Critical Phenomena and Collective Behaviour of Multi-Particle Complex Systems

Consider shuffling a pack of playing cards many times. It is reasonable to expect this action to randomize the cards and then a fair game could ensue. It would surely come as a great surprise if the pack was turned over to reveal that the red and black cards had separated out with the twenty six red cards in one half of the deck. There is a finite probability of this occurring, of course, but it is vanishingly small. In an analogous manner, it is equally counter intuitive that shaking a box containing a mixture of two similar dry granular powders will separate out the constituent components so that a completely de--mixed state is formed. However experiments have shown that when a dry granular mixture consisting of equal sized but different density particles is vibrated from side to side it can, surprisingly, completely separate out into its constituent components with probability one in certain parameter ranges.The phenomenon of de--mixing has been known to engineers for a very long time and is considered to be a nuisance in a wide range of technological processes. For example, obtaining uniform mixture of dry particles in the manufacture of medical pills is a challenging technological problem where more reliance is placed on experience and intuition. In almost all cases, the particles are of different sizes and it is not always possible to predict if the phenomenon known as `size segregation' will occur. A crucial part of the process is that gaps open up around particles when they are shaken or made to flow and percolation can occur. Large particles tend to move in preferential directions towards less dense regions of smaller particles so that large heavy objects can rise to the top of vertically shaken layers of granular materials. A common, and useful, application of this is to shake a box of muesli up and down before serving. In this way, you can select some of the best bits much to the annoyance of the rest of your household.In recent years this field has become a very active area of research in the international physics community as it became clear that not only do mixtures of dry particles segregate, but that they can also spontaneously form patterns in the process. In other words, in the playing card analogy, the cards will be sorted into their respective suits by shuffling. A striking example of this is provided by the pattern formed by shaking a thin layer of polystyrene spheres and `100's and 1,000's' cake decorations. A very obvious striped pattern forms after a few minutes of excitation and its behavior follows simple systematic rules. Moreover patterns such as these share features with the geological phenomenon of `stone striping' where loose rocks form line patterns naturally on the dirt surfaces of Alpine slopes which are subjected to solar heating cycles. Fascinating spontaneous pattern forming processes such as these have become a boom area as they provide interesting examples of the emergence of order in complex systems.

Academic Impact: TM and JMNTG have international track records for their work on granular flows. It is anticipated that equally high quality research will be achieved in the planned investigation and this will maintain our leading edge competitive stature in the field. Knowledge Transfer and Training Aspects: the post-doctoral research assistant will join the lively interdisciplinary research environment which exists in the Manchester Centre for Nonlinear Dynamics (MCND). PDRA's who have worked in our centre over the past decade have found the experience beneficial when moving to jobs in academia or the private sector. The collaborative nature of the proposal with colleagues in Greece, Holland and Belgium will also mean that the PDRA will benefitsignificantly from the planned set of network meetings. Applications and Outcomes: The issue of segregation has a number of applications in both industrial and geophysical flows. One objective of our planned work will be to test the predictions of a specific model using a rigorously controlled experiment. Dissemination of Knowledge: TM and JMNTG have a history of publishing their work in high quality international journals. These include Physical review Letters, the Journal of Fluid Mechanics and Proceedings of the Royal Society. Dissemination will also take place through attending appropriate conferences and through our www page. Collaborations: The Network involves collaborations with colleagues in Patras, Brussels and Twente. The first two of these groups are new and our research will benefit from the additional skills that they bring. Regular meetings are planned to aid an efficient transfer of ideas. Public Engagement: TM has considerable experience in public engagement with talks to local schools and societies, national venues such as the Royal Institution and media such as television and radio.