Alan Champneys
YOU?
Author Swipe
View article: Designing reaction-cross-diffusion systems with Turing and wave instabilities
Designing reaction-cross-diffusion systems with Turing and wave instabilities Open
General conditions are established under which reaction-cross-diffusion systems can undergo spatiotemporal pattern-forming instabilities. Recent work has focused on designing systems theoretically and experimentally to exhibit patterns wit…
View article: Modelling throughput through the justice system
Modelling throughput through the justice system Open
His Majesty's Courts and Tribunal Service is a complex system that criminal cases flow through. Understanding how the system works and how cases flow through the system can be used to plan and evaluate the system. We design a simple compar…
View article: Bifurcation analysis of multiple limit cycles created in boundary equilibrium bifurcations in hybrid systems
Bifurcation analysis of multiple limit cycles created in boundary equilibrium bifurcations in hybrid systems Open
A boundary equilibrium bifurcation (BEB) in a hybrid dynamical system occurs when a regular equilibrium collides with a switching surface in phase space. This causes a transition to a pseudo-equilibrium embedded within the switching surfac…
View article: An Asymptotic Analysis of Spike Self-Replication and Spike Nucleation of Reaction-Diffusion Patterns on Growing 1-D Domains
An Asymptotic Analysis of Spike Self-Replication and Spike Nucleation of Reaction-Diffusion Patterns on Growing 1-D Domains Open
In the asymptotic limit of a large diffusivity ratio, certain two-component reaction-diffusion (RD) systems can admit localized spike solutions on a 1-D finite domain in a far-from-equilibrium nonlinear regime. It is known that two distinc…
View article: Pattern Localisation in Swift-Hohenberg via Slowly Varying Spatial Heterogeneity
Pattern Localisation in Swift-Hohenberg via Slowly Varying Spatial Heterogeneity Open
Theories of localised pattern formation are important to understand a broad range of natural patterns, but are less well-understood than more established mechanisms of domain-filling pattern formation. Here, we extend recent work on patter…
View article: Pattern formation of bulk-surface reaction-diffusion systems in a ball
Pattern formation of bulk-surface reaction-diffusion systems in a ball Open
Weakly nonlinear amplitude equations are derived for the onset of spatially extended patterns on a general class of n-component bulk-surface reaction-diffusion systems in a ball, under the assumption of linear kinetics in the bulk and coup…
View article: Designing reaction-cross-diffusion systems with Turing and wave instabilities
Designing reaction-cross-diffusion systems with Turing and wave instabilities Open
General conditions are established under which reaction-cross-diffusion systems can undergo spatiotemporal pattern-forming instabilities. Recent work has focused on designing systems theoretically and experimentally to exhibit patterns wit…
View article: Amplitude equations for wave bifurcations in reaction–diffusion systems
Amplitude equations for wave bifurcations in reaction–diffusion systems Open
A wave bifurcation is the counterpart to a Turing instability in reaction–diffusion systems, but where the critical wavenumber corresponds to a pure imaginary pair rather than a zero temporal eigenvalue. Such bifurcations require at least …
View article: Measurements and linearized models for golf ball bounce on a green
Measurements and linearized models for golf ball bounce on a green Open
A detailed set of experiments are described that capture over a 1000 different instances of the bounce of a golf ball on a green. Video analysis was used to capture ball’s velocity and spin just before and after each bounce for a wide vari…
View article: Computation of Turing Bifurcation Normal Form for <i>n</i> -Component Reaction-Diffusion Systems
Computation of Turing Bifurcation Normal Form for <i>n</i> -Component Reaction-Diffusion Systems Open
General expressions are derived for the amplitude equation valid at a Turing bifurcation of a system of reaction-diffusion equations in one spatial dimension, with an arbitrary number of components. The normal form is computed up to fifth …
View article: Process modelling of NHS cardiovascular waiting lists in response to the COVID-19 pandemic
Process modelling of NHS cardiovascular waiting lists in response to the COVID-19 pandemic Open
Objective To model the referral, diagnostic and treatment pathway for cardiovascular disease (CVD) in the English National Health Service (NHS) to provide commissioners and managers with a methodology to optimise patient flow and reduce wa…
