Emergent Collective Behavior Research Articles

On-Demand Breaking of Action-Reaction Reciprocity between Magnetic Microdisks Using Global Stimuli.

Coupled physical interactions induce emergent collective behaviors of many interacting objects. Nonreciprocity in the interactions generates unexpected behaviors. There is a lack of experimental model system that switches between the reciprocal and nonreciprocal regime on demand. Here, we study a system of magnetic microdisks that breaks action-reaction reciprocity via fluid-mediated hydrodynamic interactions, on demand. Via experiments and simulations, we demonstrate that nonreciprocal interactions generate self-propulsion-like behaviors of a pair of disks; group separation in collective of magnetically nonidentical disks; and decouples a part of the group from the rest. Our results could help in developing controllable microrobot collectives. Our approach highlights the effect of global stimuli in generating nonreciprocal interactions.

Micro/Nanorobotic Swarms: From Fundamentals to Functionalities.

Swarms, which stem from collective behaviors among individual elements, are commonly seen in nature. Since two decades ago, scientists have been attempting to understand the principles of natural swarms and leverage them for creating artificial swarms. To date, the underlying physics; techniques for actuation, navigation, and control; field-generation systems; and a research community are now in place. This Review reviews the fundamental principles and applications of micro/nanorobotic swarms. The generation mechanisms of the emergent collective behaviors among the micro/nanoagents identified over the past two decades are elucidated. The advantages and drawbacks of different techniques, existing control systems, major challenges, and potential prospects of micro/nanorobotic swarms are discussed.

Magnetic Quincke rollers with tunable single-particle dynamics and collective states.

Electrohydrodynamically driven active particles based on Quincke rotation have quickly become an important model system for emergent collective behavior in nonequilibrium colloidal systems. Like most active particles, Quincke rollers are intrinsically nonmagnetic, preventing the use of magnetic fields to control their complex dynamics on the fly. Here, we report on magnetic Quincke rollers based on silica particles doped with superparamagnetic iron oxide nanoparticles. We show that their magnetic nature enables the application of both externally controllable forces and torques at high spatial and temporal precision, leading to several versatile control mechanisms for their single-particle dynamics and collective states. These include tunable interparticle interactions, potential energy landscapes, and advanced programmable and teleoperated behaviors, allowing us to discover and probe active chaining, anisotropic active sedimentation-diffusion equilibria, and collective states in various geometries and dimensionalities.

Characterization of bird formations using fuzzy modelling.

The investigation of the emergent collective behaviour in flying birds is a challenging task, yet it has always fascinated scientists from different disciplines. In the attempt of studying and modelling line formation, we collected high-precision position data of 29 free-flying northern bald ibises (Geronticus eremita) using Global Navigation Satellite System loggers, to investigate whether the spatial relationships within a flock can be explained by birds maintaining energetically advantageous positions. Specifically, we exploited domain knowledge and available literature information to model by means of fuzzy logic where the air vortices lie behind a flying bird. This allowed us to determine when a leading bird provides the upwash to a following bird, reducing its overall effort. Our results show that the fuzzy model allows to easily distinguish which bird is flying in the wake of another individual, provides a clear indication about flying flock dynamics and also gives a hint about birds' social relationships.

Microbial biofilms are shaped by the constant dialogue between biological and physical forces in the extracellular matrix.

Microbial biofilms are shaped by the constant dialogue between biological and physical forces in the extracellular matrix.

Synchronization in the network-frustrated coupled oscillator with attractive-repulsive frequencies.

We investigate the synchronization behavior of a generalized useful mode of the emergent collective behavior in sets of interacting dynamic elements. The network-frustrated Kuramoto model with interaction-repulsion frequency characteristics is presented, and its structural features are crucial to capture the correct physical behavior, such as describing steady states and phase transitions. Quantifying the effect of small-world phenomena on the global synchronization of the given network, the impact of the random phase-shift and their mutual behavior shows particular challenges. In this paper, we derive the phase-locked states and identify the significant synchronization transition points analytically with exact boundary conditions for the correlated and uncorrelated degree-frequency distributions and their full stability analysis. We find that a supercritical to subcritical bifurcation transition occurs depending on the synchronic transition points, characterized by the power scale of the network for the correlated degree frequency and the largest eigenvalue of the network in the uncorrelated case. Furthermore, our frustrated degree-frequency distribution brings us to the classical Kuramoto model with all-to-all coupling, with β=1/2 for the correlated case and λ_{N}=1 for the uncorrelated distribution. In addition, the interplay between the network topology and the frustration forms a powerful alliance, where they control the synchronization ability of the generalized model without affecting its stability.

