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SUMMARY:Geometric devils in topological dynamics\, Prof. Renzo Ricca
DTSTART:20111024T170000
DTSTAMP:20260408T133358Z
UID:8add50c1d9d5d8ba5dd797f514a8dfc8f83cb6b99250003858628fc1
CATEGORIES:Conferences - Seminars
DESCRIPTION:Abstract: Geometric features play often a crucial role in dyna
 mical and physical systems. In \nthis talk we present and discuss recent r
 esults in two different contexts\, to show how \nunexpected dynamics are o
 ften revealed by surprising geometric aspects. We first \nconsider the cas
 e of vortex dynamics under Euler equations. In ideal fluids vortex \ntopol
 ogy is frozen. By using standard analysis of projected diagrams we show th
 at \ndynamical properties can indeed be interpreted in terms of projected 
 signed area. This \nallows us to identify new\, curious behaviours that es
 caped classical analysis so far\, \nand that only recently have been subje
 ct of numerical investigation. This offers also \nan example of new method
 s that could be implemented in numerical diagnostics to \ninvestigate ener
 gy-complexity relations of complex systems. In a second case\, we \nconsid
 er the evolution and the topological transition of a soap film in the shap
 e of a \nMöbius strip (a one-sided surface)\, that under a catastrophic d
 eformation changes \nshape to become a laminar disc (two-sided). A mathema
 tical description of this \nmechanism is provided by adapting model equati
 ons to describe such type of \nevolution. The change of topology occurs as
  a twisted fold of the surface collapses in \na small region to form a cus
 p. This study reveals deep connections between \nfundamental aspects of ma
 thematical physics and key mechanisms of complex \nsystems and it helps to
  understand important aspects related to energy localization\, \nphase cha
 nge and function\, in a broad spectrum of natural sciences. 
LOCATION:MA A3 30
STATUS:CONFIRMED
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