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Conferencia: Dinámica Típica de wind-tree

 

Prof, Alba Málaga

INRIA, Francia

 Fecha y hora: 24 de julio del 2014. 15h

Abstract: In 1912 Paul and Tatiana Ehrenfest wrote a seminal article on the foundations of Statistical Mechanics in which the wind-tree model was introduced in order to interpret the work of Boltzmann and Maxwell on gas dynamics. In the wind-tree model a point particle moves without friction on the plane with infinitely many rigid obstacles re- moved, and collides elastically with the obstacles The set of all possible configurations of the Ehrenfest wind-tree model endowed with the Hausdorff topology is a compact metric space. For a typical configuration we show that the wind-tree has interesting dynamics: it is minimal, ergodic and has infinite ergodic index in almost every direction. In particular some ergodic theorems can be applied to show that if we start with a large number of ini- tially parallel particles their directions decorrelate as the dynamics evolve answering the question posed by the Ehrenfests.

Reference:

  1. Málaga Sabogal, A.M. & Troubetzkoy, S., 2018. Infinite ergodic index of the Ehrenfest wind-tree. Communications in Mathematical Physics, 358, 995-1006.
  2. Málaga Sabogal, A.M. & Troubetzkoy, S., 2017. Weakly mixing polygonal billiards. Bulletin London Mathematical Society, 49, 141-147.
  3. Málaga Sabogal, A.M. & Troubetzkoy, S., 2016. Ergodicity of the Ehrenfest wind-tree. C. R. Acad. Sci. Paris, 354, 1032-1036.
  4. Málaga Sabogal, A.M. & Troubetzkoy, S., 2016. Minimality of the Ehrenfest wind-tree. Journal Modern Dynamics, 10, 209-228.