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CATEGORIES:Partial Differential Equations seminar
SUMMARY:Orientation mixing in active suspensions - Helge D
ietert (Paris Diderot)
DTSTART;TZID=Europe/London:20220613T140000
DTEND;TZID=Europe/London:20220613T150000
UID:TALK175337AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/175337
DESCRIPTION:I will present a popular kinetic model introduced
by Saintillan and Shelley for the dynamics of susp
ensions of active elongated particles. This model\
, involving the distribution in space and orientat
ion of the particles\, is known to exhibit phase t
ransitions. We focus on the linear analysis of inc
oherence\, that is on the linearized equation arou
nd the uniform distribution\, in the regime of par
ameters corresponding to spectral (neutral) stabil
ity. I will show that in the absence of rotational
diffusion\, the supension experiences a mixing ph
enomenon similar to Landau damping\, and we provid
e optimal pointwise in time decay rates in weak to
pology. We show that this phenomenon persists for
small rotational diffusion\, and is combined with
an enhanced dissipation at time scale $\\nu^{-1/2}
$. The mathematical interest of the model is that
the usual velocity variable of kinetic models is r
eplaced by an orientation variable on the sphere.
The associated orientation mixing leads to limited
algebraic decay for macroscopic quantities.\n\nJo
int work with Michele Coti Zelati and David GĂ©rard
-Varet
LOCATION:CMS\, MR13
CONTACT:Daniel Boutros
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