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Dr Elliot Carr
Faculty of Science,
School of Mathematical Sciences
Biography
I am a Senior Lecturer in Applied and Computational Mathematics at QUT. More information can be found about me on my personal academic website: https://elliotcarr.github.io.Academic History
- Senior Lecturer, School of Mathematical Sciences, QUT, 2018-present.
- Lecturer, School of Mathematical Sciences, QUT, 2015-2018.
- ARC DECRA Research Fellow, School of Mathematical Sciences, QUT, 2015-2018.
- Postdoctoral Research Associate, Applied Modelling and Computation Group, Imperial College London, UK, 2014.
- Postdoctoral Research Fellow, Laboratory of Chemical Engineering and Materials, École Centrale Paris, France, 2013-2014.
- Postdoctoral Research Fellow, School of Mathematical Sciences, QUT, 2012-2013.
- Doctor of Philosophy (Mathematics), QUT, 2009-2012.
Awards: QUT Outstanding Doctoral Thesis Award. - Bachelor of Applied Science (Honours) (Mathematics), QUT, 2008.
Awards: University Medal, Dean’s Award - Bachelor of Applied Science (Honours) (Mathematics) (top graduate), GPA 7.0. - Bachelor of Mathematics, QUT, 2005-2007.
Awards: Dean's Award - Bachelor of Mathematics (top graduate), GPA 7.0.
Personal details
Positions
- Senior Lecturer
Faculty of Science,
School of Mathematical Sciences
Research field
Applied mathematics, Numerical and computational mathematics
Field of Research code, Australian and New Zealand Standard Research Classification (ANZSRC), 2020
Qualifications
- PhD (Queensland University of Technology)
- Bachelor of Applied Science (Honours) - Mathematics (Queensland University of Technology)
- Bachelor of Mathematics (Queensland University of Technology)
Professional memberships and associations
Member, Australian Mathematical Society (AustMS).
Member, Australian and New Zealand Industrial and Applied Mathematics (ANZIAM).
Teaching
Teaching Areas
- Computational mathematics
- Linear algebra
- Ordinary and partial differential equations
- Multivariable calculus
- Mathematical modelling
- Engineering mathematics
Recent Units
- MXB326 Computational Methods 2 (2021-present) This unit focusses on the theoretical development and practical implementation (in MATLAB) of finite volume methods and Newton-Krylov techniques for solving nonlinear partial differential equations of advection-diffusion-reaction type.
- MXB103 Introductory Computational Mathematics (2017-present) This unit focusses on the theoretical development and practical implementation (in MATLAB) of numerical methods for differentiation, integration, differential equations, interpolation and linear systems of equations.
- EGB242 Signal Analysis (2018-2021) The unit focusses on signal and system analysis in the time and frequency domain in the context of electrical and electronic circuits. I teach the maths component of this unit, which focusses on foundational mathematical knowledge in Fourier series, Fourier and Laplace transforms and related concepts.
- MXB324 Computational Fluid Dynamics (2016) This unit focussed on the theoretical development and practical implementation (in MATLAB) of finite volume methods and Newton-Krylov techniques for solving nonlinear partial differential equations applied to an industry-specific groundwater management problem.
- MXB222 Computational Linear Algebra (2015) This unit focussed on the theoretical development and practical implementation (in MATLAB) of finite difference methods for solving linear partial differential equations as well as direct and iterative methods for solving linear systems of equations.
Experience
Research
My research expertise is in the development and application of techniques and algorithms from computational and applied mathematics to solve, simulate and analyse mathematical models, particularly those involving partial differential equations. Through the use of mathematical analysis, computational simulation and high performance computing facilities, I study physical, industrial, environmental and biological applications to extract new knowledge and insight to help inform design and optimisation. Ongoing research focusses on diffusion processes, multiscale modelling and heat and mass transfer with applications to wood drying, groundwater flow, drug delivery and burn injuries.
Publications
I have published around 50 research articles in international journals including:
- Applied Mathematical Modelling
- Applied Mathematics and Computation
- Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- Royal Society Interface
- Journal of Computational Physics
- Multiscale Modeling and Simulation
- International Journal of Heat and Mass Transfer
- Journal of Computational and Applied Mathematics
- Computers & Mathematics with Applications
- International Journal for Numerical Methods in Engineering
- Transport in Porous Media
- Physical Review E
- Physica A: Statistical Mechanics and its Applications
- New Journal of Physics
- Journal of Chemical Physics
- Chemical Engineering Science
- Communications in Nonlinear Science and Numerical Simulation
- Mathematical Biosciences
- Journal of Hydrology
- Scientific Reports
- Chemical Engineering & Technology
- Annals of Forest Science
- Wood Science and Technology
A complete list of my publications can be found on my Google Scholar profile or on my personal website: https://elliotcarr.github.io.
