Prof. D.F. Parker. Analysis of nonlinear surface waves includes both the unusual (nondispersive) properties of waves adjoining a flat surface and the possible resonant effects due to corrugation and layering. Static problems of finite elasticity arising from medical engineering are also being investigated.
Dr A.B. Olde Daalhuis works in the field of exponential asymptotics for the solution of ordinary differential equations by means of power series. The exponentially small terms in divergent asymptotic series are terms beyond all orders: they play a major role in connection problems, eigenvalue problems, and the numerical computation of solutions of nonlinear ODEs.
Dr. N.F. Smyth. Modelling of all-optical devices such as switches, filters and amplifiers. Effect of radiation on optical pulses. The modelling uses a combination of perturbation and numerical techniques, and the results are compared with experimental work.
Prof. D.F. Parker, Dr. J.G. Byatt-Smith, Dr. N.F. Smyth. Water waves in regions of variable depth, soliton perturbation techniques, inverse scattering , asymptotics. Nonlinear optics - including modelling of fibre inhomogeneities, twisting, dark/bright solitons for quadratic media, etc. In all topics, computation is combined with analytic work.
Dr. H.W. Braden works in quantum field
theory. He is interested in conformal and perturbed conformal
systems together with topological field theory. In particular he
is studying a specific integrable system, the so-called Toda
field theory. More traditional topics (e.g. inverse scattering,
solvable statistical mechanical models) are also being
investigated.
Dr. J.M. Figueroa-O'Farrill does
research on the mathematics of string theory. These days he is
trying to understand the geometry of branes from several
complementary points of view, ranging from classical
differential geometry to conformal field theory. His fondness
for integrable systems might prompt him to renew his efforts in
that topic, particularly in view of its relation with branes and
supersymmetric gauge theory.
Dr. S. Richardson uses complex variable techniques to analyze free boundary problems, both steady and unsteady.
Prof. D.C. Heggie studies the dynamical evolution of stellar systems, using both the N-body equations of motion and equations based on kinetic theory and gas dynamics. Much of the work involves the use of the parallel computers at Edinburgh. The three body problem is another area in which Prof. Heggie's students have worked recently.
Dr. M. Ruffert uses computationally intensive codes to address astrophysical questions, e.g. what happens when two neutron stars merge and how does matter accrete onto a black hole?
Dr. J. Vanneste's research centres on fluid dynamics, with applications to the dynamics of the atmosphere and the oceans. He is interested in wave and instability phenomena, and in the use of Hamiltonian techniques for fluids.