Geometric devils in topological dynamics, Prof. Renzo Ricca
Event details
| Date | 24.10.2011 |
| Hour | 17:00 |
| Location |
MA A3 30
|
| Category | Conferences - Seminars |
Abstract: Geometric features play often a crucial role in dynamical and physical systems. In
this talk we present and discuss recent results in two different contexts, to show how
unexpected dynamics are often revealed by surprising geometric aspects. We first
consider the case of vortex dynamics under Euler equations. In ideal fluids vortex
topology is frozen. By using standard analysis of projected diagrams we show that
dynamical properties can indeed be interpreted in terms of projected signed area. This
allows us to identify new, curious behaviours that escaped classical analysis so far,
and that only recently have been subject of numerical investigation. This offers also
an example of new methods that could be implemented in numerical diagnostics to
investigate energy-complexity relations of complex systems. In a second case, we
consider the evolution and the topological transition of a soap film in the shape of a
Möbius strip (a one-sided surface), that under a catastrophic deformation changes
shape to become a laminar disc (two-sided). A mathematical description of this
mechanism is provided by adapting model equations to describe such type of
evolution. The change of topology occurs as a twisted fold of the surface collapses in
a small region to form a cusp. This study reveals deep connections between
fundamental aspects of mathematical physics and key mechanisms of complex
systems and it helps to understand important aspects related to energy localization,
phase change and function, in a broad spectrum of natural sciences.
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Practical information
- General public
- Free