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Applied Math Seminar — Kathryn G. Link (UC Davis)
April 4, 2022 @ 4:15 pm - 5:30 pm
Title: Viscoelastic Effects of Spontaneous Oscillations of Elastic Filaments in the Follower-Force Problem.
Abstract: It is well know that microorganisms, such as bacteria and eukaryotes, often move in intricate environments experiencing mechano-chemical dynamics. These environments consist of rheologically complex substances such as mucus and other biofilms that are more complicated than water. Spermatozoa (sperm), for example, swim in viscoelastic mucus via deformations of their flagella, which are slender threadlike structures that are powered by internal molecular motors. The motor activity generates flagellar bending, resulting in an undulatory beat. The effects of a fading-memory fluid on emergent properties of these spontaneous oscillations are not entirely known. Here we combine analysis with numerical simulations of finite-length, small-amplitude pinned filaments subject to a compressive follower force to elucidate the Hopf bifurcation that occurs with increasing forcing on the filament. Additionally, we determine characteristics of the flapping motion, specifically frequency and amplitude changes and how those changes depend on follower force strength as well as fluid elasticity.