Collective Motion Research Articles

Tunable Memory and Activity of Quincke Particles in Micellar Fluid

Memory can remarkably modify the collective behavior of active particles. We show that, in a micellar fluid, Quincke particles driven by a square-wave electric field exhibit a frequency-dependent memory. Upon increasing the frequency, a memory of directions emerges, whereas the activity of particles decreases. As the activity is dominated by interaction, Quincke particles aggregate and form dense clusters, in which the memory of the direction is further enhanced due to the stronger electric interactions. The density-dependent memory and activity result in dynamic heterogeneity in flocking and offer a new opportunity for research of collective motions.

Energetics of collective movement in vertebrates.

The collective directional movement of animals occurs over both short distances and longer migrations, and is a critical aspect of feeding, reproduction and the ecology of many species. Despite the implications of collective motion for lifetime fitness, we know remarkably little about its energetics. It is commonly thought that collective animal motion saves energy: moving alone against fluid flow is expected to be more energetically expensive than moving in a group. Energetic conservation resulting from collective movement is most often inferred from kinematic metrics or from computational models. However, the direct measurement of total metabolic energy savings during collective motion compared with solitary movement over a range of speeds has yet to be documented. In particular, longer duration and higher speed collective motion must involve both aerobic and non-aerobic (high-energy phosphate stores and substrate-level phosphorylation) metabolic energy contributions, and yet no study to date has quantified both types of metabolic contribution in comparison to locomotion by solitary individuals. There are multiple challenging questions regarding the energetics of collective motion in aquatic, aerial and terrestrial environments that remain to be answered. We focus on aquatic locomotion as a model system to demonstrate that understanding the energetics and total cost of collective movement requires the integration of biomechanics, fluid dynamics and bioenergetics to unveil the hydrodynamic and physiological phenomena involved and their underlying mechanisms.

A numerical scheme to solve Fokker–Planck control collective-motion problem

A numerical scheme to solve the optimal control problem, governed by Fokker–Planck (FP) equation, is presented. In particular, a bilinear optimal control framework is considered for the evolution of the probability density function (PDF), corresponding to collective (stochastic) motion. A FP optimality system is described and a Chang–Cooper (CC) discretization scheme is employed on staggered grids to numerically solve this optimality system. This CC scheme preserves non-negativity, conservation and second-order accuracy to the PDF. Analysis of the forward time Chang–Cooper (FT-CC) scheme is provided. For the time discretization, we use the Euler first-order time differencing scheme. Furthermore, a gradient update procedure combined with a projection step is investigated to solve the optimal control problem. Numerical results validate the proposed staggered-grid FT-CC scheme for the proposed control framework in stochastic motion.

Collective foraging of active particles trained by reinforcement learning

Collective self-organization of animal groups is a recurring phenomenon in nature which has attracted a lot of attention in natural and social sciences. To understand how collective motion can be achieved without the presence of an external control, social interactions have been considered which regulate the motion and orientation of neighbors relative to each other. Here, we want to understand the motivation and possible reasons behind the emergence of such interaction rules using an experimental model system of light-responsive active colloidal particles (APs). Via reinforcement learning (RL), the motion of particles is optimized regarding their foraging behavior in presence of randomly appearing food sources. Although RL maximizes the rewards of single APs, we observe the emergence of collective behaviors within the particle group. The advantage of such collective strategy in context of foraging is to compensate lack of local information which strongly increases the robustness of the resulting policy. Our results demonstrate that collective behavior may not only result on the optimization of behaviors on the group level but may also arise from maximizing the benefit of individuals. Apart from a better understanding of collective behaviors in natural systems, these results may also be useful in context of the design of autonomous robotic systems.

Lateral Transport of Domains in Anionic Lipid Bilayer Membranes under DC Electric Fields: A Coarse-Grained Molecular Dynamics Study.

Dynamic lateral transport of lipids, proteins, and self-assembled structures in biomembranes plays a crucial role in diverse cellular processes. In this study, we perform coarse-grained molecular dynamics simulations on a vesicle composed of a binary mixture of neutral and anionic lipids to investigate the lateral transport of individual lipid molecules and the self-assembled lipid domains upon an applied direct current (DC) electric field. Under the potential force of the electric field, a phase-separated domain rich in anionic lipids is trapped in the opposite direction of the electric field. The subsequent reversal of the electric field induces unidirectional domain motion. During the domain motion, the domain size remains constant, but a considerable amount of the anionic lipids is exchanged between the anionic-lipid-rich domain and the surrounding bulk. While the speed of the domain motion (collective lipid motion) shows a significant positive correlation with the electric field strength, the exchange of anionic lipids between the domain and bulk (individual lipid motion) exhibits no clear correlation with the field strength. The mean velocity field of the lipids surrounding the domain displays a two-dimensional (2D) source dipole. We revealed that the balance between the potential force of the applied electric field and the quasi-2D hydrodynamic frictional force well explains the dependence of the domain motions on the electric field strengths. The present results provide insight into the hierarchical dynamic responses of self-assembled lipid domains to the applied electric field and contribute to controlling the lateral transportation of lipids and membrane inclusions.

Shape-driven confluent rigidity transition in curved biological tissues

Collective cell motions underlie structure formation during embryonic development. Tissues exhibit emergent multicellular characteristics such as jamming, rigidity transitions, and glassy dynamics, but there remain questions about how those tissue-scale dynamics derive from local cell-level properties. Specifically, there has been little consideration of the interplay between local tissue geometry and cellular properties influencing larger-scale tissue behaviors. Here, we consider a simple two-dimensional computational vertex model for confluent tissue monolayers, which exhibits a rigidity phase transition controlled by the shape index (ratio of perimeter to square root area) of cells, on surfaces of constant curvature. We show that the critical point for the rigidity transition is a function of curvature such that positively curved systems are likely to be in a less rigid, more fluid, phase. Likewise, negatively curved systems (saddles) are likely to be in a more rigid, less fluid, phase. A phase diagram we generate for the curvature and shape index constitutes a testable prediction from the model. The curvature dependence is interesting because it suggests a natural explanation for more dynamic tissue remodeling and facile growth in regions of higher surface curvature. Conversely, we would predict stability at the base of saddle-shaped budding structures without invoking the need for biochemical or other physical differences. This concept has potential ramifications for our understanding of morphogenesis of budding and branching structures.

Collective motion in hcp-Fe at Earth’s inner core conditions

Earth's inner core is predominantly composed of solid iron (Fe) and displays intriguing properties such as strong shear softening and an ultrahigh Poisson's ratio. Insofar, physical mechanisms to explain these features coherently remain highly debated. Here, we have studied longitudinal and shear wave velocities of hcp-Fe (hexagonal close-packed iron) at relevant pressure-temperature conditions of the inner core using in situ shock experiments and machine learning molecular dynamics (MLMD) simulations. Our results demonstrate that the shear wave velocity of hcp-Fe along the Hugoniot in the premelting condition, defined as T/Tm (Tm: melting temperature of iron) above 0.96, is significantly reduced by ~30%, while Poisson's ratio jumps to approximately 0.44. MLMD simulations at 230 to 330 GPa indicate that collective motion with fast diffusive atomic migration occurs in premelting hcp-Fe primarily along [100] or [010] crystallographic direction, contributing to its elastic softening and enhanced Poisson's ratio. Our study reveals that hcp-Fe atoms can diffusively migrate to neighboring positions, forming open-loop and close-loop clusters in the inner core conditions. Hcp-Fe with collective motion at the inner core conditions is thus not an ideal solid previously believed. The premelting hcp-Fe with collective motion behaves like an extremely soft solid with an ultralow shear modulus and an ultrahigh Poisson's ratio that are consistent with seismic observations of the region. Our findings indicate that premelting hcp-Fe with fast diffusive motion represents the underlying physical mechanism to help explain the unique seismic and geodynamic features of the inner core.

Active Ising Models of flocking: a field-theoretic approach

Using an approach based on Doi-Peliti field theory, we study several different Active Ising Models (AIMs), in each of which collective motion (flocking) of self-propelled particles arises from the spontaneous breaking of a discrete symmetry. We test the predictive power of our field theories by deriving the hydrodynamic equations for the different microscopic choices of aligning processes that define our various models. At deterministic level, the resulting equations largely confirm known results, but our approach has the advantage of allowing systematic generalization to include noise terms. Study of the resulting hydrodynamics allows us to confirm that the various AIMs share the same phenomenology of a first-order transition from isotropic to flocked states whenever the self-propulsion speed is nonzero, with an important exception for the case where particles align only pairwise locally. Remarkably, this variant fails entirely to give flocking—an outcome that was foreseen in previous work, but is confirmed here and explained in terms of the scalings of various terms in the hydrodynamic limit. Finally, we discuss our AIMs in the limit of zero self-propulsion where the ordering transition is continuous. In this limit, each model is still out of equilibrium because the dynamical rules continue to break detailed balance, yet it has been argued that an equilibrium universality class (Model C) prevails. We study field-theoretically the connection between our AIMs and Model C, arguing that these particular models (though not AIMs in general) lie outside the Model C class. We link this to the fact that in our AIMs without self-propulsion, detailed balance is not merely still broken, but replaced by a different dynamical symmetry in which the dynamics of the particle density is independent of the spin state.Graphical .

