Collective Dynamics Research Articles

Shaping active matter from crystalline solids to active turbulence

Active matter drives its constituent agents to move autonomously by harnessing free energy, leading to diverse emergent states with relevance to both biological processes and inanimate functionalities. Achieving maximum reconfigurability of active materials with minimal control remains a desirable yet challenging goal. Here, we employ large-scale, agent-resolved simulations to demonstrate that modulating the activity of a wet phoretic medium alone can govern its solid-liquid-gas phase transitions and, subsequently, laminar-turbulent transitions in fluid phases, thereby shaping its emergent pattern. These two progressively emerging transitions, hitherto unreported, bring us closer to perceiving the parallels between active matter and traditional matter. Our work reproduces and reconciles seemingly conflicting experimental observations on chemically active systems, presenting a unified landscape of phoretic collective dynamics. These findings enhance the understanding of long-range, many-body interactions among phoretic agents, offer new insights into their non-equilibrium collective behaviors, and provide potential guidelines for designing reconfigurable materials.

Radiation reaction kinetics and collective QED signatures

Observing collective effects originating from the interplay between quantum electrodynamics and plasma physics might be achieved in upcoming experiments. In particular, the generation of electron–positron pairs and the observation of their collective dynamics could be simultaneously achieved in a collision between an intense laser and a highly relativistic electron beam through a laser frequency shift driven by an increase in the plasma density increase. In this collision, the radiation of high-energy photons will serve a dual purpose: first, in seeding the cascade of pair generation; and, second, in decelerating the created pairs for detection. The deceleration results in a detectable shift in the plasma frequency. This deceleration was previously studied considering only a small sample of individual pair particles. However, the highly stochastic nature of the quantum radiation reaction in the strong-field regime limits the descriptive power of the average behavior to the dynamics of pair particles. Here, we examine the full kinetic evolution of generated pairs in order to more accurately model the relativistically adjusted plasma density. As we show, the most effective pair energy for creating observable signatures occurs at a local minimum, obtained at finite laser field strength due to the trade-off between pair deceleration and the relativistic particle oscillation at increasing laser intensity. For a small number of laser cycles, the quantum radiation reaction may re-arrange the generated pairs into anisotropic distributions in momentum space, although, in the one-dimensional simulations considered here, this anisotropy quickly decreases.

Exploring the interplay of excitatory and inhibitory interactions in the Kuramoto model on circle topologies.

In the field of collective dynamics, the Kuramoto model serves as a benchmark for the investigation of synchronization phenomena. While mean-field approaches and complex networks have been widely studied, the simple topology of a circle is still relatively unexplored, especially in the context of excitatory and inhibitory interactions. In this work, we focus on the dynamics of the Kuramoto model on a circle with positive and negative connections paying attention to the existence of new attractors different from the synchronized state. Using analytical and computational methods, we find that even for identical oscillators, the introduction of inhibitory interactions modifies the structure of the attractors of the system. Our results extend the current understanding of synchronization in simple topologies and open new avenues for the study of collective dynamics in physical systems.

Optical assembly of multi-particle arrays by opto-hydrodynamic binding of microparticles close to a one-dimensional chain of magnetic microparticles.

Two-dimensional materials possess a large number of interesting and important properties. Various methods have been developed to assemble two-dimensional aggregates. Assembly of colloidal particles can be achieved with laser-heating-induced thermal convective flow. In this paper, an opto-hydrodynamic binding method is proposed to assemble colloidal particles dispersed in a solution into multilayer structures. First, we use polystyrene (PS) microspheres to study the feasibility and characteristics of the assembly method. PS microspheres and monodispersed magnetic silica microspheres (SLEs) are dispersed in a solution to form a binary mixture system. Under the action of an external uniform magnetic field, SLEs in the solution form chains. An SLE chain is heated by a laser beam. Due to the photothermal effect, the SLE chain is heated to produce a thermal gradient, resulting in thermal convection. The thermal convection drives the PS beads to move toward the heated SLE chain and finally stably assemble into multilayer aggregates on both sides of the SLE chain. The laser power affects the speed and result of the assembly. When the laser power is constant, the degree of constraint of the PS microbeads in different layers is also different. At the same time, this method can also assemble the biological cells, and the spacing of different layers of cells can be changed by changing the electrolyte concentration of the solution. Our work provides an approach to assembling colloidal particles and cells, which has a potential application in the analysis of the collective dynamics of microparticles and microbes.

