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Ordered, collective motions commonly arise spontaneously in systems of many interacting, active units, ranging from cellular tissues and bacterial colonies to self-propelled colloids and animal flocks. Active phases are especially rich when the active units are sufficiently anisotropic to produce liquid crystalline order and thus active nematic phenomena, with important biophysical examples provided by cytoskeletal filaments including microtubules and actin. Gliding assay experiments have provided a test bed to study the collective motions of these cytoskeletal filaments and unlocked diverse collective active phases, including states with long-range orientational order. However, it is not well understood how such long-range order emerges from the interplay of passive and active aligning mechanisms. We use Brownian dynamics simulations to study the collective motions of semiflexible filaments that self-propel in quasi-two-dimensions, in order to gain insights into the aligning mechanisms at work in these gliding assay systems. We find that, without aligning torques in the microscopic model, long-range orientational order can only be achieved when the filaments are able to overlap. The symmetry (nematic or polar) of the long-range order that first emerges is shown to depend on the energy cost of filament overlap and on filament flexibility. However, our model also predicts that a long-range-ordered active nematic state is merely transient, whereas long-range polar order is the only active dynamical steady state in systems with finite filament rigidity. 

Active nematics are an important new paradigm in soft condensed matter systems. They consist of rodlike components with an internal driving force pushing them out of equilibrium. The resulting fluid motion exhibits chaotic advection, in which a small patch of fluid is stretched exponentially in length. Using simulation, this paper shows that this system can exhibit stable periodic motion when confined to a sufficiently small square with periodic boundary conditions. Moreover, employing tools from braid theory, we show that this motion is maximally mixing, in that it optimizes the (dimensionless) “topological entropy”—the exponential stretching rate of a material line advected by the fluid. That is, this periodic motion of the defects, counterintuitively, produces more chaotic mixing than chaotic motion of the defects. We also explore the stability of the periodic state. Importantly, we show how to stabilize this orbit into a larger periodic tiling, a critical necessity for it to be seen in future experiments.