Contact details +64 (06) 356 9099  ext. 84608

Associate Professor Bruce Van Brunt

Associate Professor

Institute of Fundamental Sciences

Research Projects

Summary of Research Projects

Position Current Completed
Project Leader 0 1

Research Outputs

Journal

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.
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., Wake, G.
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., Wake, G.
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., Wake, G.
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., Wake, G.
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., Wake, G.
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.
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., Wake, G.
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., Wake, G.
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.
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.
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.
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.
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., Wake, G.
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., Wake, G.
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., Wake, G.
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.
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., Wake, G.
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., Wake, G.
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., Wake, G.
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., Wake, G.
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., Wake, G.
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.
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.
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., Wake, G.
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.
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.
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.
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.
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.

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

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.
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. University of Mauritius, Mauritius.
[Conference Oral Presentation]Authored by: Van Brunt, B.
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.
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., Wake, G.
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. Fields Institute, 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., Wake, G.
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., Wake, G.
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., Wake, G.Edited by: McKibbin, R.
Van Brunt, B. (2012, December). An initial-boundary value problem arising in a fragmentation/cell division model. Presented at New Zealand Mathematics Colloquium. Massey University, 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.
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., Wake, G.
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.
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.
van Brunt, B., & Wake, G. (2010, January). A Pantograph equation with nonconstant dispersion. . Queenstown New Zealand.
[Conference Oral Presentation]Authored by: Van Brunt, B.
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.
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.
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.(1998, December). Controller synthesis for robust performance using H-infinity with transients for structured uncertainty. PROCEEDINGS OF THE 37TH IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-4. (pp. 2828 - 2829). 0191-2216.
[Conference]Authored by: Van Brunt, B.
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.

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.
Van Brunt, B. (2016, March). On a second order initial boundary value problem that models cell division. In Math colloquium, 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.
Van Brunt, B. (2012, September). Functional Equations, Star Wars, Cell Growth. In General Talk, Massey University.
[Oral Presentation]Authored by: Van Brunt, B.
Van Brunt, B. (2004). The Calculus of Variations. Springer Verlag
[Other]Authored by: Van Brunt, B.
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.

Supervision and Teaching

Summary of Doctoral Supervision

Position Current Completed
Supervisor 3 1
Co-supervisor 2 4

Current Doctoral Supervision

Supervisor of:

  • Hammed Fatoyinbo - Doctor of Philosophy
    Pattern formation in reaction-diffusion systems with spatially varying parameters
  • Adel Almalki - Doctor of Philosophy
    The Analysis of Fragmentation Type Equations for Special Division Kernels
  • Saima Gul - Doctor of Philosophy
    Differential equations in cell growth models

Co-supervisor of:

  • Michael McVeagh - Doctor of Philosophy
    Efficient Markov bases for polytope sampling
  • Simon Murphy - Doctor of Philosophy
    Investigation into flavour and spin structure of the Nucleon Sea

Completed Doctoral Supervision

Supervisor of:

  • 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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