Md Mainul Hasan Sabbir

Active nematics in two dimensions stir themselves efficiently through internally generated chaotic flows, largely driven by motile + 1 / 2 disclinations.We investigate how this tendency toward chaotic fluid stirring can, counterintuitively, produce certain ordered, periodic flows in confinement, characterized by stable periodic orbits of + 1 / 2 disclinations. We computationally study two-dimensional active nematics in systems with boundary conditions requiring a prescribed number n of excess + 1 / 2 disclinations, using Beris-Edwards nematohydrodynamics simulations alongside an agent-based simulation approach. We find that when confinement is sufficiently strong to prevent defect pair-nucleation, but not strong enough to arrest all flow, then n = 3 defects generically follow a “golden braid” orbit as observed recently in experiments, and we predict a “silver braid” orbit of n = 4 defects. For these results and for greater numbers of defects, we show that the periodic or chaotic nature of the dynamics is determined by a balance between the number of defects and the number of vortices in the flow field, suggesting a design criterion for ordered flows in active nematics.

We model microtubule-based active nematics based on the foundational idea that an initial curve following the director field must continue to follow the director field as it evolves. The resulting model shows improved agreement with experiment.

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.

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.