Successes and Failures of
Continuous Models for
Discrete Systems

University of Bristol, 5th - 8th September 2005

This was the fourth international workshop of the Bristol Centre for Applied Nonlinear Mathematics, funded by the UK Engineering and Physical Research Council (EPSRC).

The workshop addressed fundamental issues associated with modelling discrete systems. Examples include granular media (especially soil mechanics), traffic flow, optical and atomic lattices, and cellular biological structures such as neuronal systems. In each application area, the most accurate models should respect the discrete particulate nature of the system (and so give rise to lattice or discrete element equations). However, more tractable PDE models can also be derived: the key question we wished to address was when is the continuum approximation useful ?

A particular focus was on the solutions to such models that develop localised or inhomogeneous pattern: examples include solitons in Bose-Einstein condensates, stop-and-go traffic jams, shear banding in soils, localised bursts of activity in neuron populations, and disclination waves and localised breathers in crystal lattices.

Organisers

• Eddie Wilson
• Alan Champneys
• John Hogan

Scientific Committee

• Dirk Helbing (Technische Universität Dresden, Germany)
• Bjorn Sandstede (University of Surrey)
• Steve Coombes (University of Nottingham)
• Alan Bishop (Los Alamos National Laboratory, USA)
• Jim Jenkins (Cornell University, USA)

Confirmed speakers

• Jim Keener (University of Utah, USA)
• Alan Bishop (Los Alamos National Laboratory, USA)
• Dirk Helbing (Technical University of Dresden, Germany)
• Jim Jenkins (Cornell University, USA)
• Alex Mielke (University of Stuttgart, Germany)
• Steve Sparks (University of Bristol)
• Peter Wagner (DLR institute, Germany)
• Steve Coombes (University of Nottingham)
• Erik Van Vleck (University of Kansas, USA)
• Panos Kevrekidis (University of Massachusetts, USA)
• Stefan Luding (Technical University of Delft, Netherlands)
• Gero Friesecke (University of Warwick)
• Mark Alber (University of Notre Dame, USA)
• Jim McElwain (University of Cambridge)

The Bristol Centre for Applied Nonlinear Mathematics is a £1.1 million EPSRC critical mass research centre and one of the largest mathematics projects ever funded in the UK. It has five scientific themes which provide the mathematical technologies for dynamic substructuring of engineering systems.

Topics of this workshop included:

• Traffic and pedestrian flow
• Optical lattices
• Mathematical biology
• Granular media
• Smart materials

We aimed to encourage lively debate around the general issue of when and whether continuum or discrete models provide the best tool for modelling observed physical phenomena.

Related Conference

• Multi-scale problems: modelling, analysis and applications, 12th - 14th September 2005, Bath Institute for Complex Systems.