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The Talbot effect and the evolution of Vortex Filaments

New challenges in PDE: Deterministic dynamics and randomness in high and infinite dimensional systems October 19, 2015 - October 30, 2015

October 20, 2015 (02:00 PM PDT - 03:00 PM PDT)
Speaker(s): Luis Vega (Universidad del País Vasco/Euskal Herriko Unibertsitatea)
Location: MSRI: Simons Auditorium
Tags/Keywords
  • vortex filament equation

  • singularities

  • non-linear PDE

  • Frisch-Parisi conjecture

  • Talbot effect

  • pseudo-randomness

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

14374

Abstract

I shall present some recent work done in collaboration with F. De la Hoz about the the evolution of regular polygons within the so-called Vortex Filament Equation. Each corner of the polygon generates some Kelvin waves that interact in a non-linear way that is closely related to the (linear) Talbot effect in optics.

The question of the possible connection between the Talbot effect and turbulence will be also addressed, and in particular the appearance of multi-fractals and their relation with the so called Frisch-Parisi conjecture.

Supplements
24935?type=thumb Vega_Notes 1.61 MB application/pdf Download
Video/Audio Files

14374

H.264 Video 14374.mp4 346 MB video/mp4 rtsp://videos.msri.org/data/000/024/560/original/14374.mp4 Download
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