Jan 24 2022

Analysis and Applied Mathematics Seminar: Packing and locomotion with friction, by Silas Alben

January 24, 2022

4:00 PM - 4:50 PM

Location

Zoom

Address

Chicago, IL

Silas Alben (U Michigan): Packing and locomotion with friction

We discuss two problems dealing with the motions of thin deformable bodies under frictional forces. In the first problem, elastic filaments are confined within slowly-shrinking circular boundaries. The filaments undergo deformations that are a mixture of spiraling and bifurcations, primarily the former with small friction and the latter with large friction. With zero friction, a simple model predicts that the maximum curvature and the total elastic energy scale as the wall radius to the -3/2 and -2 powers respectively. With nonzero friction, the elastic energy follows a similar scaling but with a prefactor up to 8 times larger, due to delayering and bending with a range of small curvatures. The second problem examines models of snakes as thin filaments that deform and locomote due to friction. We examine optimal motions of two-link, three-link, and smooth bodies with a variety of friction coefficients. With large friction transverse to the snake, the optimal motion is a retrograde traveling wave with amplitude scaling as the friction coefficient the -1/4 power. With zero transverse friction, a triangular direct wave is optimal. Between these extremes we find a variety of local optima including standing waves (or ratcheting motions).

Please click here to make changes to, or delete, this seminar announcement.

Contact

Ian Tobasco

Date posted

Jan 24, 2022

Date updated

Jan 24, 2022

Speakers

Silas Alben | (U Michigan)