蜜豆视频

School of Mathematical and Computational Sciences staff

Contact details +6469517608

Associate Professor Bruce Van Brunt PhD

Associate Professor in Mathematics

Doctoral Supervisor
School of Mathematical and Computational Sciences

Professional

Qualifications

  • Doctor of Philosophy - University of Oxford (1990)

Research Projects

Completed Projects

Project Title: Lattice polytope samplers: theory, methods and applications

Date Range: 2018 - 2022

Funding Bodies: University of Otago; Royal Society of New Zealand

Project Team:

Research Outputs

Journal

Hazelton, M., McVeagh, M., Tuffley, C., & VAN BRUNT, B. (2024). Some rapidly mixing hit-and-run samplers for latent counts in linear inverse problems. Bernoulli. 30(4), 2676-2699
[Journal article]Authored by: Tuffley, C., Van Brunt, B.
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Mohsin, M., Zaidi, AA., & van Brunt, B. (2024). Dynamics of cell growth: Exponential growth and division after a minimum cell size. Partial Differential Equations in Applied Mathematics. 11
[Journal article]Authored by: Van Brunt, B.
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Derfel, G., & van Brunt, B. (2024). On the Balanced Pantograph Equation of Mixed Type. Ukrainian Mathematical Journal. 75(12), 1841-1849
[Journal article]Authored by: Van Brunt, B.
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Fatoyinbo, HO., Brown, RG., Simpson, DJW., & van Brunt, B. (2022). Pattern Formation in a Spatially Extended Model of Pacemaker Dynamics in Smooth Muscle Cells. Bulletin of Mathematical Biology. 84(8)
[Journal article]Authored by: Brown, R., Simpson, D., Van Brunt, B.
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Zaidi, AA., & Van Brunt, B. (2021). Asymmetrical cell division with exponential growth. Anziam Journal. 63(1), 70-83
[Journal article]Authored by: Van Brunt, B.
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Hazelton, ML., Mcveagh, MR., & Van Brunt, B. (2021). Geometrically aware dynamic Markov bases for statistical linear inverse problems. Biometrika. 108(3), 609-626
[Journal article]Authored by: Van Brunt, B.
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Fatoyinbo, HO., Brown, RG., Simpson, DJW., & van Brunt, B. (2020). Numerical Bifurcation Analysis of Pacemaker Dynamics in a Model of Smooth Muscle Cells. Bulletin of Mathematical Biology. 82(7)
[Journal article]Authored by: Brown, R., Simpson, D., Van Brunt, B.
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Lynch, TA., Wang, Y., van Brunt, B., Pacheco, D., & Janssen, PH. (2019). Modelling thermodynamic feedback on the metabolism of hydrogenotrophic methanogens. Journal of Theoretical Biology. 477, 14-23
[Journal article]Authored by: Lynch, T., Van Brunt, B.
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Efendiev, M., van Brunt, B., Zaidi, AA., & Shah, TH. (2018). Asymmetric cell division with stochastic growth rate. Dedicated to the memory of the late Spartak Agamirzayev. Mathematical Methods in the Applied Sciences. 41(17), 8059-8069
[Journal article]Authored by: Van Brunt, B.
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Van Brunt, B., Almalki, A., Lynch, T., & Zaidi, A. (2018). On a cell division equation with a linear growth rate. Anziam Journal. 59(3), 293-312
[Journal article]Authored by: Lynch, T., Van Brunt, B.
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Efendiev, M., van Brunt, B., Wake, GC., & Zaidi, AA. (2018). A functional partial differential equation arising in a cell growth model with dispersion. Mathematical Methods in the Applied Sciences. 41(4), 1541-1553
[Journal article]Authored by: Van Brunt, B.
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Wang, Y., Janssen, PH., Lynch, TA., Brunt, BV., & Pacheco, D. (2016). A mechanistic model of hydrogen-methanogen dynamics in the rumen. Journal of Theoretical Biology. 393, 75-81
[Journal article]Authored by: Lynch, T., Van Brunt, B.
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Van Brunt, B., Gul, S., & Wake, GC. (2015). A cell growth model adapted for the minimum cell size division. ANZIAM Journal : Electronic Supplement. 57(2), 138-149
[Journal article]Authored by: Van Brunt, B.
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Van Brunt, B., Wake, GC., & Zaidi, A. (2015). Probability density function solutions to a Bessel type pantograph equation. Applicable Analysis: an international journal. 95(11), 2565-2577
[Journal article]Authored by: Van Brunt, B.
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Zaidi, AA., Van Brunt, B., & Wake, GC. (2015). Solutions to an advanced functional partial differential equation of the pantograph type. Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences. 471(2179)
[Journal article]Authored by: Van Brunt, B.
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Zaidi, AA., Van Brunt, B., & Wake, GC. (2015). A model for asymmetrical cell division. Mathematical Biosciences and Engineering. 12(3), 491-501
[Journal article]Authored by: Van Brunt, B.
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Derfel, G., van Brunt, B., & Wake, GC. (2012). A cell-growth model revisited. Journal of Functional Differential Equations. 19(1-2), 75-85
[Journal article]Authored by: Van Brunt, B.
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Van Brunt, B., & Vlieg-Hulstman, M. (2011). Eigenfunctions arising from a first-order functional differential equation in a cell growth model. Anziam Journal. 52(1), 46-58
[Journal article]Authored by: Van Brunt, B.
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Suebcharoen, T., Van Brunt, B., & Wake, GC. (2011). Asymmetric cell division in a size-structured growth model. Differential and Integral Equations. 24(7-8), 787-799
[Journal article]Authored by: Van Brunt, B.
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Van Brunt, B., & Wake, GC. (2011). A Mellin transform solution to a second-order pantograph equation with linear dispersion arising in a cell growth model. European Journal of Applied Mathematics. 22(2), 151-168
[Journal article]Authored by: Van Brunt, B.
