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Teaching

• MATH170 / EMTH171
  Mathematical Modelling and Computation
• MATH201
  Mathematics 2
• MATH363
  Dynamical systems
• MATH401
  Dynamical systems

Affiliations

• Biomathematics Research Centre
• NZ Institute for Mathematics and its Applications
• Centre for Bioengineering
• NZ Mathematics Society
• Association for Australian and NZ Industrial and Applied Mathematics
• Society for Mathematical Biology

UC Home > Departments > College of Engineering > Mathematics and Statistics

Publications

• Plank, M. J., Auger-Méthé, M. and Codling, E. A. (2012). Lévy or not? Analysing positional data from animal movement paths. In Lewis, M., Maini, P. K. and Petrovskii, S. V. (eds.) Dispersal, individual movement and spatial ecology: a mathematical perspective, Springer, in press.
• Law, R., Plank, M. J. and Kolding, J. On balanced exploitation of marine ecosystems: results from dynamic size spectra. ICES J. Mar. Sci. in press.
• Plank, M. J. Effects of diet breadth on the stability of size spectra. ANZIAM J. in press.
• Plank, M. J. and Law, R. Ecological drivers of stability and instability in marine ecosystems. Theor. Ecol. in press.
• James, A., Plank, M. J. and Edwards, A. M. (2011). Assessing Lévy walks as models of animal foraging. J. Roy. Soc. Interface. 8, 1233-1247.
• Plank, M. J., James, A. and Hannah, J. (2011). Group by subject or ability? Tertiary mathematics for engineering students. Intl. J. Math. Ed. Sci. Tech. 42, 857-865.
• Plank, M. J. and Codling, E. A. (2011). Sampling rate and misidentification of Lévy and non-Lévy movement paths: Reply. Ecol. 92, 1701-1702.
• Sellier, D., Plank, M. J. and Harrington, J. J. (2011). A mathematical framework for modelling cambial surface evolution using a level set method. Ann. Bot. 108, 1001-1011.
• Datta, S., Delius, G. W., Law, R. and Plank, M. J. (2011). A stability analysis of the power-law steady state of marine size spectra. J. Math. Biol. 63, 779-799.
• Codling, E. A. and Plank, M. J. (2011). Turn designation, sampling rate and the misidentification of power laws in movement path data using maximum likelihood estimates. Theor. Ecol. 4, 397-406.
• James, A., Pitchford, J. W. and Plank, M. J. (2010). Efficient or inaccurate? Analytical and numerical modelling of random search strategies. Bull. Math. Biol. 72, 896-913.
• Plank, M. J. and Codling, E. A. (2009). Sampling rate and misidentification of Lévy and non-Lévy movement paths. Ecol. 90, 3546-3553.
• Jones, D. S., Plank, M. J. and Sleeman, B. D. (2009). Differential equations and mathematical biology, 2nd ed., Chapman & Hall/CRC, London.
• James, A., Green, S. and Plank, M. J. (2009). Modelling the dynamic response of oxygen uptake to exercise. Discrete Continuous Dynamical Sys. B 12, 361-370.
• Law, R., Plank, M. J., James, A. and Blanchard, J. (2009). Size-spectra dynamics from stochastic predation and growth of individuals. Ecol. 90, 802-811.
• James, A., Plank, M. J. and Brown, R. (2008). Optimizing the encounter rate in biological interactions: ballistic versus Lévy versus Brownian strategies. Phys. Rev. E 78, 051128.
• Plank, M. J. and James, A. (2008). Optimal foraging: Lévy pattern or process? J. Roy. Soc. Interface 5, 1077-1086.
• Codling, E. A., Plank, M. J. and Benhamou, S. (2008). Random walk models in biology. J. Roy. Soc. Interface 5, 813-834.
