Monday, November 02, 11:30am - 12:30pm (HH410)
We introduce two methods developed by combining topology with dynamical systems for the analysis of fluid dynamics. First, we give an overview of applications that these methods can be used for. We then introduce a method that rigorously represents two-dimensional flows in a topological sense. In particular, since this method yields a topological decomposition of the space, we also show that it enables various types of analysis to be carried out topologically. This work is joint with T. Sakajo, T. Uda, et al. Finally, for time-evolving phenomena, we introduce a method for determining when and where to intervene in order to improve the situation, as well as for detecting the sensitivity of the quality of predictions, and we show that this can be applied to real-world problems such as typhoons. This work is joint with Y. Imoto.