Emergent Collective Dynamics Research Articles

Micromagnetic simulations of emergent monopole defects and magnetization reversal in connected and dipolar Square Artificial Spin Ice

Artificial spin ice (ASI) structures have garnered significant attention due to their unique properties including emergent magnetic monopoles, phase transitions, and collective switching dynamics. In this study, we employ micromagnetic simulations to investigate the magnetic microstates and magnetization reversal dynamics of square ASI with varying connectivity. In particular, we explore an intermediate or a quasi-connected system where the connectivity is altered without significantly changing the strength of dipolar interactions through the introduction of narrow gaps at the vertices. Our results reveal distinct differences in the populations of different vertex types during magnetic reversal for lattices with varying connectivity. These results suggest the possibility of engineering ASI systems in which specific vertex types can be repeatably accessed through adjustments in lattice connectivity.

Introduction to dynamical mean-field theory of randomly connected neural networks with bidirectionally correlated couplings

Dynamical mean-field theory is a powerful physics tool used to analyze the typical behavior of neural networks, where neurons can be recurrently connected, or multiple layers of neurons can be stacked. However, it is not easy for beginners to access the essence of this tool and the underlying physics. Here, we give a pedagogical introduction of this method in a particular example of random neural networks, where neurons are randomly and fully connected by correlated synapses and therefore the network exhibits rich emergent collective dynamics. We also review related past and recent important works applying this tool. In addition, a physically transparent and alternative method, namely the dynamical cavity method, is also introduced to derive exactly the same results. The numerical implementation of solving the integro-differential mean-field equations is also detailed, with an illustration of exploring the fluctuation dissipation theorem.

Micromagnetic Simulations of Emergent Monopole Defects and Magnetization Reversal in Connected and Dipolar Kagome Artificial Spin Ice

Artificial spin ice (ASI) materials, created by lithographically patterning nanoscale magnets in desired geometries, have shown a number of interesting phenomena, such as emergent magnetic monopoles (monopole defects), collective dynamics and phase transitions. The control of monopole defects with external stimuli such as magnetic and electric fields, strain, electric currents etc. would be of much interest in fabrication of future devices. In this work, we investigate the magnetization reversal as a function of the connectivity of the Kagome ASI, using micromagnetic simulations. The domain wall motion is expected to play an important role in the connected spin ice, whereas the dipolar interactions dominate for the unconnected case. The magnetic microstate of each lattice is uniquely determined by the vertex configuration, with the Kagome lattice supporting a six-fold-degenerate vertex state, obeying either a two-in/one-out (vertex charge +q) or one-in/two-out (vertex charge q) ice rule. We analyze the fraction of each vertex type to highlight changes in the magnetic microstate as a function of applied magnetic field. Our results could be correlated with magneto-transport measurements and direct imaging of vertex states in ASI using magnetic force microscopy.

Ultrafast reversible self-assembly of living tangled matter.

Tangled active filaments are ubiquitous in nature, from chromosomal DNA and cilia carpets to root networks and worm collectives. How activity and elasticity facilitate collective topological transformations in living tangled matter is not well understood. We studied California blackworms (Lumbriculus variegatus), which slowly form tangles in minutes but can untangle in milliseconds. Combining ultrasound imaging, theoretical analysis, and simulations, we developed and validated a mechanistic model that explains how the kinematics of individual active filaments determines their emergent collective topological dynamics. The model reveals that resonantly alternating helical waves enable both tangle formation and ultrafast untangling. By identifying generic dynamical principles of topological self-transformations, our results can provide guidance for designing classes of topologically tunable active materials.

Collective behaviors of stochastic agent-based models and applications to finance and optimization

In this paper, we present a survey of recent progress on the emergent behaviors of stochastic particle models which arise from the modeling of collective dynamics. Collective dynamics of interacting autonomous agents is ubiquitous in nature, and it can be understood as a formation of concentration in a state space. The jargons such as aggregation, herding, flocking and synchronization describe such concentration phenomena. Recently it became one of the emerging topics in the applied mathematics community due to possible engineering applications and close relation with nonlocal partial differential equations. When an autonomous agent system interacts with unknown environment as an open system, the effects of hidden and unidentified interactions between the environment and the autonomous system are often realized by stochastic noises in agent dynamics, and the temporal evolution of the autonomous system results in stochastic collective models. From the viewpoint of dynamical systems theory, it is very interesting how collective dynamics emerges from initial state. As concrete examples, we consider four specific stochastic collective models (stochastic Winfree and Kuramoto models for synchronization, the stochastic Cucker–Smale model for flocking, and a first-order stochastic nonlinear consensus model), and we also briefly review the state-of-the-art results for these models on the emergence of collective dynamics and discuss their applications in finance and optimization.

