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.

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 (Wageningen), and Alex Tam (Adelaide)

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

Surface interactions and diffusion; with Marta Krasowska (Adelaide), Bill Skinner (Adelaide) and David Beattie (Adelaide)

Diffusion in applied chemistry; with Anton Blencowe (Adelaide)

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
2026 - ongoing Professor of Applied Mathematics Adelaide University
2026 - ongoing Academic Lead Adelaide University
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
2026 Stokes, Y. M., Miller, T. R., & Bradshaw-Hajek, B. H. (2026). Modelling chemical signalling in the mammalian cumulus-oocyte complex. Applied Mathematical Modelling, 154, 116692-1-116692-21.
DOI
2026 Bazeed, A. Y., Bradshaw-Hajek, B. H., Wignall, A., Meakin, A. S., Morrison, J. L., Prestidge, C. A., . . . Blencowe, A. (2026). Bio-derived solvents for 𝘪𝘯 𝘴𝘪𝘵𝘶 forming implants. Journal of Controlled Release, 396, 115095-1-115095-16.
DOI
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 Scopus1
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 Scopus3 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 Scopus55 WoS51
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 Scopus3 WoS3
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 Scopus12 WoS11
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 Scopus4 WoS2
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
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
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
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 Scopus52 WoS45 Europe PMC27
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 PMC4
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
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 WoS1
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
2020 Bradshaw-Hajek, B. H., & Broadbridge, P. (2020). Analytic solutions for calcium ion fertilisation waves on the surface of eggs - Erratum. Mathematical Medicine and Biology, 37(3), 429-432.
DOI
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 Scopus14 WoS13
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 Scopus55 WoS51
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 Scopus44 WoS35
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 WoS9 Europe PMC1
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 Scopus26 WoS24
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 Scopus8 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 Scopus23 WoS23
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 Scopus11 WoS10
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 Scopus23 WoS20
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 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
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
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 Europe PMC1
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 Europe PMC2
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 Europe PMC8
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 Scopus3 WoS4
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 Europe PMC7
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 Scopus9 WoS9
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 Scopus18 WoS19
2004 Hajek, B. H., & Broadbridge, P. (2004). A robust cubic Huxley reaction diffusion equation for gene propagation. Mathematical and Computer Modelling.
DOI
2004 Bradshaw-Hajek, B. H., & Broadbridge, P. (2004). A robust cubic reaction-diffusion system for gene propagation. Mathematical and Computer Modelling, 39(9-10), 1151-1163.
DOI Scopus24 WoS22
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 Scopus24 WoS22
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
2025 Islam, N., Miklavcic, S., Hajek, B., & White, L. (2025). Asymmetric Capillary Particle Datasets.
DOI
  • ARC Centre of Excellence in Mathematics for Quantum Era Security and Trust, MathQuEST, 2026 - 2032
  • 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 X202 Differential Equations (2026)
  • 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

  • Bachelor of Mathematics

Date Role Research Topic Program Degree Type Student Load Student Name
2026 Principal Supervisor A mathematical model of water wave/ice shelf interactions incorporating energy transfer across the grounding line Master of Research Master Full Time Mr Kye Jones-Anderson
2025 Co-Supervisor Harmonic-measure distribution functions of planar and non-planar domains Doctor of Philosophy Doctorate Full Time Lamahewage Minoli Fernando
2025 Co-Supervisor Development of Implants for the Potential Treatment of Arthritis and Osteoporosis Master of Philosophy Master Full Time Ms Christina Thao Lam
2025 Co-Supervisor Hydrogel delivery systems for vaccine delivery in production animals Master of Research (Pharmaceutical Science) Master Full Time Miss Christina Thao Lam
2024 Co-Supervisor 213-Mathematical modelling of the extracellular actin scavenging system Doctor of Philosophy Doctorate Full Time Mr Matt Mack
2024 Co-Supervisor 208-Mathematical modelling and computation of biofilm growth and cell death Doctor of Philosophy Doctorate Full Time Mr Aidan Patterson
2023 Principal Supervisor Pattern formation of precursor films: a new mathematical model Doctor of Philosophy Doctorate Full Time Tharindi Amarathunge Achchige
2023 Co-Supervisor 108311-Ultrathin ionic liquid films on surfaces Doctor of Philosophy Doctorate Full Time Sowbarnika Senthilkumar
2023 Co-Supervisor 106660- Wetting, spreading, and adhesion of oils on composite mineral surfaces Doctor of Philosophy Doctorate Full Time Farzane Barzegarsattari
2021 Co-Supervisor Integration of in-stream and particle size measurements in flotation Doctor of Philosophy Doctorate Full Time Miss Amalie Moller
2021 Principal Supervisor class="MsoNormal">Shocks in reaction-diffusion equations with negative diffusivity - Doctorate Full Time Mr Tom Miller

Date Role Research Topic Program Degree Type Student Load Student Name
2021 - 2026 Co-Supervisor Liquid-liquid displacement controlled by surface properties and oil mixture interfacial tension: the first steps toward controlling particle transfer at oil-water interfaces Master of Philosophy Master Full Time Miss Amalie Moller
2019 - 2023 Principal Supervisor Diffusive processes in mineral processing Doctor of Philosophy Doctorate Full Time Miss Kirsten Louw
2019 - 2023 Co-Supervisor Harmonic-measure distribution functions, and related functions, for simply connected and multiply connected two-dimensional regions Doctor of Philosophy Doctorate Full Time Mr Arunmaran Mahenthiram
2017 - 2021 Co-Supervisor Hydrodynamic boundary conditions at fluid-liquid interfaces: from fundamentals to application Doctor of Philosophy Doctorate Full Time Mr Piotr Pawliszak
2016 - 2020 Co-Supervisor Towards multilayered emulsion applications: polyelectrolyte multilayers at interfaces Doctor of Philosophy Doctorate Part Time Miss Jessie Webber
2013 - 2016 Principal Supervisor Fluid flow and particle transport through periodic capillaries Doctor of Philosophy Doctorate Full Time Mr Nazmul Islam

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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