Emergent quantum correlations and collective behavior in noninteracting quantum systems subject to stochastic resetting

We investigate the dynamics of a non-interacting spin system, undergoing coherent Rabi oscillations, in the presence of stochastic resetting. We show that resetting generally induces long-range quantum and classical correlations both in the emergent dissipative dynamics and in the non-equilibrium stationary state. Moreover, for the case of conditional reset protocols -- where the system is reinitialized to a state dependent on the outcome of a preceding measurement -- we show that, in the thermodynamic limit, the spin system can feature collective behavior which results in a phenomenology reminiscent of that occurring in non-equilibrium phase transitions. The discussed reset protocols can be implemented on quantum simulators and quantum devices that permit fast measurement and readout of macroscopic observables, such as the magnetisation. Our approach does not require the control of coherent interactions and may therefore highlight a route towards a simple and robust creation of quantum correlations and collective non-equilibrium states, with potential applications in quantum enhanced metrology and sensing.

Metastable discrete time-crystal resonances in a dissipative central spin system

We consider the non-equilibrium behavior of a central spin system where the central spin is periodically reset to its ground state. The quantum mechanical evolution under this effectively dissipative dynamics is described by a discrete-time quantum map. Despite its simplicity this problem shows surprisingly complex dynamical features. In particular, we identify several metastable time-crystal resonances. Here the system does not relax rapidly to a stationary state but undergoes long-lived oscillations with a period that is an integer multiple of the reset period. At these resonances the evolution becomes restricted to a low-dimensional state space within which the system undergoes a periodic motion. Generalizing the theory of metastability in open quantum systems, we develop an effective description for the evolution within this long-lived metastable subspace and show that in the long-time limit a non-equilibrium stationary state is approached. Our study links to timely questions concerning emergent collective behavior in the 'prethermal' stage of a dissipative quantum many-body evolution and may establish an intriguing link to the phenomenon of quantum synchronization.

Self-organized bistability on scale-free networks

A dynamical system approaching the first-order transition can exhibit a specific type of critical behavior known as self-organized bistability (SOB). It lies in the fact that the system can permanently switch between the coexisting states under the self-tuning of a control parameter. Many of these systems have a network organization that should be taken into account to understand the underlying processes in detail. In the present paper, we theoretically explore an extension of the SOB concept on the scale-free network under coupling constraints. As provided by the numerical simulations and mean-field approximation in the thermodynamic limit, SOB on scale-free networks originates from facilitated criticality reflected on both macro- and mesoscopic network scales. We establish that the appearance of switches is rooted in spatial self-organization and temporal self-similarity of the network's critical dynamics and replicates extreme properties of epileptic seizure recurrences. Our results, thus, indicate that the proposed conceptual model is suitable to deepen the understanding of emergent collective behavior behind neurological diseases.

Selective and collective actuation in active solids

Active solids consist of elastically coupled out-of-equilibrium units performing work. They are central to autonomous processes, such as locomotion, self-oscillations and rectification, in biological systems,designer materials and robotics. Yet, the feedback mechanism between elastic and active forces, and the possible emergence of collective behaviours in a mechanically stable elastic solid remains elusive. Here we introduce a minimal realization of an active elastic solid, in which we characterize the emergence of selective and collective actuation and fully map out the interplay between activity, elasticity and geometry. Polar active agents exert forces on the nodes of a two dimensional elastic lattice. The resulting displacement field nonlinearly reorients the active agents. For large enough coupling, a collective oscillation of the lattice nodes around their equilibrium position emerges. Only a few elastic modes are actuated and, crucially, they are not necessarily the lowest energy ones. Combining experiments with the numerical and theoretical analysis of an agents model, we unveil the bifurcation scenario and the selection mechanism by which the collective actuation takes place. Our findings may provide a new mechanism for oscillatory dynamics in biological tissues and specifically confluent cell monolayers. The present selection mechanism may also be advantageous in providing meta-materials, with bona fide autonomy.

Synchronization in phase-coupled oscillator with attractive–repulsive frequencies

We investigate the synchronization behavior of a simple but quite useful mode of emergent collective behavior in ensembles of interacting dynamical elements, the Kuramoto model with attractive–repulsive frequencies features. Here, we derive a series of phase-locked (PL) states and identify the significant synchronization transition points analytically with exact boundary conditions. A detailed stability study of the model is also presented, as well as the bifurcation of the PL states set. Extremely, we show that these frequencies do not influence the stability of the system model, while the synchronization ability is considerably changed.

Crystallizing Kagome Artificial Spin Ice.

