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Professor Alan Champneys - University of Bristol. Bristol, , GB

Professor Alan Champneys Professor Alan Champneys

Professor of Applied Nonlinear Maths | University of Bristol


Using mathematical models to explore dynamics and solve problems in industry and society

Areas of Expertise (11)

Healthcare Modelling


Maths Problems

Why Structures Buckle

Buckling and Bouncing


Mathematical Models

How Balls Bounce

Applied Maths


Industrial Maths


Professor Alan Champneys is based in the Department of Engineering Mathematics at the University of Bristol. He is an expert in problem-solving, using mathematical models to understand dynamics such as swing of suspension bridges, how pumps and generators can become unstable, the impact of sudden stresses on human organs, how sports balls bounce, and why objects become distorted.

He has formed part of an online community of maths modellers who formed the UK's Virtual Centre for Knowledge Exchange in the Mathematical Sciences working with industry and government in brainstorming problems arising from the COVID-19 pandemic and beyond.

Professor Champneys is a passionate public communicator and regular contributor of popular STEM think pieces. Recent topics covered include: the importance of maths in society, the use and abuse of mathematical models, the history of science and maths, the use of data in healthcare, swarming, maths and poetry, and the mathematical principles for reopening workplaces post-lockdown.






Nonlinearity Breeds Contempt Why pedestrian bridges wobble: synchronisation and the wisdom of the crowd Professor Alan Champneys - Applied Nonlinear Mathematics - Engineering Nonlinearity Interview



Accomplishments (3)

Honoroary Doctorate in Mechanical Engineering from BME University Budapest


Alan Tayler Lecturer, St Catherine’s College Oxford


Best of Bristol Lecturers: Voted by the students


Education (2)

University of Oxford: D.Phil., Mathematics 1991

University of Birmingham: B.Sc., Mathematics 1988

Affiliations (3)

  • Member, Institute for Mathematics and Its Applications
  • Member, Scientific Steering Board of Smith Institute for Industrial Mathematics
  • Member, Society for Industrial and Applied Mathematics

Media Appearances (3)

Hundreds of thousands attend People’s Vote march in London

The Times  online


Alan Champneys, wearing a blond Boris Johnson wig, was handing out £350m notes from the “Bank of Brexit Lies” to his fellow protesters. The 51-year-old university professor, who lives in Bath, said he had joined yesterday’s People’s Vote march because “the whole ethos of Brexit: the negativity, the xenophobia, the lack of trust in expertise” ran against his values.

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Good news: The Amazon rainforest can recover

The London Economic  online


So he teamed up with Professor Alan Champneys, a theorist in the Department of Engineering Mathematics, and Dr Jo House, an expert on land use change from the School of Geographical Sciences. For the past two years they have been examining these findings rigorously and Prof Champneys said the interdisciplinary collaboration helped “in explaining seemingly unrelated phenomena.”

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Engineering Mathematics Around the World

Siam News  online


“It doesn’t really conjure up an image of who we are,” Champneys said. “Going back 40 or 50 years, it was about process modeling—about modeling mechanics and fluid flow—the traditional engineering mathematics. Now we are more into cool technology.”

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Articles (5)

Experimental characterisation of asynchronous partially contacting motion in a multiple-degree-of-freedom rotor system

Mechanical Systems and Signal Processing

2020 Recent theory has predicted the onset of asynchronous bouncing motion at speeds beyond those of internal resonance in multi-degree-of-freedom rotating systems with intermittent contact. This paper provides the first attempt to experimentally validate the theory. Vibrations incorporating rotor-stator contact are recorded from a vertically ounted rotordynamics test rig comprising two rigid shaft-disk assemblies that are axially joined by a bellows coupling.

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Explanation of the onset of bouncing cycles in isotropic rotor dynamics; a grazing bifurcation analysis

The Royal Society A Mathematical Physical and Engineering Sciences

2020 The dynamics associated with bouncing-type partial contact cycles are considered for a 2 degree-of-freedom unbalanced rotor in the rigid-stator limit. Specifically, analytical explanation is provided for a previously proposed criterion for the onset upon increasing the rotor speed Ω of single-bounce-per-period periodic motion, namely internal resonance between forward and backward whirling modes.

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Happy Catastrophe: Recent Progress in Analysis and Exploitation of Elastic Instability

Frontiers in Applied Mathematics and Statistics

2019 A synthesis of recent progress is presented on a topic that lies at the heart of both structural engineering and non-linear science. The emphasis is on thin elastic structures that lose stability subcritically—without a nearby stable post-buckled state—a canonical example being a uniformly axially-loaded cylindrical shell.

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Tropical tree cover in a heterogeneous environment: A reaction-diffusion model

PLoS One

2019 Observed bimodal tree cover distributions at particular environmental conditions and theoretical models indicate that some areas in the tropics can be in either of the alternative stable vegetation states forest or savanna.

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Identifying dynamical instabilities in supply networks using generalized modeling

Journal of Operations Management

2019 Supply networks need to exhibit stability in order to remain functional. Here, we apply a generalized modeling (GM) approach, which has a strong pedigree in the analysis of dynamical systems, to study the stability of real‐world supply networks. It goes beyond purely structural network analysis approaches by incorporating material flows, which are defining characteristics of supply networks.

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