Velocity Alignment Research Articles

Emergent behaviors of two thermodynamically consistent inertial spin models

We propose two thermodynamically consistent inertial spin models generalizing the inertial spin model for the ensemble of mechanical particles with spin. For the collective dynamics modeling consistent with an entropy principle, we use two modeling ideas based on Hamiltonian formulation and flocking formalism for the coupling of the inertial spin model and temperatures introduced by Ha and Ruggeri [Arch. Ration. Mech. Anal. 223, 1397 (2017)]. The resulting models admit several constants of motions and are consistent with the entropy principle. We present several sufficient frameworks leading to the asymptotic vanishing of spins and velocity alignment. We also implement several numerical simulations and compare them with analytical results.

Emergent behaviors of relativistic flocks with adaptive coupling laws

In this paper, we investigate the emergent behaviors of the relativistic Cucker–Smale (RCS) model equipped with adaptive couplings. To do this, we first divide adaptive couplings into two types, Hebbian or anti-Hebbian. For the Hebbian case, we demonstrate the asymptotic flocking of the RCS model in two ways based on the Lyapunov functional approach and continuous argument. Meanwhile, for the anti-Hebbian case, depending on the regularity of the adaptive law at the origin, we prove the various emergent behaviors such as the slow velocity alignment or the group formation.

Rigid Formation Control on a Sphere: A Heterogeneous System Approach.

We consider a heterogeneous multiagent system for tracking multiple targets with a rigid formation on a unit sphere, where the targets and chasing agents are governed by single- and double-integrator models, respectively. To make asymptotic rendezvous between agents and their corresponding targets, we use an autonomous system consisting of attraction forces and velocity alignments. If the target's position, velocity, and acceleration information are available, we derive a multiagent system for complete rendezvous and obtain its exponential convergence result. If we have only the location and velocity information of the targets, we provide an autonomous system for practical rendezvous and the corresponding mathematical analysis. To prove the main results, we employ frame-rotation-structure decomposition for the double-integrator model and the geometric properties of a rigid formation on a sphere. We also provide numerical simulations to confirm our mathematical results and apply them to multiagent dynamics with a rigid formation that patrols the boundary line for a certain area on the sphere.

Global well-posedness and asymptotic behavior for the Euler-alignment system with pressure

We study the Cauchy problem of the compressible Euler system with strongly singular velocity alignment. We establish a global well-posedness theory for the system with small smooth initial data. Additionally, we derive asymptotic emergent behaviors for the system, providing time decay estimates with optimal decay rates. Notably, the optimal decay rate we obtain does not align with the corresponding fractional heat equation within our considered range, where the parameter α∈(0,1). This highlights the distinct feature of the alignment operator.

Aerodynamic and production comparison of wind farms with downwind versus conventional upwind turbines

Ever-increasing turbine scales and their associated logistical challenges have reignited questions about the performance of downwind rotor configurations. A particular potential benefit of downwind rotor configurations is the farm-scale power increase that may be conferred by tilt-driven downward wake entrainment and associated wake recovery. In this work, a comprehensive aerodynamic analysis is carried out to understand the mechanisms for wake entrainment and recovery across a spectrum of velocity and inflow alignment conditions on a small, structured farm in order to understand the impact of downwind rotors on farm production. The results show that the benefits demonstrated previously in the literature for downwind-rotor farms in aligned flows are fragile, and, outside of strong farm/flow alignment conditions, power production benefits for small farms with downwind rotor configurations are significantly if not completely mitigated by misalignment effects. The work indicates that farm-scale benefits for downwind rotors must be realized either from large-scale entrainment benefits, with more exotic farm arrangements that can take advantage of the aerodynamic effects, or from beneficial fatigue impacts from entrainment of less turbulent outer boundary layer flows.

Asymptotic stability of rarefaction wave for compressible Euler system with velocity alignment

In this paper, we study the asymptotic stability of the rarefaction wave for the one-dimensional compressible Euler system with nonlocal velocity alignment. Namely, for the initial data approaching to rarefaction wave, we prove the corresponding solution converges toward the rarefaction wave. Moreover, we obtain this system has weak alignment behavior. We develop some promoted estimates for the smooth approximate rarefaction wave and new a priori estimates by Fourier analysis tools. Moreover, we introduce the weighted energy method and Besov spaces to obtain the key high-order derivative estimates, in which we overcome the difficulties caused by the nonlocal velocity alignment. It is worth mentioning that this is the first stability result of rarefaction wave for compressible Euler system with velocity alignment.

Navigating Open Set Scenarios for Skeleton-Based Action Recognition

In real-world scenarios, human actions often fall outside the distribution of training data, making it crucial for models to recognize known actions and reject unknown ones. However, using pure skeleton data in such open-set conditions poses challenges due to the lack of visual background cues and the distinct sparse structure of body pose sequences. In this paper, we tackle the unexplored Open-Set Skeleton-based Action Recognition (OS-SAR) task and formalize the benchmark on three skeleton-based datasets. We assess the performance of seven established open-set approaches on our task and identify their limits and critical generalization issues when dealing with skeleton information.To address these challenges, we propose a distance-based cross-modality ensemble method that leverages the cross-modal alignment of skeleton joints, bones, and velocities to achieve superior open-set recognition performance. We refer to the key idea as CrossMax - an approach that utilizes a novel cross-modality mean max discrepancy suppression mechanism to align latent spaces during training and a cross-modality distance-based logits refinement method during testing. CrossMax outperforms existing approaches and consistently yields state-of-the-art results across all datasets and backbones. We will release the benchmark, code, and models to the community.

Local well‐posedness of classical solutions for the kinetic self‐organized model of Cucker–Smale type

We study in this paper the local well‐posedness of classical solutions to the Cauchy problem for a kinetic self‐organized model of Cucker–Smale type for collective motions, which includes two cases of velocity alignment mechanisms: normalized and nonnormalized reorientation cases. The main concern is the a priori estimates for both cases. Our treatments rely on two key ingredients: One point is to deal with the possible singularity and high nonlinearity arising from the normalized/nonnormalized mean velocity, and the other is to control the growth with respect to the microscopic velocity variable in the whole space by employing weighted estimates.

Data-driven model selections of second-order particle dynamics via integrating Gaussian processes with low-dimensional interacting structures

In this paper, we focus on the data-driven discovery of a general second-order particle-based model that contains many state-of-the-art models for modeling the aggregation and collective behavior of interacting agents of similar size and body type. This model takes the form of a high-dimensional system of ordinary differential equations parameterized by two interaction kernels that appraise the alignment of positions and velocities. We propose a Gaussian Process-based approach to this problem, where the unknown model parameters are marginalized by using two independent Gaussian Process (GP) priors on latent interaction kernels constrained to dynamics and observational data. This results in a nonparametric model for interacting dynamical systems that accounts for uncertainty quantification. We also show that our estimators can be efficiently derived through the use of preconditioned techniques, ensuring scalability. Moreover, we perform a theoretical analysis to interpret the methodology and investigate the conditions under which the kernels can be recovered. We demonstrate the effectiveness of the proposed approach on various prototype systems, including the selection of the order of the systems and the types of interactions. In particular, we present applications to modeling two real-world fish motion datasets that display flocking and milling patterns up to 248 dimensions. Despite the use of small datasets, the GP-based approach learns an effective representation of the nonlinear dynamics in these spaces and outperforms competitor methods.

Collective behavior of self-steering active particles with velocity alignment and visual perception

The formation and dynamics of swarms is widespread in living systems, from bacterial biofilms to schools of fish and flocks of birds. We study this emergent collective behavior via agent-based simulations in a model of active Brownian particles with visual-perception-based steering and alignment interactions. The dynamics, shape, and internal structure of the emergent aggregates, clusters, and swarms of these intelligent active Brownian particles are determined by the maneuverabilities Ωv and Ωa, quantifying the steering based on the visual signal and polar alignment, respectively, the propulsion velocity, characterized by the Péclet number Pe, the vision angle θ, and the orientational noise. Various nonequilibrium dynamical aggregates—like motile wormlike swarms and milling, and close-packed or dispersed clusters—are obtained. Small vision angles imply the formation of small clusters, while large vision angles lead to more complex clusters. In particular, a strong polar-alignment maneuverability Ωa favors elongated wormlike swarms, which display superdiffusive motion over a much longer time range than individual ABPs, whereas a strong vision-based maneuverability Ωv favors compact, nearly immobile aggregates. Swarm trajectories show long persistent directed motion, interrupted by sharp turns. Milling rings, where a wormlike swarm bites its own tail, emerge for an intermediate regime of Pe and vision angles. Our results offer insights into the behavior of animal swarms and provide design criteria for swarming microbots. Published by the American Physical Society 2024

Global well-posedness and asymptotic behavior in critical spaces for the compressible Euler system with velocity alignment

In this paper, we study the Cauchy problem of the compressible Euler system with strongly singular velocity alignment. We prove the existence and uniqueness of global solutions in critical Besov spaces to the considered system with small initial data. The local-in-time solvability is also addressed. Moreover, we show the large-time asymptotic behaviour and optimal decay estimates of the solutions as .

Flocking Behaviors of a Body Attitude Coordination Model with Velocity Alignment

Flocking Behaviors of a Body Attitude Coordination Model with Velocity Alignment

Particle-wall alignment interaction and active Brownian diffusion through narrow channels.

We numerically examine the impacts of particle-wall alignment interactions on active species diffusion through a structureless narrow two-dimensional channel. We consider particle-wall interaction to depend on the self-propulsion velocity direction whereby some specific particle's alignments with respect to the boundary walls are stabilized more. Further, the alignment interaction is meaningful as long as particles are close to the confining boundaries. Unbiased diffusion of active particles for various possible stable velocity alignments against the walls has been examined. We show that for the most stable configuration leading to the self-propulsion velocity direction perpendicular to the wall, diffusivity becomes inversely proportional to the square of the alignment interaction torque. On the other hand, when the self-propulsion velocity direction making an acute angle to the channel walls is the most stable configuration, diffusion exponentially grows with strengthening alignment interaction. Hence, particle-wall interaction plays a pivotal role in the transport control of active particles through narrow channels. Moreover, the impacts of the alignment interactions on diffusion largely depend on the particle's self-propulsion properties and its chirality. Our simulation results can potentially be used to understand unbiased diffusion of artificial or living micro/nano-objects (such as virus, bacteria, Janus particles, etc.) though narrow confined structures.

Synchronous and Fully Steerable Active Particle Systems for Enhanced Mimicking of Collective Motion in Nature.

The collective motion observed in living active matter, such as fish schools and bird flocks, is characterized by its dynamic and complex nature, involving various moving states and transitions. By tailoring physical interactions or incorporating information exchange capabilities, inanimate active particles can exhibit similar behavior. However, the lack of synchronous and arbitrary control over individual particles hinders their use as a test system for the study of more intricate collective motions in living species. Herein, a novel optical feedback control system that enables the mimicry of collective motion observed in living objects using active particles is proposed. This system allows for the experimental investigation of the velocity alignment, a seminal model of collective motion (known as the Vicsek model), in a microscale perturbed environment with controllable and realistic conditions. The spontaneous formation of different moving states and dynamic transitions between these states is observed. Additionally, the high robustness of the active-particle group at the critical density under the influence of different perturbations is quantitatively validated. These findings support the effectiveness of velocity alignment in real perturbed environments, thereby providing a versatile platform for fundamental studies on collective motion and the development of innovative swarm microrobotics.

Artificial patterns in spatially discrete models of cell migration and how to mitigate them

Several discrete models for diffusive motion are known to exhibit checkerboard artifacts, absent in their continuous analogues. We study the origins of the checkerboard artifact in the discrete heat equation and show that this artifact decays exponentially in time when following either of two strategies: considering the present state of each lattice site to determine its own future state (self-contributions), or using non-square lattice geometries. Afterwards, we examine the effects of these strategies on nonlinear models of biological cell migration with two kinds of cell-cell interactions: adhesive and polar velocity alignment. In the case of adhesive interaction, we show that growing modes related to pattern formation overshadow artifacts in the long run; nonetheless, artifacts can still be completely prevented following the same strategies as in the discrete heat equation. On the other hand, for polar velocity alignment we show that artifacts are not only strengthened, but also that new artifacts can arise in this model which were not observed in the previous models. We find that the lattice geometry strategy works well to alleviate artifacts. However, the self-contribution strategy must be applied more carefully: lattice sites should contribute to both their own density and velocity values, and their own velocity contribution should be high enough. With this work, we show that these two strategies are effective for preventing artifacts in spatial models based on the discrete continuity equation.

Vectorial active matter on the lattice: polar condensates and nematic filaments

We introduce a novel lattice-gas cellular automaton (LGCA) for compressible vectorial active matter with polar and nematic velocity alignment. Interactions are, by construction, zero-range. For polar alignment, we show the system undergoes a phase transition that promotes aggregation with strong resemblance to the classic zero-range process. We find that above a critical point, the states of a macroscopic fraction of the particles in the system coalesce into the same state, sharing the same position and momentum (polar condensate). For nematic alignment, the system also exhibits condensation, but there exist fundamental differences: a macroscopic fraction of the particles in the system collapses into a filament, where particles possess only two possible momenta. Furthermore, we derive hydrodynamic equations for the active LGCA model to understand the phase transitions and condensation that undergoes the system. We also show that generically the discrete lattice symmetries—e.g. of a square or hexagonal lattice—affect drastically the emergent large-scale properties of on-lattice active systems. The study puts in evidence that aligning active matter on the lattice displays new behavior, including phase transitions to states that share similarities to condensation models.

An Alignment-Free Explanation for Collective Predator Evasion in Moving Animal Groups

Moving animal groups consist of many distinct individuals but can operate and function as one unit when performing different tasks. Effectively evading unexpected predator attacks is one primary task for many moving groups. The current explanation for predator evasion responses in moving animal groups require the individuals in the groups to interact via (velocity) alignment. However, experiments have shown that some animals do not use alignment. This suggests that another explanation for the predator evasion capacity in at least these species is needed. Here we establish that effective collective predator evasion does not require alignment, it can be induced via attraction and repulsion alone. We also show that speed differences between individuals that have directly observed the predator and those that have not influence evasion success and the speed of the collective evasion process, but are not required to induce the phenomenon. Our work here adds collective predator evasion to a number of phenomena previously thought to require alignment interactions that have recently been shown to emerge from attraction and repulsion alone. Based on our findings we suggest experiments and make predictions that may lead to a deeper understanding of not only collective predator evasion but also collective motion in general.

Collective behavior of self-propelled particles with heading estimation via focal observation

Animals, including humans, often achieve velocity alignment by observing their neighbors from their own perspective rather than form a bird’s-eye view. In this study, we explore a particular implementation of this idea, where particles estimate the heading of their neighbors based on their own focal view observations, thereby achieving velocity alignment. Two types of observations are used to estimate the heading of neighbors in this study: the relative position of neighbors at two adjacent moments, and the movement of the focal particle itself. Simulation results show that noise amplitude η arising during observations and the weight parameter s denoting the ratio of noise contained in the two types of observations can induce continuous order–disorder phase transition. The probability density distribution of the noise contained in different models is statistically analyzed, and results show that the type of phase transition mainly depends on the variance of the noise. Furthermore, an optimal value of s is found in our model that makes the model tolerate large noise amplitude. Our findings suggest that the focal view observation plays an important role in collective motion.

Asymptotic behaviors for the compressible Euler system with nonlinear velocity alignment

We consider the compressible Euler system with a family of nonlinear velocity alignments. The system is a nonlinear extension of the Euler-alignment system in collective dynamics. We show the asymptotic emergent phenomena of the system: alignment and flocking. Different types of nonlinearity and nonlocal communication protocols are investigated, resulting in a variety of different asymptotic behaviors.

On some collinear configurations in the planar three-body problem

In this paper, we further investigate the planar Newtonian three-body problem with a focus on collinear configurations, where either the three bodies or their velocities are aligned. We provide an independent proof of Montgomery’s result (Montgomery 2007 Ergod. Theory Dyn. Syst. 27 311–40), stating that apart from the Lagrange’s solution, all negative energy solutions to the zero angular momentum case result in syzygies, i.e. collinear configurations of positions. The concept of generalised syzygies, inclusive of velocity alignments, was previously explored by the author for bounded solutions in Tsygvintsev (2023 C. R. Acad. Sci., Paris 361 331–5). In this study, we broaden our scope to encompass negative energy cases and provide new bounds. Our methodology builds upon the elementary Sturm–Liouville theory and the Wintner-Conley ‘linear’ form of the three-body problem, as previously explored in the works of Albouy and Chenciner (1997 Invent. Math. 131 151–84); Albouy (2004 Mutual Distances in Celestial Mechanics (Lectures at Nankai Institute)); Chenciner (2013 Acta Math. Vietnam. 38 165–86).