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From the Viscous Sewing Machine to the Cowboy’s Lasso
Part I : The fluid mechanical sewing machine
A thin thread of viscous fluid falls onto a moving conveyer belt and lays down in a plethora of complex "stitch" patterns depending on the belt speed and the height of fall. This experiment is well documented in the literature and we used direct numerical simulations to reproduce and investigate the typical yet unexplained patterns. In particular the Fourier analysis of the motion of the thread’s contact point with the belt suggests a new classification of these patterns patterns. Indeed, they result from the combination of simple ratios of the natural frequency of the thread \Omega_c. Of particular interest is the alternating loops pattern witch frequencies are locked on the first five multiple of \Omega_c/3. Furthermore, we built up on these observations to propose a toy model for such a complex system.
Part II : The lasso
How does a cowboy manage to form a flat loop when spinning a lasso in the air ? and why is so difficult to realize such a trick ? Trick roping is an art derived from the original ability of Mexican Charros and American Cowboys to catch cattle. Of particular interest for us is the mathematical scaffold upon which trick roping is built. We combine analytics (continuation and matched asymptotics) with experiments to build up a representative model of the lasso that ultimately provides a recipe to successfully realize basic rope tricks.