Thomas J Bridges

Professor of Applied Mathematics


Seminars and Conferences
 
  2012-2014
 
  BAMC 2012
University College London, 27-29 March 2012.
  SIAM Nonlinear Waves and Coherent Structures
University of Washington, Seattle, 13-16 June 2012.

Minisymposium on "Hamiltonian & Symplectic Methods in the theory of nonlinear waves" 

  Nonlinear Waves in Fluids
Loughborough University, 12-14 September 2012.
  Workshop: Spectral analysis, stability and bifurcation in modern nonlinear physical systems
Banff International Research Station, Canada, 4-9 November 2012.
  Industrial and Computational Mathematics Seminar
University of Nottingham, 20 February 2013.
  IUTAM Symposium on Nonlinear Interfacial Wave Phenomena
Limassol, Cyprus, 14 to 18 April 2013.
  Conference: Geometric Mechanics and Control Theory
Indian Institute of Science, Bangalore, 19-31 August 2013.
  Theory of Water Waves
Isaac Newton Institute for Mathematical Sciences, 14 July to 8 August 2014.
 
  2008-2011
 
  IMA Conference on Nonlinearity and Coherent Structures
University of Reading, 6-8 July 2011.
  British Applied Mathematics Colloquium 2011
University of Birmingham, 11-13 April 2011.
  PDE Seminar
Trinity College, Dublin, 15 February 2011.
  Fluid Dynamics Seminar
Imperial College, 02 February 2011.
  Seminar in Applied Mathematics
University of Birmingham, 03 December 2010.
  Applied Mathematics Seminar
University of Bergen, Norway, April 2010.
  Mathematics Seminar
University College Dublin, Ireland, February 2010.
  Nonlinear Waves and the Maslov Index
Mathematics Institute, University of Warwick, November 2009.
  Dynamical Systems Seminar
School of Mathematics, University of Manchester, 11 February 2009.
  Workshop on Large Amplitude Internal Waves
ICMS Edinburgh, 1-4 December 2008.
  Conference on Nonlinear PDEs
OxPDE, St Anne's College, Oxford University, 5 June 2008.
  Applied Dynamics and Geometric Mechanics
Mathematisches Forschungsinsitut Oberwolfach, Germany, 20-26 July 2008.
  Colloquium in Mathematics
University of Reading, Friday 15 February 2008.
 
  Pre-2008 events
  MaGiC 2005: Manifolds and Geometric Integration Colloquia,
in Ustaoset, Norway, 14-18 February.

Click here for
The Ustaoset Lecture Slides

 
 
