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SUMMARY:Patrick Farrell
DTSTART:20260408T070000Z
DTEND:20260408T080000Z
DTSTAMP:20260422T121745Z
UID:MathMAC/57
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MathMAC/57/"
 >A kinetic theory approach to ordered fluids</a>\nby Patrick Farrell as pa
 rt of Modelling of materials - theory\, model reduction and efficient nume
 rical methods (UNCE MathMAC)\n\n\nAbstract\nBoltzmann derived the kinetic 
 equation for monatomic gases in 1872. It took 85 years before Curtiss deve
 loped the extension to polyatomic gases\, enlarging the phase space with E
 uler angles to describe the orientations of the molecules. What is the rig
 ht kinetic equation for molecules with other kinds of internal ordering\, 
 such as the rodlike molecules constituting liquid crystals? This talk pres
 ents a framework that aims to address exactly this question.\n\nThe intern
 al structure of a molecule is described by a point on an order parameter m
 anifold\, a concept introduced by Capriz in continuum mechanics in 1989. W
 ith this manifold\, a group action describing how rotations change orderin
 g\, and the intermolecular potential\, we derive a general BBGKY hierarchy
  and a Vlasov—Boltzmann kinetic equation that governs the evolution the 
 one-particle density function.\n\nWe prove that in certain situations the 
 system thermalises to a Maxwellian distribution\, simulate the resulting n
 ovel kinetic equation for liquid crystals with direct simulation Monte Car
 lo\, and discuss taking hydrodynamic closures to derive novel models at th
 e level of continuum mechanics.\n
LOCATION:https://researchseminars.org/talk/MathMAC/57/
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