Growth and nonlinearity]. Progress report

Abstract

The research centered on the physics of growth. One particular focus was the spiral patterns seen in excitable media, such as the chemical reaction of Belousov and Zhabatinskii, and the aggregation of the slime mold, Dictyostelium Discoideum. Another area of interest is the statistical roughness of the growth front itself. For example, when growing thin films, the roughness of the surface is very important for the ultimate quality of the film. Besides its direct technological relevance, this problem is intimately connected to many fundamental problems in statistical physics. In addition work was done in the related area of statistical properties of flux-flow motion in superconductors. Substantial progress was also made on techniques and applications of the analysis of complex systems. Methods of time series analysis were generalized to the analysis of complex spatio-temporal patterns. In the examples studied most, turbulence and electroencephalograms, the spatio-temporal patterns are very complex and fleeting, and can easily be misken for random noise. Nevertheless, substantial progress was made in developing and applying methods to these systems that indicate the presence of nonrandom time-varying spatial patterns.