Liquid Crystals, Soft-matter Packing, and Active Systems: Materials and Biological Applications

The abundance of partially-ordered liquid crystal phases in both natural and synthetic settings have had a major impact in the display industry and have played a central role in the understanding of soft matter.  A central thrust in liquid crystal research is the ability to control macroscopic-sized regions of uniform molecular alignment, an example of which are found in optical and display devices by electromagnetic fields.  A compelling direction in current liquid crystal research aims at the topological control of the systems, with liquid crystal colloids and chromonic materials playing prominent roles.  

In this setting, colloids, consisting of dispersed particles in a liquid crystal matrix, present complex defect structures, ranging from point, line, and Saturn rings defects, to order parameter knot networks resembling those in DNA.  From a dynamics perspective, such systems exhibit low Reynolds number turbulence and also give rise to nonlinear electrokinetic effects that enable electrophoretic processes driven by alternating fields.

Chromonic liquid crystals, unlike their rigid-rod molecular counterparts, consist of disk-like, plank molecules that may form isotropic, nematic, and columnar lyotropic phases. Their compatibility with water makes them amenable to the modeling of biological processes, especially those related to cellular organization and DNA confinement. An example of the latter can be found in the mechanical and geometric analogies between bacteriophage viruses and ionically-controlled chromonic clusters. From a different point of view, nematic chromonic liquid crystals are also excellent hosts for bacteria, with such active systems being explored for nanofluidic and particle transport devices.  

Liquid crystal research touches upon mathematical and computational methods involving topological fluid dynamics, electrokinetics, free boundary problems, particle coarsening approaches, and topology of knots. This workshop will be highly interdisciplinary involving mathematicians and researchers from the materials and biological sciences communities.