/S11538-013-9834-5
Abstract: We have developed a mathematical model for in-host virus dynamics that includes spatial chemotaxis and diffusion across a two-dimensional surface representing the vaginal or rectal epithelium at primary HIV infection. A linear stability analysis of the steady state solutions identified conditions for Turing instability pattern formation. We have solved the model equations numerically using parameter values obtained from previous experimental results for HIV infections. Simulations of the model for this surface show hot spots of infection. Understanding this localization is an important step in the ability to correctly model early HIV infection. These spatial variations also have implications for the development and effectiveness of microbicides against HIV.
Time Fractional Fisher–KPP and Fitzhugh–Nagumo Equations
Publisher: MDPI AG
Date: 16-09-2020
DOI: 10.3390/E22091035
Abstract: A standard reaction–diffusion equation consists of two additive terms, a diffusion term and a reaction rate term. The latter term is obtained directly from a reaction rate equation which is itself derived from known reaction kinetics, together with modelling assumptions such as the law of mass action for well-mixed systems. In formulating a reaction–subdiffusion equation, it is not sufficient to know the reaction rate equation. It is also necessary to know details of the reaction kinetics, even in well-mixed systems where reactions are not diffusion limited. This is because, at a fundamental level, birth and death processes need to be dealt with differently in subdiffusive environments. While there has been some discussion of this in the published literature, few ex les have been provided, and there are still very many papers being published with Caputo fractional time derivatives simply replacing first order time derivatives in reaction–diffusion equations. In this paper, we formulate clear ex les of reaction–subdiffusion systems, based on equal birth and death rate dynamics, Fisher–Kolmogorov, Petrovsky and Piskunov (Fisher–KPP) equation dynamics, and Fitzhugh–Nagumo equation dynamics. These ex les illustrate how to incorporate considerations of reaction kinetics into fractional reaction–diffusion equations. We also show how the dynamics of a system with birth rates and death rates cancelling, in an otherwise subdiffusive environment, are governed by a mass-conserving tempered time fractional diffusion equation that is subdiffusive for short times but standard diffusion for long times.
Serum Levels of Human MIC-1/GDF15 Vary in a Diurnal Pattern, Do Not Display a Profile Suggestive of a Satiety Factor and Are Related to BMI
Publisher: Public Library of Science (PLoS)
Date: 24-07-2015
Division plane placement in pleomorphic archaea is dynamically coupled to cell shape
Publisher: Wiley
Date: 11-06-2019
DOI: 10.1111/MMI.14316
Continuous Time Random Walks with Reactions Forcing and Trapping
Publisher: EDP Sciences
Date: 2013
Pattern formation on networks with reactions: A continuous-time random-walk approach
Publisher: American Physical Society (APS)
Date: 08-03-2013
Intrinsic Discontinuities in Solutions of Evolution Equations Involving Fractional Caputo–Fabrizio and Atangana–Baleanu Operators
Publisher: MDPI AG
Date: 13-11-2020
DOI: 10.3390/MATH8112023
Abstract: There has been considerable recent interest in certain integral transform operators with non-singular kernels and their ability to be considered as fractional derivatives. Two such operators are the Caputo–Fabrizio operator and the Atangana–Baleanu operator. Here we present solutions to simple initial value problems involving these two operators and show that, apart from some special cases, the solutions have an intrinsic discontinuity at the origin. The intrinsic nature of the discontinuity in the solution raises concerns about using such operators in modelling. Solutions to initial value problems involving the traditional Caputo operator, which has a singularity inits kernel, do not have these intrinsic discontinuities.
From stochastic processes to numerical methods: A new scheme for solving reaction subdiffusion fractional partial differential equations
Publisher: Elsevier BV
Date: 02-2016
Solutions of Initial Value Problems with Non-Singular, Caputo Type and Riemann-Liouville Type, Integro-Differential Operators
Publisher: MDPI AG
Date: 11-08-2022
DOI: 10.3390/FRACTALFRACT6080436
Abstract: Motivated by the recent interest in generalized fractional order operators and their applications, we consider some classes of integro-differential initial value problems based on derivatives of the Riemann–Liouville and Caputo form, but with non-singular kernels. We show that, in general, the solutions to these initial value problems possess discontinuities at the origin. We also show how these initial value problems can be re-formulated to provide solutions that are continuous at the origin but this imposes further constraints on the system. Consideration of the intrinsic discontinuities, or constraints, in these initial value problems is important if they are to be employed in mathematical modelling applications.
Noise induced aperiodic rotations of particles trapped by a non-conservative force
Publisher: AIP Publishing
Date: 04-2018
DOI: 10.1063/1.5018443
Abstract: We describe a mechanism whereby random noise can play a constructive role in the manifestation of a pattern, aperiodic rotations, that would otherwise be d ed by internal dynamics. The mechanism is described physically in a theoretical model of overd ed particle motion in two dimensions with symmetric d ing and a non-conservative force field driven by noise. Cyclic motion only occurs as a result of stochastic noise in this system. However, the persistence of the cyclic motion is quantified by parameters associated with the non-conservative forcing. Unlike stochastic resonance or coherence resonance, where noise can play a constructive role in lifying a signal that is otherwise below the threshold for detection, in the mechanism considered here, the signal that is detected does not exist without the noise. Moreover, the system described here is a linear system.
Generalized fractional diffusion equations for subdiffusion in arbitrarily growing domains
Publisher: American Physical Society (APS)
Date: 26-10-2017
A General Framework for Fractional Order Compartment Models
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2021
DOI: 10.1137/21M1398549
Generalized fractional power series solutions for fractional differential equations
Publisher: Elsevier BV
Date: 04-2020
A Fractional-Order Infectivity and Recovery SIR Model
Publisher: MDPI AG
Date: 17-11-2017
DOI: 10.3390/FRACTALFRACT1010011
Abstract: The introduction of fractional-order derivatives to epidemiological compartment models, such as SIR models, has attracted much attention. When this introduction is done in an ad hoc manner, it is difficult to reconcile parameters in the resulting fractional-order equations with the dynamics of in iduals. This issue is circumvented by deriving fractional-order models from an underlying stochastic process. Here, we derive a fractional-order infectivity and recovery Susceptible Infectious Recovered (SIR) model from the stochastic process of a continuous-time random walk (CTRW) that incorporates a time-since-infection dependence on both the infectivity and the recovery of the population. By considering a power-law dependence in the infectivity and recovery, fractional-order derivatives appear in the generalised master equations that govern the evolution of the SIR populations. Under the appropriate limits, this fractional-order infectivity and recovery model reduces to both the standard SIR model and the fractional recovery SIR model.
A time-fractional generalised advection equation from a stochastic process
Publisher: Elsevier BV
Date: 09-2017
Related Organisations
Related Funding Activities
Discovery Projects - Grant ID: DP200100345
Start Date: 2020
End Date: 06-2024
Amount: $385,000.00
Funder: Australian Research Council
View Funded Activity