Polar order, shear banding, and clustering in confined active matter.

We investigate the collective behavior of sterically interacting self-propelled particles confined in a harmonic potential. Our theoretical and numerical study unveils the emergence of distinctive collective polar organizations, revealing how different levels of interparticle torques and noise influence the system. The observed phases include the shear-banded vortex, where the system self organizes in two concentric bands rotating in opposite directions around the potential center; the uniform vortex, where the two bands merge into a close packed configuration rotating uniformly as a quasi-rigid body; and the orbiting polar state, characterized by parallel orientation vectors and the cluster revolving around the potential center, without rotation, as a rigid body. Intriguingly, at lower filling fractions, the vortex and polar phases merge into a single phase where the trapped cluster breaks into smaller polarized clusters, each one orbiting the potential center as a rigid body.

Structural phases of classical 2D clusters with competing two-body and three-body interactions.

In modeling systems of interacting particles, many-body terms beyond pairwise interactions are often overlooked. Nevertheless, in certain scenarios, even small contributions from three-body or higher-order terms can disrupt significant changes in their collective behavior. Here we investigate the effects of three-body interactions on the structure and stability of 2D, harmonically confined clusters. We consider clusters with three distinct pairwise interactions:logr,1/r, ande-κr/r, thus covering a wide range of condensed and soft matter systems, such as vortices in mesoscopic superconductors, charged colloids, and dusty plasma. In each case, we evaluate the energetics and normal mode spectra of equilibrium and metastable configurations as the intensity of an attractive, Gaussian three-body potential is varied. We demonstrate that, above a threshold value of the three-body energy strength, the cluster shrinks and eventually becomes self-sustained, that is, it remains cohesive after the confinement potential is shut down. Depending on the strengths of the two-body and three-body interaction terms, this compaction can be continuous or abrupt. The latter case is characterized by a discontinuous jump in the particle density and coexsitence of the compact and non-compact phases as metastable states, as in a first-order phase transition. For some values of the particle number, the compaction is preceded by one or more structural changes, resulting in configurations not usually seen in purely pairwise-additive clusters.

Coexisting orbits and chaotic dynamics of a confined self-propelled particle.

We investigate theoretically the dynamics of a confined active swimmer with velocity and orientation axis coupled to each other via a self-alignment torque. For an isotropic harmonic potential, this system is known to exhibit two distinct dynamical phases: a climbing one, where the particle is oriented radially and undergoes angular Brownian motion, and a circularly orbiting phase. Here we show that for nonradially symmetric confinement an assortment of complex phenomena emerge. For an elliptic harmonic potential the orbiting phase splits into several periodic orbits with a diversity of shapes: ovals, lemniscates, and generalized lemniscates with multiple lobes. These orbits can coexist in the parameter space and decay into one another induced by noise. For anharmonic confining potentials, we report transitions from periodic to chaotic dynamics, as one changes the intensity of the self-alignment torque and noise-induced complex orbits. These results demonstrate that the combination of the shape of the trapping potential and self-alignment torque can induce a rich variety of nontrivial dynamical states of a confined active particle.

Formation and stability of conformal spirals in confined 2D crystals.

We investigate the ground-state and dynamical properties of nonuniform two-dimensional (2D) clusters of long-range interacting particles. We demonstrate that, when the confining external potential is designed to produce an approximate 1/r2density profile, the particles crystallize into highly ordered structures featuring spiral crystalline lines. Despite the strong inhomogeneity of the observed configurations, most of them are characterized by small density of topological defects, typical of conformal crystals, and the net topological charge induced by the simply-connected geometry of the system is concentrated near the cluster center. These crystals are shown to be robust with respect to thermal fluctuations up to a certain threshold temperature, above which the net charge is progressively redistributed from the center to the rest of the system and the topological order is lost. The crystals are also resilient to the shear stress produced by a small nonuniform azimuthal force field, rotating as a rigid body (RB). For larger forces, topological defects proliferate and the RB rotation gives place to plastic flow.

Self-assembled vortex crystals induced by inhomogeneous magnetic textures.

We investigate the self-assembly of vortices in a type-II superconducting disk subjected to highly nonuniform confining potentials produced by inhomogeneous magnetic textures. Using a series of numerical experiments performed within the Ginzburg-Landau theory, we show that vortices can arrange spontaneously in highly nonuniform, defect-free crystals, reminiscent of conformal lattices, even though the strict conditions for the conformal crystal are not fulfilled. These results contradict continuum-limit theory, which predicts that the order of a nonuniform crystal is unavoidably frustrated by the presence of topological defects. By testing different cooling routes of the superconductor, we observed several different self-assembled configurations, each of which corresponding to one in a set of allowed conformal transformations, which depends on the magnetic and thermal histories of the system.