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Information: Computational Mathematics Group
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School of CMIS
University of Brighton
Watts Building
Lewes Road
Brighton BN2 4GJ
England

Tel: +44 (0)1273 642428
Fax: +44 (0)1273 642405

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PRINCIPAL STAFF:  Dr. Roma Chakrabarti, Dr. Steve Ellacott, Dr. Paul Harris, Dr. David Henwood, Mr. Keith Parramore and Dr. William Wilkinson.

For further information about staff, look at the CMIS Staff Search.

CURRENT RESEARCH STUDENTS: David Chappell, Philip Newman

The Computational Mathematics Group is involved with a number of on-going research projects. The details of some of these are listed below.
 

The Boundary Element Method
Previous research has covered a variety of application areas, notably bubble dynamics. However current activity focuses on acoustics.
The group is currently working on the modelling of the transient sound field radiated by a loud-speaker cone as part of a long-standing collaboration between the University of Brighton and B&W Loudspeakers Ltd. Prediction of the sound field enables the design process to be simplified.
Calculated results are compared to actual measurements obtained using a laser interferometer and anechoic chamber at B&W. The animation shows the calculated pressure field generated on the surface of the loudspeaker cone by an axisymmetric oscillation of the cone.

The group is also collaborating with the University of Liverpool on precondtioners for iterative solution of boundary element equations.

Paul Harris is on the steering/scientific committee for two upcoming conferences. They are the 5th UK Boundary Integral Method conference in Liverpool, 12th-13th September 2005 and the 9th International Conference on Integral Methods in Science and Engineering, 23 - 27 July 2006 in Niagra Falls, Canada.

Space Plasmas
The group's research interest in space plasmas focuses on the various aspects of collisionless shock waves; quasi-perpendicular and quasi-parallel shock structure; shock thermalization processes; particle dynamics at shocks; upstream and downstream wave phenomena; particle distributions and wave-particle interactions and co-rotating interaction regions in the solar wind. The work involves theoretical and computer simulation studies supported by some analysis of spacecraft  measurements.
The supersonic solar wind is deflected past the Earth by a standing shock wave (pink in the picture). This picture is from the ESA/NASA SOHO spacecraft portfolio and is courtesy of NASA.
Phase plot The plasma is heated as it passes through the shock. Phase space analysis allows the particle distribution to be determined. On the diagram, the dots show the calculated velocity distribution (white dots, one standard deviation; black dots, mode and two standard deviations), and the ellipses indicate a Gaussian approximation to the distribution. The diagram is taken from Ellacott and Wilkinson, 2003 (see publications below).

Recent PhD
H. Wang, Boundary integral modelling of transient wave propagation with application to acoustic radiation from loudspeakers, University of Brighton, 2004

Recent Publications
Boundary Elements

K. Chen and P. J. Harris, On efficient preconditioners for iterative solution of a Galerkin boundary element equation for the three dimensional exterior Helmholtz problem, The Journal of Computational and Applied Mathematics, 156, pp. 303-318, 2003.

H. Wang, P. J. Harris, R. Chakrabarti and D. Henwood, Modelling transient acoustic radiation using the retarded potential integral equation method, Proc. Third UK Conference on Boundary Integral Methods (ed. S. Amini), University of Salford, pp. 57-66, 2003.

P. J. Harris, An investigation into the use of the boundary integral method to model the motion of a single gas or vapour bubble in a liquid, Proc. Third UK Conference on Boundary Integral Methods (ed. S. Amini), University of Salford, pp. 37-46, 2003.

K. Chen, S. Hawkins and P. J. Harris, Easily inverted approximation type preconditioners for matrices arising from wavelet discretisations of boundary integral equations, Proc. Third UK Conference on Boundary Integral Methods (ed. S. Amini), University of Salford, pp. 165-174, 2003.

P. J. Harris and K. Chen, A discontinuous linear boundary element method for solving the three-dimensional exterior Helmholtz problem, Proc. Third UK Conference on Boundary Integral Methods (ed. S. Amini), University of Salford, pp. 57-66, 2003.

P. J. Harris, An investigation into the use of the boundary integral method to model the motion of a single gas or vapour bubble in a liquid, Engineering Analysis with Boundary Elements, 28, Issue 4, pp. 325-332, 2004.

P. J. Harris, W. K. Soh and H. Al-Awadi, An investigation into the effects of heat transfer on the motion of a spherical bubble ANZAM J 45, pp. 361-371, 2004.

P. J. Harris, H. Wang, R. Chakrabarti and D. Henwood, A method for modelling non-harmonic periodic acoustic radiation from a loudspeaker, Proceedings of Integral Methods in Science and Engineering 2002, Ed. C. Constanda, Birkhauser, Boston, 2004.

Space Plasma Physics

P. J. Moran, A. R. Breen, C. A. Varley, P. J. S. Williams, W. P. Wilkinson and J. Markkanen Measurements of the direction of the solar wind using interplanetary scintillations", Annales Geophysicae, 16 (10), pp. 1259-1264, 1998.

A. R. Breen, P. J. Moran, C. A. Varley, W. P. Wilkinson, P. J. S. Williams, W. A. Coles, A. Lecinski and J. Markkanen, Interplanetary scintillation observations of interaction regions in the solar wind, Annales Geophysicae, 16 (10), pp. 1265-1282, 1998.  

W. P. Wilkinson, Multiple encounters of a specularly reflected ion with planar quasi-perpendicular shocks, Planetary and Space Science 47(3-4), pp. 529-543, 1999.

W. P. Wilkinson, Constraints from the theory of magnetohydrodynamics on the supersonic interaction of two coplanar plasmas Journal of Technical Physics 40 (1), pp. 49-52, 1999.

W. P.  Wilkinson What the Rankine-Hugoniot relations tell us about co-rotating interaction regions in the solar wind, and what they don´t, Proceedings of the Les Woolliscroft Memorial Conference/Sheffield Space Plasma Meeting: Multi-Point Measurements versus Theory, Sheffield (UK), 24-26 April 2001, European Space Agency Special Publication SP-492 (ed. B. Warmbein), pp. 45-52, July 2001.

W. P. Wilkinson The Earth's quasi-parallel bow shock: review of observations and perspectives for Cluster, Planetary and Space Science 51 (11), pp. 629-647, 2003. (Invited review article for a special issue of the journal).

S. W. Ellacott and W.P. Wilkinson, Heating of directly transmitted ions at low mach number perpendicular shocks: new insights from a statistical physics formulation, J. Geophys Res., vol.108, no. A11, 1409, 2003.

S. W. Ellacott and W.P. Wilkinson, Irreversibility and entropy issues concerning the heating of directly transmitted ions at low mach number perpendicular collisionless shocks, to appear in J. Advances in Space Research. Click here for a preprint.

Other

S. W. Ellacott, The arithmetical structure of Celtic key patterns, Mathematics Today, vol.36 no.5 pp142-150, October 2000.

Computational Mathematics Research Group, Brighton

 

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