BMC/BAMC2015: Some Intriguing Dynamical Systems Inspired by Plants (Prof. Jacques Dumais) скачать в хорошем качестве

BMC/BAMC2015: Some Intriguing Dynamical Systems Inspired by Plants (Prof. Jacques Dumais)

The feature that most clearly distinguishes plants from their animal and fungal counterparts is the near perfect regularity of their microscopic and macroscopic architecture. Thus, it is no wonder that plants have been used repeatedly to illustrate mathematical concepts such as self-similarity, symmetry groups, packing, and dynamical systems. In this talk, I will discuss recent developments in the mathematical analysis of cell division. Empirical evidence indicates that tensional forces within the cytoskeleton constrain plant cells to adopt area-minimising configurations as they divide. By framing this cell division rule as a dynamical system, it is possible to identify several attractors that are predictive of cell patterns observed in plants. In the case of geometrically simple systems, such as the two-dimensional thallus of Coleochaete, the entire phase space can be characterised in precise mathematical terms. In more complex systems, such as the shoot apical meristem of plants, various attractors are predicted - many of which are observed in Nature. Finally, I will show how simple transformations of the cell division fixed points reproduce other dynamical systems observed elsewhere in plants and beyond. The IMA Lighthill Plenary lecture by Prof. Jacques Dumais. Given at the 4th join British Mathematics Colloquium (BMC) and British Applied Mathematics Colloquium (BAMC) 2015 in Cambridge, UK.