WS 2015/16 Physics of Dissipative Patterns - An Introduction

Lecturer: PD Dr. Falko Ziebert
Time: 2 hours, Mon 14-16
Tutorial: 1 hour on appointment
Place: SR II
Start: 19.10.2015

Programme:

Pattern formation is one of the most fascinating and intriguing phenomena in nature. It takes place in a wide variety of physical, chemical and biological systems and on very different spatial and temporal scales: examples are convection phenomena in geosciences and meteorology, but also patterns occurring in chemical reactions and bacterial colonies. In some circumstances, pattern formation is undesired, for instance the formation of spiral waves leading to cardiac arrhythmias in the heart muscle. In other contexts, pattern formation is even essential for the functioning of a system as in embryo development.

We will give an introduction to the basic phenomena in pattern formation. We will discuss how and which kind of instabilities can occur in dissipative, i.e. out-of-equilibrium, driven systems and how these instabilities lead to bifurcations to stationary vs. oscillatory and long-wavelength vs. finite wavelength structures.

We will then discuss generic models for pattern formation and deduce the universal description of nonlinear pattern dynamics via amplitude equations (also called center manifolds), leading to the famous complex Ginzburg-Landau equation.
 

Literature:

•     Ball P, The Self-Made Tapestry: Pattern Formation in Nature (Oxford, Oxford Univ. Press, 1998).
•     Cross M C and Hohenberg P C, Rev. Mod. Phys. 1993.
•     Cross M C and Greenside H, Pattern formation and dynamics in nonequilibrium systems (Cambridge, Cambridge Univ. Press, 2009).