Dynamics offers wider views

When complex wholes from carnivore populations to global weather phenomena are being studied, the future can be predicted on the basis of the current situation with the help of dynamic models. These models and related mathematical phenomena are the domain of research of the Centre of Excellence in Analysis and Dynamics Research.

“Even Newton employed dynamic models in determining the movements of heavenly bodies. Core concepts in current research include turbulence and random fractals, which have to do with the dynamics of very complex phenomena,” explains the Director of the Centre, Academy Professor Antti Kupiainen.

Kupiainen himself studies turbulence exhibited in such physical phenomena as the movement of liquids and gases. Other research interests are population models associated with mathematical biology and regular patterns occurring in nature, fractals. Applied research includes gas dynamics and wireless technology.

“If in the future each mobile phone functions as a base station, there are going to be graph-theoretical problems. Mobile phones form a large quantity of randomly chosen points between which there either is a connection or not. Utilising certain dynamic ideas, we can examine how this kind of base station grid would work,” says Kupiainen.

The background of the eleven researchers in the Centre is mostly in pure mathematics but they share an interest in applications. According to Kupiainen, applications also contribute to the development of theories. The theory behind the dynamics research is based on the fruitful interaction between pure mathematics and its applications.

“Our aim is to reform the study and research of mathematics in Finland. Nowadays, postgraduates specialise from an early stage. More diverse backgrounds and interaction between different disciplines will lead to improved opportunities,” Kupiainen says.

Professor Kupiainen was awarded his doctorate at Princeton University in the US in 1980 in mathematical physics, after which he served as Professor of Mathematics at Rutgers, also in the USA. Kupiainen was appointed Academy Professor in 1999. The Centre is affiliated with the Universities of Helsinki and Jyväskylä, from which it draws its staff of eleven senior researchers and some forty other researchers and postgraduate students.

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Text: Tiina Männistö
Photo: Veikko Somerpuro
Translation: Valtasana Oy