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Discrete Geometric Mechanics of Elastic Rods and Viscous Threads

Tuesday, November 1, 3:30PM – 5PM
6.304

Eitan Grinspun, Associate Professor, Computer Science, Columbia University

The deformation of slender bodies is characterized by buckling, coiling, folding, or broadly by strong nonlinearities arising primarily from geometry. Whereas in some contexts these deformations are associated with failure, recent research emphasizes their role as functional units for applications spanning transoceanic cable deposition, carbon nanotube synthesis, stretchable electronic construction, fiber spinning, visual effects, and so forth.

We develop a computational model of Kirchhoff elastic rods and viscous liquid threads by focusing on the geometry. We describe the kinematics in terms of framed curves, emphasizing that the classical notion of parallel transport sheds light on the competition between twisting and bending modes, providing an analogy to the isoparametric problem on the unit sphere. After presenting the smooth kinematics we then build a discrete picture from the ground up, mimicking the axioms, structures, and symmetries of the smooth setting. The result is an economical, unified treatment of viscous threads and elastic rods demonstrating canonical coiling, folding, and breakup in dynamic simulations, and reproducing with good agreement a variety of fascinating physical phenomena, including hysteretic transitions between coiling regimes, competition between surface tension and gravity, and the first numerical fluid-mechanical sewing machine.

Short Bio: He was Professeur d'Université Invité at l'Université Pierre et Marie Curie in 2009, a Research Scientist at the Courant Institute of Mathematical Sciences from 2003-2004, and a graduate student at the California Institute of Technology from 1997-2003. He was an NVIDIA Fellow in 2001, an Everhart Distinguished Lecturer in 2003, an NSF CAREER Award recipient in 2007, and is currently an Alfred P. Sloan Research Fellow honored by Popular Science magazine as one of the 2011 "Brilliant Ten."

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