Training session

"Mathematical modelling and analysis of industrial problems"

From 13 of Abril to 14 of Abril

This will consist of short courses on mathematical modelling and problem solving, aiming at familiarising participants with the type of situation that will be met at a typical study group. The course will be based on case studies from previous study groups and students will work in groups on these problems under the guidance of invited experts who have a wide experience of tackling industrial problems.

The Training Session will be led by

• Prof Alistair Fitt (Univ. of Southampton, UK)
• Prof Andrew Lacey (Heriot-Watt University, UK)

The idea of this session will be to introduce students to modelling in a variety of different areas and to give them some experience of working collaboratively.

It will be a shorter version of the very successful ECMI modelling weeks which are run for students each year.

The session will start with an introductory lecture on modelling followed by the presentation of a number of Case Studies. The students will be divided into groups of 5-8 to work on these problems with the help of a local leader. (This could be a senior doctoral student or a postdoc or a faculty member). Each group will present their solution (or progress towards a solution) to the others at the end of the second day.

Case Study 1: Traffic flow

One group study will consider some simple models for traffic flow which might be useful next week.

Case Study 2: Behaviour of fish food pellets on fish farms

A growth industry in Scotland over recent years has been fish farming. Fish are raised in large cages kept within sea inlets or estuaries or lakes. The fish are fed with food pellets which are scattered onto the water above the cages. Ideally the pellets sink within 15 seconds and can then be eaten by the caged fish. Sometimes there are problems at fish farms with the fish food floating for too long, whereas in simple laboratory experiments with the same batch of pellets, throwing a handful onto water in a bucket, the pellets are observed to sink quickly. The aim is to understand why.

Lectures to be drawn from:

• Study groups
• Industrial problems
• Asymptotics of DEs
• Non-dimensionalisation
• Homelessness and housing allocation
• Bread crust formation

Useful references

"Mathematical Modeling", Ellis Cumberbatch and Alistair Fitt (Editors)