In materia implementation strategies of physical reservoir computing with memristive nanonetworks

Physical reservoir computing (RC) represents a computational framework that exploits information-processing capabilities of programmable matter, allowing the realization of energy-efficient neuromorphic hardware with fast learning and low training cost. Despite self-organized memristive networks have been demonstrated as physical reservoir able to extract relevant features from spatiotemporal input signals, multiterminal nanonetworks open the possibility for novel strategies of computing implementation. In this work, we report on implementation strategies of in materia RC with self-assembled memristive networks. Besides showing the spatiotemporal information processing capabilities of self-organized nanowire networks, we show through simulations that the emergent collective dynamics allows unconventional implementations of RC where the same electrodes can be used as both reservoir inputs and outputs. By comparing different implementation strategies on a digit recognition task, simulations show that the unconventional implementation allows a reduction of the hardware complexity without limiting computing capabilities, thus providing new insights for taking full advantage of in materia computing toward a rational design of neuromorphic systems.

On the relativistic flocks over the unit sphere and the hyperboloid in a bonding force field

We study emergent collective dynamics for the relativistic Cucker–Smale (RCS) model in a bonding force field on an abstract Riemannian manifold. The abstract RCS model in a bonding force field contains forcing terms involved with geometric quantities, such as parallel transport, Riemannian metric tensor, and logarithm mapping on manifolds. We consider two explicit realizations of the RCS model on the Euclidean unit sphere and the hyperboloid and present refined emergent dynamics of the explicit RCS models and asymptotic behaviors. We also show that the explicit RCS models reduce to the relativistic Kuramoto-type models with a memory effect for a one-dimensional setting.

Clustering and flocking of repulsive chiral active particles with non-reciprocal couplings

Recently, non-reciprocal systems have become a focus of growing interest. Examples occur in soft and active matter, but also in engineered quantum materials and neural (brain) networks. Here, we investigate the impact of non-reciprocity on the collective behavior of a system of (dry) chiral active matter. Specifically, we consider a mixture of ‘circle swimmers’ with steric interactions and non-reciprocal alignment couplings. Based on hydrodynamic equations which we derive from a set of Langevin equations, we explore the interplay of non-reciprocity, finite size, and chirality. We first consider, as a reference, one-species systems with reciprocal couplings. Based on a linear stability analysis and numerical simulations, we here observe three different types of collective behavior, that is, flocking, motility-induced phase separation, and a combination of both. Turning then to a non-reciprocal system, we find that non-reciprocity can turn otherwise stationary instabilities into oscillatory ones, affect the relative orientation of flocks, and, crucially, change the general type of instability. This illustrates the drastic impact of non-reciprocity on the emergent collective dynamics of chiral active matter systems, with potentially far-reaching biological implications.

Passive electrolocation in terrestrial arthropods: Theoretical modelling of location detection

The recent discovery that some terrestrial arthropods can detect, use, and learn from weak electrical fields adds a new dimension to our understanding of how organisms explore and interact with their environments. For bees and spiders, the filiform mechanosensory systems enable this novel sensory modality by carrying electric charge and deflecting in response to electrical fields. This mode of information acquisition opens avenues for previously unrealised sensory dynamics and capabilities. In this paper, we study one such potential: the possibility for an arthropod to locate electrically charged objects.We begin by illustrating how electrostatic interactions between hairs and surrounding electrical fields enable the process of location detection. After which we examine three scenarios: (1) the determination of the location and magnitude of multiple point charges through a single observation, (2) the learning of electrical and mechanical sensor properties and the characteristics of an electrical field through several observations, (3) the possibility that an observer can infer their location and orientation in a fixed and known electrical field (akin to “stellar navigation”).To conclude, we discuss the potential of electroreception to endow an animal with thus far unappreciated sensory capabilities, such as the mapping of electrical environments. Electroreception by terrestrial arthropods offers a renewed understanding of the sensory processes carried out by filiform hairs, adding to aero-acoustic sensing and opening up the possibility of new emergent collective dynamics and information acquisition by distributed hair sensors.