 
  List of publications click here
 
Some recent papers and preprints
 
  TJB [2013] A universal form for the emergence of the Korteweg-de Vries equation, Proc. Roy. Soc. Lond. A 469 20120707. Journal website
  M.R. Turner & TJB [2013] Nonlinear energy transfer between fluid sloshing and vessel motion, J. Fluid Mech 719 606-636. Preprint .pdf
  TJB, J. Pennant & S. Zelik [2014] Degenerate hyperbolic conservation laws with dissipation: reduction to and validity of a class of Burgers-type equations. Arch. Rat. Mech. Anal. (in press). Preprint .pdf
  TJB [2012] Emergence of unsteady dark solitary waves from coalescing spatially-periodic patterns, Proc. Royal Soc. London A 468 3754-3803. Preprint .pdf
  TJB & F. Chardard [2012] Transversality of homoclinic orbits, the Maslov index, and the symplectic Evans function. Preprint .pdf
  H. Alemi Ardakani, TJB & M.R. Turner [2012] Resonance in a model for Cooker's sloshing experiment, Eur. J. Mech. B/Fluids 36 25-38. Final form Preprint .pdf  
  TJB [2012] Geometric lift of paths of Hamiltonian equilibria and homoclinic bifurcation, Inter. J. Bif. & Chaos 22 1250304. Final form Preprint .pdf
  TJB & D.J. Needham [2011] Breakdown of the shallow water equations due to growth of the horizontal vorticity, J. Fluid Mech. 679 655-666. Final form Preprint .pdf   JFM Page
  H. Alemi Ardakani & TJB [2011] Shallow-water sloshing in vessels undergoing prescribed rigid-body motion in three dimensions, J. Fluid Mech. 667 474-519. Final form Preprint .pdf
  F. Dias, TJB & J.M. Dudley [2011] Rogue waves, Preprint Downloadable Preprint .pdf
  F. Chardard, F. Dias & TJB [2011] Computing the Maslov index of solitary waves. Part 2: Phase space with dimension greater than four Physica D 240 1334-1344 Downloadable Preprint .pdf
  TJB & N.M. Donaldson [2011] Variational principles for water waves from the viewpoint of a time-dependent moving mesh, Mathematika 57 147-173. Mathematika website   Downloadable Preprint .pdf
  TJB, P.E. Hydon & J.K. Lawson [2010] Multisymplectic structures and the variational bicomplex, Math. Proc. Camb. Phil. Soc. 148 159-178, Surrey Preprint .pdf
  D. Avitabile & TJB [2010] Numerical implementation of complex orthogonalization, parallel transport on Stiefel bundles, and analyticity, Physica D 239 1038-1047. Surrey Preprint .pdf
  F. Chardard, F. Dias & TJB [2009] Computing the Maslov index of solitary waves. Part 1: Hamiltonian systems on a four-dimensional phase space, Physica D 238 1841-1867, Surrey Preprint .pdf
  F. Chardard, F. Dias & TJB [2009] On the Maslov index of multi-pulse homoclinic orbits, Proc. Royal Soc. London A 465 2897-2910, Surrey Preprint .pdf
  TJB [2008] Degenerate relative equilibria, curvature of the momentum map, and homoclinic bifurcation, J. Diff. Eqns. 244 1629-1674   JDE website @ Sciencedirect.com   Surrey Preprint .pdf
  TJB & G Derks [2003] Dimension breaking of nonlinear elliptic PDEs: satisfying the spectral condition geometrically,   Surrey Preprint
Contact information:

Address: Department of Mathematics
University of Surrey
Guildford
Surrey GU2 7XH
ENGLAND
Telephone: +44 (0)1483 689642
Fax: +44 (0)1483 686071
Mail to: t.bridges@surrey.ac.uk
Home page: http://www.maths.surrey.ac.uk/profiles?s_id=2039
Local Weather:
Lectures
2011-2012 Academic Year
 
  MATM016
Nonlinear Wave Equations

upcoming
 
  MAT2047
Curves and Surfaces

Autumn 2012
 
Current Postgraduate Research Students
 
  Hamid Alemi Ardakani
Rigid-body motion with interior shallow-water sloshing
 
  Natalie Douglas
Self-rotating life forms, connections and a numerical simulation of deformable bodies in inviscid flow
 
Open projects for PhD Research
 
  Numerical analysis on Grassmannian manifolds
  Multi-symplectic structures and pattern formation
  Any aspect of the theory of water waves
  Stability and dynamics of solitary waves
  Fluid sloshing in moving containers
 
 

  See the Postgraduate Research page for further details.
Grasshopper's Guide
to Research Interests
 
  Symplectic pattern formation -->
  Grassmann and Stiefel manifolds
  Absolute and convective instabilities
  Stability of multi-periodic and quasiperiodic patterns
  Dynamics of coupled pendulums
  Hydrodynamic stability and the Orr-Sommerfeld equation
  Dynamical systems and Hamiltonian mechanics
  Symplectic geometry
  Water waves
  Solitary waves and fronts
  Transition to turbulence in shear flows
  Equivariant symplectic maps
  Springer Lecture Notes in Mathematics website
  Nonlinear Kelvin-Helmholtz problem
Book in preparation on:

Symplectic Pattern Formation

 
  Full table of contents to appear here soon!
  Multi-symplectic structures
  Dimension breaking of patterns
  Multi-periodic patterns
  solitary waves and fronts
  quasiperiodic patterns
  geometry of patterns in oceanography
  multi-symplectic Melnikov theory
  multi-symplectic structure of water waves