Artificial spin ices are engineered arrays of dipolarly coupled nanobar magnets. They enable direct investigations of fascinating collective phenomena from their diverse microstates. However, experimental access to ground states in the geometrically frustrated systems has proven difficult, limiting studies and applications of novel properties and functionalities from the low energy states. Here, we introduce a convenient approach to control the competing diploar interactions between the neighboring nanomagnets, allowing us to tailor the vertex degeneracy of the ground states. We achieve this by tuning the length of selected nanobar magnets in the spin ice lattice. We demonstrate the effectiveness of our method by realizing multiple low energy microstates in a kagome artificial spin ice, particularly the hardly accessible long range ordered ground state-the spin crystal state. Our strategy can be directly applied to other artificial spin systems to achieve exotic phases and explore new emergent collective behaviors.

Explosive behaviors on coupled fractional-order system

Fractional derivatives provide a prominent platform for various chemical and physical system with memory and hereditary properties, while most of the previous differential systems used to describe dynamic phenomena including oscillation quenching are integer order. Here, effects of fractional derivative on the transition process from oscillatory state to stationary state are illustrated for the first time on mean-filed coupled oscillators. It is found the fractional derivative could induce the emergence of a first-order discrete transition with hysteresis between oscillatory and stationary state. However, if the fractional derivative is smaller than the critical value, the transition will be invertible. Besides, the theoretical conditions for the steady state are calculated via Lyapunov indirect method which probe that, the backward transition point is unrelated to mean-field density. Our result is a step forward in enlightening the control mechanism of explosive phenomenon, which is of great importance to highlight the function of fractional-order derivative in the emergence of collective behaviors on coupled nonlinear model.

A mathematical model for inter‐specific interactions in seagrasses

Seagrasses are vital organisms in coastal waters, and the drastic demise of their population in the last decades has worrying implications for marine ecosystems. Spatial models for seagrass meadows provide a mathematical framework to study their dynamical processes and emergent collective behavior. These models are crucial to predict the response of seagrasses to different global warming scenarios, analyze the resilience of existing seagrass distributions, and optimize restoration strategies. In this article, we propose a model that includes interactions among different species based on the clonal growth of seagrasses. We present a theoretical analysis of the model considering the specific case of the seagrass–seaweed interaction between Cymodocea nodosa and Caulerpa prolifera. Our simulations successfully reproduce field observations of shoot densities in mixed meadows in the Ebro River Delta in the Mediterranean Sea. Besides, the proposed model allows us to investigate the possible underlying mechanisms that mediate the interaction among the two macrophytes.

From Modelling Turbulence to General Systems Modelling

Complex adaptive and evolutionary systems can, at least in principle, be modelled in ways that are similar to modelling of complex mechanical (or physical) systems. While quantitative modelling of turbulent reacting flows has been developed over many decades due to availability of experimental data, modelling of complex evolutionary systems is still in its infancy and has huge potential for further development. This work analyses recent trends, points to the similarity of modelling approaches used in seemingly different areas, and suggests a basic classification for such approaches. Availability of data in the modern computerised world allows us to use tools previously developed in physics and applied mathematics in new domains of scientific inquiry that previously were not amendable by quantitative evaluation and modelling, while raising concerns about the associated ethical and legal issues. While the utility of big data has been repeatedly demonstrated in various practical applications, these applications, as far as we can judge, do not involve the scientific goal of conceptual modelling of emergent collective behaviour in complex evolutionary systems.

Synchronization with prescribed transient behavior: Heterogeneous multi-agent systems under funnel coupling

In this paper, we introduce a nonlinear time-varying coupling law, which can be designed in a fully decentralized manner and achieves approximate synchronization with arbitrary precision, under only mild assumptions on the individual vector fields and the underlying (undirected) graph structure. The proposed coupling law is motivated by the so-called funnel control method studied in adaptive control under the observation that arbitrary precision synchronization can be achieved for heterogeneous multi-agent systems by a high-gain coupling; consequently we call our novel synchronization method ‘(node-wise) funnel coupling.’ By adjusting the conventional proof technique in the funnel control study, we are even able to obtain asymptotic synchronization with the same funnel coupling law. Moreover, the emergent collective behavior that arises for a heterogeneous multi-agent system when enforcing arbitrary precision synchronization by the proposed funnel coupling law, is analyzed in this paper. In particular, we introduce a single scalar dynamics called ‘emergent dynamics’ which describes the emergent synchronized behavior of the multi-agent system under funnel coupling. Characterization of the emergent dynamics is important because, for instance, one can design the emergent dynamics first such that the solution trajectory behaves as desired, and then, provide a design guideline to each agent so that the constructed vector fields yield the desired emergent dynamics. We illustrate this idea via the example of a distributed median solver based on funnel coupling.