Preprint Highlight: Automatic detection of spatiotemporal signaling patterns in cell collectives.

Propagation of signal between cells drives many biological processes, but the field lacks systematic quantification methods. This study presents Automatic Recognition of COllective Signalling (ARCOS), a general-purpose computational method to visualize and quantify intercellular propagation of signaling events. The method detects single-cell signaling activation events, groups these events across space and time, and extracts quantitative measurements of the spatiotemporal dynamics of collective signaling events. The authors demonstrated the application of ARCOS on diverse experimental systems, with implementation and documentation publicly available in R and Python and as a NAPARI plugin. ARCOS could be used to explore and decipher rules governing emergent collective cell dynamics.

Defect-induced monopole injection and manipulation in artificial spin ice

Lithographically defined arrays of nanomagnets are well placed for application in areas such as probabilistic computing or reconfigurable magnonics due to their emergent collective dynamics and writable magnetic order. Among them are artificial spin ice (ASI), which are arrays of binary in-plane macrospins exhibiting geometric frustration at the vertex interfaces. Macrospin flips in the arrays create topologically protected magnetic charges, or emergent monopoles, which are bound to an antimonopole to conserve charge. In the absence of controllable pinning, it is difficult to manipulate individual monopoles in the array without also influencing other monopole excitations or the counter-monopole charge. Here, we tailor the local magnetic order of a classic ASI lattice by introducing a ferromagnetic defect with shape anisotropy into the array. This creates monopole injection sites at nucleation fields below the critical lattice switching field. Once formed, the high energy monopoles are fixed to the defect site and may controllably propagate through the lattice under stimulation. Defect programing of bound monopoles within the array allows fine control of the pathways of inverted macrospins. Such control is a necessary prerequisite for the realization of functional devices, e. g. reconfigurable waveguide in nanomagnonic applications.

From Single to Collective Motion of Social Amoebae: A Computational Study of Interacting Cells

The coupling of the internal mechanisms of cell polarization to cell shape deformations and subsequent cell crawling poses many interdisciplinary scientific challenges. Several mathematical approaches have been proposed to model the coupling of both processes, where one of the most successful methods relies on a phase field that encodes the morphology of the cell, together with the integration of partial differential equations that account for the polarization mechanism inside the cell domain as defined by the phase field. This approach has been previously employed to model the motion of single cells of the social amoeba Dictyostelium discoideum, a widely used model organism to study actin-driven motility and chemotaxis of eukaryotic cells. Besides single cell motility, Dictyostelium discoideum is also well-known for its collective behavior. Here, we extend the previously introduced model for single cell motility to describe the collective motion of large populations of interacting amoebae by including repulsive interactions between the cells. We performed numerical simulations of this model, first characterizing the motion of single cells in terms of their polarity and velocity vectors. We then systematically studied the collisions between two cells that provided the basic interaction scenarios also observed in larger ensembles of interacting amoebae. Finally, the relevance of the cell density was analyzed, revealing a systematic decrease of the motility with density, associated with the formation of transient cell clusters that emerge in this system even though our model does not include any attractive interactions between cells. This model is a prototypical active matter system for the investigation of the emergent collective dynamics of deformable, self-driven cells with a highly complex, nonlinear coupling of cell shape deformations, self-propulsion and repulsive cell-cell interactions. Understanding these self-organization processes of cells like their autonomous aggregation is of high relevance as collective amoeboid motility is part of wound healing, embryonic morphogenesis or pathological processes like the spreading of metastatic cancer cells.

Emergent collective dynamics of pusher and puller squirmer rods: swarming, clustering, and turbulence.

