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:
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
Non-autonomous Turing conditions for reaction-diffusion systems on
evolving domains
Full text available
Asymptotic Dynamics of Stochastic $p$-Laplace Equations on Unbounded
Domains
Full text available
Amplitude death criteria for coupled complex Ginzburg–Landau systems
Nonlinear Dynamics
(1 January 2019)
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