Professor Alan Champneys
B.Sc.(Birm.), D.Phil.(Oxon.)
Current positions
Professor of Applied Non-linear Mathematics
School of Engineering Mathematics and Technology
Contact
Press and media
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Research interests
- Applied dynamical Systems. Understanding complicated dynamics in physical systems governed byordinary, partial or lattice dierential equations in terms of bifurcation theory, especially global bifurcations (homoclinic and heteroclinic orbits). Bifurcation analysis of piecewise-smooth systems. Application to mechanical, civil, aero and eletrical engineering including rotating machines; valve dynamics; parametric resonance. Friction and impact modelling including the Painleve paradox.
- Nonlinear waves and coherent structures. Localised pattern formation ('homoclinic snaking') in Swift-Hohenberg and other models of bi-stable media. Application to nonlinear elastic buckling of cylinders, rods and struts. Application to ecology and biology. Solitary waves in fuids, solids and nonlinear optics.
- Mathematical biology. Modelling active hearing in the mammalian inner ear; the bio-mechanics of mosquito hearing and consequent swarming. Metabolomic modelling, especially within plant cells. Cellular pattern formation and polarity formation. Mathematical modelling of neuronal dynamics including the neural control of high blood pressure.
- Mathematical modelling and industrial mathematics Smart energy; tidal stream energy devices, economics of energy technology and market transition, power grid stability. Rotordynamics with application to drillstrings. Ecosystem feedback models. The dynamics of industrial supply networks. Design advice for pressure-relief valve instability prevention. Biosensor design. Digital healthcare using routinely collected ward data. Mutiscale modelling of hydroponic systems. Friction and impact modelling in industrial processes and sports science.
Projects and supervisions
Research projects
Machine learning for intensive care decision support
Principal Investigator
Role
Co-Investigator
Description
Developing bespoke clinical decision support software for intensive care discharge using machine learning.Managing organisational unit
Department of Engineering MathematicsDates
01/10/2018 to 31/12/2019
Dynamic supply chains
Principal Investigator
Managing organisational unit
Department of Engineering MathematicsDates
01/09/2013 to 01/03/2017
Tipping points; bifurcations in realistic atmospheric models and data workshop
Principal Investigator
Description
This project received funding from the Cabot Institute's Open Call for funding.Managing organisational unit
Department of Engineering MathematicsDates
Bridging the Gaps - Cross-Disciplinary Feasability Account
Principal Investigator
Managing organisational unit
Department of Engineering MathematicsDates
01/10/2009 to 01/04/2011
LOCALISED STRUCTURES OF LIGHT DISSIPATIVE NONLINEAR LATTICES
Principal Investigator
Managing organisational unit
Department of Engineering MathematicsDates
01/02/2007 to 01/02/2010
Thesis supervisions
Localised structures in reaction-diffusion equations
Supervisors
Multi-hazard exposure of cities and implications for urban infrastructure
Supervisors
Oscillations and Coupling in Neural Circuits
Supervisors
Application of Director Theory to Models of Flow in Straight and Curved Pipes
Supervisors
Development of a novel cell-based biosensor for the detection of cytotoxic effects using astrocyte cell lines
Supervisors
Investigation into the golf ball and turf interaction
Supervisors
Habitat loss and species interaction
Supervisors
Publications
Recent publications
01/04/2025From snaking to isolas
Wave Motion
Amplitude equations for wave bifurcations in reaction–diffusion systems
Nonlinearity
Wave-pinned patterns for cell polarity — a catastrophe theory explanation
SIAM Journal on Applied Dynamical Systems
Analysis of point-contact models of the bounce of a hard spinning ball on a compliant frictional surface
IMA Journal of Applied Mathematics
A new phase model of the spatiotemporal relationships between three circadian oscillators in the brainstem
Scientific Reports
Related people
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Dr Robert Szalai
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Dr Alberto Gambaruto
Senior Lecturer in Mechanical Engineering
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Dr Stanislaw Biber
Honorary Teaching Associate
School of Engineering Mathematics and Technology