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Van Brunt, B., & Vlieg-Hulstman, M. (2010). An eigenvalue problem involving a functional differential equation arising in a cell growth model. Anziam Journal. 51(4), 383-393
[Journal article]Authored by: Van Brunt, B.
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van Brunt, B., Kim, HO., & Derfel, G. (2010). Holomorphic solutions to functional differential equations. Journal of Mathematical Analysis and Applications. 368(1), 350-357
[Journal article]Authored by: Van Brunt, B.
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Senarath, P., Thornley, G., & Van Brunt, B. (2007). A system of PDES for Riemannian spaces. Journal of the Australian Mathematical Society. 82(2), 249-262
[Journal article]Authored by: Van Brunt, B.
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Van Brunt, B., & Vlieg Hulstman, M. (2008). Evolution equations having conservation laws with flux characteristics. Anziam Journal. 49(1), 39-52
[Journal article]Authored by: Van Brunt, B.
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Basse, B., Wake, GC., Wall, DJ., & Van Brunt, B. (2004). On a cell-growth model for plankton. Mathematical Medicine and Biology. 21, 49-61
[Journal article]Authored by: Van Brunt, B.
Basse, B., Wake, GC., Wall, DJN., & Van Brunt, B. (2004). On a cell-growth model for plankton. Mathematical Medicine and Biology. 21(1), 49-61
[Journal article]Authored by: Van Brunt, B.
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Basse, B., Baguley, BC., Marshall, ES., Joseph, WR., Van Brunt, B., Wake, G., . . . Wall, DJN. (2004). Modelling cell death in human tumour cell lines exposed to the anticancer drug paclitaxel. Journal of Mathematical Biology. 49(4), 329-357
[Journal article]Authored by: Van Brunt, B.
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Marshall, JC., van-Brunt, B., & Wake, GC. (2004). A natural boundary for solutions to the second order pantograph equation. Journal of Mathematical Analysis and Applications. 299(2), 314-321
[Journal article]Authored by: Marshall, J., Van Brunt, B.
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Van Brunt, B., Pidgeon, D., Vlieg-Hulstman, M., & Halford, WD. (2004). Conservation laws for second-order parabolic partial differential equations. Anziam Journal. 45(3), 333-348
[Journal article]Authored by: Van Brunt, B.
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van Brunt, B., Marshall, JC., & Wake, GC. (2004). Holomorphic solutions to pantograph type equations with neutral fixed points. Journal of Mathematical Analysis and Applications. 295(2), 557-569
[Journal article]Authored by: Marshall, J., Van Brunt, B.
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Van Brunt, B., Marshall, JC., & Wake, GC. (2003). An Eigenvalue problem for holomorphic solutions to a certain class of functional differential equations. European Journal of Applied Mathematics. 14(5), 571-585
[Journal article]Authored by: Marshall, J., Van Brunt, B.
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Basse, B., Baguley, BC., Marshall, ES., Joseph, WR., Van Brunt, B., Wake, G., . . . Wall, DJN. (2003). A mathematical model for analysis of the cell cycle in cell lines derived from human tumors. Journal of Mathematical Biology. 47(4), 295-312
[Journal article]Authored by: Van Brunt, B.
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Marshall, JC., Van Brunt, B., & Wake, GC. (2002). Natural boundaries for solutions to a certain class of functional differential equations. Journal of Mathematical Analysis and Applications. 268(1), 157-170
[Journal article]Authored by: Marshall, J., Van Brunt, B.
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Van Brunt, B., Wake, GC., & Kim, HK. (2001). On a singular Sturm-Liouville problem involving an advanced functional differential equation. European Journal of Applied Mathematics. 12(6), 625-644
[Journal article]Authored by: Van Brunt, B.
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Wiles, PG., & Van Brunt, B. (2001). Optimal location of transshipment depots. Transportation Research Part A Policy and Practice. 35(8), 745-771
[Journal article]Authored by: Van Brunt, B.
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Selvaratnam, AR., Vlieg-Hulstman, M., Van-Brunt, B., & Halford, WD. (2001). On the solution of a class of second-order quasi-linear pdes and the gauss equation. Anziam Journal. 42(3), 312-323
[Journal article]Authored by: Van Brunt, B.
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Wake, GC., Cooper, S., Kim, H., & Van Brunt, B. (2000). Functional differential equations for cell-growth models with dispersion. Communications in Applied Analysis. 4(4), 561-573
[Journal article]Authored by: Cooper, S., Van Brunt, B.
Milliken, P., Marsh, C., & van Brunt, B. (1999). Minimax controller design for a class of uncertain linear systems. Automatica. 35(4), 583-590
[Journal article]Authored by: Van Brunt, B.
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Van-Brunt, B., & Grant, K. (1996). Potential applications of Weingarten surfaces in CAGD, part I: Weingarten surfaces and surface shape investigation. Computer Aided Geometric Design. 13(6), 569-582
[Journal article]Authored by: Van Brunt, B.
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Van-Brunt, B., & Grant, K. (1994). Hyperbolic Weingarten surfaces. Mathematical Proceedings of the Cambridge Philosophical Society. 116(3), 489-504
[Journal article]Authored by: Van Brunt, B.
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Van-Brunt, B. (1994). Mathematical possibility of certain systems in geometrical optics. Journal of the Optical Society of America A Optics and Image Science and Vision. 11(11), 2905-2914
[Journal article]Authored by: Van Brunt, B.
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van-Brunt, B., & Ockendon, JR. (1992). A lens focusing light at two different wavelengths. Journal of Mathematical Analysis and Applications. 165(1), 156-179
[Journal article]Authored by: Van Brunt, B.
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Book

