Prof A R Champneys
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Alan R Champneys
Professor of Applied Nonlinear Mathematics
Applied Nonlinear Mathematics Group,
Department of Engineering Mathematics,
University of Bristol,
Queen's Building, University Walk,
Bristol BS8 1TR, United Kingdom
Tel: +44 (0)117 331 5643
Fax: +44 (0)117 331 5636
Home Tel: +44 (0)1225-317803
Date of and place of birth: 17/4/67,
Tunbridge Wells , Kent, U.K.
Status Married to Sharon since 1992. Two sons: Max 19/6/95,
Dominic 10/5/97. Daughter Emma 19/11/00
- 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
- 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.
EPSRC Advanced Fellowship
- 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'.
across engineering to aircraft and structural dynamics, power electronics,
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.
Localised phenomena . 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.
- Phd Students:
Mario di Bernardo 1995-1998 Controlling chaos
(joint supervision with Prof David Stoten,
Patrick Woods 1995-1999 Localised elastic buckling
Rob Clewley 1997-2001 Dynamical models of neural networks
- Bart Oldeman 1998-2001 Homoclinic doubling bifurcations
(joint supervision with Dr Bernd Krauskopf)
- Matt Pearce 2000 - Embedded solitons in nonliear optics
- Richard Eyres 2001- Modelling lag dampers on helicopter
rotos (joint supervision with Dr Nick Lieven
- Aerospace Engineering - & John Hogan)
- Csoba Hos 2002 Visiting student from
Technical University of Budapest.
complete listing is available including downloadable versions
Group Preprint Server
A downloadable site for the
ANM group preprints since 1995
- Champneys, A.R. 1991 Homoclinic orbits in the dynamics of
articulated pipes conveying fluid. Nonlinearity 4,
- Champneys, A.R., Kuznetsov, Yu.A. & Sandstede, B. 1996
A numerical toolbox for homoclinic bifurcation analysis.
International Journal of Bifurcation and Chaos 6, 867-887.
- Champneys, A.R. 1998 Homoclinic orbits in reversible systems
and their applications in mechanics, fluids and optics
Physica D 112 , 158-186.
- Champneys, A.R., Hunt G.H. and Thompson, J.M.T. (Eds.) 1999
Localization and solitary waves in solid mechanics.
World Scientific Advanced Series in Nonlinear Dynamics. Volume 12.
- Champneys, A.R. and Fraser, W.B. 2000 The `Indian rope trick'
for a parametrically excited flexible rod: I linearised analysis.
Proc. Roy. Soc. Lond. A 456 553-570.
- Skryabin, D.V, Champneys, A.R. and Firth W.J. 2000
by soliton excitation in nondegenerate intracavity downconversion.
Physical Review Letters 84 463-466.
- di Bernardo, M., Budd, C.J. and Champneys, A.R. 2001
Grazing and Border--Collision in Piecewise-smooth Systems:
A Unified Analytical Framework. Physical Review Letters
- Champneys, A.R., Vanden-Broek J.-M. and Lord, G.J. 2002
Do true elevation solitary waves exist? A numerical investigation.
J.Fluid Mech. 454 403-417.
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HomCont, jointly developed with Yuri A.
Kuznetsov of the University of Utrecht,
Ohio State Univeristy. A toolbox for
numerical homoclinic bifurcation analysis.
the numerical continuation package AUTO
wrtiten by Eusebius Doedel of Concordia University.
Specifically, it deals with continuation of codim 1 homoclinic orbits to
hyperbolic and saddle-node equilibria, including the detection of many
codim 2 singularities and the continuation of these singularities in 3
or more parameters.
Version 3.0 is available prepackaged with AUTO97
which is freely available from
the auto website or by annonymous ftp from
ftp.cs.concordia.ca directory pub/doedel/auto/ .
- 1994-1996 Numerical Computation of Homoclinic Tangencies to
Nuffield Foundation ``Newly appointed science
lecturer'' 4,000 pounds.
- 1994 British Council Travel Grant to visit Poul G. Hjorth of the
Technical University of Denmark to
work on adiabatic invariants in Hamiltonian systems.
- 1994 Novel Aspects of Codimension-Two Homoclinic Bifurcations.
EPSRC Visiting Fellowship Grant to fund the visits of Bjoern Sandstede
of the Weierstrass-Institute for Applied Analysis and Stochastics,
Berlin and Joerg Haerterich of the
Free University of Berlin.
- 1994-1997 Homoclinic Orbits and Localised Buckling of
Axially-Compressed Cylindrical Shells.
With Giles Hunt (Mechanical Engineering, University of
Bath). EPSRC Applied Nonlinear Mathematics Initiative, 100,000
pounds to employ Gabriel Lord
as a postdoctoral Research Assistant.
- 1997-2000 Localized homoclinic buckling of rods using
nonlinear dynamics and bifurcation theory. With J.M.T. Thompson FRS.
EPSRC Applied Nonlinear Mathematics (ANM) grant to fund a postdoc
at UCL starting April 1997. 100,000 pounds (payable to UCL)
Gert van der Heijden.
1998 An Ethel Raybold Foundation grant to visit the University of
Queensland to work with Dave Stump for 5 weeks in Sept-Oct 1998
on buckling of long rods hanging under gravity.
- 1999 A Benjamin Meaker grant for Boris Malomed of the University of
Tel Aviv to visit for four weeks in March 1999.
- 1999 An NWO (Dutch Research Council) grant for Dr Paul Zegeling
of the University of Utrecht to visit for 1 week in March 2000.
- 2000 An EPSRC visiting fellowship to fund Barrie Fraser of the University
of Sydney to visit Bristol for 3 months in Summer 2000.
BLADE Project JIF bid from the UK government. Part of the
scientific case for this 15 Million pounds(!) award to
revamp the Queen's Building into a state of
the art facility for Advanced Dynamic Engineering
- 2000-2002 A Global Approach to Understanding Localized
Structures in Nonlinear Dispersive Wave Systems.
Co-principle investigator with Vassilis Rothos
(University of Loughborough) to fund a postdoc and international
visitor programme. Funds
Value 100,000 pounds.
- 2000-2001 London Mathematical Society network grant to found meetings
of the ``Southern Bifurcation Theory'' network at Bristol, Exeter,
Southampton and Imperial College.
- 2001 EPSRC Mathematics Programme Workshop Grant
to fund meeting on
``Nonlinear Dynamics and
Chaos; Where Should We Go From Here?'' One of orgainising
committee of 6.
Value 16,630 pounds + 4,000 pounds from
Colston Research Society and 2,000 pounds from LMS.
- 2001 ``Local Bifurcations with Global Reinjection.'' Co-investigator on
fast track EPSRC proposal by Bernd Krauskopf. Value 60,000 pounds.
- 2002 ``Numerical Methods for Nonlinear Dynamics \& Bifurcations'' EPSRC
and LMS workshop funding. One of four co-investigators.
Value 10,000 pounds.
- 2002 ``Bristol Centre for Applied Nonlinear Mathematics.'' Major
interdisciplinary grant from the EPSRC Mathematics programme to
fund RAs and research workshops/visitors 2002-2007. 2nd named
investigator. Value 1.067 million pounds.
2002 EPSRC visting fellowship for Keith Promislow (Vancouver) to
visit Bath and Bristol May-June 2002. Co-investigator. Value
$\approx \pounds 2K$
- 2002 EU IST Framework V grant ``SICONOS: SImulation and COntrol
of NOn-smooth Systems'' co-ordinator of Bristol node. 2002-2006
Network of approx 9 sites. Total value 2 million euro.
Bristol's share 330,000 euro.
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