Splitting the spacetime: a systematic analysis of foliation dependence in cosmic averaging

It is a fundamental unsolved question in general relativity how to unambiguously characterize the effective collective dynamics of an ensemble of fluid elements sourcing the local geometry, in the absence of exact symmetries.In a cosmological context this is sometimes referred to as the averaging problem.At the heart of this problem in relativity is the non-uniqueness of the choice of foliation within which the statistical properties of the local spacetime are quantified,which can lead to ambiguity in the formulated average theory. This has led to debate in the literature on how to best construct and view such a coarse-grained hydrodynamic theory.Here, we address this ambiguity by performing the first quantitative investigation of foliation dependence in cosmological spatial averaging. Starting from the aim of constructing slicing-independent integral functionals (volume, mass, entropy, etc.) as well as average functionals (mean density, average curvature, etc.) defined on spatial volume sections, we investigate infinitesimal foliation variations and derive results on the foliation dependence of functionals and on extremal leaves.Our results show that one may only identify fully foliation-independent integral functionals in special scenarios, requiring the existence of associated conserved currents.We then derive bounds on the foliation dependence of integral functionals for general scalar quantities under finite variations within physically motivated classes of foliations.Our findings provide tools that are useful for quantifying, eliminating or constraining the foliation dependence in cosmological averaging.

Transformation of the Symbolic Space of the City of Halych in the Mid to Late 20th – Early 21st Century

The transformation of the symbolic space of the city of Halych from the second half of the 20th century to the beginning of the 21st century is investigated in the article. The work is based on the analysis of archival and historical documents, field materials collected by the author through the method of participant observation during the 2022–2023. The symbolic space term is used currently in various scientific studies: in cultural anthropology (O. Hrytsenko, H. Bondarenko), in semiotics (R. Barthes), in urban studies (E. Soja, R. Čepaitienė and others), in Ukrainian sociology (V. Sereda, O. Obukhova). The planning and architecture of the city, its landscape, toponymy, monuments as well as the elements of external design of the streets, squares and buildings are used together to create a symbolic space, where collective memory, identity and social dynamics of local communities are formed. In the 1930s, the places of worship have dominated in the urban space of Halych: the Greek-Catholic Church of Christmas (the 14th century), the Roman-Catholic Church of the Assumption of the Blessed Virgin Mary, St. Volodymyr’s Orthodox Church, the synagogue and the Karaite Kenesa, thus reflecting the ethnic and confessional structure of the population of the city. Part of the walls of Halych Castle is preserved on the Castle Hill, being the evidence of the historical significance of the city. The process of communization has started after the incorporation to the Soviet Union (September, 1939): streets and squares are renamed, Soviet monuments are erected. The places of worship are destroyed or reequipped. The Church of Christmas has become an Orthodox one forcibly and the only active. Participation in parades and meetings to commemorate the Soviet holidays has become a common practice for the population. A tradition to lay flowers at the monument to Lenin by the newly wedded couple has appeared. The central part of the city is a zone of official, formal events of ideological matter at that time as well as the Halych Castle remains a favourite place of family, youth leisure, the space for informal intercourse. Essential transformations of the urban public space of the city of Halych start after Ukraine has gained independence. In 1990 the monument to Lenin is dismantled and the central square of the city has got the Christmas Square name. In 1988 a monumental equestrian sculpture to King Danylo Halytskyi has appeared there. The process of streets’ renaming continues. New churches and chapels (over 20) are built, a number of commemorative plaques and monuments to the participants of the Ukrainian national resistance, public and cultural figures of the city and the region (about 10) have been placed on municipal houses. Nine memorial annotation plaques are dedicated to soldiers died in the Russian-Ukrainian war. Christmas Square today is the main symbolic space of the city, a place where various activities and communications take place (both public and private). Halych Castle continues to occupy an important place in the cultural life of the city. Many significant scientific and cultural events representing Ukrainian historical and musical heritage occur here, influencing the formation of the identity of the local population.

