Research Interests

Nonlinear Partial Differential Equations, Pattern formation, Bifurcation theory, Numerical Analysis.

Further details can be found on my personal web page.

Publications

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

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

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, pdf, movie_nonlocalised_stripes.mpg, movie_change_curvature.mpg

E Dalah, D Bradley, D 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 pdf

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

M Beck, J Knobloch, DJB Lloyd, B Sandstede and T Wagenknecht, Snakes, ladders, and isolas of localised patterns, SIAM J. Math. Anal. 41(3) 936-972, 2008, pdf

DJB Lloyd, B Sandstede, D Avitabile and AR Champneys, Localized hexagon patterns in the planar Swift-Hohenberg equation, SIAM J. Appl. Dyn. Sys. 7(3) 1049-1100, 2008. pdf, hexagon movie, ladder movie

DJB Lloyd, AR Champneys and RE Wilson, Robust heteroclinic cycles in the one-dimensional complex Ginzburg-Landau equation, Physica D, 204 (3-4):240-268, 2005.

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

Teaching

In Spring 2009, I teach MAT1025 Experiment and MAT3007 Chaos and Fractals.

PhD Projects

I am happy to discuss possible PhD projects. Available projects can be found here.