62 citations · 134 across the 11 of their papers we have counts for
14 papers
Combining Dynamic Mode Decomposition with Ensemble Kalman Filtering for Tracking and Forecasting
Stephen A Falconer, David J. B. Lloyd, Naratip Santitissadeekorn
Data assimilation techniques, such as ensemble Kalman filtering, have been shown to be a highly effective and efficient way to combine noisy data with a mathematical model to track…
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…
Adaptive stochastic continuation with a modified lifting procedure applied to complex systems
Clemens Willers, Uwe Thiele, Andrew J. Archer +2
Many complex systems occurring in the natural or social sciences or economics are frequently described on a microscopic level, e.g., by lattice- or agent-based models. To analyze t…
Hexagon Invasion Fronts Outside the Homoclinic Snaking Region in the Planar Swift-Hohenberg Equation
David J. B. Lloyd
Stationary fronts connecting the trivial state and a cellular (distorted) hexagonal pattern in the Swift-Hohenberg equation with a quadratic-cubic nonlinearity are known to undergo…
Invasion Fronts Outside the Homoclinic Snaking Region in the Planar Swift-Hohenberg Equation
David J. B. Lloyd
In this paper, we carry out numerical bifurcation analysis of depinning of fronts near the homoclinic snaking region, involving a spatial stripe cellular pattern embedded in a quie…
Existence of stationary fronts in a system of two coupled wave equations with spatial inhomogeneity
Jacob Brooks, Gianne Derks, David J. B. Lloyd
We investigate the existence of stationary fronts in a coupled system of two sine-Gordon equations with a smooth, "hat-like" spatial inhomogeneity. The spatial inhomogeneity corres…
Pattern formation on the free surface of a ferrofluid: spatial dynamics and homoclinic bifurcation
Mark D. Groves, David J. B. Lloyd, Athanasios Stylianou
We establish the existence of spatially localised one-dimensional free surfaces of a ferrofluid near onset of the Rosensweig instability, assuming a general (nonlinear) magnetisati…
A Web-based Tool for Identifying Strategic Intervention Points in Complex Systems
Sotiris Moschoyiannis, Nicholas Elia, Alexandra S. Penn +2
Steering a complex system towards a desired outcome is a challenging task. The lack of clarity on the system's exact architecture and the often scarce scientific data upon which to…
Continuation and Bifurcation of Grain Boundaries in the Swift-Hohenberg Equation
David J. B. Lloyd, Arnd Scheel
We study grain boundaries between striped phases in the prototypical Swift-Hohenberg equation. We propose an analytical and numerical far-field-core decomposition that allows us to…
On the interaction of uni-directional and bi-directional buckling of a plate supported by an elastic foundation
M. Khurram Wadee, David J. B. Lloyd, Andrew P. Bassom
A thin flat rectangular plate supported on its edges and subjected to in-plane loading exhibits stable post-buckling behaviour. However, the introduction of a nonlinear (softening)…
Homoclinic snaking near the surface instability of a polarizable fluid
David J. B. Lloyd, Christian Gollwitzer, Ingo Rehberg +1
We report on localized patches of cellular hexagons observed on the surface of a magnetic fluid in a vertical magnetic field. These patches are spontaneously generated by jumping i…
Continuation of localised coherent structures in nonlocal neural field equations
James Rankin, Daniele Avitabile, Javier Baladron +2
We study localised activity patterns in neural field equations posed on the Euclidean plane; such models are commonly used to describe the coarse-grained activity of large ensemble…