Dynamics of topological solitons, knotted streamlines, and transport of cargo in liquid crystals.

Active colloids and liquid crystals are capable of locally converting the macroscopically supplied energy into directional motion and promise a host of new applications, ranging from drug delivery to cargo transport at the mesoscale. Here we uncover how topological solitons in liquid crystals can locally transform electric energy to translational motion and allow for the transport of cargo along directions dependent on frequency of the applied electric field. By combining polarized optical video microscopy and numerical modeling that reproduces both the equilibrium structures of solitons and their temporal evolution in applied fields, we uncover the physical underpinnings behind this reconfigurable motion and study how it depends on the structure and topology of solitons.

Numerical quadrature over smooth, closed surfaces.

The numerical approximation of definite integrals, or quadrature, often involves the construction of an interpolant of the integrand and its subsequent integration. In the case of one dimension it is natural to rely on polynomial interpolants. However, their extension to two or more dimensions can be costly and unstable.

Some observations regarding steady laminar flows past bluff bodies.

Steady laminar flows past simple objects, such as a cylinder or a sphere, have been studied for well over a century. Theoretical, experimental and numerical methods have all contributed fundamentally towards our understanding of the resulting flows. This article focuses on developments during the past few decades, when mostly numerical and asymptotical advances have provided insights also for steady, although unstable, high-Reynolds-numbers flow regimes.