UK Nonlinear News, May 1998

Situations Vacant


Department of Engineering

PhD Studentship in Fracture Mechanics and Dynamics

Project Title: An Influence of Chaotic and Stochastic Dynamic Loading on Fatigue Life of Mechanical Elements

Applications are invited for a three year PhD studentship available NOW for a home or EC student to work in the areas of fracture mechanics and dynamics. We seek a suitably-qualified student with an engineering and mathematical background who is willing to undertake an experimental and analytical work on the project outlined briefly below. An increasing demand for higher fatigue life of mechanical components requires to establish a consistent methodology for evaluating damage done by irregular loading. Since the majority of loading has a random or non-linear nature, the current code based on periodic loading cannot provide a reliable answer about the fatigue life for many structures. The developed methodology will be applicable to many materials used in different engineering structures.

For further particulars and application forms please contact

Dr. M. Wiercigroch Telephone 01124 272509 E-mail:
Dr. W.F. Deans Telephone 01124 272795 E-mail:

Source: Marian Wiercigroch (


EPSRC Studentship in Mathematical Biology

Supervisors: Dr. Mark Chaplain and Dr. Kees Weijer, Departments of Mathematics and Anatomy and Physiology, University of Dundee.

Project Title Mathematical modelling of cell movement during multicellular development.

Start Date: September/October 1998. (Closing date for applications 3rd July 1998).

One of the most important problems in developmental biology is to determine the mechanisms responsible for morphogenesis. Morphogenesis happens mostly during embryonic development and involves regulated cell division of the fertilised egg to produce many cells that differentiate into a number of cell types. These are then arranged in a well ordered spatial pattern in a defined temporal sequence. The aim of this PhD thesis research programme is to understand the cellular basis of morphogenesis of a simple organism, the slime mould Dictyostelium discoideum. Based on previous experiments we have developed a working hypothesis to explain the control of cell movement during Dictyostelium morphogenesis. Slime mould cells proliferate as unicellular amoebae, which feed on bacteria in the soil. When food becomes limited, the amoebae enter an aggregation phase, leading to the formation of a multi cellular aggregate, the mound. In the mound cells differentiate into several cell types and the mound then transforms into a motile structure, the slug, with a clear polarity and an axial pattern formed by differentiated cells. The slug moves to a suitable place to produce a fruiting body, which consists of several stalk and spore cells. The spores disperse, germinate and the cycle can start over again. Development up to the early mound stage (wave propagation, chemotaxis stream formation) is now relatively well understood. However the later stages of development slug formation and migration and culmination are less well understood both experimentally and theoretically. The aim of this work is to investigate the control of cell sorting leading to slug formation and migration as well as the mechanism of slug movement. There are several exciting and challenging problems that need to be addressed both experimentally and theoretically.

The mathematical modelling of the system will consider two approaches. The first approach is to use a hydrodynamic model by considering the multi-cellular aggregate as a liquid where chemotaxis is modelled as an internally arising force which causes the flows inside the liquid. This hydro-dynamical approach has already been used successfully to model mound formation. The novel mathematics will involve the 3-dimensional numerical simulation of an incompressible fluid with a free boundary/surface. An alternative way to model these processes is to use a cellular automata (CA) model to describe the cells. The advantage of this type of model is that it is easy to generate different cell types with different relay and movement properties in accordance with the known facts. It will be more difficult to model cell movement in a densely packed mass of cells using rules which are relevant to experimental measurable variables. One possibility will be to model cells as entities which are able to change their shape so that they can glide over each other (i.e a cell occupies many grid points). Adhesion can be described by simple rules involving minimalisation of the free energy of cell cell contacts. The description of the chemotactic response will be in terms of forces (as described above in the hydrodynamic model). At the same time we also intend to develop a (classical) pde model describing the movement of the cells and then use the discretised version of the pde as a basis for the rules of the cellular automata - a type of deterministic cellular automata. In this way we will utilise the strengths of the continuum-pde approach (qualitative solutions, analysis of travelling wave solutions) with the strengths of the CA approach (ability to model different cell types with different properties).

We seek either an applied mathematics or theoretical physics graduate with strong and demonstrable biological interests, or a biologist with an excellent mathematical background. The project will be genuinely interdisciplinary, and intending applicants should keep this clearly in mind.

Applications, with full CV and the names of two referees should be addressed to:

Dr Mark Chaplain, Department of Mathematics, University of Dundee, DUNDEE DD1 4HN,, telephone: 01382-345369


Dr C.J. Weijer, Department of Anatomy and Physiology, University of Dundee, DUNDEE DD1 4HN,, telephone 01382-345191

either of whom are happy to answer informal enquiries. BBSRC PhD Studentship in Mathematical Biology.

Source: Mark Chaplain.


BBSRC Studentship in Mathematical Biology

Supervisors: Dr. Mark Chaplain and Dr. Steve Hubbard, Departments of Mathematics and Biological Sciences, University of Dundee.

Project Title The spatial and temporal dynamics of horizontal and vertical transmission of the intracellular parasite Wolbachia in insect populations.

