Bronwyn Hajek

Research Interests

Dynamical Systems in Applications Partial Differential Equations

Prof Bronwyn Hajek

Professor of Applied Mathematics

School of Mathematical Sciences

College of Science

Eligible to supervise Masters and PhD - email supervisor to discuss availability.

Bronwyn’s research interests lie in developing and solving mathematical models using nonlinear partial differential equations. She is motivated by many areas of application, including biological invasions, cell biology, viscous flow, and physical chemistry. She has a particular focus on the use of Lie symmetry techniques to construct analytic solutions of nonlinear reaction-diffusion equations.
Bronwyn is an enthusiastic teacher of mathematics.

Coloid and surface science

Surface interactions; with Marta Krasowska (UniSA) and David Beattie (UniSA)

Modelling with nonlinear PDEs and symmetry analysis

A video about this aspect of my research can be found on the Sydney Mathematics Research Institute website.

Shocks in reaction-nonlinear diffusion; with Martin Wechselberger and Robert Marangell (the University of Sydney) and Peter van Heijster (QUT)

Calcium fertilisation waves; with Phil Broadbridge (La Trobe University) and Yvonne Stokes (the University of Adelaide)

Problems with nonlinear diffusion; with Phil Broadbridge (La Trobe University) and Joel Moitsheki (University of the Witwatersrand)

Compactly supported solutions of nonlinear reaction-diffusion equations; with Maureen Edwards (University of Wollongong) and Bob Anderssen (CSIRO)

Selected invited conferences and seminars

Reaction-diffusion, symmetries and solutions, plenary speaker, ANZIAM conference, 2022

Analytic solutions of various reaction-diffusion models, keynote speaker, AustMS Annual Meeting, 2021

Analytic solutions of nonlinear reaction-diffusion equations with applications in biology, ANZIAM Lecturer, New Zealand Mathematics Colloquium, 2019

Analytic solutions for a reaction-diffusion model of calcium waves on the surface of amphibian eggs, Australia-Japan Workshop on Dynamical Systems and the Life Sciences, Biei, Japan, 2018

Analytical solutions of nonlinear reaction-diffusion equations in various coordinate systems, Mathematical Society of Japan Seasonal Institute: The role of metrics in the theory of PDEs, Sapporo, Japan, 2018

Analytic solutions to nonlinear reaction-diffusion equations on the surface of a sphere, Workshop on Waves in Neural Media, The Fields Institute, Toronto, 2017

Electrokinetics behaviour concentrated suspensions, Workshop on Wave Transport of Ionic Species, The Fields Institute, Toronto, 2017

Date Position Institution name
2024 - 2025 Professor of Applied Mathematics University of South Australia
2022 - 2025 Professorial Lead University of South Australia
2021 - 2023 Associate Professor University of South Australia
2016 - 2020 Senior Lecturer University of South Australia
2013 - 2015 Lecturer University of South Australia
2007 - 2012 Postdoctoral Researcher University of South Australia
2004 - 2007 Postdoctoral Researcher University of Adelaide

Date Institution name Country Title
2000 - 2004 University of Wollongong Australia Doctor of Philosophy
1998 - 1999 University of Wollongong Australia Master of Environmental Science (Honours)
1995 - 1997 University of Adelaide Australia Bachelor of Science

