Boris Buffoni: Heteroclinic orbits describing convective patterns with orthogonal walls

Date: 2023-09-28

Time: 10:00 - 11:00

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Boris Buffoni, EPFL


The 6-dimensional system
    A´´´´ &=       A ( 1 – A^2 – g B^2  )\\
    B´´ & = e^2 B ( -1 + g A^2 + B^2 )
appears in an approximation of the classical Bénard-Rayleigh problem near the convective instability threshold, where \(e>0\) and \(g>1\) are two parameters.

Heteroclinic orbits from \((A,B)=(1,0)\) to \((0,1)\) correspond to configurations in which two families of convective rolls with orthogonal orientations coexist (“orthogonal walls”).

The derivation of the system will be briefly described and heteroclicinic orbits obtained by a variational method.

Two limiting cases will be considered more carefully: \(e>0\) small and \(g-1>0\) small.

This is joint work with M. Haragus and G. Iooss.