David Lloyd

Lecturer
Dynamics and Numerical Analysis

Contact Details

Address: Department of Mathematics School of Electronics and Physical Sciences University of Surrey Guildford GU2 7XH UK Office: 14 AA 04 Telephone: +44 (0)1483-68 Fax: +44 (0)1483 686071 E-mail: d.j.lloyd@surrey.ac.uk

Position

Lecturer
Department of Mathematics, University of Surrey, UK.

Research projects and interests

Localised Pattern formation

Localised patterns in the 2D Swift-Hohenberg equation,
Localised hexagon preprint can be found here,
Movies: Localised hexagon movie hexagons.mpg, Ladder movie ladders.mov

Collaborators: Drs. Daniele Avitabile (Bristol), John Burke (Boston) and Profs. Edgar Knobloch (UC, Berkeley), Bjorn Sandstede

I am happy to discuss possible PhD projects informally. Possible projects on Localised patterns can be found here.

Tumour modelling

Modelling oxygen and tracer distribution in cancer tumours.

Collaboration with Entesar Dalah (Surrey), Drs. Anne Skeldon (Surrey, Maths), David Bradley (Department of Physics, Surrey), and Prof. Andrew Nisbet (Department of Physics/Royal Surrey County Hospital).

Mountain Pass Algorithms

Development of Mountain Pass and minimum energy paths algorithms for quasi-linear PDEs.

Collaboration with Jeremy Chamard (Surrey) and Josef Otta (University of West Bohemia).

Numerical Continuation of 2D/3D localised pulses

Efficient numerical continuation routines for 2D and 3D localised pulses ('light bullets')

Robust heteroclinic cycles

Existence and bifurcations of robust heteroclinic cycles in the Complex Ginzburg-Landau equation

Publications

Preprints

J Chamard, J Otta and DJB Lloyd, Computation of Minimum Energy Paths for Quasi-Linear Problems, Submitted 2010, Preprint

J Knobloch, DJB Lloyd, B Sandstede and T Wagenknecht, Isolas of 2-pulse solutions in homoclinic snaking scenarios, Submitted 2010, Preprint

D Avitabile, DJB Lloyd, J Burke, E Knobloch and B Sandstede, To snake or not to snake in the planar Swift-Hohenberg equation, Submitted 2010, Preprint, movie_nonlocalised_stripes.mpg, movie_change_curvature.mpg

E Dalah, D Bradley, DJB Lloyd, AC Skeldon and A Nisbet, Simulating the heterogeneous distribution of O_2 partial pressure in 2D vasculature using a reaction-diffusion model, Submitted 2009, Preprint

In Journals

M Beck, J Knobloch, DJB Lloyd, B Sandstede, T Wagenknecht, Snakes, ladders, and isolas of localised patterns. 2009 SIAM J. Math. Ana. 41(3) 936-972, 2009

DJB Lloyd, B Sandstede, Localized radial solutions of the Swift-Hohenberg equation. Nonlinearity 22(2) 485-524, 2009 Preprint)

DJB Lloyd, B Sandstede, D Avitabile, AR Champneys, Localised patterns in the 2D Swift-Hohenberg equation, SIADS 7(3) 1049-1100, 2008, Preprint,
Movies: Localised hexagon movie hexagons.mpg, Ladder movie ladders.mov

DJB Lloyd, AR Champneys and RE Wilson, Robust heteroclinic cycles in the one-dimensional complex Ginzburg-Landau equation Physica D, 2005. [Abstract+Preprint version]

DJB Lloyd and AR Champneys, Efficient numerical continuation and stability analysis of spatiotemporal quadratic optical solitons, SIAM Journal of Scientific Computing, 2005 27(3) 759-773. [Abstract+Preprint version]

Thesis

Localised Solutions of Partial Differential Equations, PhD Thesis, University of Bristol, 2005 [Download]

A study of localised solutions of PDEs in higher dimensions.

Teaching

Experiment (MAT1025)

Course outline can be found here

Chaos and Fractals (MAT3007)

Course outline can be found here

Hobbies

Surfing

I go surfing in South Wales, North Devon, Cornwall and South West France (ok this isn't me but I was 10miles up the beach surfing waves like these!)
Photos of me surfing in France 2006 Photo 1 and Photo 2
New photo of me surfing in France 2008 Photo

Snowboarding

Hiking

The three peaks challenge 2005
Hiked to the botton of the Grand Canyon and back within a day June 2005 (meeting James Bond at the bottom by the Colorado river!)