Year Citation
2025 Miller, T., Tam, A. K. Y., Marangell, R., Wechselberger, M., & Bradshaw Hajek, B. H. (2025). Shock selection in reaction-diffusion equations with partially negative diffusivity using nonlinear regularisation. Physica D: Nonlinear Phenomena, 474(134561), 1-14.
DOI
2024 Miller, T., Tam, A. K. Y., Marangell, R., Wechselberger, M., & Bradshaw Hajek, B. H. (2024). Analytic shock-fronted solutions to a reaction-diffusion equation with negative diffusivity. Studies in Applied Mathematics, 153(1, article no. e12685), 1-23.
DOI Scopus2 WoS2
2024 Pawliszak, P., Bradshaw-Hajek, B. H., Skinner, W., Beattie, D. A., & Krasowska, M. (2024). Frothers in flotation: A review of performance and function in the context of chemical classification. Minerals Engineering, 207, 11 pages.
DOI Scopus39 WoS34
2024 Bradshaw Hajek, B. H., Lizarraga, I., Marangell, R., & Wechselberger, M. (2024). A geometric singular perturbation analysis of shock selection rules in composite regularized reaction-nonlinear diffusion models. SIAM Journal on Applied Dynamical Systems, 23(3), 2099-2137.
DOI Scopus2 WoS2
2023 Louw, K. I., Bradshaw Hajek, B. H., & Hill, J. M. (2023). van der Waals interaction energies for ferric ion sensors using prismatic and cylindrical pore approximations for a MOF pore. Royal Society Open Science, 10(5, article no. 230232), 1-17.
DOI
2023 Broadbridge, P., Bradshaw Hajek, B. H., & Hutchinson, A. J. (2023). Conditionally integrable PDEs, non-classical symmetries and applications. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 479(2276, article no. 20230209), 1-27.
DOI Scopus9 WoS8
2022 Palinski, T. J., Guan, B., Bradshaw Hajek, B. H., Lienhard, M. A., Priest, C., & Miranda, F. A. (2022). Reversible colorimetric sensing of volatile analytes by wicking in close proximity to a photonic film. RSC Advances, 12(55), 36150-36157.
DOI
2022 Louw, K. I., Bradshaw Hajek, B. H., & Hill, J. M. (2022). Ferric ion diffusion for MOF-polymer composite with internal boundary sinks. Nanomaterials, 12(5, article no. 887), 1-19.
DOI Scopus1 WoS1 Europe PMC1
2022 Louw, K. I., Bradshaw Hajek, B. H., & Hill, J. M. (2022). Interaction of ferric ions with europium metal organic framework and application to mineral processing sensing. Philosophical Magazine, 102(13), 1231-1246.
DOI Scopus4 WoS3
2022 McCue, S. W., Bradshaw Hajek, B. H., & Simpson, M. J. (2022). Exact time-dependent solutions of a Fisher-KPP-like equation obtained with nonclassical symmetry analysis. Applied Mathematics Letters, 132(108151), 1-8.
DOI Scopus3 WoS1
2022 Wylie, J. J., & Bradshaw Hajek, B. H. (2022). Bounds for systems of coupled advection-diffusion equations with application to the Poisson-Nernst-Plank equations. Physical Review E, 106(4, article no. 044208), 1-7.
DOI
2021 Pawliszak, P., Ulaganathan, V., Bradshaw-Hajek, B. H., Miller, R., Beattie, D. A., & Krasowska, M. (2021). Can small air bubbles probe very low frother concentration faster?. Soft Matter, 17(43), 9916-9925.
DOI Scopus7 WoS7 Europe PMC3
2021 Pawliszak, P., Bradshaw-Hajek, B. H., Greet, C., Skinner, W., Beattie, D. A., & Krasowska, M. (2021). Interfacial tension sensor for low dosage surfactant detection. Colloids and Interfaces, 5(1), 12 pages.
DOI Scopus10 WoS11
2021 Webber, J. L., Namivandi-Zangeneh, R., Drozdek, S., Wilk, K. A., Boyer, C., Wong, E. H. H., . . . Beattie, D. A. (2021). Incorporation and antimicrobial activity of nisin Z within carrageenan/chitosan multilayers. Scientific Reports, 11(1), 15 pages.
DOI Scopus48 WoS44 Europe PMC26
2021 Webber, J. L., McMillin, R., Ferri, J. K., Bradshaw-Hajek, B. H., Krasowska, M., & Beattie, D. A. (2021). Mechanical properties of thin films at the dodecane-water interface, for multilayered emulsion applications. Colloids and Surfaces A Physicochemical and Engineering Aspects, 626(article no. 127051), 12 pages.
DOI Scopus2 WoS2
2021 Webber, J. L., Bradshaw-Hajek, B. H., Krasowska, M., & Beattie, D. A. (2021). Polyelectrolyte multilayer formation on protein layer supports. Colloids and Surfaces A Physicochemical and Engineering Aspects, 629(article no, 127470), 9 pages.
DOI Scopus4 WoS4
2020 Binder, C., Lageder, B., Bradshaw Hajek, B. H., Fischmann, A. J., & Priest, C. (2020). Microvolume screening of extraction and phase behavior in a liquid-liquid microsystem. Analytical Chemistry, 92(11), 7831-7835.
DOI
2020 Nelson, M. I., & Bradshaw Hajek, B. H. (2020). An analysis of organic carbon removal in a two-reactor cascade with recycle and a two-reactor step-feed cascade with recycle. Asia-Pacific Journal of Chemical Engineering, 15(1), 1-11.
DOI Scopus2 WoS2
2019 Trenholm, S., Hajek, B., Robinson, C., Chinnappan, M., Albrecht, A., & Ashman, H. (2019). Investigating undergraduate mathematics learners' cognitive engagement with recorded lecture videos. International journal of mathematical education in science and technology, 50(1), 3-24.
DOI Scopus40 WoS31
2019 Bradshaw Hajek, B. H. (2019). Nonclassical symmetry solutions for non-autonomous reaction-diffusion equations. Symmetry, 11(2, article no. 208), 1-13.
DOI Scopus13 WoS11
2019 Bradshaw Hajek, B. H., & Wylie, J. J. (2019). Front and pulse solutions for a system of reaction-diffusion equations with degenerate source terms. Physical review E, 99(2, article no. 022214), 1-10.
DOI
2019 Bradshaw Hajek, B. H., & Broadbridge, P. (2019). Analytic solutions for calcium ion fertilisation waves on the surface of eggs. Mathematical medicine and biology, 36(4), 549-562.
DOI Scopus10 WoS8 Europe PMC1
2019 Pawliszak, P., Ulaganathan, V., Bradshaw-Hajek, B. H., Manica, R., Beattie, D. A., & Krasowska, M. (2019). Mobile or Immobile? Rise Velocity of Air Bubbles in High-Purity Water. Journal of Physical Chemistry C, 123(24), 15131-15138.
DOI Scopus51 WoS47
2019 Krasowska, M., Kor, M., Pawliszak, P., Bernardis, F. L., Bradshaw-Hajek, B. H., & Beattie, D. A. (2019). Controlling Bubble-Solid Surface Interactions with Environmentally Benign Interfacial Modifiers. Journal of Physical Chemistry C, 123(6), 3645-3656.
DOI Scopus13 WoS12
2018 Krasowska, M., Zawala, J., Bradshaw-Hajek, B. H., Ferri, J. K., & Beattie, D. A. (2018). Interfacial characterisation for flotation: 1. Solid-liquid interface. Current Opinion in Colloid and Interface Science, 37, 61-73.
DOI Scopus25 WoS23
2018 Bradshaw Hajek, B. H., Islam, N., Miklavcic, S. J., & White, L. R. (2018). Convective and diffusive particle transport in channels of periodic cross-section: comparison with experiment. Journal of engineering mathematics, 111(1), 1-13.
DOI Scopus4 WoS3
2017 Islam, N., Miklavcic, S. J., Bradshaw Hajek, B. H., & White, L. R. (2017). Convective and diffusive effects on particle transport in asymmetric periodic capillaries. PLoS one, 12(8, article no. e0183127), 1-21.
DOI Scopus7 WoS6 Europe PMC2
2016 Wylie, J., Bradshaw-Hajek, B., & Stokes, Y. (2016). The evolution of a viscous thread pulled with a prescribed speed. Journal of Fluid Mechanics, 795, 380-408.
DOI Scopus6 WoS5
2016 Broadbridge, P., & Bradshaw Hajek, B. H. (2016). Exact solutions for logistic reaction-diffusion equations in biology. Zeitschrift fur angewandte mathematik und physik, 67(4, article no. 93), 1-13.
DOI Scopus22 WoS21
2015 Islam, N., Bradshaw Hajek, B. H., Miklavcic, S. J., & White, L. R. (2015). The onset of recirculation flow in periodic capillaries: geometric effects. European journal of mechanics B : fluids, 53, 119-128.
DOI Scopus7 WoS6
2015 Bradshaw Hajek, B., & Moitsheki, R. J. (2015). Symmetry solutions for reaction-diffusion equations with spatially dependent diffusivity. Applied mathematics and computation, 254, 30-38.
DOI Scopus10 WoS9
2015 Broadbridge, P., Bradshaw Hajek, B. H., & Triadis, D. (2015). Exact non-classical symmetry solutions of Arrhenius reaction-diffusion. Proceedings of the Royal Society A, 471(2184, article no. 20150580), 15 pages.
DOI Scopus22 WoS18
2014 Makinde, O. D., Moitsheki, R. J., Jana, R. N., Bradshaw Hajek, B. H., & Khan, W. A. (2014). Nonlinear fluid flow and heat transfer. Advances in mathematical physics, 2014(article no. 719102), 1-2.
DOI Scopus2 WoS1
2013 Bradshaw Hajek, B. H., Miklavcic, S. J., & Ward, D. A. (2013). A composite Level Set and Extended-Domain-Eigenfunction Method for simulating 2D Stokes flow involving a free surface. Journal of computational and applied mathematics, 237(1), 389-402.
DOI Scopus1 WoS1
2013 Moitsheki, R. J., & Bradshaw Hajek, B. H. (2013). Symmetry analysis of a heat conduction model for heat transfer in a longitudinal rectangular fin of a heterogeneous material. Communications in nonlinear science and numerical simulation, 18(9), 2374-2387.
DOI Scopus12 WoS11
2011 Aarão, J., Bradshaw Hajek, B. H., Miklavcic, S. J., & Ward, D. A. (2011). Numerical implementation of the EDEM for modified Helmholtz BVPs on annular domains. Journal of computational and applied mathematics, 235(5), 1342-1353.
DOI Scopus5 WoS5
2011 Stokes, Y., Bradshaw-Hajek, B., & Tuck, E. (2011). Extensional flow at low Reynolds number with surface tension. Journal of Engineering Mathematics, 70(1-3), 321-331.
DOI Scopus10 WoS10
2010 Bradshaw Hajek, B. H., Miklavcic, S. J., & White, L. R. (2010). High-frequency behavior of the dynamic mobility and dielectric response of concentrated colloidal dispersions. Langmuir, 26(3), 1656-1665.
DOI Scopus4 WoS4
2010 Bradshaw Hajek, B. H., Miklavcic, S. J., & White, L. R. (2010). The actual dielectric response function for a colloidal suspension of spherical particles. Langmuir, 26(11), 7875-7884.
DOI Scopus4 WoS4
2010 Aarao, J., Bradshaw Hajek, B. H., Miklavcic, S. J., & Ward, D. A. (2010). The extended-domain-eigenfunction method for solving elliptic boundary value problems with annular domains. Journal of physics a: mathematical and theoretical, 43(18), 18 pages.
DOI Scopus16 WoS6
2009 Bradshaw Hajek, B. H., Miklavcic, S. J., & White, L. R. (2009). Dynamic dielectric response of concentrated colloidal dispersions: comparison between theory and experiment. Langmuir, 25(4), 1961-1969.
DOI Scopus19 WoS19
2008 Hajek, B. H., Miklavcic, S. J., & White, L. R. (2008). Frequency-dependant electrical conductivity of concentrated dispersions of spherical colloidal particles. Langmuir, 24(9), 4512-4522.
DOI Scopus15 WoS16
2008 Hajek, B. H., Broadbridge, P., & Williams, G. (2008). Evolving gene frequencies in a population with three possible alleles at a locus. Mathematical and Computer Modelling, 47(1/2), 210-217.
DOI Scopus2 WoS3
2007 Hajek, B., Stokes, Y., & Tuck, E. (2007). Computation of extensional fall of slender viscous drops by a one-dimensional eulerian method. Siam Journal on Applied Mathematics, 67(4), 1166-1182.
DOI Scopus8 WoS8
2007 Hajek, B. H., Edwards, M., Broadbridge, P., & Williams, G. (2007). Nonclassical symmetry solutions for reaction-diffusion equations with explicit spatial dependence. Nonlinear Analysis - Theory Methods and Applications, 67(9), 2541-2552.
DOI Scopus16 WoS17
2004 Hajek, B. H., & Broadbridge, P. (2004). A robust cubic Huxley reaction diffusion equation for gene propagation. Mathematical and Computer Modelling.
DOI
2002 Broadbridge, P., Hajek, B. H., Fulford, G., & Aldis, G. K. (2002). Huxley and fisher equations for gene propagation : an exact solution. Australian and New Zealand Industrial And Applied Mathematics Journal, 44(1), 11-20.
DOI Scopus23 WoS21
1984 HAJEK, B. (1984). SEMIMARTINGALES, A COURSE ON STOCHASTIC-PROCESSES - METIVIER,M. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 11(1), 198-203.
DOI