Little, CH., Teo, K., & Van Brunt, B.(2003). The number systems of analysis. River Edge, NJ: World Scientific
[Authored Book]Authored by: Van Brunt, B.

Conference

Fatoyinbo, HO., Brown, RG., Simpson, DJW., & Van Brunt, B. (2022). Effects of ion channels conductance on spontaneous electrical activity in smooth muscles. In Virtual 13th International Conference Dynamical Systems Applied to Biology and Natural Sciences (DSABNS) 2022 Book of Abstracts(pp. 142 - 142). , Virtual 13th International Conference Dynamical Systems Applied to Biology and Natural Sciences (DSABNS) 2022 Bilbao, Spain: Dynamical Systems Applied to Biology and Natural Sciences (DSABNS)
[Conference Abstract]Authored by: Simpson, D., Van Brunt, B.
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Doumic, M., & Van Brunt, B. (2018). Explicit Solution and Fine Asymptotics for a Critical Growth-Fragmentation Equation. In P. Gabriel, L. Dumas, M. Dauhoo, & P. Lafitte (Eds.) ESAIM: PROCEEDINGS AND SURVEYS. Vol. 62 (pp. 30 - 42). : CIMPA School on Mathematical Models in Biology and Medicine
[Conference Paper in Published Proceedings]Authored by: Van Brunt, B.
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Van Brunt, B., Zaidi, AA., & Lynch, T. (2018). Cell Division And The Pantograph Equation. In D. Chafaï, P. Lafitte, & T. Lelièvre (Eds.) ESAIM: PROCEEDINGS AND SURVEYS. Vol. 62 (pp. 158 - 167).
[Conference Paper in Published Proceedings]Authored by: Lynch, T., Van Brunt, B.
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Van Brunt, B. (2017, March). Analytical solutions to certain equations from a cell division equation. Presented at Workshop on: Coagulation and Fragmentation Equations. Vienna, Austria.
[Conference Oral Presentation]Authored by: Van Brunt, B.
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Van Brunt, B. (2016, December). On a simple model for size structured asymmetric cell division. Presented at CIMPA 2016 Research School Mathematical Models in Biology and Medicine. Mauritius, East Africa.
[Conference Oral Presentation]Authored by: Van Brunt, B.

