The quality of your next air flight may be influenced by a little Irish magic known as singularly perturbed heat equations. Remember that name.
They come from the world of advanced mathematical computation. In particular, they can be used to describe a system influenced by thin layers - for example, air passing over an aircraft wing or water rushing along the surface of a hull.
Dublin City University last week honoured one of its re search academics from the school of mathematical sciences for his "internationally acclaimed" work on singularly perturbed heat equations.
Dr Eugene O'Riordan received the inaugural DCU President's Research Award, worth £2,000.
He and collaborators in Trinity, the University of Limerick, the Russian Academy of Sciences and Kent State University in the US cracked a particularly difficult mathematical nut with their work on singularly perturbed systems.
Dr O'Riordan had worked on them for 10 years but had failed to solve them.
The simplest way to understand what these equations do is to consider air flowing over the wing of an aircraft. The challenge is to use computational mathematics on a computer to describe how a given wing design will interact with moving air.
Mathematical modelling allows designs to be tested without having to build them. It was known through experimentation that there is a very thin layer, perhaps 2 mm, of still air just above the wing surface, which exists despite the 1,000 k.p.h. air movement just above it when the aircraft is in flight.
For years this still layer was ignored as insignificant. Mathematicians would model the wing system by taking sample or "mesh" points all around the wing and then try to calculate how air would move over the wing.
The results of these calculations, however, did not gel with built models. Increasing the number of samples usually increases the quality of the results, but with these singularly perturbed systems, error often increased as the sample size increased.
As so often occurs with re search, the day was won by adopting the KISS approach - keep it simple, stupid. The source of this inspiration, conveyed in less condensed form, was the Russian collaborator, Dr Grigorii Ivano vich Shishkin. "He looked at it theoretically and said that a standard approach to these problems would fail," Dr O'Riordan explained. He also offered a recipe for how the calculations might be made to work.
The recipe was no more than a few sentences long, delivered as Dr O'Riordan accompanied Dr Shishkin back to Dublin after a speaking engagement in Cork.
"If you want to get a whole view [of a system with a thin layer effect], you have to concentrate half your total sample effort within the layer. Because the layer over the wing is minuscule, one would assume you could ignore it, but you can't ignore this thin film effect."
The research group has dub bed the new approach the "Shishkin mesh". The calculations were adjusted to allow half of the sample points to be within the thin layer and almost immediately the computational errors dropped away. As expected, increased sample size did result in reduced error size.
This enables the mathematician to predict the effect of design changes. "It worked and has continued to work no matter what we apply it to," Dr O'Riordan said. "We think there is something here for the general application of science."
The calculations could be applied to any system where there was a thin film or layer which could affect system performance, he said. There was an immediate application of this mathematical approach in a variety of science and engineering areas, including semi-conductor design, heat transfer and exchange systems, and wing and hull design.
Dr O'Riordan still marvels at the simplicity of the approach. "They were such complicated problems and such a simple thing cracked them all open."
A KISS really can work wonders.
