62 citations · 134 across the 11 of their papers we have counts for
6 papers · 1 filter
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…
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…
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…