Laboratoire Matière et Systèmes Complexes

January 25th 2021. 11h30

There will be a live diffusion with Zoom. Contact Michael Berhanu to attend the video seminar.

Pr. Piotr Szymczak

Institute of Theoretical Physics, Faculty of Physics
University of Warsaw, Poland

Knotted Loops Fall Flat

Long-chain molecules, like DNA, can develop knots, and these knots in turn affect how the molecules move through a liquid. To understand this behavior, together with a Giovanni Dietler group from EPFL Lausanne we have devised an experiment with knotted loops made of steel beaded chain. Surprisingly, all the loops settled into horizontally flat configurations as they fell—no matter how they were initially dropped. The loops in this configuration perform a highly concerted motion, which is a superposition of downward translation, rotation of the individual strands around each other and much slower rotation of the entire structure around the vertical axis. Interestingly, a very similar motion has been reported previously in a completely different context of knotted vortices in an ideal fluid. We then study this motion in a more detail using Stokesian Dynamics simulations of a flexible chain represented in terms of the bead-and-spring model.

We also consider the sedimentation of unknotted loops and show that at relatively small bending stiffness, a rich zoology of periodic orbits and stationary states appear, including double and triple loops, rotating figure-of-eight, swinging periodic motions or tank-treading solutions. These solutions are characterized by different sedimentation velocities, which can be used to differentiate them experimentally. These results are important not only for elucidating the link between topology and dynamics of filamentous objects but also for understanding of the appearance of periodic solutions in the sedimentation of many-particle systems in a viscous fluid.