SCIENCE FOUNDATION IRELAND:A consortium of Irish universities have joined forces to use applied mathematics to solve everyday business issues from chicken farming to conference calls to puring the perfect pint
WHAT HAVE the bubbles in a can of draught Guinness, acid etchings on crystal glass, commercial chicken rearing and telephone conference voice quality got in common?
They are all areas where applied mathematics can offer solutions in terms of process and efficiency improvements and thanks to the work of the Science Foundation Ireland funded Macsi (Mathematics Applications Consortium for Science and Industry), these real-world issues and many more besides are being addressed in Ireland.
Based in the University of Limerick, Macsi encompasses a network of applied mathematicians working across the country in UCC, NUIG, DIT, UCD, DCU and TCD and aims to develop a coherent strategy for a mathematical solution of problems which arise in science, engineering and industry in Ireland.
The consortium’s day-to-day work sees it working with a wide variety of companies throughout Ireland in solving the everyday problems they encounter. This may not sound much like the mathematics most of us did in school and that’s because it isn’t, as Stephen O’Brien, professor of applied mathematics at the University of Limerick and principal investigator with Macsi, explains.
“It is important to understand that applied mathematics encompasses a much broader field than the present Leaving Certificate syllabus,” he says. “Applied mathematical modelling is a philosophy of asking how things work where emphasis is placed on the application of mathematics in non-mathematical disciplines such as finance, economics, biology, physics, chemistry or industry. A problem or phenomenon of some sort occurs outside mathematics and mathematics is used to explain, to understand or to improve it.”
This is where applied mathematics differs from pure mathematics and explains why Macsi is so unique in Ireland. “Ireland has lagged behind the rest of the world in this regard for many years,” says O’Brien. “The issue is that Ireland has been very traditional in terms of maths. Third-level maths fractures into two groups – applied and pure – and Ireland has concentrated on pure mathematics. Pure mathematics is intellectually interesting and challenging but focuses on solving the problems which occur in mathematics rather than the real world. But you can apply maths to solving almost any problem and that’s what we do.”
With Macsi the focus is on the use of mathematics to understand phenomena in the non-mathematical world. For example, mathematical models can be developed to predict the wavelength of the waves in a settling pint of stout or the cooling time of a block of cheese when placed in brine.
The University of Limerick became home to a large group of applied mathematicians in recent years owing partly to what O’Brien describes as an accident of history.
“There hasn’t been enough interest in applied mathematics over the years, but possibly because we are a younger university here, we started developing in a different direction. We only make appointments in applied mathematics here and 95 per cent of our mathematicians are applied mathematicians – this makes us as unique in Ireland.”
A key activity of the consortium is its annual study group. This involves the coming together of mathematicians, scientists and industry collaborators for a week of interaction and co-operation where they work together to find solutions to problems proposed by the industry partners. This year’s study group took place from June 27nd to July 2nd in the University of Limerick and was part of a wider series of European Study Groups which has been taking place for more than 30 years. Indeed, this year’s event in Limerick was the 75th such European study group but just the third held in Ireland.
The study group format is fairly standard. On the first morning, industry representatives present their problems, which are usually not mathematical problems to begin with, but descriptions of a complicated industrial process that is not well understood from a scientific point of view.
When all problems have been presented, the mathematicians select the problems they would like to work on and split into different groups. That is followed by the various subgroups meeting with the industry representatives to ask more detailed questions. By the end of the first day, the teams should have defined in broad terms their goals for the week.
During the rest of the week, the group works on the problems and progresses towards a solution. Participants may choose two strategies. Either they focus on a single problem all week or they decide to hover between different problems. Some people like to work intensively on one problem others prefer to make smaller contributions to a number of problems. On the final day, all the groups present their results to the industry representatives and the other academics.
“What we’re doing here is bringing 90 people from across the world to Limerick to provide free consultancy to industries because that’s what scientists do,” O’Brien points out. “If we were lawyers or accountants we’d be charging hundreds of thousands of euro for this. But that’s not what we’re about and long may it continue to be so.”
At the end of the week, if real progress is being made, this may result in further research being undertaken in UL with the company sponsoring a post-graduate student or team. But this is very much what happens in Macsi in any case.
“The study group is only one aspect of our interaction with industry,” O’Brien notes. “About half of all of our work is working on solutions with enterprise partners. We are always anxious to here from any companies or indeed researchers in other scientific fields who have problems which they think might have mathematical solutions. If we can’t help them we won’t waste their time; we are usually able to tell people within 20 minutes if we are going to be able to help them.”
One of the more unusual problems brought to this year’s study group related to chicken farming. Manor Farm Chickens produce chickens for the Irish market and have encountered difficulties regarding a mismatch between supply and demand.
Supermarkets order chickens in various weight categories and demand for them varies from day to day and week to week. The company forecasts this demand up to 13 weeks in advance but doesn’t know the actual demand until the day in question. If it doesn’t have sufficient chickens in the weight category required it has to substitute them with higher weight chickens therefore giving them away at a lower price. The group was asked to develop an algorithm to schedule egg incubation and chicken slaughtering times in order to minimise this mismatch – in other words, to establish a just-in-time production system for the company.
“We made quite a lot of progress on this during the week,” says O’Brien. “We also made a lot of progress on an issue brought to us by Intel in relation to conference calls.”
The problem was that if there were 10 people on a call, the software couldn’t figure out which voice was the one to relay to everyone else. The solution arrived at by the Macsi study group was for the software to recognise the loudness of each voice during the encoding process and to relay the loudest voice to each of the participants.
And then there is Guinness. Lovers of the canned draught product often wonder at the technology involved which makes the product behave remarkably like the stuff they get in the pub. The technology is actually quite simple.
It is a plastic widget which is akin to a table tennis ball with a hole in it secured to the bottom of the can. “This helps form the bubbles which give the product its draught characteristics,” O’Brien explains. “But the problem is that whenever they change anything like the size or the shape of the can everything else changes and the bubbles don’t form in the same way. Because they don’t understand how the widget actually works they have to keep trying different sizes of widget and hole to try to get the same results as before. They came to us for help with a mathematical solution to the problem and we have made quite a lot of progress on this as well.”
For further information see macsi.ie, e-mail macsi@ul.ie or tel: 061-202293