Publications
- Oliver, D., Turner, I. & Carr, E. (2024). Dual-grid mapping method for the advection-diffusion-reaction equation in a heterogeneous medium. Computers and Mathematics with Applications, 154, 78–90. https://eprints.qut.edu.au/244900
- Carr, E., Simpson, M., Drovandi, C., Warne, D. & Maclaren, O. (2024). Generalised likelihood profiles for models with intractable likelihoods. Statistics and Computing, 34(1). https://eprints.qut.edu.au/244862
- Carr, E. & Pontrelli, G. (2024). Modelling functionalized drug release for a spherical capsule. International Journal of Heat and Mass Transfer, 222. https://eprints.qut.edu.au/245400
- Lin, Y., Huang, J., Carr, E., Hsieh, T., Zhan, H. & Yu, H. (2023). A temporally relaxed theory of physically or chemically non-equilibrium solute transport in heterogeneous porous media. Journal of Hydrology, 620. https://eprints.qut.edu.au/239435
- Carr, E. & Filippini, L. (2023). Analytical formulas for calculating the thermal diffusivity of cylindrical shell and spherical shell samples. International Journal of Heat and Mass Transfer, 202. https://eprints.qut.edu.au/237148
- Filippini, L., Simpson, M. & Carr, E. (2023). Simplified models of diffusion in radially-symmetric geometries. Physica A: Statistical Mechanics and its Applications, 626. https://eprints.qut.edu.au/243546
- Klowss, J., Browning, A., Murphy, R., Carr, E., Plank, M., Gunasingh, G., Haass, N. & Simpson, M. (2022). A stochastic mathematical model of 4D tumour spheroids with real-time fluorescent cell cycle labelling. Journal of the Royal Society, Interface, 19(189). https://eprints.qut.edu.au/230289
- Carr, E., Oliver, D. & Simpson, M. (2022). Approximate analytical solution for transient heat and mass transfer across an irregular interface. Communications in Nonlinear Science and Numerical Simulation, 108. https://eprints.qut.edu.au/227422
- Carr, E., (2022). Exponential and Weibull models for spherical and spherical-shell diffusion-controlled release systems with semi-absorbing boundaries. Physica A: Statistical Mechanics and its Applications, 605. https://eprints.qut.edu.au/236219
- Carr, E., Vandenheuvel, D., Wilson, J. & Simpson, M. (2022). Mean exit time in irregularly-shaped annular and composite disc domains. Journal of Physics A: Mathematical and Theoretical, 55(10). https://eprints.qut.edu.au/230142
QUT ePrints
For more publications by Elliot, explore their research in QUT ePrints (our digital repository).
Awards
- Type
- Keynote Speaker/Expert Panel Member/Invited Speaker for a Conference
- Reference year
- 2023
- Details
- Plenary speaker "Random walks with absorbing boundaries". ANZIAM Conference, Cairns, Australia, 5-9 February, 2023.
- Type
- Academic Honours, Prestigious Awards or Prizes
- Reference year
- 2022
- Details
- JH Michell Medal for distinguished research in applied mathematics. Awarded by the ANZIAM division of the Australian Mathematical Society.
- Type
- Keynote Speaker/Expert Panel Member/Invited Speaker for a Conference
- Reference year
- 2020
- Details
- Keynote speaker "Semi-analytical solutions for transport PDEs in heterogeneous media". Monash Workshop on Numerical Differential Equations and Applications (MWNDEA), Melbourne, Australia, 10-14 February, 2020.
- Type
- Keynote Speaker/Expert Panel Member/Invited Speaker for a Conference
- Reference year
- 2019
- Details
- Invited speaker "Coarse-scale simulation of heterogeneous flows: application to groundwater modelling". Forum "Math-for-Industry" (FMFI), Auckland, New Zealand, 18-21 November, 2019.
- Type
- Academic Honours, Prestigious Awards or Prizes
- Reference year
- 2016
- Details
- Vice-Chancellor's Performance Award (Mathematics Work Integrated Learning team)
- Type
- Keynote Speaker/Expert Panel Member/Invited Speaker for a Conference
- Reference year
- 2016
- Details
- Invited speaker "Multiscale Modelling of Groundwater Flow". Forum "Math-for-Industry" (FMFI), Brisbane, 21-23 November, 2016.
- Type
- Recipient of an Australia Council Grant or Australia Council Fellowship
- Reference year
- 2015
- Details
- Discovery Early Career Researcher Award (DECRA)
- Type
- Academic Honours, Prestigious Awards or Prizes
- Reference year
- 2012
- Details
- Outstanding Doctoral Thesis Award (awarded to the top 5% of graduates university-wide)
- Type
- Academic Honours, Prestigious Awards or Prizes
- Reference year
- 2008
- Details
- University Medal (awarded to the top 0.5% of graduates university-wide)
Selected research projects
- Title
- Transforming Australian bio-based industries through multiscale modelling
- Primary fund type
- CAT 1 - Australian Competitive Grant
- Project ID
- DP230102299
- Start year
- 2023
- Keywords
- Title
- Two-scale numerical modelling of coupled transport in heterogeneous media
- Primary fund type
- CAT 1 - Australian Competitive Grant
- Project ID
- DE150101137
- Start year
- 2015
- Keywords
- multiscale modelling; exponential integrators; groundwater contamination
- Title
- Improving returns from Southern Pine Plantations through innovative Resource Characterisation
- Primary fund type
- CAT 1 - Australian Competitive Grant
- Project ID
- Start year
- 2015
- Keywords
- Mathematical Modelling; Numerical Simulation
Projects listed above are funded by Australian Competitive Grants. Projects funded from other sources are not listed due to confidentiality agreements.
Supervision
Current supervisions
- Deterministic and stochastic modelling of cell movement in the brain informed by diffusion MRIs
PhD, Principal Supervisor
Other supervisors: Dr Adrianne Jenner - Player List Management Optimisation in the Australian Football League
PhD, Associate Supervisor
Other supervisors: Professor Paul Corry, Professor Chris Drovandi - Computational methods for advection-diffusion-reaction processes in heterogeneous media
PhD, Principal Supervisor
Other supervisors: Professor Ian Turner
Completed supervisions (Doctorate)
Completed supervisions (Masters by Research)
Supervision topics
- Branching processes, stochastic simulations and travelling waves
- Design, derivation, and implementation of mesh-free finite volume solvers based on 3D unit cell morphology to estimate biomass particle effective parameters
- Mathematical and computational techniques for advection diffusion reaction models
- Mean exit time calculations in complicated geometries
- Exact and approximate solutions of diffusion on evolving domains
- First passage time for diffusion
- Mathematical tools for stochastic and continuum transport models
The supervisions listed above are only a selection.