Research in Laboratory for Applied Mathematics

Experimental research at the interface between mathematics and physics has a long history in Manchester, starting with the pioneering work of Osborne Reynolds in the late nineteenth century. His observations of the transition to turbulence in pipe flow raised fundamental questions about nonlinear dynamics in fluids, which have have kept applied mathematicians busy ever since - and are still not fully resolved today! Nonlinear systems are ubiquitous in nature and thus, their understanding is of great technological importance. The complexity of their dynamics is often best addressed through a combination of theoretical analysis and experiments. Hence, the School of Mathematics is one of a few in the UK to have invested in laboratory facilities for applied mathematics. Our laboratory offers a unique opportunity for post-graduate students to get involved in inter-disciplinary work of mathematical interest.

Examples of current experimental projects are:

• The mechanics of airway reopening.
• Frozen-wave formation in two liquid layers.
• Interfacial instabilities in granular slurries.
• Pattern formation in particle-laden flows.
• Viscous fingering of an oscillating, viscous interface.
• Secondary flows in rotating fluids.
• Avalanches and segregation in granular materials

The laboratory for applied mathematics is an integral part of the Manchester Centre for Nonlinear Dynamics (MCND), an initiative taken by the University of Manchester to promote inter-disciplinary research into nonlinear systems. The centre is formed by researchers from within the School of Mathematics and the School of Physics and Astronomy. The laboratories are housed within the School of Physics and Astronomy.

Research within the MCND group is based upon the application of a combined approach of theoretical modelling, computation and detailed quantitative experimental investigations of nonlinear phenomena. For instance, researchers in the centre have developed a modern version of Reynolds' experiment, which is helping to settle long-standing questions about the transition to turbulence. Broadly speaking, research interests in MCND currently include fluid dynamics, granular flows, liquid crystals and optics. Thus, MCND provides an exceptionally attractive environment, unique in the UK, for interdisciplinary research into nonlinear phenomena.

Postgraduate students benefit from a vibrant research environment, which exposes them to a broad variety of problems and techniques, and which encourages interaction, through multiple forums for discussion, as well as with the many visitors to the centre.

There are currently 18 students and 5 PDRAs in MCND and the group has a healthy current grant portfolio of £1,900,000 to support research activities. Industrial collaborations are established with QINETIQ, Samsung, Sharp, Merck and De Beers.

Further information can be found on the MCND website at http://www.mcnd.man.ac.uk

Members of staff involved