Nonlinear Growth Dynamics of Neuronal Cells Cultured on Directional Surfaces.

During the development of the nervous system, neuronal cells extend axons and dendrites that form complex neuronal networks, which are essential for transmitting and processing information. Understanding the physical processes that underlie the formation of neuronal networks is essential for gaining a deeper insight into higher-order brain functions such as sensory processing, learning, and memory. In the process of creating networks, axons travel towards other recipient neurons, directed by a combination of internal and external cues that include genetic instructions, biochemical signals, as well as external mechanical and geometrical stimuli. Although there have been significant recent advances, the basic principles governing axonal growth, collective dynamics, and the development of neuronal networks remain poorly understood. In this paper, we present a detailed analysis of nonlinear dynamics for axonal growth on surfaces with periodic geometrical patterns. We show that axonal growth on these surfaces is described by nonlinear Langevin equations with speed-dependent deterministic terms and gaussian stochastic noise. This theoretical model yields a comprehensive description of axonal growth at both intermediate and long time scales (tens of hours after cell plating), and predicts key dynamical parameters, such as speed and angular correlation functions, axonal mean squared lengths, and diffusion (cell motility) coefficients. We use this model to perform simulations of axonal trajectories on the growth surfaces, in turn demonstrating very good agreement between simulated growth and the experimental results. These results provide important insights into the current understanding of the dynamical behavior of neurons, the self-wiring of the nervous system, as well as for designing innovative biomimetic neural network models.

Delay-adaptive compensation for 3-D formation control of leader-actuated multi-agent systems

This paper focuses on the control of collective dynamics in large-scale multi-agent systems (MAS) operating in a 3-D space, with a specific emphasis on compensating for the influence of an unknown delay affecting the actuated leaders. The communication graph of the agents is defined on a mesh-grid 2-D cylindrical surface. We model the agents’ collective dynamics by a complex- and a real-valued reaction–advection–diffusion 2-D partial differential equations (PDEs) whose states represent the 3-D position coordinates of the agents. The leader agents on the boundary suffer unknown actuator delay due to the cumulative computation and information transmission time. We design a delay-adaptive controller for the 2-D PDE by using PDE backstepping combined with a Lyapunov functional method, where the latter is employed to design an update law that generates real-time estimates of the unknown delay. Capitalizing on our recent result on the control of 1-D parabolic PDEs with unknown input delay, we use Fourier series expansion to bridge the control of 1-D PDEs to that of 2-D PDEs. To design the update law for the 2-D system, a new target system is defined to establish the closed-loop local boundedness of the system trajectories in H2 norm and the regulation of the states to zero assuming a measurement of the spatially distributed plant’s state. We illustrate the performance of the delay-adaptive controller by numerical simulations.

Collective incentives reduce over-exploitation of social information in unconstrained human groups

Collective dynamics emerge from countless individual decisions. Yet, we poorly understand the processes governing dynamically-interacting individuals in human collectives under realistic conditions. We present a naturalistic immersive-reality experiment where groups of participants searched for rewards in different environments, studying how individuals weigh personal and social information and how this shapes individual and collective outcomes. Capturing high-resolution visual-spatial data, behavioral analyses revealed individual-level gains—but group-level losses—of high social information use and spatial proximity in environments with concentrated (vs. distributed) resources. Incentivizing participants at the group (vs. individual) level facilitated adaptation to concentrated environments, buffering apparently excessive scrounging. To infer discrete choices from unconstrained interactions and uncover the underlying decision mechanisms, we developed an unsupervised Social Hidden Markov Decision model. Computational results showed that participants were more sensitive to social information in concentrated environments frequently switching to a social relocation state where they approach successful group members. Group-level incentives reduced participants’ overall responsiveness to social information and promoted higher selectivity over time. Finally, mapping group-level spatio-temporal dynamics through time-lagged regressions revealed a collective exploration-exploitation trade-off across different timescales. Our study unravels the processes linking individual-level strategies to emerging collective dynamics, and provides tools to investigate decision-making in freely-interacting collectives.

