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ACMS Abstracts: Fall 2022

James Hanna (UN-Reno)

Title: A snapping singularity

Abstract: I will discuss our preliminary work (with A. Dehadrai) on the focusing of kinetic energy and the amplification of various quantities during the snapping motion of the free end of a string or chain. This brief but violent event, with its remarkably large spikes in velocity, acceleration, and tension, is an essentially unavoidable feature of flexible structure dynamics, induced by generic initial and boundary conditions. We are guided by an analytical solution for a geometrically singular limit that features a finite-time singularity in other quantities. Regularization of this singularity does not arise from discretization of the continuous string equations or, equivalently, from the physical discreteness of a chain. It is instead associated with a length scale arising from the geometry of the problem, which evolves according to an anomalously slow curvature scaling.

Thomas Chandler (UW)

Title: Fluid–body interactions in liquid crystals: A complex variable approach

Abstract: Fluid anisotropy, or direction-dependent response to deformation, can be observed in biofluids like mucus or, at a larger scale, self-aligning swarms of swimming bacteria. A model fluid used to investigate such environments is a liquid crystal. Large colloidal bodies undergo shape-dependent interactions when placed in such an environment, whilst deformable bodies like red blood cells tend to be stretched, offering a passive means of measuring cell material properties. While numerous methods exist for studying the liquid crystalline configurations and fluid–body interaction for a single body, there are exceedingly few analytical results for the interaction of two or more bodies. In this talk, we will bring the power of complex variables to bear on this problem, presenting a simple methodology to analytically solve for the interactions inside a liquid crystalline environment. This approach allows for the solution of a wide range of problems, opening the door to studying the role of body shape and orientation, liquid crystal anchoring conditions, and body deformability.