We study the interplay of steric and hydrodynamic interactions in suspensions of elongated microswimmers by simulating the full hydrodynamics of squirmer rods in the quasi two-dimensional geometry of a Hele-Shaw cell. To create pusher or puller-type squirmer rods, we concentrate the surface slip-velocity field more to the back or to the front of the rod and thereby are able to tune the rod's force-dipole strength. We study a wide range of aspect ratios and area fractions and provide corresponding state diagrams. The flow field of pusher-type squirmer rods destabilizes ordered structures and favors the disordered state at small area fractions and aspect ratios. Only when steric interactions become relevant, we observe a turbulent and dynamic cluster state, while for large aspect ratios a single swarm and jammed cluster occurs. The power spectrum of the turbulent state shows two distinct energy cascades at small and large wave numbers with power-law scaling and non-universal exponents. Pullers show a strong tendency to form swarms instead of the disordered state found for neutral and pusher rods. At large area fractions a dynamic cluster is observed and at larger aspect ratio a single swarm or jammed cluster occurs.

Emergent properties in the responses of tropical corals to recurrent climate extremes

The frequency, intensity, and spatial scale of climate extremes are changing rapidly due to anthropogenic global warming.1,2 A growing research challenge is to understand how multiple climate-driven disturbances interact with each other over multi-decadal time frames, generating combined effects that cannot be predicted from single events alone.3-5 Here we examine the emergent dynamics of five coral bleaching events along the 2,300km length of the Great Barrier Reef that affected >98% of the Reef between 1998 and 2020. We show that the bleaching responses of corals to a given level of heat exposure differed in each event and were strongly influenced by contingency and the spatial overlap and strength of interactions between events. Naive regions that escaped bleaching for a decade or longer were the most susceptible to bouts of heat exposure. Conversely, when pairs of successive bleaching episodes were close together (1-3 years apart), the thermal threshold for severe bleaching increased because the earlier event hardened regions of the Great Barrier Reef to further impacts. In the near future, the biological responses to recurrent bleaching events may become stronger as the cumulative geographic footprint expands further, potentially impairing the stock-recruitment relationships among lightly and severely bleached reefs with diverse recent histories. Understanding the emergent properties and collective dynamics of recurrent disturbances will be critical for predicting spatial refuges and cumulative ecological responses, and for managing the longer-term impacts of anthropogenic climate change on ecosystems.

Collective P-Wave Orbital Dynamics of Ultracold Fermions.

We consider the nonequilibrium orbital dynamics of spin-polarized ultracold fermions in the first excited band of an optical lattice. A specific lattice depth and filling configuration is designed to allow the p_{x} and p_{y} excited orbital degrees of freedom to act as a pseudospin. Starting from the full Hamiltonian for p-wave interactions in a periodic potential, we derive an extended Hubbard-type model that describes the anisotropic lattice dynamics of the excited orbitals at low energy. We then show how dispersion engineering can provide a viable route to realizing collective behavior driven by p-wave interactions. In particular, Bragg dressing and lattice depth can reduce single-particle dispersion rates, such that a collective many-body gap is opened with only moderate Feshbach enhancement of p-wave interactions. Physical insight into the emergent gap-protected collective dynamics is gained by projecting the Hamiltonian into the Dicke manifold, yielding a one-axis twisting model for the orbital pseudospin that can be probed using conventional Ramsey-style interferometry. Experimentally realistic protocols to prepare and measure the many-body dynamics are discussed, including the effects of band relaxation, particle loss, spin-orbit coupling, and doping.

Impact of Variable Speed on Collective Movement of Animal Groups

The collective dynamics and structure of animal groups has attracted the attention of scientists across a broad range of fields. A variety of agent-based models have been developed to help understand the emergence of coordinated collective behavior from simple interaction rules. A common, simplifying assumption of such collective movement models, is that individual agents move with a constant speed. In this work we critically re-asses this assumption. First, we discuss experimental data showcasing the omnipresent speed variability observed in different species of live fish and artificial agents (RoboFish). Based on theoretical considerations accounting for inertia and rotational friction, we derive a functional dependence of the turning response of individuals on their instantaneous speed, which is confirmed by experimental data. We then investigate the interplay of variable speed and speed-dependent turning on self-organized collective behavior by implementing an agent-based model which accounts for both these effects. We show that, besides the average speed of individuals, the variability in individual speed can have a dramatic impact on the emergent collective dynamics: a group which differs to another only in a lower speed variability of its individuals (groups being identical in all other behavioral parameters), can be in the polarized state while the other group is disordered. We find that the local coupling between group polarization and individual speed is strongest at the order-disorder transition, and that, in contrast to fixed speed models, the group’s spatial extent does not have a maximum at the transition. Furthermore, we demonstrate a decrease in polarization with group size for groups of individuals with variable speed, and a sudden decrease in mean individual speed at a critical group size (N= 4 for Voronoi interactions) linked to a topological transition from an all-to-all to a distributed spatial interaction network. Overall, our work highlights the importance to account for fundamental kinematic constraints in general, and variable speed in particular, when modeling self-organized collective dynamics.