Pair filamentation and laser scattering in beam-driven QED cascades.

We report the observation of longitudinal filamentation of an electron-positron pair plasma in a beam-driven QED cascade. The filaments are created in the "pair-reflection" regime, where the generated pairs are partially stopped and reflected in the strong laser field. The density filaments form near the center of the laser pulse and have diameters similar to the laser wavelength. They develop and saturate within a few laser cycles and do not induce sizable magnetostatic fields. We rule out the onset of two-stream instability or Weibel instability and attribute the origin of pair filamentation to laser ponderomotive forces. The small plasma filaments induce strong scattering of laser energy to large angles, serving as a signature of collective QED plasma dynamics.

A Comparative Computational Study of the Solidification Kinetic Coefficients for the Soft-Sphere BCC-Melt and the FCC-Melt Interfaces

Using the non-equilibrium molecular dynamics (NEMD) simulations and the time-dependent Ginzburg–Landau (TDGL) theory for solidification kinetics, we study the crystal-melt interface (CMI) kinetic coefficients for both the soft-sphere (SS) BCC-melt and the FCC-melt interfaces, modeled with the inverse-power repulsive potential (n=8). The collective dynamics of the interfacial liquids at four equilibrium CMIs are calculated and employed to eliminate the discrepancy between the predictions of the kinetic coefficient using the NEMD simulations and the TDGL solidification theory. The speedup of the two modes of the interfacial liquid collective dynamics (at wavenumbers equal to the principal and the secondary reciprocal lattice vector of the grown crystal) at the equilibrium FCC CMI is observed. The calculated local collective dynamics of the SS BCC CMIs are compared with the previously reported data for the BCC Fe CMIs, validating a hypothesis proposed recently that the density relaxation times of the interfacial liquids at the CMIs are anisotropic and material dependent. With the insights provided by the improved application of the TDGL solidification theory, an attempt has been made to interpret the variation physics of the crystal-structure dependence of the solidification kinetic coefficient.

Unraveling the forces shaping foraging dynamics in harvester ant colonies: Recruitment efficiency and environmental variability

The collective foraging behavior of ant colonies is a central focus in behavioral ecology. This paper enhances the classical model of foraging dynamics in harvester ant colonies by introducing a nonlinear recruitment rate and considering environmental variability. Initially, we analyze the existence and stability of steady states in the deterministic model. The results suggest that an increase in mean recruitment time can reduce the foraging threshold, leading to both forward and backward bifurcations. Furthermore, both average recruitment time and the interference intensity of recruiters impact the number of workers in each subgroup. Subsequently, we conduct an analysis of the long-term and transient dynamics of collective foraging in random environments, providing sufficient conditions for the colony to sustain foraging activity. The findings emphasize the scene-dependent impact of environmental stochasticity on foraging dynamics. When ant colonies deterministically cease foraging, environmental stochasticity may unexpectedly prolong the foraging state. Conversely, when colonies deterministically persist in foraging, environmental stochasticity may disrupt this continuity. Additionally, the effect of environmental stochasticity on foraging status varies with the initial worker size. Sizes near the boundary of the basin of attraction between non-foraging and foraging states exhibit greater sensitivity to environmental stochasticity, and sufficiently large stochasticity can impact foraging dynamics across a broader range of initial worker sizes. These findings underscore the intricate interplay between intrinsic factors (e.g., recruitment efficiency and interference intensity) and extrinsic factors (e.g., environmental stochasticity) in shaping the collective foraging dynamics of ant colonies.