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Van Brunt, B. (2016, July). Exact solutions and higher order asymptotics for a cell division equation. Presented at 10th European Conference on Mathematical and Theoretical Biology. Nottingham, United Kingdom.
[Conference Oral Presentation]Authored by: Van Brunt, B.
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Van Brunt, B. (2016, May). Exact Solutions and higher order asymptotics for a cell division equation. Presented at International Conference on Differential Equations and Applications. Lahore University of Management Sciences, Lahore, Pakistan.
[Conference Oral Presentation]Authored by: Van Brunt, B.
Van Brunt, B., Zaidi, A., & Wake, G. (2015, November). A Second Order Initial Boundary Value Problem for Cell Growth. Presented at New Zealand Mathematical Colloquium 2015. Christchurch, New Zealand.
[Conference Oral Presentation]Authored by: Van Brunt, B.
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Van Brunt, B. (2015, May). Higher order asymptotics of solutions to initial-boundary value problems involving a functional argument. Presented at Differential equations with variable delay. Toronto, Canada.
[Conference Oral Presentation]Authored by: Van Brunt, B.
Van Brunt, B., Gul, S., & Wake, GC.A CELL GROWTH MODEL ADAPTED FOR THE MINIMUM CELL SIZE DIVISION.
[Conference Oral Presentation]Authored by: Van Brunt, B.
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Van Brunt, B., Wake, G., & Zaidi, A. (2014, December). On the solution to a nonlocal PDE from a cell growth model. Presented at 8th Australia-New Zealand Mathematics Convention. Melbourne, Australia.
[Conference Oral Presentation]Authored by: Van Brunt, B.
Van Brunt, B. (2014, February). An initial-boundary value problem arising in a fragmentation/cell division model. Presented at ANZIAM. Rotorua, New Zealand.
[Conference Oral Presentation]Authored by: Van Brunt, B.
Van Brunt, B. (2013, December). Eigenfunction expansions for solutions to a nonlocal PDE from a cell growth model. Presented at New Zealand Mathematics Colloquium. Tauranga, New Zealand.
[Conference Oral Presentation]Authored by: Van Brunt, B.
Van Brunt, B., Wake, G., & Zaidi, A. (2014). Tumour cell biology and some new non-local calculus. In M. Wakayama, R. McKibbin, R. Anderssen, J. Cheng, K. Polthier, & K. Toh (Eds.) The Impact of Applications on Mathematics: Proceedings of the Forum lf Mathematics for Industry. Vol. 1 (pp. 27 - 33). Japan: Mathematics for Industry
[Conference Paper in Published Proceedings]Authored by: Van Brunt, B.
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Van Brunt, B. (2012, December). An initial-boundary value problem arising in a fragmentation/cell division model. Presented at New Zealand Mathematics Colloquium. 蜜豆视频, Palmerston North.
[Conference Oral Presentation]Authored by: Van Brunt, B.
Van Brunt, B. (2011, November). Eigenfunctions from a cell growth model. Presented at 14th Manawatu-Wellington Applied Mathematics Meeting. Industrial Research, Wellington.
[Conference Oral Presentation]Authored by: Van Brunt, B.
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Zaidi, AA., van-Brunt, B., & Wake, GC.Probability density function solutions to a Bessel type pantograph equation.
[Conference Oral Presentation]Authored by: Van Brunt, B.
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Van Brunt, B. (2010, June). The Pantograph Equation. Presented at Industrial Mathematics Intiative 2010. KAIST, Daejeon South Korea.
[Conference Oral Presentation]Authored by: Van Brunt, B.
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Van Brunt, B. (2010, April). Conservation Laws and Characteristics for Certain Classes of Evolution Equations. Presented at KAIST-NIMS International Workshop on Nonlinear Partial Differential Equations: theory, application and numerical computing. Daejeon, South Korea.
[Conference Oral Presentation]Authored by: Van Brunt, B.
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van Brunt, B., & Wake, G. (2010, January). A Pantograph equation with nonconstant dispersion. . Queenstown New Zealand.
[Conference Oral Presentation]Authored by: Van Brunt, B.
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Van Brunt, B. (2010, December). A singular Sturm-Liouville problem arising from a cell growth model. Presented at New Zealand Mathematical Society Colloquium 2010. Dunedin.
[Conference Oral Presentation]Authored by: Van Brunt, B.
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Van Brunt, B. (2008, December). Holomorphic solutions for a class of functional differential equations. Presented at 7th Joint Australia-New Zealand Mathematics Convention 2008. Christchurch New Zealand.
[Conference Oral Presentation]Authored by: Van Brunt, B.
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Van Brunt, B., & Marshall, JC. (2005). Holomorphic solutions to linear first-order functional differential equations. Electronic Journal of Differential Equations. Vol. 12 (pp. 39 - 46). San Marcos, TX: 2004 Conference on Differential Equations and Applications in Mathematical Biology
[Conference Paper in Published Proceedings]Authored by: Van Brunt, B.
Milliken, P., Marsh, C., & van Brunt, B.Controller synthesis for robust performance using H ∞ with transients for structured uncertainty. Proceedings of the IEEE Conference on Decision and Control. (pp. 2828 - 2829). 0191-2216.
[Conference]Authored by: Van Brunt, B.
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Milliken, P., Marsh, C., & van Brunt, B.(1997, June). State feedback minimax and guaranteed cost controllers for linear systems with integral quadratic constraint uncertainty descriptions. ROBUST CONTROL DESIGN (ROCODN'97). (pp. 347 - 352).
[Conference]Authored by: Van Brunt, B.

