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University of Oxford
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Radcliffe Observatory Quarter
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
Full text available
Asymptotic Dynamics of Stochastic $p$-Laplace Equations on Unbounded
Full text available
Amplitude death criteria for coupled complex Ginzburg–Landau systems
Nonlinear Dynamics (1 January 2019)
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.
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