Collective dynamics of actin and microtubule and its crosstalk mediated by FHDC1.

The coordination between actin and microtubule network is crucial, yet this remains a challenging problem to dissect and our understanding of the underlying mechanisms remains limited. In this study, we used travelling waves in the cell cortex to characterize the collective dynamics of cytoskeletal networks. Our findings show that Cdc42 and F-BAR-dependent actin waves in mast cells are mainly driven by formin-mediated actin polymerization, with the microtubule-binding formin FH2 domain-containing protein 1 (FHDC1) as an early regulator. Knocking down FHDC1 inhibits actin wave formation, and this inhibition require FHDC1's interaction with both microtubule and actin. The phase of microtubule depolymerization coincides with the nucleation of actin waves and microtubule stabilization inhibit actin waves, leading us to propose that microtubule shrinking and the concurrent release of FHDC1 locally regulate actin nucleation. Lastly, we show that FHDC1 is crucial for multiple cellular processes such as cell division and migration. Our data provided molecular insights into the nucleation mechanisms of actin waves and uncover an antagonistic interplay between microtubule and actin polymerization in their collective dynamics.

Hydrodynamic correlation and spectral functions of perfect cubic crystals

We investigate the collective dynamics of the perfect cubic crystal by deriving from the hydrodynamic equations the time-dependent correlation and the spectral functions characterizing the fluctuations of mass and momentum densities. We show that the seven hydrodynamic modes of the perfect crystal can be identified from the resonances of these spectral functions. The comparison with those of a fluid is discussed. Using the numerical values of the thermodynamic, elastic, and transport coefficients computed in our previous paper (J Mabillard and P Gaspard 2024 J. Stat. Mech. 023208) for a system of hard spheres, the theoretical expressions for the correlation and spectral functions are compared to the same functions directly computed using molecular dynamics simulations. The excellent agreement between theory and simulation provides strong support for the microscopic hydrodynamic theory of perfect crystals based on the local-equilibrium approach. This work sheds light on the fundamental mechanisms governing the collective behavior of matter in the solid state.

Flock members experience gas pressures higher than lone individuals

Local interactions between flock members in absence of centralized control generate collective dynamics characterized by coherent large-scale patterns. We investigate whether aggregates of individuals like birds, swarms and fishes behaving in concert with their neighbors may modify the physical properties of the fluid medium in which they are embedded. Using the K-Nearest Neighbors algorithm to simulate collective animal behavior, we showed that the occurrence of collective dynamics can modify the physical parameters of the phase space in which the interacting individuals’ trajectories take place. This means that lone individuals experience the nearby fluid medium (i.e., the air in case of birds/insects and the water in case of fishes) differently from flock members. In particular, our framework suggests that a bird belonging to a group and acting collectively with its neighbors perceives the nearby atmosphere as denser, compared with an isolated bird.

Precision touch DNA sampling on plastic bag knots for improved profiling of packer and holder contributions

In forensic DNA analysis, evidence sampling stands as a pivotal step setting the ground for the quality of the forensic profiling. The collection of touch DNA from objects, when guidelines are scarce or absent, is usually governed by ad hoc decisions based on the available case circumstances. In our laboratory, in the context of illicit drug-related crimes, similar objects are frequently encountered, offering an opportunity for the standardization of evidence treatment. This study aims to develop an effective method for sampling touch DNA from knots on plastic bags. We examine both the exposed and hidden areas of knots, considering the latter as "protected" zones less likely to accumulate biological material during subsequent handling. The study contrasts a single sample method (whole knot surface sampling, Method 1) with dual-sample methods that separate exterior (exposed) and interior (hidden) surfaces of the knot. Notably, our study consistently reveals higher DNA yields from exterior surfaces of the knots as opposed to interior samples. Importantly, our findings demonstrate that utilizing a single sample may produce DNA profiles that are not interpretable, while employing a dual-sample approach may allow for the differentiation between the genetic contributions of the person who tied the knot, the packer, from the person who held the package, the holder. We have refined the dual-sample method to reduce holder DNA in the interior sample while maintaining it on the exterior, also allowing the packer's DNA to be detected on both surfaces. We explore four dual-sample collection methods. Method 2 involves taking the first sample from the exterior and the second from the interior of an untied knot. Method 3 visually differentiates between the original exposed and hidden surfaces for precise sampling. Method 4 employs tools to open the knot for interior sampling. Method 5 uses Diamond dye to highlight cell-free DNA on both surfaces before sampling. In conclusion, this study not only clarifies the complex dynamics of touch DNA transfer and collection on plastic bag knots, but also offers insights into standardizing evidence collection in similar cases.

