However it is also true that the "devil lies in the detail" when it comes to comparing different types of singularity. In other words different systems might have some common features such as self-similarity, but also unique aspects that require specialised study. One aim of the workshop therefore was to identify the common methods that could be applied as a foundation for more detailed specific study of a particular type of singularity.
This was reflected in the wide range of systems discussed. One such system, dealing with cracks in structures or rock formations, was presented by Jay Fineberg from the Hebrew University in Jerusalem. He talked about new experiments involving gels, allowing the structure of the crack to be determined in great detail down to very small microscopic dimensions, yielding some unexpected findings. "In particular, the structure of a crack is often more complicated than anticipated. Instead of one single crack path, the crack splits and has many small side branches, which appear to have complicated, if not fractal, structure," said Eggers. Fractal structure here means much the same as self-similarity, involving a geometrical pattern that looks unchanged under magnification or reduction.
Another example of everyday relevance concerned the singularities of crumpling in paper, presented by Tom Witten from the James Franck Institute in Chicago. A crumpled piece of paper comprises many ridges and tips, which defy easy analysis. As Eggers noted, there are many unanswered questions even in describing each individual cone-shaped tip. Yet understanding the underlying mathematics would not just help understand what happens when we crumple up a piece of paper to throw away, but also other physical systems involving ridges and tips, such as the folding of proteins during their manufac
|Contact: Jens Eggers|
European Science Foundation