There are two ways to build a better mouse-trap. You can tinker with what you already have in the hope of making improvements or you can define what the mousetrap does in abstract terms and use this to dream up new innovations.
A similar process is constantly under way in the complex world of advanced electronics. Engineers have physical devices made up of electronic components and can make improvements by changing these. They also use highly complex mathematics to describe what goes on inside those components to guide them towards useful changes.
Dr Orla Feely, a senior lecturer in UCD's Department of Electronic and Electrical Engineering, is involved in the abstract mathematics-driven side of this activity. In effect she uses a pencil and paper to make your CD deliver better sound.
She does this using "non-linear dynamics" a form of mathematics originally devised about a century ago which went through rapid refinement in the 1970s and 1980s when chaos theory began to emerge as a way to understand complex systems.
The way electronics produce and handle signals is a classic area for chaos theory mathematics, or more accurately, non-linear dynamics. Dr Feely's area of specialisation is the "non-linear dynamics of electronic circuits". Many electronic circuit systems are non-linear, either because they were made that way or because of quirks in the circuitry, she explained.
She uses the mathematics of non-linearity to describe exactly what is going inside the circuits on the basis of the signals going into and coming from the components. "I provide insights and explanations for the phenomenon that can then work its way back into the [circuit] design," she said. "The interface between engineering design and the mathematical theory that underlies it is very important."
She has studied the digital-to-analog converters found in CD players in an effort to find ways to eliminate "non-linear defects". The mathematics describes what the signal is doing as it is processed by the electronics, and this in turn helps to suggest ways that the defect can be removed through new circuit designs.
Phase-locked loops are used in mobile phones and televisions to help these devices lock on to broadcast signals. They are subject to a phenomenon known as "phase jitter". The device takes the signal but allows minute variations that degrade the signal quality.
This was initially studied by a final-year engineering student, Mr David Naughton, working with Dr Feely. The work was developed with others, and their findings were presented in 1997 at the European Conference on Circuit Theory and Design and won the award for best paper. Since then two postgraduates have continued the work with Dr Feely.
She typically has from two to four researchers working with her on these projects and currently has students from Ukraine and Bulgaria. "This kind of research goes on in Ireland, and people are coming here to participate," she said. she believes Ireland's researchers can set themselves apart on the international stage by tackling the difficult problems in science and engineering.
Her work is now being applied in other disciplines by other researchers, including studies of neural networks and image-processing. "Exactly the same mathematics can be applied to a wide range of activities," she said. "There is this universality in non-linear systems."