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Studies of active particle systems have demonstrated that particle anisotropy can impact the collective behavior of a system, motivating a systematic study. Here, we report a systematic computational investigation of the role of anisotropy in shape and active force director on the collective behavior of a two-dimensional active colloidal system. We find that shape and force anisotropy can combine to produce critical densities both lower and higher than those of disks. We demonstrate that changing particle anisotropy tunes what we define as a "collision efficiency" of inter-particle collisions in leading to motility-induced phase separation (MIPS) of the system. We use this efficiency to determine the relative critical density across systems. Additionally, we observe that local structure in phase-separated clusters is the same as the particle's equilibrium densest packing, suggesting a general connection between equilibrium behavior and non-equilibrium cluster structure of self-propelled anisotropic particles. In engineering applications for active colloidal systems, shape-controlled steric interactions such as those described here may offer a simple route for tailoring emergent behaviors.

Active matter systems are of great interest for their novel out-of-equilibrium collective behavior. Active Brownian particles (ABPs) are known to exhibit clustering and motility-induced phase separation, and there have been many studies revealing this rich behavior in the overdamped limit of Brownian motion, where inertial effects are insignificant. Here we simulate an Active Inertial Particle (AIP) model where we focus on the underdamped, rather than overdamped limit, to study the interplay between particle inertia and collective behavior, such as phase separation. We show that inertia reduces particle motility due to collisions and a longer time delay for particles to regain speed, thereby suppressing phase separation relative to that observed in the overdamped limit. Additionally, we observe interesting oscillatory behavior between a phase separated steady-state and a homogeneous fluid state that results from inertia-induced collective motion within active clusters due to momentum transfer. Such oscillatory behavior has been reported for ABP systems with particle shape anisotropy, where collective motion is mediated by particle shape anisotropy. Furthermore, we confirm that there is no single characteristic frequency for the oscillatory behavior. The power spectral density is a power law in the high frequency domain, with an exponent close to -2.5.

Self-propelled particles phase-separate into coexisting dense and dilute regions above a critical density. The statistical nature of their stochastic motion lends itself to various theories that predict the onset of phase separation. However, these theories are ill-equipped to describe such behavior when noise becomes negligible. To overcome this limitation, we present a predictive model that relies on two density-dependent timescales: τ&#95;{F}, the mean time particles spend between collisions; and τ&#95;{C}, the mean lifetime of a collision. We show that only when τ&#95;{F}<τ&#95;{C} do collisions last long enough to develop a growing cluster and initiate phase separation. Using both analytical calculations and active particle simulations, we measure these timescales and determine the critical density for phase separation in both two and three dimensions.

We investigate emergent behavior in binary mixtures comprised of passive particles and contact-triggered active particles (CAPs), where a propulsion force is applied on CAPs towards passive particles when the two are in contact. We show that such mixtures phase separate into distinct dense and dilute phases with as few as 10% CAPs. Furthermore, the structure of the dense phase can be tuned by varying the fraction of CAPs and the strength of their propulsion force. The dense phase is classified into seven structure types, which includes both 6-fold and 4-fold ordered crystals, and kinetically arrested gels and clusters. Mixtures with fewer than 35% CAPs exhibit traveling density waves such that one end of the dense phase recedes while the other propagates. This phenomenon results from the spontaneous symmetry breaking of particle flux at the dense-dilute interface. We show that contact-triggered activity can be employed to develop materials with a wide range of structures and dynamics.

Like meridian lines on a globe, two lines on a Gaussian-curved surface cannot be simultaneously straight and parallel everywhere. We find that this inescapable property of Gaussian curvature has important consequences for the clustering and swarming behavior of active matter. Focusing on the case of self-propelled particles confined to the surface of a sphere, we find that for high curvature, particles converge to a common orbit to form symmetry-breaking microswarms. We prove that this microswarm flocking behavior is distinct from other known examples in that it is a result of the curvature, and not incorporated through Vicsek-like alignment rules or collision-induced torques. Additionally, we find that clustering can be either enhanced or hindered as a consequence of both the microswarming behavior and curvature-induced changes to the shape of a cluster's boundary. Furthermore, we demonstrate how surfaces of non-constant curvature lead to behaviors that are not explained by the simple averaging of the total curvature. These observations demonstrate a promising method for engineering the emergent behavior of active matter via the geometry of the environment.

In assemblies, the geometric frustration of a locally preferred packing motif leads to anomalous behaviours, from self-limiting growth to defects in the ground state. Here, we demonstrate that geometric frustration selects the equilibrium morphology of cohesive bundles of chiral filaments, an assembly motif critical to a broad range of biological and synthetic nanomaterials. Frustration of inter-filament spacing leads to optimal shapes of self-twisting bundles that break the symmetries of packing and of the underlying inter-filament forces, paralleling a morphological instability in spherical two-dimensional crystals. Equilibrium bundle morphology is controlled by a parameter that characterizes the relative costs of filament bending and the straining of cohesive bonds between filaments. This parameter delineates the boundaries between stable, isotropic cylindrical bundles and anisotropic, twisted-tape bundles. We also show how the mechanical and interaction properties of constituent amyloid fibrils may be extracted from the mesoscale dimensions of the anisotropic bundles that they form.

Densely packed and twisted assemblies of filaments are crucial structural motifs in macroscopic materials (cables, ropes, and textiles) as well as synthetic and biological nanomaterials (fibrous proteins). We study the unique and nontrivial packing geometry of this universal material design from two perspectives. First, we show that the problem of twisted bundle packing can be mapped exactly onto the problem of disc packing on a curved surface, the geometry of which has a positive, spherical curvature close to the center of rotation and approaches the intrinsically flat geometry of a cylinder far from the bundle center. From this mapping, we find the packing of any twisted bundle is geometrically frustrated, as it makes the sixfold geometry of filament close packing impossible at the core of the fiber. This geometrical equivalence leads to a spectrum of close-packed fiber geometries, whose low symmetry (five-, four-, three-, and twofold) reflect non-euclidean packing constraints at the bundle core. Second, we explore the ground-state structure of twisted filament assemblies formed under the influence of adhesive interactions by a computational model. Here, we find that the underlying non-euclidean geometry of twisted fiber packing disrupts the regular lattice packing of filaments above a critical radius, proportional to the helical pitch. Above this critical radius, the ground-state packing includes the presence of between one and six excess fivefold disclinations in the cross-sectional order.