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Professor Alan Champneys
Professor Alan Champneys
Professor of Applied Non-linear Mathematics
Applied dynamical systems
. Understanding complicated dynamics (e.g. chaos) in physical systems governed by ordinary or partial differential equations in terms of bifurcation theory. Global bifurcations (homoclinic and heteroclinic orbits). Bifurcations (grazing and sliding) unique to piecewise-smooth systems. Parametric resonance; the `Indian Rope trick'. Application across engineering to aircraft and structural dynamics, power electronics, fluid-structure interaction.
Numerical bifurcation theory
. Path-following; use of the codes AUTO and CONTENT. Numerical analysis of homoclinic and heteroclinic bifurcations, including homoclinic orbits to periodic orbits, numerical branch-switching and stability calculations. Algorithms for periodic orbits of large systems.
. Existence theories for multiplicities of homoclinic orbits in Hamiltonian and reversible systems. Applications to nonlinear elastic buckling. Localised buckling of cylinders , rods and struts. Solitary waves in suspension bridges. Applications to solitary water waves with surface tension, and generalised solitary waves (homoclinics to periodics). Applications to nonlinear optics; "embedded" solitons, second-harmonic generation, optical parametric oscillators. Localised modes of higher-oder continuum models for lattice equations.
Brief Career History
- 1985-1988 BSc. in Mathematics, University of Birmingham Graduated with first class honours.
- 1988-1991 PhD. in Mathematics, Wadham College University of Oxford. Thesis title The nonlinear dynamics of articulated pipes conveying fluid, supervisor T. Brooke Benjamin FRS.
- 1992-1993 Postdoctoral Research Assistant in the School of Mathematical Sciences, University of Bath sponsored by the EPSRC (formerly SERC) on Numerical computation of invariant manifold bifurcations. Jointly supervised by John Toland and Alastair Spence .
- 1993- Lecturer in Nonlinear Systems. Department of Engineering Mathematics, University of Bristol. Reader since 1998. Professor since 2001.
- 1997-2002 EPSRC Advanced Fellowship
- Vlajic, N, Champneys, AR & Balachandran, B, 2017, Nonlinear Dynamics of a Jeffcott Rotor with Torsional Deformations and Rotor-Stator Contact. International Journal of Non-Linear Mechanics.
- Alexander, N, Macdonald, J & Champneys, A, 2017, Numerical investigation of a simple model of human jumping on an oscillating structure. in: Procedia Engineering: X International Conference on Structural Dynamics, EURODYN 2017.
- Champneys, AR & Varkonyi, P, 2016, The Painlevé paradox in contact mechanics. IMA Journal of Applied Mathematics, vol 81., pp. 538-588
- Aldersley, AJ, Champneys, AR, Homer, ME & Robert, D, 2016, Quantitative analysis of harmonic convergence in mosquito auditory interactions. Journal of the Royal Society Interface, vol 13.
- Hős, C, Champneys, A, Paul, K & McNeely, M, 2016, Dynamic behaviour of direct spring loaded pressure relief valves: III valves in liquid service. Journal of Loss Prevention in the Process Industries, vol 43., pp. 1-9
- Briant, LJB, Paton, JFR, Pickering, AE & Champneys, AR, 2015, Modelling the vascular response to sympathetic postganglionic nerve activity. Journal of Theoretical Biology, vol 371., pp. 102-116
- Breña-Medina, VF, Avitabile, D, Champneys, AR & Ward, MJ, 2015, Stripe to spot transition in a plant root hair initiation model. SIAM Journal on Applied Mathematics, vol 75., pp. 1090-1119
- Berdeni, Y, Champneys, A & Szalai, R, 2015, The two-ball bounce problem. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol 471., pp. 1-20
- Briant, L, O'Callaghan, E, Champneys, A & Paton, J, 2015, Respiratory modulated sympathetic activity: a putative mechanism for developing vascular resistance?. Journal of Physiology, vol 593., pp. 5341?5360
- Neild, S, Champneys, A, Wagg, D, Hill, T & Cammarano, A, 2015, The use of normal forms for analysing nonlinear mechanical vibrations. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol 373.
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