Status:
Personal website:
+44 1865 615166
ORCID iD:
https://orcid.org/0000-0001-9638-7278
Research groups:
Address
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG
Recent Publications:
Amplitude death criteria for coupled complex Ginzburg–Landau systems
Nonlinear Dynamics
(4 May 2019)
Hybrid approach to modeling spatial dynamics of systems with generalist predators
Journal of Theoretical Biology
volume 462
page 26-47
(7 February 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)
Turing-Hopf patterns on growing domains: The torus and the sphere.
Journal of theoretical biology
(25 September 2018)
Coupled complex Ginzburg-Landau systems with saturable nonlinearity and asymmetric cross-phase modulation
ANNALS OF PHYSICS
volume 396
page 397-428
(September 2018)
Full text available
Effects of tidal torques on 1I/2017 U1 ('Oumuamua)
ICARUS
volume 311
page 170-174
(1 September 2018)
Full text available
Lattice and continuum modelling of a bioactive porous tissue scaffold.
Mathematical medicine and biology : a journal of the IMA
(10 August 2018)
Predator-prey-subsidy population dynamics on stepping-stone domains with dispersal delays.
Journal of theoretical biology
volume 451
page 19-34
(August 2018)
Stochastic epidemic metapopulation models on networks: SIS dynamics and control strategies.
Journal of theoretical biology
volume 449
page 35-52
(July 2018)
Heterogeneity induces spatiotemporal oscillations in reaction-diffusion systems.
Physical review. E
issue 5-1
volume 97
page 052206-
(May 2018)
Chaotic Dynamics in the Planar Gravitational Many-Body Problem with Rigid Body Rotations
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
issue 5
volume 28
(May 2018)
Full text available
Emergent structures in reaction-advection-diffusion systems on a sphere.
Physical review. E
issue 4-1
volume 97
page 042215-
(April 2018)
Two-Species Migration and Clustering in Two-Dimensional Domains.
Bulletin of mathematical biology
issue 10
volume 79
page 2302-2333
(October 2017)
Continuous dispersal in a model of predator-prey-subsidy population dynamics
ECOLOGICAL MODELLING
volume 354
page 115-122
(24 June 2017)
Full text available
Dynamics of the non-autonomous stochastic p-Laplace equation driven by multiplicative noise
APPLIED MATHEMATICS AND COMPUTATION
volume 246
page 365-376
(1 November 2014)
Full text available
Pullback attractors of non-autonomous stochastic degenerate parabolic equations on unbounded domains
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
issue 2
volume 417
page 1018-1038
(15 September 2014)
Full text available
From One Pattern into Another: Analysis of Turing Patterns in
Heterogeneous Domains via WKBJ
Full text available
Diffusive instabilities and spatial patterning from the coupling of reaction-diffusion processes with Stokes flow in complex domains
Journal of Fluid Mechanics
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:
TA: MT 2014-C5.7 Topics in Fluid Mechanics, HT 2015-MMSC B5.2 Applied Partial Differential Equations, MT 2015-MMSC Supplementary Applied Mathematics, HT 2016-MMSC Further Mathematical Methods
Departmental Tutor: MT 2016-C5.12 Mathematical Physiology
Pembroke Stipendiary Lectureship: MT 2017-Prelims Introductory Calculus, Part A Differential Equations I, HT 2018-Prelims Dynamics, Part A Differential Equations II, Waves and Fluids, Statistics, TT Part A Mathematical Biology, MT 2018-Prelims Calculus, Part A DEI, Quantum Theory
St. Anne's Stipendiary Lectureship: MT 2015-Prelims Introductory Calculus, Geometry, HT 2016-Part A Differential Equations 2, Integral Transforms