BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Laurel Ohm (Courant Institute) DTSTART:20210322T160000Z DTEND:20210322T165000Z DTSTAMP:20260423T005850Z UID:anpdews/55 DESCRIPTION:Title: Mathematical foundations of slender body theory\nby Laurel Ohm (Coura nt Institute) as part of HA-GMT-PDE Seminar\n\n\nAbstract\nMarch 22\, Mond ay\, 11:00am-11:50am (CDT) - Laurel Ohm (Courant Institute\, New York) Zo om link. https://umn.zoom.us/j/97214138395\nTitle. Mathematical foundation s of slender body theory \nAbstract. Slender body theory (SBT) facilitate s computational simulations of thin filaments in a 3D viscous fluid by app roximating the hydrodynamic effect of each fiber as the flow due to a line force density along a 1D curve. Despite the popularity of SBT in computat ional models\, there had been no rigorous analysis of the error in using S BT to approximate the interaction of a thin fiber with fluid. In this talk \, we develop a PDE framework for analyzing the error introduced by this a pproximation. In particular\, given a 1D force along the fiber centerline\ , we define a notion of `true' solution to the full 3D slender body proble m and obtain an error estimate for SBT in terms of the fiber radius. This places slender body theory on firm theoretical footing. In addition\, we p erform a complete spectral analysis of the slender body PDE in a simple ge ometric setting\, which sheds light on the use of SBT in approximating the `slender body inverse problem\,' where we instead specify the fiber veloc ity and solve for the 1D force density. Finally\, we make some comparisons to the method of regularized Stokeslets and offer thoughts on improvement s to SBT.\n LOCATION:https://researchseminars.org/talk/anpdews/55/ END:VEVENT END:VCALENDAR