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UNIVERSITY OF SURREY Institute of Advanced Studies Seminar on Theoretical Aspects of Pattern Formation Tuesday 20 September 2005 |
| Ahlers, G |
| The legacy of Henri Bénard and Lord Rayleigh |
| This talk will trace the major breakthroughs in the study of Rayleigh-Bénard convection since the experiments of Henri Bénard a century ago. A few selected topics of current interest will be presented in somewhat more detail. These include the effect of thermal noise on the bifurcation to convection and spatio-temporal chaos. |
| Newell, A |
| Patterns on plants |
| Plant patterns, namely the tiling of plant surfaces into regular polygonal shapes, and plant phyllotaxis, the arrangements of leaves and stickers, has fascinated natural scientists for over four hundred years. In this lecture, I will outline some of the ideas of Patrick Shipman and myself (about to appear in J. Theor. Bio.) which provide a rational explanation for many observations including the prevalence of Fibonacci sequences of spiral families. |
| Scheel, A |
| Following coherent structures |
| Spiral waves, sources and sinks, and line defects, are examples of localized structures embedded in a background of waves with characteristic wavenumbers. We will discuss how these structures change as system parameters are varied. Although coherent structures often appear to be very robust, the generic persistence already turns out to be a delicate question due to essential spectrum caused by the background waves. We show how methods from dynamical systems can be used to prove robustness and bifurcation theorems, hence enabling a pathfollowing type exploration of large-scale nonequilibrium systems. We also present examples where our approach exhibits structural barriers to pathfollowing: coherent structures can suddenly disappear. |
| Wayne, CE |
| Long-time asymptotics and coherent structures in Navier-Stokes flows in R2 and R3 |
| I will describe how one can combine ideas from dynamical systems theory and kinetic theory to describe the long-time behavior of solutions of the Navier-Stokes equations. In two dimensions this leads to a very complete description of the behavior of solutions whose initial vorticity is at least slightly localized. In three dimensions it gives a better understanding of the existence of the Burgers vortex and its variants. |