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  1. Active fluids have potential applications in micromixing, but little is known about the mixing kinematics of such systems with spatiotemporally-varying activity. To investigate, UV-activated caged ATP was used to activate controlled regions of microtubule-kinesin active fluid inducing a propagating active-passive interface. The mixing process of the system from non-uniform to uniform activity as the interface advanced was observed with fluorescent tracers and molecular dyes. At low Péclet numbers (diffusive transport), the active-inactive interface progressed toward the inactive area in a diffusion-like manner and at high Péclet numbers (convective transport), the active-inactive interface progressed in a superdiffusion-like manner. The results show mixing in non-uniform active fluid systems evolve from a complex interplay between the spatial distribution of ATP and its active transport. This active transport may be diffusion-like or superdiffusion-like depending on Péclet number and couples the spatiotemporal distribution of ATP and the subsequent localized active stresses of active fluid. Our work will inform the design of future microfluidic mixing applications and provide insight into intracellular mixing processes. *T.E.B., E.H.T., J.H.D., and K.-T.W. acknowledge support from the National Science Foundation (NSF-CBET-2045621). C.-C. C. was supported through the National Science and Technology Council (NSTC), Taiwan (111-2221-E-006-102-MY3). M.M.N. was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences (DE-SC0022280). 
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  2. Active fluids with spatiotemporally varying activity have potential applications to micromixing; however previously existing active fluids models are not prepared to account for spatiotemporally-varying active stresses. Our experimental work used UV-activated caged ATP to activate controlled regions of microtubule-kinesin active fluid inducing a propagating active-passive interface. Here, we recapitulate our experimental results with two models. The first model redistributes an initial ATP distribution by Fick's law and translates the ATP distribution into a velocity profile by Michaelis-Menton kinetics. This model reproduces our experimental measurements for the low-Péclet number limit within 10% error without fitting parameters. However, as the model is diffusion based, it fails to capture the convective based superdiffusive-like behaviour at high Péclet numbers. Our second model introduces a spatiotemporally varying ATP field to an existing nematohydrodynamic active fluid model and then couples the active stresses to local ATP concentrations. This model is successful in qualitatively capturing the superdiffusive-like progression of the active-inactive interface for high Peclet number (convective transport) experimental cases. Our results show that new model frameworks are necessary for capturing the behaviour of active fluid with spatiotemporally varying activity. *T.E.B., E.H.T., J.H.D., and K.-T.W. acknowledge support from the National Science Foundation (NSF-CBET-2045621). C.-C. C. was supported through the National Science and Technology Council (NSTC), Taiwan (111-2221-E-006-102-MY3). M.M.N. was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences (DE-SC0022280). 
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  3. Confinement can be used to systematically tame turbulent dynamics occurring in active fluids. Although periodic channels are the simplest geometries to study confinement numerically, the corresponding experimental realizations require closed racetracks. Here, we computationally study 2D active nematics confined to such a geometry—an annulus. By systematically varying the annulus inner radius and channel width, we bridge the behaviors observed in the previously studied asymptotic limits of the annulus geometry: a disk and an infinite channel. We identify new steady-state behaviors, which reveal the influence of boundary curvature and its interplay with confinement. We also show that, below a threshold inner radius, the dynamics are insensitive to the presence of the inner hole. We explain this insensitivity through a simple scaling analysis. Our work sheds further light on design principles for using confinement to control the dynamics of active nematics. 
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  4. Abstract Active fluids have applications in micromixing, but little is known about the mixing kinematics of systems with spatiotemporally-varying activity. To investigate, UV-activated caged ATP is used to activate controlled regions of microtubule-kinesin active fluid and the mixing process is observed with fluorescent tracers and molecular dyes. At low Péclet numbers (diffusive transport), the active-inactive interface progresses toward the inactive area in a diffusion-like manner that is described by a simple model combining diffusion with Michaelis-Menten kinetics. At high Péclet numbers (convective transport), the active-inactive interface progresses in a superdiffusion-like manner that is qualitatively captured by an active-fluid hydrodynamic model coupled to ATP transport. Results show that active fluid mixing involves complex coupling between distribution of active stress and active transport of ATP and reduces mixing time for suspended components with decreased impact of initial component distribution. This work will inform application of active fluids to promote micromixing in microfluidic devices. 
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  5. In networks of nonlinear oscillators, symmetries place hard constraints on the system that can be exploited to predict universal dynamical features and steady states, providing a rare generic organizing principle for far-from-equilibrium systems. However, the robustness of this class of theories to symmetry-disrupting imperfections is untested in free-running (i.e., non-computer-controlled) systems. Here, we develop a model experimental reaction-diffusion network of chemical oscillators to test applications of the theory of dynamical systems with symmeries in the context of self-organizing systems relevant to biology and soft robotics. The network is a ring of four microreactors containing the oscillatory Belousov-Zhabotinsky reaction coupled to nearest neighbors via diffusion. Assuming homogeneity across the oscillators, theory predicts four categories of stable spatiotemporal phase-locked periodic states and four categories of invariant manifolds that guide and structure transitions between phase-locked states. In our experiments, we observed that three of the four phase-locked states were displaced from their idealized positions and, in the ensemble of measurements, appeared as clusters of different shapes and sizes, and that one of the predicted states was absent. We also observed the predicted symmetry-derived synchronous clustered transients that occur when the dynamical trajectories coincide with invariant manifolds. Quantitative agreement between experiment and numerical simulations is found by accounting for the small amount of experimentally determined heterogeneity in intrinsic frequency. We further elucidate how different patterns of heterogeneity impact each attractor differently through a bifurcation analysis. We show that examining bifurcations along invariant manifolds provides a general framework for developing intuition about how chemical-specific dynamics interact with topology in the presence of heterogeneity that can be applied to other oscillators in other topologies. 
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  6. Experiments and models were used to determine the extent to which aqueous bromine permeated into, and reacted with, the elastomer polydimethylsiloxane (PDMS). Thin films of PDMS were immersed in bromine water, and the absorbance of bromine in the aqueous phase was measured as a function of time. Kinetics were studied as a function of mass and thickness of the immersed PDMS films. We attribute the decrease of bromine in solution to permeation into PDMS, followed by a combination of diffusion, reversible binding, and an irreversible reaction with PDMS. In order to decouple the irreversible reaction from the reversible processes, kinetics were also studied for bromine-passivated PDMS films. Fits of the models to a variety of experiments yielded the partition coefficient of bromine between the water and PDMS phases, the diffusion constant of bromine in PDMS, the irreversible reaction constant between bromine and PDMS, the molar concentration of the reactive sites within PDMS, and the on and off rates of reversible binding of bromine to PDMS. Developing a quantitative reaction-diffusion model accounting for the transport of bromine through PDMS is necessary for the design of microfluidic devices fabricated using PDMS, which are used in experimental studies of the nonlinear dynamics of reaction-diffusion networks containing Belousov-Zhabotinsky chemical oscillators. 
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    Active nematics are a class of far-from-equilibrium materials characterized by local orientational order of force-generating, anisotropic constitutes. Traditional methods for predicting the dynamics of active nematics rely on hydrodynamic models, which accurately describe idealized flows and many of the steady-state properties, but do not capture certain detailed dynamics of experimental active nematics. We have developed a deep learning approach that uses a Convolutional Long-Short-Term-Memory (ConvLSTM) algorithm to automatically learn and forecast the dynamics of active nematics. We demonstrate our purely data-driven approach on experiments of 2D unconfined active nematics of extensile microtubule bundles, as well as on data from numerical simulations of active nematics. 
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