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SUMMARY:CCM Colloquium: Laurel Ohm (Princeton)
DTSTART;VALUE=DATE-TIME:20211215T150000Z
DTEND;VALUE=DATE-TIME:20211215T161500Z
DTSTAMP;VALUE=DATE-TIME:20220523T022300Z
UID:indico-event-2683@indico.flatironinstitute.org
DESCRIPTION:Title: Mathematical foundations of slender body theory\n\nAbs
tract: Slender body theory (SBT) facilitates computational simulations of
thin filaments in a 3D viscous fluid by approximating the hydrodynamic ef
fect of each fiber as the flow due to a line force density along a 1D curv
e. Despite the popularity of SBT in computational models\, there had been
no rigorous analysis of the error in using SBT to approximate the interact
ion of a thin fiber with fluid. In this talk\, we develop a PDE framework
for analyzing the error introduced by this approximation. Given a 1D force
along the fiber centerline\, we define a notion of `true' solution to the
full 3D slender body problem and obtain an error estimate for SBT in term
s of the fiber radius. This places slender body theory on firm theoretical
footing. In addition\, we perform a complete spectral analysis of the sl
ender body PDE in a simple geometric setting\, which sheds light on the u
se of SBT in approximating the `slender body inverse problem\,' where we
instead specify the fiber velocity and solve for the 1D force density. Fi
nally\, we introduce a numerical method based on a boundary integral formu
lation of the slender body PDE and discuss numerical comparisons with slen
der body theory.\n\nhttps://www.math.princeton.edu/people/laurel-ohm\n\n
\n\nIf you would like to attend\, please email crampersad@flatironinstitut
e.org for the Zoom link. \n\nhttps://indico.flatironinstitute.org/event/2
683/
LOCATION:3rd floor classroom & zoom
URL:https://indico.flatironinstitute.org/event/2683/
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