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School of CMIS
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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 MethodPrevious research has covered a variety of application areas, notably bubble dynamics. However current activity focuses on acoustics.
The group is also collaborating with the University of Liverpool on precondtioners
for iterative solution of boundary element equations.
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.
S. W. Ellacott, The arithmetical structure of Celtic key patterns, Mathematics Today, vol.36 no.5 pp142-150, October 2000.