Universality Classes for Spatio-Temporal Chaos Guenter Ahlers, UC Santa Barbara DMR Many systems that cover a region of space, such as a thin layer of an ordinary liquid, or of a nematic liquid crystal (NLC) like those in your flat-screen TV or your wrist watch display, can form patterns that vary irregularly as a function of position and of time. We call this phenomenon “Spatio-Temporal Chaos” or STC. Physicists have questioned for a long time whether there are different types, or “universality classes”, of STC, perhaps in analogy to the universality classes for equilibrium critical points. Here we show, in the left column, three different realizations of STC. The top one is from convection of a horizontal layer of fluid heated from below and rotated about a vertical axis. The middle comes from electro-convection (EC) of a nematic film driven by an applied voltage. Here the NLC molecules are oriented on average perpendicular to the film. The third is also from EC, but this time the molecules are oriented parallel to the film. The right column gives the corresponding power spectra, which are representations of the strengths of all the plane-wave modes that are needed to reproduce the patterns. We see, and quantitative analysis confirms, that the three examples have quite different symmetries, and we suggest that these symmetries provide a way to sort the different types of STC into universality classes. Sheng-Qi Zhou and Guenter Ahlers, Phys. Rev. E, submitted. Sheng-Qi Zhou, Nandor Eber, Agnes Buka, Werner Pesch, and Guenter Ahlers, Phys. Rev. E, in press. Nathan Becker and Guenter Ahlers, Phys. Rev. E 73, (2006). Examples of three different types of spatio-temporal chaos (left), and their power spectra (right).

Universality Classes for Spatio-Temporal Chaos Guenter Ahlers, UC Santa Barbara DMR Broad impact on fundamental science: The realization that critical points could be grouped in a small number of universality classes according to the symmetry properties of the order parameter was one of the major breakthroughs of the 1960’s. For the last two decades scientists have asked whether a similar classification is possible also for STC. We believe that we now have experimental evidence that supports this idea. Impact on other fields: STC occurs in many astrophysical, geophysical, industrial, and biological situations. Developing a better understanding of STC can lead to greater efficiency of industrial processes and a deeper knowledge of the Earth, our atmosphere, our oceans, our environment, and our bodies. Impact on education: We provide excellent training of undergraduate students, graduate students, and post-doctoral scholars who participate in our research. During the last year our effort produced two new Ph.D.’s, and two undergraduate students from our group have gone on to top graduate schools. The Sun Disordered patterns on animal skins Spiral waves in the heart Patterns in crystal growth Cloud streets in the sky