RESUMEN
This work examines self-mixing in active nematics, a class of fluids in which mobile topological defects drive chaotic flows in a system comprised of biological filaments and molecular motors. We present experiments that demonstrate how geometrical confinement can influence the braiding dynamics of the defects. Notably, we show that confinement in cardioid-shaped wells leads to realization of the golden braid, a maximally efficient mixing state of exactly three defects with no defect creation or annihilation. We characterize the golden braid state using different measures of topological entropy and the Lyapunov exponent. In particular, topological entropy measured from the stretching rate of material lines agrees well with an analytical computation from braid theory. Increasing the size of the confining cardioid produces a transition from the golden braid, to the fully chaotic active turbulent state.
RESUMEN
The formation of biopolymer-based active phases has become an important technique for researchers interested in exploring the emerging field of active liquid crystals and their possible roles in cell biology. These novel systems consist of self-driven sub-units that consume energy locally, producing an out-of-equilibrium dynamic fluid. To form the active liquid crystal phase described in this report, purified protein components including biopolymers and molecular motors are combined, and the active nematic phase spontaneously forms in the presence of adenosine triphosphate (ATP). To observe the nematic state, the material must be confined in a suitable geometry for microscopy at a high enough density. This article describes two different methods for the formation of an active nematic phase using microtubules and kinesin motors: assembly of a two-dimensional active layer at an oil and water interface and assembly under an oil layer using an elastomeric well. Techniques to insert the active material into small wells of different shapes are also described.