Start Date: September/October 1998. (Closing date for applications 3rd July 1998)

Wolbachia is a genus of closely related proteobacteria found in obligatory intracellular association with a wide variety of arthropods, including most major insect orders (Werren et al, 1995, Proc. Roy. Soc. B). These Rickettsia-like micro-organisms are maternally inherited, and are maintained in host populations by three distinct alterations of host sexuality; cytoplasmic incompatibility (CI), parthenogenesis (P), and the feminisation (F) of genetically determined males. A great deal of recent interest has centred on the possible role of Wolbachia in speciation through reproductive isolation, and in the biological control of insect pests (Braig et al, 1994, Nature). Given that the Wolbachia common ancestor evolved around 20-80 million years ago, compared to 300 million years for insects, it is likely that horizontal transfer (HT) of the parasite is still occurring, and one obvious group of vectors for HT are insect parasitoids; preliminary results obtained recently in the laboratory of one of us show that parasitoids do indeed act as HT vectors at frequencies between 2 and 10%, but the consequences of this for insect population and evolutionary dynamics have yet to be fully explored. The aim of this project is to develop mathematical models describing the horizontal and vertical transmission of Wolbachia in a host-parasitoid system on both ecological and evolutionary timescales. These models will be compared and tested with on-going experimental work.

To model the spatio-temporal dynamics of horizontal transmission the student will initially develop a system of partial differential equations describing the interaction between the hosts and the parasitoids within a given 2-dimensional domain. These equations will yield spatio-temporal distributions of each species throughout the domain in terms of density per unit area. From these equations we will generate a biased random walk model from a discretised form of the pdes. This technique will enable individual insects and their interactions to be followed. This will also introduce a stochastic element to the model - at each encounter between host and parasitoid there will be a probability of host infection. Each infection in turn will have a probability of affecting the host in one of three ways (CI, P, F) describer above. The results of the spatio-temporal dynamics of the horizontal transmission will then be used to determine the vertical transmission of Wolbachia to successive generations. The modelling techniques used here will be nonlinear dynamical systems theory (nonlinear difference and nonlinear ordinary differential equations). The student will also use cellular automata and coupled-map lattice models for the horizontal dynamics and compare the results of the different models.

We seek either an applied mathematics or theoretical physics graduate with strong and demonstrable biological interests, or a biologist with an excellent mathematical background. The project will be genuinely interdisciplinary, and intending applicants should keep this clearly in mind.

Applications, with full CV and the names of two referees should be addressed to:

Dr Mark Chaplain, Department of Mathematics, University of Dundee, DUNDEE DD1 4HN,, 01382-345369


Dr S.F. Hubbard, Department of Biological Sciences, University of Dundee, DUNDEE DD1 4HN,, 01382-344291

either of whom are happy to answer informal enquiries.

Source: Mark Chaplain.


PhD Studentships in Nonlinear Mathematics

PhD studentships will be available from September next year in the following general areas:

For more details contact:

Dr. P.S. Addison
Department of Civil and Transportation Engineering
Napier University
Merchiston Campus
10 Colinton Road
EH10 5DT

Tel. 0131 455 2552
Fax. 0131 455 2239

Source: P.S. Addison (


CASE AWARD for graduate study in Nonlinear Prediction

The Mathematical Institute of Oxford University of Oxford has a CASE studentship in Nonlinear Prediction in association with the European Centre for Medium Range Weather Forecasting. The project will focus on the prediction and predictability of nonlinear dynamical systems ranging from analytically tractable systems to operational weather models. Those interested should contact:

Leonard Smith (44) 1865 270 518 (direct)
Mathematical Institute (44) 1865 270 515 (fax)
26-29 St Giles
Oxford OX1 3LB

Source: Leonard Smith (


PhD Studentship in Dynamical Systems Theory Applied to Eye Movement

Dave Broomhead in Mathematics at UMIST has an already funded EPSRC studentship for 3 years starting this summer for work on the use of Dynamical Systems theory in the study of eye movement and its control. This work is being done in collaboration with Dr Richard Abadi in the Department of Optometry and Vision Science at UMIST. The project will need a person with a mathematics background who is interested in developing nonlinear dynamical models, using information derived from experimental studies of the way in which people control (or fail to control) their eye movements. If you are interested, or would like more information, please contact:

Professor D.S. Broomhead
Department of Mathematics Tel: +44 (0)161-200-3689
PO Box 88
Manchester M60 1QD FAX: +44 (0)161-200-3669
U.K. E-mail:

Source: Dave Broomhead (


Post Graduate Research Associate in Fluid Dynamics

Supervisor: Dr Peter Thomas, Engineering Department (University of Warwick, England).

Project Title: Flow over granular media in rotating fluids.

Applications are invited for a Post Graduate Research Associate in Experimental Fluid Dynamics. Applicants should have a good honours degree in Physics, Engineering or a related subject. The successful applicant will be expected to carry out fundamental research related to the boundary-layer flow over layers of granular media in rotating fluids (Note: please see Journal of Fluid Mechanics, 1994, vol 274, pp. 23-41 to see what it is all about). The research is initially purely experimental but is expected to involve some numerical modelling during the later stages of the project. The position is available immediately. The successful candidate will have the opportunity to register for a PhD. The post is intended to be half-time for 3 years but applicants wishing to work 18 months full time will be considered. The salary is pro-rata to the RA1B scale 15,159-16,927 pounds.

Unfortunately we can only consider those applicants which are either EC nationals or who already have a work permit for the UK.

Dr. Peter J. Thomas,
Fluid Dynamics Research Centre
Department of Engineering
University of Warwick
Coventry CV4 7AL

Tel.: +44 (0)1203 522200,

Source: Gregory P. King on behalf of Peter Thomas (

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Last Updated: 1st May 1998.