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Hydrodynamic limit for a disordered harmonic chain

Presented by: 
Cedric Bernardin
Thursday 13th December 2018 - 10:00 to 11:00
INI Seminar Room 1
We consider a one-dimensional unpinned chain of harmonic oscillators with random masses. We prove that after hyperbolic scaling of space and time the distributions of the elongation, momentum and energy converge to the solution of the Euler equations. Anderson localization decouples the mechanical modes from the thermal modes, allowing the closure of the energy conservation equation even out of thermal equilibrium. This example shows that the derivation of Euler equations rests primarily on scales separation and not on ergodicity.

Joint with F. Huveneers and S. Olla
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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons