Self-propelled Vicsek particles at low speed and low density

Persistent and responsive collective motion with adaptive time delay

It is beneficial for collective structures to simultaneously have high persistence to environmental noise and high responsivity to nontrivial external stimuli. However, without the ability to differentiate useful information from noise, there is always a tradeoff between persistence and responsivity within the collective structures. To address this, we propose adaptive time delay inspired by the adaptive behavior observed in the school of fish. This strategy is tested using particles powered by optothermal fields coupled with an optical feedback-control system. By applying the adaptive time delay with a proper threshold, we experimentally observe the responsivity of the collective structures enhanced by approximately 1.6 times without sacrificing persistence. Furthermore, we integrate adaptive time delay with long-distance transportation and obstacle-avoidance capabilities to prototype adaptive swarm microrobots. This research demonstrates the potential of adaptive time delay to address the persistence-responsivity tradeoff and lays the foundation for intelligent swarm micro/nanorobots operating in complex environments.

Motional consensus of self-propelled particles

The motional consensus of self-propelled particles is studied in both noise-free cases and cases with noise by the standard Vicsek model. In the absence of noise, we propose a simple method, using grid-based technique and defining the normalized variance of the ratio of the number of particles locally to globally, to quantitatively study the movement pattern of the system by the spatial distribution of the particles and the degree of aggregation of particles. It is found that the weaker correlation of velocity leads to larger degree of aggregation of the particles. In the cases with noise, we quantify the competition between velocity alignment and noise by considering the difference of the variety of order parameter result from the velocity alignment and noise. The variation of the effect of noise on motional consensus is non-monotonic for the change of the probability distribution of noise from uniform to non-uniform. Our results may be useful and encourage further efforts in exploring the basic principles of collective motion.

Modeling three-dimensional bait ball collective motion

Collective motion of animal groups such as fish schools and bird flocks in three-dimensional (3D) space are modeled by considering a topological (Voronoi) neighborhood. The tridimensionality of the group is quantified. Apart from the patterns of swarming, schooling, and milling, we identify a 3D bait ball around the phase transition boundary. More significantly, we find that by considering a blind angle in this topology based model, an individual interacts statistically with six to seven neighbors, consistent precisely with the previous field observations of the starling flocks. This model could be expected to enable more insightful investigation on realistic collective motion of shoals or flocks.

Short-time dynamics in active systems: the Vicsek model

We study the short-time dynamics (STD) of the Vicsek model (VM) with vector noise. The study of STD has proved to be very useful in the determination of the critical point, critical exponents and spinodal points in equilibrium phase transitions. Here we aim is to test its applicability in active systems. We find that, despite the essential non-equilibrium characteristics of the VM (absence of detailed balance, activity), the STD presents qualitatively the same phenomenology as in equilibrium systems. From the STD one can distinguish whether the transition is continuous or discontinuous (which we have checked also computing the Binder cumulant). When the transition is continuous, one can determine the critical point and the critical exponents.

Noisy multistate voter model for flocking in finite dimensions

We study a model for the collective behavior of self-propelled particles subject to pairwise copying interactions and noise. Particles move at a constant speed v on a two-dimensional space and, in a single step of the dynamics, each particle adopts the direction of motion of a randomly chosen neighboring particle within a distance R=1, with the addition of a perturbation of amplitude η (noise). We investigate how the global level of particles' alignment (order) is affected by their motion and the noise amplitude η. In the static case scenario v=0 where particles are fixed at the sites of a square lattice and interact with their first neighbors, we find that for any noise η>0 the system reaches a steady state of complete disorder in the thermodynamic limit, while for η=0 full order is eventually achieved for a system with any number of particles N. Therefore, the model displays a transition at zero noise when particles are static, and thus there are no ordered steady states for a finite noise (η>0). We show that the finite-size transition noise vanishes with N as η_{c}^{1D}∼N^{-1} and η_{c}^{2D}∼(NlnN)^{-1/2} in one- and two-dimensional lattices, respectively, which is linked to known results on the behavior of a type of noisy voter model for catalytic reactions. When particles are allowed to move in the space at a finite speed v>0, an ordered phase emerges, characterized by a fraction of particles moving in a similar direction. The system exhibits an order-disorder phase transition at a noise amplitude η_{c}>0 that is proportional to v, and that scales approximately as η_{c}∼v(-lnv)^{-1/2} for v≪1. These results show that the motion of particles is able to sustain a state of global order in a system with voter-like interactions.