Bootstrapped Motion of an Agent on an Adaptive Resource Landscape

We theoretically show that isolated agents that locally and symmetrically consume resources and sense positive resource gradients can generate constant motion via bootstrapped resource gradients in the absence of any externally imposed gradients, and we show a realization of this motion using robots. This self-generated agent motion can be coupled with neighboring agents to act as a spontaneously broken symmetry seed for emergent collective dynamics. We also show that in a sufficiently weak externally imposed gradient, it is possible for an agent to move against an external resource gradient due to the local resource depression on the landscape created by an agent. This counter-intuitive boot-strapped motion against an external gradient is demonstrated with a simple robot system on an light-emitting diode (LED) light-board.

Development of swarm behavior in artificial learning agents that adapt to different foraging environments.

Collective behavior, and swarm formation in particular, has been studied from several perspectives within a large variety of fields, ranging from biology to physics. In this work, we apply Projective Simulation to model each individual as an artificial learning agent that interacts with its neighbors and surroundings in order to make decisions and learn from them. Within a reinforcement learning framework, we discuss one-dimensional learning scenarios where agents need to get to food resources to be rewarded. We observe how different types of collective motion emerge depending on the distance the agents need to travel to reach the resources. For instance, strongly aligned swarms emerge when the food source is placed far away from the region where agents are situated initially. In addition, we study the properties of the individual trajectories that occur within the different types of emergent collective dynamics. Agents trained to find distant resources exhibit individual trajectories that are in most cases best fit by composite correlated random walks with features that resemble Lévy walks. This composite motion emerges from the collective behavior developed under the specific foraging selection pressures. On the other hand, agents trained to reach nearby resources predominantly exhibit Brownian trajectories.

Constants of motion for the finite-dimensional Lohe type models with frustration and applications to emergent dynamics

We present constants of motion for the finite-dimensional Lohe type aggregation models with frustration, and apply them to the analysis of collective behaviors. The Lohe type models have been proposed as possible non-abelian and higher-dimensional generalizations of the Kuramoto model, which is a prototype phase model for synchronization. In this paper, we study the emergent collective dynamics of these models under the effect of (interaction) frustration, which generalizes phase-shift frustrations in the Kuramoto model. To this end, we provide constants of motion, i.e., conserved quantities along the flow generated by the models under consideration. From the perspective of the low-dimensional dynamics, we derive several results on the emergent asymptotic patterns of the Kuramoto and Lohe sphere models.

Emergent collective dynamics of bottom-heavy squirmers under gravity

.We present the results of hydrodynamic simulations using the method of multi-particle collision dynamics for a system of squirmer microswimmers moving under the influence of gravity at low Reynolds numbers. In addition, the squirmers are bottom-heavy so that they experience a torque which aligns them along the vertical. The squirmers interact hydrodynamically by the flow fields of a stokeslet and rotlet, which are initiated by the acting gravitational force and torque, respectively, and by their own flow fields. By varying the ratio of swimming to bulk sedimentation velocity and the torque, we determine state diagrams for the emergent collective dynamics of neutral squirmers as well as strong pushers and pullers. For low swimming velocity and torque we observe conventional sedimentation, while the sedimentation profile becomes inverted when their values are increased. For neutral squirmers we discover convective rolls of circulating squirmers between both sedimentation states, which sit at the bottom of the system and are fed by plumes made of collectively sinking squirmers. At larger torques porous clusters occur that spawn single squirmers. The two latter states can also occur transiently starting from a uniform squirmer distribution and then disappear in the long-time limit. For strong pushers and pullers only weak plume formation is observed.Graphical abstract