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Personal profile

Research interests

I formulate, analyse and apply mathematical and computational models to describe biological processes. Particular applications of my work include understanding the basic mechanisms that allow cells to organise into tissues and organs, the key transitions that operate during pathological processes such as cancer growth and the cues that allow animals to navigate through complex environments

Biography

I have been in the Department of Mathematics at Heriot-Watt University since 2000. Prior to joining Heriot-Watt, I undertook a degree in Applied Mathematics at the University of Warwick (1991-1994) before moving to the University of Oxford (1994-1998) to study for a Doctor of Philosophy. Following the completion of my Doctorate, I spent two years as a Research Associate in the United States, divided between the Universities of Utah and Minnesota, before moving to Heriot-Watt University in early 2000.

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Chemotaxis Mathematics
Cell Mathematics
Theoretical Models Medicine & Life Sciences
Model Mathematics
Aggregation Mathematics
Global Existence Mathematics
Adhesion Mathematics
Anisotropic Diffusion Mathematics

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Selected Research Output 1997 2019

  • 52 Article
  • 6 Chapter (peer-reviewed)
  • 1 Literature review
cancer
tensors
fibers
anisotropy
cells

Spatio-temporal chaos in a chemotaxis model

Painter, K. J. & Hillen, T., 15 Feb 2011, In : Physica D: Nonlinear Phenomena. 240, 4-5, p. 363-375 13 p.

Research output: Contribution to journalArticle

chemotaxis
chaotic dynamics
embryonic development
bifurcation
tumor

A user's guide to PDE models for chemotaxis

Hillen, T. & Painter, K. J., 2009, In : Journal of Mathematical Biology. 58, 1-2, p. 183-217 35 p.

Research output: Contribution to journalArticle

Chemotaxis
Keller-Segel Model
Finite Time Blow-up
Formulation
Tractability

Modelling cell migration strategies in the extracellular matrix

Painter, K. J., Apr 2009, In : Journal of Mathematical Biology. 58, 4-5, p. 511-543 33 p.

Research output: Contribution to journalArticle

Tumors
Cells
Infiltration
Fibers

A continuum approach to modelling cell-cell adhesion

Armstrong, N. J., Painter, K. J. & Sherratt, J. A., 7 Nov 2006, In : Journal of Theoretical Biology. 243, 1, p. 98-113 16 p.

Research output: Contribution to journalArticle

Cell Adhesion
Adhesives
Population
Cell Adhesion Molecules
Embryonic Development

Global Existence for a Parabolic Chemotaxis Model with Prevention of Overcrowding

Hillen, T. & Painter, K., May 2001, In : Advances in Applied Mathematics. 26, 4, p. 280-301 22 p.

Research output: Contribution to journalArticle

Chemotaxis
Keller-Segel Model
Global Existence
Quorum Sensing
Cross-diffusion

Stripe formation in juvenile Pomacanthus explained by a generalized Turing mechanism with chemotaxis

Painter, K., Maini, P. K. & Othmer, H. G., 1999, In : Proceedings of the National Academy of Sciences. 96, 10, p. 5549-5554 6 p.

Research output: Contribution to journalArticle