8 citations · 16 across the 7 of their papers we have counts for
8 papers
Global bifurcation of localised 2D patterns emerging from spatial heterogeneity
Dan J. Hill, David J. B. Lloyd, Matthew R. Turner
We present a general approach to prove the existence, both locally and globally in amplitude, of fully localised multi-dimensional patterns in partial differential equations contai…
The role of spatial dimension in the emergence of localised radial patterns from a Turing instability
Dan J. Hill
The emergence of localised radial patterns from a Turing instability has been well studied in two and three dimensional settings and predicted for higher spatial dimensions. We pro…
Localized Patterns
Jason J. Bramburger, Dan J. Hill, David J. B. Lloyd
Localized patterns are coherent structures embedded in a quiescent state and occur in both discrete and continuous media across a wide range of applications. While it is well-under…
Radial amplitude equations for fully localised planar patterns
Dan J. Hill, David J. B. Lloyd
Isolated patches of spatially oscillating pattern have been found to emerge near a pattern-forming instability in a wide variety of experiments and mathematical models. However, th…
Predicting the emergence of localised dihedral patterns in models for dryland vegetation
Dan J. Hill
Localised patterns are often observed in models for dryland vegetation, both as peaks of vegetation in a desert state and as gaps within a vegetated state, known as `fairy circles'…
Dihedral rings of patterns emerging from a Turing bifurcation
Dan J. Hill, Jason J. Bramburger, David J. B. Lloyd
Collective organisation of patterns into ring-like configurations has been well-studied when patterns are subject to either weak or semi-strong interactions. However, little is kno…
Approximate localised dihedral patterns near a Turing instability
Dan J. Hill, Jason J. Bramburger, David J. B. Lloyd
Fully localised patterns involving cellular hexagons or squares have been found experimentally and numerically in various continuum models. However, there is currently no mathemati…
Localised Radial Patterns on the Free Surface of a Ferrofluid
Dan J. Hill, David J. B. Lloyd, Matthew R. Turner
This paper investigates the existence of localised axisymmetric (radial) patterns on the surface of a ferrofluid in the presence of a uniform vertical magnetic field. We formally i…