Year Citation
- Miklavcic, S., Islam, N., Hajek, B., & White, L. (n.d.). Asymmetric Capillary Particle Datasets.
DOI

  • Pattern formation of precursor films: a new mathematical model, ARC - Discovery Projects, 01/01/2022 - 31/12/2026

  • Unlocking complex resources through lean processing, BHP Billiton Olympic Dam Corporation Pty Ltd, 01/06/2018 - 31/08/2024

  • Unlocking complex resources through lean processing, SA Dept of Innovation and Skills (formerly DSD), 01/06/2018 - 31/08/2024

Courses I teach

  • MATH 2023 Differential Equations 1 (2025)
  • MATH 2023 Differential Equations 1 (2024)
  • MATH 3040 Topics in Mathematics 1 (2024)
  • MATH 4049 Advanced Honours Topics in Mathematics 1 (2024)
  • MATH 4050 Advanced Honours Topics in Mathematics 2 (2024)

Programs I'm associated with

  • LBMH - Bachelor of Mathematics

Date Role Research Topic Program Degree Type Student Load Student Name
2025 Co-Supervisor - Doctor of Philosophy Doctorate Full Time Lamahewage Minoli Fernando
2025 Co-Supervisor - - Master Full Time Ms Christina Thao Lam
2024 Co-Supervisor - Doctor of Philosophy Doctorate Full Time Mr Matt Mack
2024 Co-Supervisor - Doctor of Philosophy Doctorate Full Time Mr Aidan Patterson
2023 Co-Supervisor - Doctor of Philosophy Doctorate Full Time Farzane Barzegarsattari
2023 Principal Supervisor - Doctor of Philosophy Doctorate Full Time Tharindi Amarathunge Achchige
2023 Co-Supervisor - Doctor of Philosophy Doctorate Full Time Sowbarnika Senthilkumar
2021 Co-Supervisor - Doctor of Philosophy Doctorate Full Time Miss Amalie Moller
2021 Principal Supervisor - Doctor of Philosophy Doctorate Full Time Mr Tom Miller

Date Role Editorial Board Name Institution Country
2022 - ongoing Associate Editor Proceedings of the Royal Society A Royal Society United Kingdom
2021 - ongoing Associate Editor Acta Applicandae Mathematicae Springer United Kingdom

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