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- Publication Date:
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- Frontiers in Applied Mathematics and Statistics
- Sponsoring Org:
- National Science Foundation
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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 tomore »
Inferring the size of a collective of self-propelled Vicsek particles from the random motion of a single unit
Inferring the size of a collective from the motion of a few accessible units is a fundamental problem in network science and interdisciplinary physics. Here, we recognize stochasticity as the commodity traded in the units’ interactions. Drawing inspiration from the work of Einstein-Perrin-Smoluchowski on the discontinuous structure of matter, we use the random motion of one unit to identify the footprint of every other unit. Just as the Avogadro’s number can be determined from the Brownian motion of a suspended particle in a liquid, the size of the collective can be inferred from the random motion of any unit. For self-propelled Vicsek particles, we demonstrate an inverse proportionality between the diffusion coefficient of the heading of any particle and the size of the collective. We provide a rigorous method to infer the size of a collective from measurements of a few units, strengthening the link between physics and collective behavior.
Active matter is differentiated from conventional passive matter due to its unique capability of locally consuming fuels to generate kinetic energy. Such a unique feature of active matter has led to unprecedented phenomena and associated applications. While active matter has been developed for decades, its significance is not recognized by the public. To remedy this gap, we developed an online teaching module introducing collective dynamics of active matter, targeting high school and undergraduate students. The collective dynamics were illustrated via the Vicsek model-based simulation because it reveals the collective dynamics of active matter with one simple rule: nearest-neighbor alignment. With this rule, the simulation demonstrated the collective motion of active matter particles depended on particle number, radius of neighbor aligning, and noise that disturbed alignment. To allow students to hands-on experience the simulation, we developed a graphical user interface, allowing users to perform the Vicsek simulation without a programming background. The simulation and teaching module are available on an online platform: The Partnership for Integration of Computation into Undergraduate Physics, allowing teachers in the US to bring the active matter lecture to their classrooms.
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.
Assemblies of self-rotating particles are gaining interest as a novel realization of active matter with unique collective behaviors such as edge currents and non-trivial dynamic states. Here, we develop a continuum model for a system of fluid-embedded spinners by coarse-graining the equations of motion of the discrete particles. We apply the model to explore mixtures of clockwise and counterclockwise rotating spinners. We find that the dynamics is sensitive to fluid inertia; in the inertialess system, after transient turbulent-like motion the spinners segregate and form steady traffic lanes. At small but finite Reynolds number instead, the turbulent-like motion persists and the system exhibits a chirality breaking transition leading to a single rotation sense state. Our results shed light on the dynamic behavior of non-equilibrium materials exemplified by active spinners.