Scientists at the University of Liverpool are exhibiting at Manchester’s Festival of Mathematics and its Applications, to show how they solved a mathematical problem that has challenged researchers for more than four decades.
The team’s work is related to phase-locking, a phenomenon where two oscillating systems interact with each other, like two pendulum clocks hanging on the same wall that eventually synchronize. This was first observed by scientists Christiaan Huygens in the 17th century, and has since been seen to occur in a diverse range of systems, including the interaction between rates of breathing and heartbeats in humans.
In the 1960s, the famous Russian mathematician Vladimir Arnol’d introduced a simple model to study phase-locking phenomena, now known as the Arnol’d Family. The model is meant to describe a periodic motion on a circle affected by an external force, and has been used as a simplified model for a large number of physical and biological systems, such as a beating heart.
Professor Lasse Rempe-Gillen, at the University’s School of Physical Sciences, together with Professor Sebastian van Strien at Imperial College, were able to verify that this family has a certain property which had long been hypothesised, but never confirmed.
The research findings are the focus of an exhibition at the Festival of Mathematics and its Applications at the University of Manchester from Thursday, 3 July to Friday, 4 July 2014.
The work was partially funded by the EPSRC and the Leverhulme trust and will be published in the Duke Mathematical Journal.