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Other

Van Brunt, B. (2016, July). On a functional differential equation arising in a cell division model. In Mathematics Department, Munich Technical University, Munich Germany.
[Oral Presentation]Authored by: Van Brunt, B.
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Van Brunt, B. (2016, March). On a second order initial boundary value problem that models cell division. In Math colloquium. Presented at Ben Gurion University, Beer Sheva Israel.
[Oral Presentation]Authored by: Van Brunt, B.
Van Brunt, B., Little, C., & Teo, K. (2015). Real Analysis via Sequences and Series. Springer Verlag
[Other]Authored by: Van Brunt, B.
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Van Brunt, B. (2012, September). Functional Equations, Star Wars, Cell Growth. In General Talk, 蜜豆视频.
[Oral Presentation]Authored by: Van Brunt, B.
Van Brunt, B. (2004). The Calculus of Variations. Springer Verlag
[Other]Authored by: Van Brunt, B.
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Van Brunt, B., Little, C., & Teo, K. (2003). Number Systems of Analysis. World Scientific
[Other]Authored by: Van Brunt, B.
Van Brunt, B., & Carter, M. (2000). The Lebesgue-Stieltjes Integral. Springer Verlag
[Other]Authored by: Van Brunt, B.
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Teaching and Supervision

Contact Supervisor

Summary of Doctoral Supervision

Position Current Completed
Main Supervisor 0 5
Co-supervisor 1 4

Current Doctoral Supervision

Co-supervisor of:

  • Brandon Jones - Doctor of Philosophy
    Mathematical modelling of growth and metabolism in anaerobic microbes

Completed Doctoral Supervision

Main Supervisor of:

  • 2021 - Michael McVeagh - Doctor of Philosophy
    Efficient Markov bases for Z-polytope sampling
  • 2021 - Hammed Fatoyinbo - Doctor of Philosophy
    Pattern Formation in Electrically Coupled Pacemaker Cells
  • 2020 - Adel Almalki - Doctor of Philosophy
    The Analysis of Fragmentation Type Equations for Special Division Kernels
  • 2019 - Saima Gul - Doctor of Philosophy
    Differential equations arising in the study of a cell growth model
  • 2006 - Jonathan Marshall - Doctor of Philosophy
    Holomorphic Solutions to Functional Differential Equations

Co-supervisor of:

  • 2017 - Yuancheng Wang - Doctor of Philosophy
    Mechanistic modelling of enteric methane production
  • 2015 - Ali Ashher Zaidi - Doctor of Philosophy
    Mathematics of Cell Growth
  • 2013 - Fleur McDonald - Doctor of Philosophy
    Travelling Wave Solutions of Multisymplectic Discretisations of Wave Equations
  • 2000 - Paul Milliken - Doctor of Philosophy
    Minimax approaches to Robust Control.

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Last updated on Friday 16 May 2025