Swarmalators under competitive time-varying phase interactions

Swarmalators are entities with the simultaneous presence of swarming and synchronization that reveal emergent collective behavior due to the fascinating bidirectional interplay between phase and spatial dynamics. Although different coupling topologies have already been considered, here we introduce time-varying competitive phase interaction among swarmalators where the underlying connectivity for attractive and repulsive coupling varies depending on the vision (sensing) radius. Apart from investigating some fundamental properties like conservation of center of position and collision avoidance, we also scrutinize the cases of extreme limits of vision radius. The concurrence of attractive–repulsive competitive phase coupling allows the exploration of diverse asymptotic states, like static π, and mixed phase wave states, and we explore the feasible routes of those states through a detailed numerical analysis. In sole presence of attractive local coupling, we reveal the occurrence of static cluster synchronization where the number of clusters depends crucially on the initial distribution of positions and phases of each swarmalator. In addition, we analytically calculate the sufficient condition for the emergence of the static synchronization state. We further report the appearance of the static ring phase wave state and evaluate its radius theoretically. Finally, we validate our findings using Stuart–Landau oscillators to describe the phase dynamics of swarmalators subject to attractive local coupling.

Will sailing in formation reduce energy consumption? Numerical prediction of resistance for ships in different formation configurations

In nature, emergent collective behaviors suggest that the followers would obtain energy benefit from positive interaction with the leader’s wake by certain configurations. This article answers the question about the motivation of formation control research -- “will sailing in formation reduce energy consumption”. We carried out a series of numerical analyses on the relationship between resistance and formation configurations using the Reynolds Averaged Navier-Stokes (RANS) method in combination with the Shear Stress Transport (SST) k-ω turbulence model. At the first stage, verification and four-separate-distance benchmark cases are conducted to test grid discretization and numerical methods. Then, parametric studies are performed at various longitudinal offsets and transverse separations in tandem, parallel, and triangle formations. The numerical results indicate that specific formation configurations could bring resistance reduction and achieve energy benefit from the perspective of the whole convoy and the individual ship. Discussions on the resistance, energy consumption, and formation configuration are provided, respectively. Five energy consumption regions are established based on the resistance variations under different formation configurations. In terms of energy preservation, tandem formation is the optimal fleet configuration, followed by the triangle and parallel formation. Besides, for better maneuverability, specific longitudinal distances and lateral gaps are given to eliminate the additional lateral force and yaw moment caused by the ship-ship interaction.

Evidence of the Triaxial Structure of ^{129}Xe at the Large Hadron Collider.

The interpretation of the emergent collective behavior of atomic nuclei in terms of deformed intrinsic shapes is at the heart of our understanding of the rich phenomenology of their structure, ranging from nuclear energy to astrophysical applications across a vast spectrum of energy scales. A new window into the deformation of nuclei has been recently opened with the realization that nuclear collision experiments performed at high-energy colliders, such as the CERN Large Hadron Collider (LHC), enable experimenters to identify the relative orientation of the colliding ions in a way that magnifies the manifestations of their intrinsic deformation. Here we apply this technique to LHC data on collisions of ^{129}Xe nuclei to exhibit the first evidence of nonaxiality in the ground state of ions collided at high energy. We predict that the low-energy structure of ^{129}Xe is triaxial (a spheroid with three unequal axes) and show that such deformation can be determined from high-energy data. This result demonstrates the unique capabilities of precision collider machines such as the LHC as new means to perform imaging of the collective structure of atomic nuclei.

Emergent collective behavior of active Brownian particles with visual perception.

Systems comprised of self-steering active Brownian particles are studied via simulations for a minimal cognitive flocking model. The dynamics of the active Brownian particles is extended by an orientational response with limited maneuverability to an instantaneous visual input of the positions of neighbors within a vision cone and a cut-off radius. The system exhibits large-scale self-organized structures, which depend on selected parameter values, and, in particular, the presence of excluded-volume interactions. The emergent structures in two dimensions, such as worms, worm-aggregate coexistence, and hexagonally close-packed structures, are analysed and phase diagrams are constructed. The analysis of the particle's mean-square displacement shows ABP-like dynamics for dilute systems and the worm phase. In the limit of densely packed structures, the active diffusion coefficient is significantly smaller and depends on the number of particles in the cluster. Our analysis of the cluster-growth dynamics shows distinct differences to processes in systems of short-range attractive colloids in equilibrium. Specifically, the characteristic time for the growth and decay of clusters of a particular size is longer than that of isotropically attractive colloids, which we attribute to the non-reciprocal nature of the directed visual perception. Our simulations reveal a strong interplay between ABP-characteristic interactions, such as volume exclusion and rotational diffusion, and cognitive-based interactions and navigation.