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1. Collective motion of driven semiflexible filaments tuned by soft repulsion and stiffness

   https://doi.org/10.1039/D0SM01036G  

   Moore, Jeffrey M.; Thompson, Tyler N.; Glaser, Matthew A.; Betterton, Meredith D. (October 2020, Soft Matter)

   null (Ed.)

   In active matter systems, self-propelled particles can self-organize to undergo collective motion, leading to persistent dynamical behavior out of equilibrium. In cells, cytoskeletal filaments and motor proteins form complex structures important for cell mechanics, motility, and division. Collective dynamics of cytoskeletal systems can be reconstituted using filament gliding experiments, in which cytoskeletal filaments are propelled by surface-bound motor proteins. These experiments have observed diverse dynamical states, including flocks, polar streams, swirling vortices, and single-filament spirals. Recent experiments with microtubules and kinesin motor proteins found that the collective behavior of gliding filaments can be tuned by altering the concentration of the crowding macromolecule methylcellulose in solution. Increasing the methylcellulose concentration reduced filament crossing, promoted alignment, and led to a transition from active, isotropically oriented filaments to locally aligned polar streams. This emergence of collective motion is typically explained as an increase in alignment interactions by Vicsek-type models of active polar particles. However, it is not yet understood how steric interactions and bending stiffness modify the collective behavior of active semiflexible filaments. Here we use simulations of driven filaments with tunable soft repulsion and rigidity in order to better understand how the interplay between filament flexibility and steric effects can lead to different active dynamic states. We find that increasing filament stiffness decreases the probability of filament alignment, yet increases collective motion and long-range order, in contrast to the assumptions of a Vicsek-type model. We identify swirling flocks, polar streams, buckling bands, and spirals, and describe the physics that govern transitions between these states. In addition to repulsion and driving, tuning filament stiffness can promote collective behavior, and controls the transition between active isotropic filaments, locally aligned flocks, and polar streams. 

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2. Directional self-locomotion of active droplets enabled by nematic environment

   https://doi.org/10.1038/s41567-020-01055-5  

   Rajabi, Mojtaba; Baza, Hend; Turiv, Taras; Lavrentovich, Oleg D. (October 2020, Nature Physics)

   null (Ed.)

   Active matter composed of self-propelled interacting units holds a major promise for the extraction of useful work from its seemingly chaotic dynamics. Streamlining active matter is especially important at the microscale, where the viscous forces prevail over inertia and transport requires a non-reciprocal motion. Here we report that microscopic active droplets representing aqueous dispersions of swimming bacteria Bacillus subtilis become unidirectionally motile when placed in an inactive nematic liquid-crystal medium. Random motion of bacteria inside the droplet is rectified into a directional self-locomotion of the droplet by the polar director structure that the droplet creates in the surrounding nematic through anisotropic molecular interactions at its surface. Droplets without active swimmers show no net displacement. The trajectory of the active droplet can be predesigned by patterning the molecular orientation of the nematic. The effect demonstrates that broken spatial symmetry of the medium can be the reason for and the means to control directional microscale transport. 

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3. Steady states of active Brownian particles interacting with boundaries

   https://doi.org/10.1088/1742-5468/ac42cf  

   Wagner, Caleb G; Hagan, Michael F; Baskaran, Aparna (January 2022, Journal of Statistical Mechanics: Theory and Experiment)

   Abstract An active Brownian particle is a minimal model for a self-propelled colloid in a dissipative environment. Experiments and simulations show that, in the presence of boundaries and obstacles, active Brownian particle systems approach nontrivial nonequilibrium steady states with intriguing phenomenology, such as accumulation at boundaries, ratchet effects, and long-range depletion interactions. Nevertheless, theoretical analysis of these phenomena has proven difficult. Here, we address this theoretical challenge in the context of non-interacting particles in two dimensions, basing our analysis on the steady-state Smoluchowski equation for the one-particle distribution function. Our primary result is an approximation strategy that connects asymptotic solutions of the Smoluchowski equation to boundary conditions. We test this approximation against the exact analytic solution in a 2D planar geometry, as well as numerical solutions in circular and elliptic geometries. We find good agreement so long as the boundary conditions do not vary too rapidly with respect to the persistence length of particle trajectories. Our results are relevant for characterizing long-range flows and depletion interactions in such systems. In particular, our framework shows how such behaviors are connected to the breaking of detailed balance at the boundaries. 

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4. Dynamics and thermodynamics of air-driven active spinners

   https://doi.org/10.1039/c8sm00403j  

   Farhadi, Somayeh; Machaca, Sergio; Aird, Justin; Torres Maldonado, Bryan O.; Davis, Stanley; Arratia, Paulo E.; Durian, Douglas J. (January 2018, Soft Matter)

   We report on the collective behavior of active particles in which energy is continuously supplied to rotational degrees of freedom. The active spinners are 3D-printed disks, 1 cm in diameter, that have an embedded fan-like structure, such that a sub-levitating up-flow of air forces them to spin. Single spinners exhibit Brownian motion with a narrow Gaussian velocity distribution function, P ( v ), for translational motion. We study the evolution of P ( v ) as the packing fraction and the average single particle spin speeds are varied. The interparticle hydrodynamic interaction is negligible, and the dynamics is dominated by hyperelastic collisions and dissipative forces. As expected for nonequilibrium systems, P ( v ) for a collection of many spinners deviates from Gaussian behavior. However, unlike translationally active systems, phase separation is not observed, and the system remains spatially homogeneous. We then search for a near-equilibrium counterpart for our active spinners by measuring the equation of state. Interestingly, it agrees well with a hard-sphere model, despite the dissipative nature of the single particle dynamics. 

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5. Chaos, dynamic trapping, and transport of swimming microbes in a vortex chain flow

   https://doi.org/10.1063/5.0270869  

   Le, Nghia; Solomon, Thomas_H (June 2025, Chaos: An Interdisciplinary Journal of Nonlinear Science)

   We present experiments on chaotic motion of self-propelled (active) particles in a time-independent, two-dimensional vortex chain flow. We track Tetraselmis microbes and calculate the variance of a spreading distribution of these microbes in the flow. For small non-dimensional swimming speed v0, we find subdiffusion with variance ⟨x2⟩∼tγ with γ<1; transport is diffusive (γ=1) for larger v0. Subdiffusion for small v0 is due to dynamic trapping of microbes to islands of ordered trajectories surrounded by a sea of chaotic motion; these islands disappear for larger v0. We calculate Lagrangian-averaged trajectories (LATs) from the experimental data and use the LATs to measure trapping time probability distributions P(t). We find regimes with P(t)∼t−ν with ν<2 for small v0, consistent with the measured subdiffusion. 

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