Recovery of dynamical similarity from lossy representations of collective behavior of midge swarms.

Understanding emergent collective phenomena in biological systems is a complex challenge due to the high dimensionality of state variables and the inability to directly probe agent-based interaction rules. Therefore, if one wants to model a system for which the underpinnings of the collective process are unknown, common approaches such as using mathematical models to validate experimental data may be misguided. Even more so, if one lacks the ability to experimentally measure all the salient state variables that drive the collective phenomena, a modeling approach may not correctly capture the behavior. This problem motivates the need for model-free methods to characterize or classify observed behavior to glean biological insights for meaningful models. Furthermore, such methods must be robust to low dimensional or lossy data, which are often the only feasible measurements for large collectives. In this paper, we show that a model-free and unsupervised clustering of high dimensional swarming behavior in midges (Chironomus riparius), based on dynamical similarity, can be performed using only two-dimensional video data where the animals are not individually tracked. Moreover, the results of the classification are physically meaningful. This work demonstrates that low dimensional video data of collective motion experiments can be equivalently characterized, which has the potential for wide applications to data describing animal group motion acquired in both the laboratory and the field.

The role of hydrodynamics in collective motions of fish schools and bioinspired underwater robots.

Collective behaviour defines the lives of many animal species on the Earth. Underwater swarms span several orders of magnitude in size, from coral larvae and krill to tunas and dolphins. Agent-based algorithms have modelled collective movements of animal groups by use of social forces, which approximate the behaviour of individual animals. But details of how swarming individuals interact with the fluid environment are often under-examined. How do fluid forces shape aquatic swarms? How do fish use their flow-sensing capabilities to coordinate with their schooling mates? We propose viewing underwater collective behaviour from the framework of fluid stigmergy, which considers both physical interactions and information transfer in fluid environments. Understanding the role of hydrodynamics in aquatic collectives requires multi-disciplinary efforts across fluid mechanics, biology and biomimetic robotics. To facilitate future collaborations, we synthesize key studies in these fields.

Dynamics in Nuclei

The nucleus is a complex many-body system with some remarkable emergent collective properties of multiple nucleons acting together. Bohr and Mottelson [1] provided a description of collective motion in nuclei based on geometrical shapes with superimposed oscillations around those shapes. Later, Lie algebras and symmetries were used to describe nuclear dynamics [2], followed by advances in the shell model approach [3] with new effective nucleon-nucleon two- and three-body interactions, and more recently with Hartree-Fock-Bogoliubov approximations within the extended generator coordinate method [4]. Yet, the underlying science question has remained the same. In nuclei, where there is explicit deformation in the ground state, “are the low-lying 0+ states collective vibrations built on the ground state or are they minima of a coexisting shape?” Ref. [4] has shown that for a significant percentage of K = 0+ excitations built on the deformed ground state (g.s.) should, in fact, be a collective vibration. The question has remained open due to sufficiently convincing experimental data with lifetimes, transfer reaction cross sections, and E0 transitions [5]. This paper summarizes the experimental situation regarding the lifetimes of 0+ states.

Generator coordinate method for nuclear octupole excitations: Status and perspectives

Strong octupole correlations have been observed in the low-lying states of atomic nuclei across various mass regions. In this paper, we provide an overview of Beyond Mean-Field (BMF) studies of nuclear octupole collective motions with Generator Coordinate Method (GCM) in combination with quantum-number projections that are implemented to restore the broken symmetries in nuclear mean-field states. We highlight recent developments within this framework and their applications to excitation spectra and electromagnetic transition rates in octupole-shaped nuclei and hypernuclei. We discuss the novel phenomena of nucleon clustering in light nuclei. Additionally, we explore the phase transition from octupole vibrations to rotational motions as spin increases in heavy nuclei. Lastly, we examine the status and future prospects of studies on octupole deformation effects in nuclear Schiff moments. These studies, along with the upper limits of atomic Electric Dipole Moment (EDM), impose stringent constraints on beyond-standard-model time-reversal-violating nucleon–nucleon interactions.

Gaussian process regression for the side-by-side foil pair

The mutual interaction among multiple fish during schooling has significant implication on motion pattern control and hydrodynamic optimization. However, the collective motion of multiple objects in a flow field forms a vast parameter space, causing difficulty in comprehensively analyzing and considering each parameter. To address this issue, the problem is simplified to a foil pair oscillating in a side-by-side configuration in a two-dimensional flow. Moreover, the Gaussian process regression predictive algorithm is combined with the fast and robust boundary data immersion method CFD algorithm to form a iteration loop for value prediction of the large parameter space. Through a relatively small number of simulations (around 1000 data points), we obtained predictions for the entire four-dimensional parameter space that consists of more than 160 000 parameter sets, greatly improving the computational efficiency. After obtaining the predicted space, we analyzed the interactions between different parameters and specially described the mechanism that gives rise to the unique effect of phase difference on the efficiency of the overall system and individual foils.

Fish-inspired robotic algorithm: mimicking behaviour and communication of schooling fish.

This study aims to present a novel flocking algorithm for robotic fish that will aid the study of fish in their natural environment. The algorithm, fish-inspired robotic algorithm (FIRA), amalgamates the standard flocking behaviors of attraction, alignment, and repulsion, together with predator avoidance, foraging, general obstacle avoidance, and wandering. The novelty of the FIRA algorithm is the combination of predictive elements to counteract processing delays from sensors and the addition of memory. Furthermore, FIRA is specifically designed to work with an indirect communication method that leads to superior performance in collision avoidance, exploration, foraging, and the emergence of realistic behaviors. By leveraging a high-latency, non-guaranteed communication methodology inspired by stigmergy methods inherent in nature, FIRA successfully addresses some of the obstacles associated with underwater communication. This breakthrough enables the realization of inexpensive, multi-agent swarms while concurrently harnessing the advantages of tetherless communication. FIRA provides a computational light control algorithm for further research with low-cost, low-computing agents. Eventually, FIRA will be used to assimilate robots into a school of biological fish, to study or influence the school. This study endeavors to demonstrate the effectiveness of FIRA by simulating it using a digital twin of a bio-inspired robotic fish. The simulation incorporates the robot's motion and sensors in a realistic, real-time environment with the algorithm used to direct the movements of individual agents. The performance of FIRA was tested against other collective flocking algorithms to determine its effectiveness. From the experiments, it was determined that FIRA outperformed the other algorithms in both collision avoidance and exploration. These experiments establish FIRA as a viable flocking algorithm to mimic fish behavior in robotics.

Evolution of schooling drives changes in neuroanatomy and motion characteristics across predation contexts in guppies

One of the most spectacular displays of social behavior is the synchronized movements that many animal groups perform to travel, forage and escape from predators. However, elucidating the neural mechanisms underlying the evolution of collective behaviors, as well as their fitness effects, remains challenging. Here, we study collective motion patterns with and without predation threat and predator inspection behavior in guppies experimentally selected for divergence in polarization, an important ecological driver of coordinated movement in fish. We find that groups from artificially selected lines remain more polarized than control groups in the presence of a threat. Neuroanatomical measurements of polarization-selected individuals indicate changes in brain regions previously suggested to be important regulators of perception, fear and attention, and motor response. Additional visual acuity and temporal resolution tests performed in polarization-selected and control individuals indicate that observed differences in predator inspection and schooling behavior should not be attributable to changes in visual perception, but rather are more likely the result of the more efficient relay of sensory input in the brain of polarization-selected fish. Our findings highlight that brain morphology may play a fundamental role in the evolution of coordinated movement and anti-predator behavior.

Microrollers flow uphill as granular media

Pour sand into a container and only the grains near the top surface move. The collective motion associated with the translational and rotational energy of the grains in a thin flowing layer is quickly dissipated as friction through multibody interactions. Alternatively, consider what will happen to a bed of particles if one applies a torque to each individual particle. In this paper, we demonstrate an experimental system where torque is applied at the constituent level through a rotating magnetic field in a dense bed of microrollers. The net result is the grains roll uphill, forming a heap with a negative angle of repose. Two different regimes have been identified related to the degree of mobility or fluidisation of the particles in the bulk. Velocimetry of the near surface flowing layer reveals the collective motion of these responsive particles scales in a similar way to flowing bulk granular flows. A simple granular model that includes cohesion accurately predicts the apparent negative coefficient of friction. In contrast to the response of active or responsive particles that mimic thermodynamic principles, this system results in macroscopic collective behavior that has the kinematics of a purely dissipative granular system.

Synchronization in collectively moving inanimate and living active matter

Whether one considers swarming insects, flocking birds, or bacterial colonies, collective motion arises from the coordination of individuals and entails the adjustment of their respective velocities. In particular, in close confinements, such as those encountered by dense cell populations during development or regeneration, collective migration can only arise coordinately. Yet, how individuals unify their velocities is often not understood. Focusing on a finite number of cells in circular confinements, we identify waves of polymerizing actin that function as a pacemaker governing the speed of individual cells. We show that the onset of collective motion coincides with the synchronization of the wave nucleation frequencies across the population. Employing a simpler and more readily accessible mechanical model system of active spheres, we identify the synchronization of the individuals’ internal oscillators as one of the essential requirements to reach the corresponding collective state. The mechanical ‘toy’ experiment illustrates that the global synchronous state is achieved by nearest neighbor coupling. We suggest by analogy that local coupling and the synchronization of actin waves are essential for the emergent, self-organized motion of cell collectives.

Multi-scale dynamic imaging reveals that cooperative motility behaviors promote efficient predation in bacteria

Many species, such as fish schools or bird flocks, rely on collective motion to forage, prey, or escape predators. Likewise, Myxococcus xanthus forages and moves collectively to prey and feed on other bacterial species. These activities require two distinct motility machines enabling adventurous (A) and social (S) gliding, however when and how these mechanisms are used has remained elusive. Here, we address this long-standing question by applying multiscale semantic cell tracking during predation. We show that: (1) foragers and swarms can comprise A- and S-motile cells, with single cells exchanging frequently between these groups; (2) A-motility is critical to ensure the directional movement of both foragers and swarms; (3) the combined action of A- and S-motile cells within swarms leads to increased predation efficiencies. These results challenge the notion that A- and S-motilities are exclusive to foragers and swarms, and show that these machines act synergistically to enhance predation efficiency.

Nearest Neighbour Node Deployment Algorithm for Mobile Sensor Networks.

Many animal aggregations display remarkable collective coordinated movements on a large scale, which emerge as a result of distributed local decision-making by individuals. The recent advances in modelling the collective motion of animals through the utilisation of Nearest Neighbour rules, without the need for centralised coordination, resulted in the development of self-deployment algorithms in Mobile Sensor Networks (MSNs) to achieve various types of coverage essential for different applications. However, the energy consumption associated with sensor movement to achieve the desired coverage remains a significant concern for the majority of algorithms reported in the literature. In this paper, the Nearest Neighbour Node Deployment (NNND) algorithm is proposed to efficiently provide blanket coverage across a given area while minimising energy consumption and enhancing fault tolerance. In contrast to other algorithms that sequentially move sensors, NNND leverages the power of parallelism by employing multiple streams of sensor motions, each directed towards a distinct section of the area. The cohesion of each stream is maintained by adaptively choosing a leader for each stream while collision avoidance is also ensured. These properties contribute to minimising the travel distance within each stream, resulting in decreased energy consumption. Additionally, the utilisation of multiple leaders in NNND eliminates the presence of a single point of failure, hence enhancing the fault tolerance of the area coverage. The results of our extensive simulation study demonstrate that NNND not only achieves lower energy consumption but also a higher percentage of k-coverage.

Modeling Surface Vibrations and Their Role in Molecular Adsorption: A Generalized Langevin Approach.

The atomic vibrations of a solid surface can play a significant role in the reactions of surface-bound molecules, as well as their adsorption and desorption. Relevant phonon modes can involve the collective motion of atoms over a wide array of length scales. In this paper, we demonstrate how the generalized Langevin equation can be utilized to describe these collective motions weighted by their coupling to individual sites. Our approach builds upon the generalized Langevin oscillator (GLO) model originally developed by Tully. We extend the GLO by deriving parameters from atomistic simulation data. We apply this approach to study the memory kernel of a model platinum surface and demonstrate that the memory kernel has a bimodal form due to coupling to both low-energy acoustic modes and high-energy modes near the Debye frequency. The same bimodal form was observed across a wide variety of solids of different elemental compositions, surface structures, and solvation states. By studying how these dominant modes depend on the simulation size, we argue that the acoustic modes are frozen in the limit of macroscopic lattices. By simulating periodically replicated slabs of various sizes, we quantify the influence of phonon confinement effects in the memory kernel and their concomitant effect on simulated sticking coefficients.