Selected Publications
2024
D.J. Hill, "The role of spatial dimension in the emergence of localised radial patterns from a Turing instability" (2024), preprint
J.J. Bramburger, D.J. Hill & D.J.B. Lloyd, "Localized Multi-Dimensional Patterns" (2024), preprint
M.D. Groves & D.J. Hill, "On function spaces for radial functions" (2024), preprint
D.J. Hill & D.J.B. Lloyd, "Radial amplitude equations for fully localised planar patterns" (2024), preprint
D.J. Hill, "Predicting the emergence of localised dihedral patterns in models for dryland vegetation", J. Nonlinear Sci. 34, 67 (2024), doi, preprint
D.J. Hill, J.J. Bramburger & D.J.B. Lloyd, "Dihedral rings of patterns emerging from a Turing instability", Nonlinearity, (2024), doi, preprint
2023
D.J. Hill, J.J. Bramburger & D.J.B. Lloyd, "Approximate localised dihedral patterns near a Turing instability", Nonlinearity, (2023), doi, preprint
2022
D.J. Hill, "Existence of localised radial patterns in a model for dryland vegetation", IMA J. Appl. Math. (2022), doi, preprint
2021
2021
D.J. Hill, "Existence of small amplitude localised patterns on the surface of a ferrofluid", Doctoral Thesis, pdf
2017
D.J. Hill, "3D incompressible Navier-Stokes equations in a thin spherical shell", MMath Thesis, pdf