Topological knots in droplets with holes

From a topological point of view, a sphere and a cube are equivalent, since we can transform one into the other through continuous deformations. Making holes or knots is a way to produce more complex topological objects. For instance, we could make a hole in the sphere to produce a torus, or could take two torii and intertwine them to produce knots. These knotted structures are not only important in mathematics but are also relevant to many areas of physics, including cosmology, hydrodynamics, optics, condensed matter, particle, nuclear, and atomic physics. They appear when studying fields and are called solitons, due to their particle-like behavior. Our goal is to create and study these topological knots in a chiral nematic liquid crystal, where rod-like molecules align with each other yielding an orientational director field. Recent simulations have shown that complex knots could be stabilized in toroidal droplets of this sort of liquid crystal. Here the stability of topological knots is enhanced by the chiral medium’s tendency to twist the director field and the toroidal confinement. We are interested in experimentally studying these problems by using a recently developed technique that allows us to produce droplets with holes. This project is in collaboration with Ivan Smalyukh, from the University of Colorado, and Alberto Fernandez-Nieves, from the Georgia Institute of Technology.

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