UK Nonlinear News, May 1996

Situations Vacant

(See also the THES online: )


Two EPSRC Ph.D. Studentships

A dynamical systems analysis of
lateral vibrations in oil-well drillstrings

Alan Champneys

The project will involve an application of nonlinear dynamics and chaos to a real-world Engineering problem in the oil industry. Violent, self-supporting lateral vibrations in oil well drillstrings are known to cause millions of dollars worth of damage each year to complex drilling apparatus. A simplified differential equation model has shown the basic mechanism for the onset of these vibrations. Depending on the rotation speed of the drillstring and other critical parameters, this model is known to feature chaotic solutions. The aim of this project is to develop a more realistic model and to analyse its dynamics in order to suggest control strategies for the vibrations. A mixture of theoretical and numerical methods will be used. It will also involve collaboration with industry, notably Schlumberger and possibly Shell or BP. Interest in differential equations and some experience with scientific computing and/or numerical analysis would be useful.

This project has guaranteed funding from the Applied Nonlinear Mathematics Programme of the EPSRC.

Fractal dimension of medical images

Supervisors: Prof S.J. Hogan and Dr. P. Goddard

This is an interdisciplinary project between the university of Bristol and the Bristol Royal Infirmary. The purpose of the project is to use methods from nonlinear dynamics to produce models of various diseases in the lungs, based on information taken from medical images produced by a method known as magnetic resonance. The work will be a mixture of mathematical modelling using analytic techniques and comparison with field data. No medical knowledge is needed but some familiarity with reaction-diffusion equations would be useful. This is an excellent opportunity to get involved with a real medical problem which at the same time poses tremendous mathematical challenges.

Funding for this project is guaranteed through a grant from Bristol Royal Infirmary.

For informal equiries about either project, contact:
A.R.Champneys ( or
S.J.Hogan (
Department of Engineering Mathematics, University of Bristol
Tel. 0117 928 7754
Deadline for applications: 1st July 1996

University College, London; and
Southhampton Oceanography Centre

CASE Ph.D. Studentship

Geophysical Dynamics of Ocean Eddies:
Comparison of Observations and Models of Agulhas Rings

Climate modelling and observations form the basis for important economic decisions. For example, the possible imposition of Carbon Taxes has grave economic consequences. It is thus vital that climate models are as accurate as possible. It is becoming clear that the Agulhas system (the area of ocean off South Africa, between the South Atlantic and the Indian Ocean), and the rings of fluid spawned from it may play a significant role in the global heat budget and so in determining climate. Observing and modelling these Rings and their generation is an important but challenging task. A current project "Agulhas Rings - their propagation and generation" has been funded by NERC to develop at UCL a series of ocean models that should retain far finer eddy details and more rapidly-varying topography than present models. The project will deliver eddy statistics to enable direct comparison with altimetry from the Remote Sensing group of the Rennell Division of the Southampton Oceanography Centre.

Applications are invited for a 3-year CASE research studentship supported by NERC World Ocean Circulation Experiment (WOCE) Special Topic funding to join this collaboration between the Rennell Division of SOC and the Geophysical Fluid Dynamics group at UCL.

The successful applicant will spend year one at SOC working with Peter Challenor, the Head of Satellite Remote Sensing, learning techniques for analysing altimetry data and producing eddy statistics. The second and third years will be spent between UCL and SOC comparing these statistics with output from currently available models like OCCAM and collaborating on the new models developed at UCL. This intercomparison of models and data is a vital component of both.

Send a curriculum vitae and two reference letters to:
Professor Ted Johnson (
Department of Mathematics
University College London, Gower Street, London, WC1E 6BT, UK.


Two EPSRC Ph.D. Studentships

Two EPSRC funded PhD studentships will be available from September 1996 in the Physics Department at the University of Manchester. The studentships will be for research in the new Nonlinear Dynamics Group (see the news section, this issue) which will be established under the direction of Professor Tom Mullin. The topics of the research will be concerned with

(1) Spatio-Temporal Dynamics in "Open Flows" and
(2) Low-Dimensional Dynamics and Chaos in Non-Newtonian Flows.

Applicants should have, or expect to get, a first or upper second class degree in Physics. British students will receive full funding and EU students tuition fees only. Initial enquiries should be made directly to Tom Mullin (


Ph.D. Studentship

Modelling of Non-Fickian, Turbulent Diffusion
using Fractional Brownian Motions.

A Ph.D. studentship is on offer in the Department of Civil and Transportation Engineering at Napier University, Edinburgh.

Accurate prediction of pollutant dispersion is an important area of environmental research. The proposed programme of research will concern itself with the use of fractal geometry in the characterisation of the natural fractal structure of particle paths in fluids. Such characterisation will aid in the development of enhanced numerical models for the prediction of turbulent diffusion. The study will involve the abstraction of fractal characteristics (namely the Hurst exponent, H, and fractal dimension, D) from satellite tracked ocean surface drifter trajectories. These characteristics will then be used as input data for numerical simulations of non-Fickian, fractal diffusion.

Contact: Dr. Paul Addison (
Tel: 0131 455 2552 ; Fax: 0131 455 2239

BRIMS; or Overseas

EC Alapedes Programme

It is expected that up to 8 postdoctoral or PhD positions will become available in October 1996 at the various nodes of ALAPEDES. (See the
article in this issue).

Because of the multidisciplinary nature of this Network, the positions will be attractive to candidates from a wide range of backgrounds in mathematics, computer science or engineering. Candidates should take note of the following restrictions imposed by the European Commission.

  • A candidates must be a national of a member state of the EC or of an associated state.
  • A candidate must not be a national of the state in which he or she takes up an appointment.

    To apply for a position, or to seek further information regarding ALAPEDES, please contact Geert-Jan Olsder, the Network Coordinator:
    Geert-Jan Olsder (
    Delft University of Technology
    Faculty of Technical Mathematics and Informatics, PO Box 5031, 2600 GA Delft, Holland
    Tel: +31 15 278 1912; Fax: +31 15 278 7209

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    Last Updated: 8th May 1996.