Professor Alan Champneys
B.Sc.(Birm.), D.Phil.(Oxon.)
Current positions
Professor of Applied Non-linear Mathematics
Department of Engineering Mathematics
Contact
Media contact
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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
Publications
Recent publications
28/01/2023General conditions for Turing and wave instabilities in reaction -diffusion systems
Journal of Mathematical Biology
Modelling a Dynamic Magneto-Agglutination Bioassay
Biosensors and Bioelectronics
Spikes and localised patterns for a novel Schnakenberg model in the semi-strong interaction regime
European Journal of Applied Mathematics
Bistability, wave pinning and localisation in natural reaction-diffusion systems?
Physica D: Nonlinear Phenomena
Conveyance of texture signals along a rat whisker
Scientific Reports
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