by Martin Homer, University of Bristol, UK

The Bristol Centre for Applied Nonlinear Mathematics (BCANM) at the University of Bristol has a unique and proven track record for collaborative research between mathematicians, engineers and applied scientists. It benefits from its position in the Department of Engineering Mathematics within the internationally renowned Faculty of Engineering, and was recently part of the successful JIF bid for £15M to fund the Bristol Laboratory for Advanced Dynamic Engineering (BLADE), Europe's most advanced dynamics engineering facilities, due for completion in February 2004. BCANM is supported by a £1.1M grant from the Engineering and Physical Sciences Research Council, the UK Government's funding agency for research and training in engineering and the physical sciences. It is one of the largest mathematics projects ever funded in the UK.

The mission of BCANM is to address both the mathematical themes of the BLADE, and the grand engineering challenge of real-time dynamic substructuring. Building on the internationally leading interdiscipinary base of the Applied Nonlinear Mathematics group, founded in 1992 by Prof. John Hogan, the members of BCANM will address these aims with five postdoctoral research assistants, appointed on a rolling programme over five years, to work on specific projects within each theme, and a series of workshops and extensive visitor programme centered on the themes. The mathematical themes the programme will address are:

• Dynamical systems with delays
• Dynamics of piecewise smooth systems
• Qualitative numerical analysis of high-dimensional nonlinear systems
• Modelling spatially extended systems; continuous vs discrete

 

In addition, the permanent academic members of BCANM have a wide range of research interests, including analysis and control of piecewise smooth systems, analysis of local and global bifurcations, numerical continuation of global bifurcations and solitary waves, computation of invariant manifolds, control and synchronisation of chaotic systems, nonlinear dynamics of laser systems, liquid crystal dynamics, electrical control of porous media flows, non-integrable nonlinear optics, localised elastic buckling in long structures, nonlinear dynamics of power electronics systems and fractal analysis of medical images.

There are currently 7 full time staff members in the group headed by Prof. John Hogan, with 8 research assistants and 12 postgraduates. esearch assistants and visitors are housed in one large open-plan office, which has become a natural focus for the BCANM's activities. There is significant synergy within the group between staff, students and visitors, with an extensive series of group activities e.g. several 1 or 2 day mini-meetings throughout the year centering on individual methods or approaches or visiting researchers, weekly formal seminars, bi-weekly informal seminars, weekly working seminars and daily research coffee meetings. BCANM has strong links, both internally within the Faculty of Engineering, the Department of Mathematics and the Department of Physics, as well as locally with the Centre for Nonlinear Mechanics at the University of Bath, and with many research groups all over the world. One of the main contacts of BCANM is with the €2M, 13 groups, 7 nations EU project

SICONOS

(Modelling, Simulation and Control of Nonsmooth Dynamical Systems). In addition, BCANM members have many active contacts with industry, involving companies such as Westland, Jaguar, QinetiQ and British Oxygen.

 

Photo taken at the Colston meeting, June 2001.
From left to right: Hinke Osinga, John Hogan, Martin Homer, Eddie Wilson, Bernd Krauskopf, Alan Champneys, and Mario di Bernardo.

 

A crucial part of the multidisciplinary research of BCANM is a programme that allows us to attract the world's leading experts for research visits on a continuous rolling programme. Visitors will be able to conduct collaborative research towards each theme's objectives, and make full use of the world-class facilities of BLADE. Follow-up visits are also encouraged, to continue collaboration. Each visitor will be encouraged to visit other UK institutions, and also to present a set of tutorial lectures, which will take place at Bristol, but be advertised nationally.

The members of BCANM have organised many successful conferences; the first of five workshops of the BCANM took place in September 2003, on Delay Equations and their Applications, stimulating interaction between practitioners and theoreticians of all levels. The meeting opened with tutorial presentations from Jack Hale (Georgia Institute of Technology, USA) and Gábor Stépán (Technical University of Budapest, Hungary). These lectures were video taped and will appear shortly on the web. BCANM members were involved with the organisation of the European study group with industry, held at University of Bristol in April 2003. In June 2001 the ANM group hosted the highly successful meeting Nonlinear Dynamics and Chaos: Where do we go from here?, sponsored by the EPSRC, LMS and Colston Research Society. The spirit of the meeting was captured in the book Nonlinear Dynamics and Chaos: where do we go from here? jointly edited by all the permanent members of BCANM, published by IoP Publishing.