Dr. John Norbury

Publications

Travelling Shock Waves arising in a Model of Malignant Invasion - SIAM Applied Mathematics Journal. B. P. Marchant, J. Norbury and A. J. Perumpanani

Dynamics of Constrained Differential Delay Equations - Journal of Computational and Applied Mathematics, John Norbury and R. Eddie Wilson.

The Numerical Computation of Axisymmetric, Swirling Vortex Rings, John Norbury and Rhys Williams.

The Location and Stability of Interface Solutions of an Inhomogeneous Parabolic Problem - SIAM Applied Mathematics Journal. John Norbury and Li-Chen Yeh.

Recent D.Phil Supervision

Stuart H. Doole, 1993 - Research Assistant of Bristol University, now in Investment Banking, London

"Steady gravity waves on flows with vorticity: bifurcation theory and variational principles"

Stuart and I were interested in the appearance of wave motion on sheared streams of ideal fluid flowing horizontally with gravity acting vertically. We related these waves on streams to their values of pressure head R and flow force S.

The Bifurcation of Steady Gravity Water Waves in (R,S) Parameter Space, Journal of Fluid Mechanics, vol. 302 (1995), pp.287-305

Jan H. van Vuuren, 1995 - Senior Lecturer at Stellenbosch University, Matieland 7602, South Africa

"Permanence and asymptotic stability in diagonally convex reaction – diffusion systems"

Jan and I continue to work on competitive/co-operative species and their survival in changing habitats

Permanence and Asymptotic Stability in Diagonally Convex Reaction –

Diffusion Systems, Proceedings of the Royal Society of Edinburgh, vol. 123A (1998), pp. 147-172. vol. 42 (2000), pp. 195-223

Conditions for Permanence in Well-Known Biological Competition Models,

Anziam J, - Junior Research Fellow, Oxford and the Harvard Medical School, now a Business consultant, Perth, Western Australia

Abbey J. Perumpanani, 1996

"Malignant and morphogenetic waves"

Mathematical Modelling of Capsule Formation and Multinodularity in Benign Tumour Growth, Nonlinearity, vol. 10 (1997), pp. 1599-1614

Laurence J. H. O. Mays, 1997 - Lecturer and research assistant, Lincoln and Mansfield Colleges, Oxford

"Existence of solutions of nonlinear problems using positive square root operators"

Laurence and I are working on the developments of clustering behaviour in ceratin Keller-Segel biological models – this has application in various areas of science and economics

A Note on Solitary and Periodic Waves of a New Kind, Proceedings of the Royal Society of London A, vol. 454 (1998)

Bifurcation of Positive Solutions for a Neumann Boundary Value Problem, Journal of the Australian Mathematical Society: Series B, vol. B42 (2000), pp. 1-17

Brenda Allen, 1997 - Senior scientific civil service, now in Investment Banking, London Richard E. Wilson, 1998 - Lecturer in Department of Engineering Mathematics, University of Bristol

"Non-smooth differential equations"

"Modelling, analysis, and simulation of road traffic networks"

Rhys L. Williams, 1998 - Volunteer service abroad teacher in Africa

"Exact, asymptotic and numerical solutions to certain steady, axisymmetric, ideal fluid flow problems in 3D"

Volunteer service abroad teacher in Africa

Timo I. Taskinen, 1999 - Head of Design Engineering, Nokia, Vekaratie 4, Aanekoski, Finland

"On the steady-state flow of an elastic-plastic material past cones and wedges"

On the Steady Flow of an Incompressible Elastic-Plastic Material Past Thin Cones: Numerical Results, Computers and Geotechnics, vol. 20, no. 2 (1997), pp.143-159

Li-Chin Yeh, 1999 - Lecturer, Department of Applied Mathematics, National Dong Hwa University, Haalien, Taiwan

"Patterned solutions in a reaction diffusion problem with convex nonlinearity"

Leslie and I looked at the large scale shapes and patterns of interaction fronts between competing states when there is variation in the growth and capacity of the states depending on position. These large scale patterns stably evolve from local small scale interactions, and are a general feature of these reaction-small diffusion models The Location and Stability of Interface Solutions of an Inhomogeneous Parabolic Problem, OCIAM Research Report 269, Oct 2000, to appear in SIAM journal of applied math 2001

Ben Marchant, 1999 - Post doctoral research post, Biotechnology and Biological Sciences Research Council, Silsoe Research Institute, Wrest Park, Silsoe, Milton Keynes

"Modelling tumour invasion"

Ben and I are interested in new features of travelling waves of invading cells (that first arose in Perumpanani’s post graduate work). We found out that jumps in concentration were possible when chemotaxis/haptotaxis mechanisms are present at the invasion front, and that these blunt invasion profiles could be both stable and of the most physical relevance.

Travelling Shock Waves Arising in a Model of Malignant Invasion, Society for Industrial and Applied Mathematics, vol. 60, no. 2 (2000), pp. 463-476

Submitted Articles