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We study the universal behavior of a class of active colloids whose design is inspired by the collective dynamics of natural systems such as schools of fish and flocks of birds. These colloids, with off-center repulsive interaction sites, self-organize into polar swarms exhibiting long-range order and directional motion without significant hydrodynamic interactions. Our simulations show that the system transitions from motile perfect crystals to solid-like, liquid-like, and gas-like states depending on noise levels, repulsive interaction strength, and particle density. By analyzing swarm polarity and hexatic bond order parameters, we demonstrate that effective volume fractions based on force-range and torque-range interactions explain the system's universal behavior. This work lays a groundwork for biomimetic applications utilizing the cooperative polar dynamics of active colloids. 

By introducing geometry-based phoresis kernels, we establish a direct connection between the translational and rotational velocities of a phoretic sphere and the distributions of the driving fields or fluxes. The kernels quantify the local contribution of the field or flux to the particle dynamics. The field kernels for both passive and active particles share the same functional form, depending on the position-dependent surface phoretic mobility. For uniform phoretic mobility, the translational field kernel is proportional to the surface normal vector, while the rotational field kernel is zero; thus, a phoretic sphere with uniform phoretic mobility does not rotate. As case studies, we discuss examples of a self-phoretic axisymmetric particle influenced by a globally-driven field gradient, a general scenario for axisymmetric self-phoretic particle and two of its special cases, and a non-axisymmetric active particle. 

We revisit Brenner's seminal work on the Stokes resistance of a slightly deformed sphere (Chem. Engng Sci., vol. 19, 1964, p. 519), evaluate its range of validity and extend its applicability to higher deformations for axisymmetric particles, using hydrodynamic radius as the measure of Stokes resistance. Brenner's method solves the flow around a slightly deformed sphere through two mapping steps: the first mapping translates the surface velocity on the deformed sphere to that over a reference sphere of arbitrary radius using an asymptotic expansion of the flow field in terms of deformation amplitude and a Taylor expansion of the velocity field around the surface of the reference sphere. Subsequently, the second mapping extrapolates the velocity field from the surface of the reference sphere to any point in the fluid using Lamb's general solution for Stokes flow. While the original work addresses slightly deformed spheres to a linear order in deformation amplitude, we demonstrate that the first mapping, in combination with axisymmetric spectral modes (J. Fluid Mech., vol. 936, 2022, R1), can accommodate significant deformations to arbitrary orders of perturbation, and thus is not limited to slightly deformed spheres. Also, while first-order analysis is suitable for nearly spherical particles, second-order terms can provide a reasonable range for significantly higher deformations. 

Abstract Active colloidal microcrystallites capable of generating flow patterns around or through their porous network are introduced, which in combination with “free microspheres,” create self‐assembled active clusters with multiple moving parts. Fluid flow draws microspheres within a microcrystallite's local environment toward—and aggregate at—the edge of the microcrystallite, where the previously translational movement transitions to continuous spinning. These experiments show that the spinning frequency decreases with an increase in diameter and that when the center of mass of a spinning particle is shifted off‐center—here Janus spheres—a time‐varying angular frequency is observed. Weight‐anisotropy also leads to a particularly intriguing phenomenon, which manifests as the spontaneous realignment of the rotational axis to a preferential direction; this effect is attributed to a gravitropic self‐correcting mechanism. Thus, the dynamics of the self‐assembled active structure remains stable over long time periods, despite being subjected to significant noise, for example, Brownian forces. 

Abstract Artificial self‐propelled colloidal particles have recently served as effective building blocks for investigating many dynamic behaviors exhibited by nonequilibrium systems. However, most studies have relied upon excluded volume interactions between the active particles. Experimental systems in which the mobile entities interact over long distances in a well‐defined and controllable manner are valuable so that new modes of multiparticle dynamics can be studied systematically in the laboratory. Here, a system of self‐propelled microscale Janus particles is engineered to have contactless particle–particle interactions that lead to long‐range attraction, short‐range repulsion, and mutual alignment between adjacent swimmers. The unique modes of motion that arise can be tuned by modulating the system's parameters.