Mathematical foundations of slender body theory

Abstract: March 22, Monday, 11:00am-11:50am (CDT) - Laurel Ohm (Courant Institute, New York) Zoom link. umn.zoom.us/j/97214138395 Title. Mathematical foundations of slender body theory Abstract. Slender body theory (SBT) facilitates computational simulations of thin filaments in a 3D viscous fluid by approximating 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 computational models, there had been no rigorous analysis of the error in using SBT 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 approximation. In particular, 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 terms of the fiber radius. This places slender body theory on firm theoretical footing. In addition, we perform a complete spectral analysis of the slender body PDE in a simple geometric setting, which sheds light on the use of SBT in approximating the `slender body inverse problem,' where we instead specify the fiber velocity and solve for the 1D force density. Finally, we make some comparisons to the method of regularized Stokeslets and offer thoughts on improvements to SBT.

analysis of PDEsclassical analysis and ODEsfunctional analysismetric geometry

Audience: researchers in the topic

HA-GMT-PDE Seminar

Series comments: Description: A senior graduate student/postdoc series in harmonic analysis, geometric measure theory, and partial differential equations.

Meetings will be weekly, and usually will occur on Monday, with some exceptions. For each talk, the Zoom link is made available in the website too. Contact Bruno Poggi at poggi008@umn.edu if you would like to subscribe to the seminar mailing list.