Clustering and anisotropic correlated percolation in polar flocks

Percolation transitions in a binary mixture of active Brownian particles with different softness

Homogeneous active Brownian particle (ABP) systems with purely repulsive interactions are considered to exhibit a simple phase behavior, but various physical attributes of active entities can lead to variation in the collective dynamics. Recent studies have shown that even homogeneous ABPs exhibit complex behavior due to an interplay between particle softness and motility. However, the heterogeneity in the composition of ABPs has not been explored yet. In this paper, we study the structural properties of a binary mixture of ABPs with different particle softness by varying the relative softness and composition. We found that upon varying the motility parameter, the system underwent a motility-induced phase separation (MIPS) followed by a percolation transition similar to the homogeneous systems. However, we observed a novel feature: the formation of a space-filling structure made of particles with higher stiffness, within the dense cluster of MIPS containing both types of particles. Our systematic analysis shows that this structure formation occurs only if the difference in softness of both types of particles is sufficiently large. Furthermore, the presence of a non-linear scaling for different compositions of binary ABPs suggests that there is a complex relationship between the composition and the structural properties. Our study demonstrates that the composition heterogeneity of ABPs can lead to complex phase behavior.

Swarming Transition in Super-Diffusive Self-Propelled Particles

A super-diffusive Vicsek model is introduced in this paper that incorporates Levy flights with exponent α. The inclusion of this feature leads to an increase in the fluctuations of the order parameter, ultimately resulting in the disorder phase becoming more dominant as α increases. The study finds that for α values close to two, the order-disorder transition is of the first order, while for small enough values of α, it shows degrees of similarities with the second-order phase transitions. The article formulates a mean field theory based on the growth of the swarmed clusters that accounts for the decrease in the transition point as α increases. The simulation results show that the order parameter exponent β, correlation length exponent ν, and susceptibility exponent γ remain constant when α is altered, satisfying a hyperscaling relation. The same happens for the mass fractal dimension, information dimension, and correlation dimension when α is far from two. The study reveals that the fractal dimension of the external perimeter of connected self-similar clusters conforms to the fractal dimension of Fortuin-Kasteleyn clusters of the two-dimensional Q=2 Potts (Ising) model. The critical exponents linked to the distribution function of global observables vary when α changes.

Universal Critical Behavior of Percolation in Orientationally Ordered Janus Particles and Other Anisotropic Systems

We combine percolation theory and Monte Carlo simulation to study in two dimensions the connectivity of an equilibrium lattice model of interacting Janus disks which self-assemble into an orientationally ordered stripe phase at low temperature. As the patch size is increased or the temperature is lowered, clusters of patch-connected disks grow, and a percolating cluster emerges at a threshold. In the stripe phase, the critical clusters extend longer in the direction parallel to the stripes than in the perpendicular direction, and percolation is thus anisotropic. It is found that the critical behavior of percolation in the Janus system is consistent with that of standard isotropic percolation, when an appropriate spatial rescaling is made. The rescaling procedure can be applied to understand other anisotropic systems, such as the percolation of aligned rigid rods and of the q-state Potts model with anisotropic interactions.

Percolation transition in phase-separating active fluid

The motility-induced phase separation exhibited by active particles with repulsive interactions is well known. We show that the interaction softness of active particles destabilizes the highly ordered dense phase, leading to the formation of a porous cluster which spans the system. This soft limit can also be achieved if the particle motility is increased beyond a critical value, at which the system clearly exhibits all the characteristics of a standard percolation transition. We also show that in the athermal limit, active particles exhibit similar transitions even at low motility. With these additional new phases, the phase diagram of repulsive active particles is revealed to be richer than what was previously conceived.

Aggregation of self-propelled particles with sensitivity to local order

We study a system of self-propelled particles (SPPs) in which individual particles are allowed to switch between a fast aligning and a slow nonaligning state depending upon the degree of the alignment in the neighborhood. The switching is modeled using a threshold for the local order parameter. This additional attribute gives rise to a mixed phase, in contrast to the ordered phases found in clean SPP systems. As the threshold is increased from zero, we find the sudden appearance of clusters of nonaligners. Clusters of nonaligners coexist with moving clusters of aligners with continual coalescence and fragmentation. The behavior of the system with respect to the clustering of nonaligners appears to be very different for values of low and high global densities. In the low density regime, for an optimal value of the threshold, the largest cluster of nonaligners grows in size up to a maximum that varies logarithmically with the total number of particles. However, on further increasing the threshold the size decreases. In contrast, for the high density regime, an initial abrupt rise is followed by the appearance of a giant cluster of nonaligners. The latter growth can be characterized as a continuous percolation transition. In addition, we find that the speed differences between aligners and nonaligners is necessary for the segregation of aligners and nonaligners.

Phases and homogeneous ordered states in alignment-based self-propelled particle models

We study a set of models of self-propelled particles that achieve collective motion through similar alignment-based dynamics, considering versions with and without repulsive interactions that do not affect the heading directions. We explore their phase space within a broad range of values of two nondimensional parameters (coupling strength and Peclet number), characterizing their polarization and degree of clustering. The resulting phase diagrams display equivalent, similarly distributed regions for all models with repulsion. The diagrams without repulsion exhibit differences, in particular for high coupling strengths. We compare the boundaries and representative states of all regions, identifying various regimes that had not been previously characterized. We analyze in detail three types of homogeneous polarized states, comparing them to existing theoretical and numerical results by computing their velocity and density correlations, giant number fluctuations, and local order-density coupling. We find that they all deviate in one way or another from the theoretical predictions, attributing these differences either to the remaining inhomogeneities or to finite-size effects. We discuss our results in terms of the generic or specific features of each model, their thermodynamic limit, and the high mixing and low mixing regimes. Our study provides a broad, overarching perspective on the multiple phases and states found in alignment-based self-propelled particle models.