
Status:
Personal website:
ORCID iD:

Research groups:
Address
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG
Highlighted Publications:
From one pattern into another: analysis of Turing patterns in heterogeneous domains via WKBJ
Journal of the Royal Society Interface
issue 162
volume 17
(15 January 2020)
Diffusive instabilities and spatial patterning from the coupling of reaction-diffusion processes with Stokes flow in complex domains
Journal of Fluid Mechanics
volume 877
page 759-823
(27 August 2019)
Beyond Onsager–Casimir Relations: Shared Dependence of Phenomenological Coefficients on State Variables
The Journal of Physical Chemistry Letters
page 7021-7025
(5 December 2018)
Influence of Curvature, Growth, and Anisotropy on the Evolution of Turing Patterns on Growing Manifolds
Bulletin of Mathematical Biology
(3 December 2018)
Heterogeneity induces spatiotemporal oscillations in reaction-diffusion systems
Physical Review E
issue 5
volume 97
page 052206-
(14 May 2018)
Recent Publications:
Predicting bone formation in mesenchymal stromal cell- seeded hydrogels using experiment-based mathematical modelling
Tissue Engineering: Parts A
issue 17-18
volume 26
page 1014-1023
(17 September 2020)
A Non-local Cross-Diffusion Model of Population Dynamics II: Exact, Approximate, and Numerical Traveling Waves in Single- and Multi-species Populations
Bulletin of Mathematical Biology
issue 8
volume 82
(11 August 2020)
A Non-local Cross-Diffusion Model of Population Dynamics I: Emergent Spatial and Spatiotemporal Patterns
Bulletin of Mathematical Biology
issue 8
volume 82
(11 August 2020)
Unstaggered-staggered solitons on one- and two-dimensional two-component discrete nonlinear Schrödinger lattices
Communications in Nonlinear Science and Numerical Simulation
volume 85
(1 June 2020)
Mix and Match: Phenotypic Coexistence as a Key Facilitator of Cancer Invasion.
Bulletin of mathematical biology
issue 1
volume 82
page 15-
(17 January 2020)
Research interests:
I am broadly interested in nonlinear dynamical systems, with applications to mathematical biology and other areas. I am particularly interested in understanding and overcoming the limits of current methodologies to capture spatial and temporal complexity in situations of scientific interest. I am currently active in the following research areas:
- Reaction-Diffusion Systems: pattern formation, diffusion-driven (Turing) instabilities, spatiotemporal phenomena (including chaos and heterogeneity), RD systems on static and growing manifolds, with applications to developmental biology, population dynamics, and tissue engineering.
- Spatial Population Dynamics: discrete patch and spatially continuous models, random and deterministic dispersal, synchronization of metapopulations, and applications to ecological and epidemiological metapopulation models.
-
Nonlinear Dynamical Systems: dissipative dynamics (attractors and absorbing sets), numerical bifurcation analysis, and stochastic differential equations.
In all of these cases I am interested both in the scientific field or application, as well as in the theoretical or computational tools used. I primarily approach problems from a dynamical systems point of view, and I am keen to see applications motivate new theory in this field. However, I am much more motivated by developing approaches to solve problems as they are, rather than trying to force them into a particular shape in order to use a specific hammer. While I have used several tools in the past, I am more than happy to pick up new methodologies in order to address an interesting problem. I am also happy to pursue questions outside of my main research interests, as long as I am able to provide a useful perspective in addressing them.
Teaching:
I have taught at St Annes and Pembroke Colleges as well as in the department in a variety of roles since 2014. Please see my CV for further details.