• Kleinstreuer, N., David, T., Plank, M. J. and Endre, Z. H. (2008). Dynamic myogenic autoregulation in the rat kidney: a whole organ model. Am. J. Physiol. Renal Physiol. 294, F1453-1464.
• Basse, B. and Plank, M. J. (2008). Modelling biological invasions over homogeneous and inhomogeneous landscapes using level set methods. Biol. Invasions 10, 157-167.
• Comerford, A., David, T. and Plank, M. J. (2008). Endothelial nitric oxide synthase and calcium production in arterial geometries: an integrated fluid mechanics/cell model. J. Biomech. Eng. 308, 011010.
• Chapman, S. J., Plank, M. J., James, A. and Basse, B. (2007). A nonlinear model of size-structured populations with applications to cell cycles. ANZIAM J. 49, 151-169.
• James, A. and Plank, M. J. (2007). On fitting power laws to ecological data. arXiv:0712.0613v1.
• James, A., Dungan, R., Plank, M. J. and Ito, R. (2007). A dynamical model of honeydew droplet production by sooty-beech scale insects (Ultracoelostoma spp.) in New Zealand Nothofagus forest. Ecol. Modelling 209, 323-332.
• James, A., Pitchford, J. W. and Plank, M. J. (2007). An event-based model of superspreading in epidemics. Proc. Roy. Soc. B 274, 741-747.
• Plank, M. J., Wall, D. J. N. and David, T. (2007). The role of endothelial calcium and nitric oxide in the localisation of atherosclerosis. Math. Biosci. 207, 26-39.
• Mann, J. L., Plank, M. J. and Wilkins, A. (2007). Tree growth and wood formation — applications of anisotropic surface growth. Proc. Math. Ind. Study Group 2006, 153-192.
• Plank, M. J., Comerford, A., Wall, D. J. N. and David, T. (2007). Modelling the early stages of atherosclerosis. In: Mathematical modelling of biological systems, volume I, Deutsch, A., Brusch, L., Byrne, H., de Vries, G. and Herzel, H. (eds.), Birkhäuser, Boston, pp. 263-274.
• Plank, M. J., Comerford, A., David, T. and Wall, D. J. N. (2006). Concentration of blood-borne agonists at the endothelium. Proc. Roy. Soc. A 462, 671-688.
• Comerford, A., David, T. and Plank, M. J. (2006). Effects of arterial bifurcation geometry on nucleotide concentration at the endothelium. Ann. Biomed. Eng. 34, 605-617.
• Plank, M. J., Wall, D. J. N. and David, T. (2006). Atherosclerosis and calcium signalling in endothelial cells. Prog. Biophys. Mol. Biol. 91, 287-313.
• Plank, M. J., Comerford, A., David, T. and Wall, D. J. N. (2005). Modelling the localisation of cardiovascular disease. Proc. Intl. Conf. Biomed. Eng. 1B1-01.
• Plank, M. J. and Sleeman, B. D. (2004). Lattice and non-lattice models of tumour angiogenesis. Bull. Math. Biol. 66, 1785-1819.
• Plank, M. J., Sleeman, B. D. and Jones, P. F. (2004). A mathematical model of tumour angiogenesis, regulated by vascular endothelial growth factor and the angiopoietins. J. Theor. Biol. 229, 435-454.
• Plank, M. J., Sleeman, B. D. and Jones, P. F. (2004). The role of the angiopoietins in tumour angiogenesis. Growth Factors 22, 1-11.
• Plank, M. J. and Sleeman, B. D. (2003). Tumour-induced angiogenesis: a review. J. Theor. Med. 5, 137-153.
• Plank, M. J. and Sleeman, B. D. (2003). A reinforced random walk model of tumour angiogenesis and anti-angiogenic strategies. Math. Med. Biol. 20, 135-181.
• Plank, M. J., Sleeman, B. D. and Jones, P. F. (2003). A mathematical model of an in vitro experiment to investigate endothelial cell migration. J. Theor. Med. 4, 251-270.
• Plank, M. J. (2003). Cell-based models of tumour angiogenesis. PhD Thesis, Department of Applied Mathematics, University of Leeds.