View article: Analysis of point-contact models of the bounce of a hard spinning ball on a compliant frictional surface
Analysis of point-contact models of the bounce of a hard spinning ball on a compliant frictional surface Open
Inspired by the turf–ball interaction in golf, this paper seeks to understand the bounce of a ball that can be modelled as a rigid sphere and the surface as supplying a viscoelastic contact force in addition to Coulomb friction. A general …
View article: A new phase model of the spatiotemporal relationships between three circadian oscillators in the brainstem
A new phase model of the spatiotemporal relationships between three circadian oscillators in the brainstem Open
Analysis of ex vivo Per2 bioluminescent rhythm previously recorded in the mouse dorsal vagal complex reveals a characteristic phase relationship between three distinct circadian oscillators. These signals represent core clock gene expressi…
View article: Measurements and linearized models for golf ball bounce
Measurements and linearized models for golf ball bounce Open
A detailed set of experiments are described that capture over a 1000 different instances of the bounce of a golf ball. Video analysis is used to capture velocity and spin immediately prior to and subsequent to each bounce for a wide variet…
View article: Getting the most out of maths: How to coordinate mathematical modelling research to support a pandemic, lessons learnt from three initiatives that were part of the COVID-19 response in the UK
Getting the most out of maths: How to coordinate mathematical modelling research to support a pandemic, lessons learnt from three initiatives that were part of the COVID-19 response in the UK Open
In March 2020 mathematics became a key part of the scientific advice to the UK government on the pandemic response to COVID-19. Mathematical and statistical modelling provided critical information on the spread of the virus and the potenti…
View article: Modelling a dynamic magneto-agglutination bioassay
Modelling a dynamic magneto-agglutination bioassay Open
The process of developing an end-to-end model of a magneto-immunoassay is described, simulating the agglutination effect due to the specific binding of bacteria to paramagnetic particles. After establishing the properties of the dose-speci…
View article: Analysis of point-contact models of the bounce of a hard spinning ball on a compliant frictional surface
Analysis of point-contact models of the bounce of a hard spinning ball on a compliant frictional surface Open
Inspired by the turf-ball interaction in golf, this paper seeks to understand the bounce of a ball that can be modelled as a rigid sphere and the surface as supplying an elasto-plastic contact force in addition to Coulomb friction. A gener…
View article: Organization of spatially localized structures near a codimension-three cusp-Turing bifurcation
Organization of spatially localized structures near a codimension-three cusp-Turing bifurcation Open
A wide variety of stationary or moving spatially localized structures is present in evolution problems on unbounded domains, governed by higher-than-second-order reversible spatial interactions. This work provides a generic unfolding in on…
View article: Optimisation of Fluid Mixing in a Hydrosac Growing Module
Optimisation of Fluid Mixing in a Hydrosac Growing Module Open
A mathematical model is proposed for the flow of nutrients in an inflatable hydroponics module being developed by Phytoponics. Simple experiments were performed via the injection of dye into the system enabling a basic understanding of the…
View article: Understanding the Fundamentals of Motor Current Signature Analysis
Understanding the Fundamentals of Motor Current Signature Analysis Open
Motor current signal analysis is a method to perform on-line monitoring of the condition of electrical motors by examining the spectrum of the residual current of the motor for sidebands around the main frequencies. The interpretation of t…
View article: Supplementary material for model development to optimise CVD waiting lists
Supplementary material for model development to optimise CVD waiting lists Open
This file contains the infomation used and the porcess and mathematical techniques to develop the model of UK CVD England waiting lists.
View article: Wiggly canards: Growth of traveling wave trains through a family of fast-subsystem foci
Wiggly canards: Growth of traveling wave trains through a family of fast-subsystem foci Open
A class of two-fast, one-slow multiple timescale dynamical systems is considered that contains the system of ordinary differential equations obtained from seeking travelling-wave solutions to the FitzHugh-Nagumo equations in one space dime…