Macroscopic modeling of social crowds

Social behavior in crowds, such as herding or increased interpersonal spacing, is driven by the psychological states of pedestrians. Current macroscopic crowd models assume that these are static, limiting the ability of models to capture the complex interplay between evolving psychology and collective crowd dynamics that defines a “social crowd”. This paper introduces a novel approach by explicitly incorporating an “activity” variable into the modeling framework, which represents the evolving psychological states of pedestrians and is linked to crowd dynamics. To demonstrate the role of activity, we model pedestrian egress when this variable captures stress and awareness of contagion. In addition, to highlight the importance of dynamic changes in activity, we examine a scenario in which an unexpected incident necessitates alternative exits. These case studies demonstrate that activity plays a pivotal role in shaping crowd behavior. The proposed modeling approach thus opens avenues for more realistic macroscopic crowd descriptions with practical implications for crowd management.

Collective dynamics of coupled Lorenz oscillators near the Hopf boundary: Intermittency and chimera states.

We study collective dynamics of networks of mutually coupled identical Lorenz oscillators near a subcritical Hopf bifurcation. Such systems exhibit induced multistable behavior with interesting spatiotemporal dynamics including synchronization, desynchronization, and chimera states. For analysis, we first consider a ring topology with nearest-neighbor coupling and find that the system may exhibit intermittent behavior due to the complex basin structures and dynamical frustration, where temporal dynamics of the oscillators in the ensemble switches between different attractors. Consequently, different oscillators may show a dynamics that is intermittently synchronized (or desynchronized), giving rise to intermittent chimera states. The behavior of the intermittent laminar phases is characterized by the characteristic time spent in the synchronization manifold, which decays as a power law. Such intermittent dynamics is quite general and is also observed in an ensemble of a large number of oscillators arranged in variety of network topologies including nonlocal, scale-free, random, and small-world networks.

Emergent Chirality and Hyperuniformity in an Active Mixture with Nonreciprocal Interactions.

We investigate collective dynamics in a binary mixture of programmable robots in experiments and simulations. While robots of the same species align their motion direction, interaction between species is distinctly nonreciprocal: species A aligns with B and species B antialigns with A. This nonreciprocal interaction gives rise to the emergence of collective chiral motion that can be stabilized by limiting the robot angular speed to be below a threshold. Within the chiral phase, increasing the robot density or extending the range of local repulsive interactions can drive the system through an absorbing-active transition. At the transition point, the robots exhibit a remarkable capacity for self-organization, forming disordered hyperuniform states.

Low-order modeling of collective dynamics of four ring-coupled turbulent thermoacoustic oscillators

We investigate the low-order modeling of collective dynamics in a can-annular combustor consisting of four ring-coupled turbulent lean-premixed combustors. Each combustor is treated as an individual thermoacoustic oscillator, and the entire combustion system is modeled using four Van der Pol oscillators ring-coupled with dissipative, time-delay, and reactive coupling terms. We show that this model, despite its simplicity, can reproduce many collective dynamics observed in experiments under various combinations of equivalence ratios and combustor lengths, such as 2-can anti-phase synchronization, alternating anti-phase synchronization, pairwise anti-phase synchronization, spinning azimuthal mode, and 4 steady thermoacoustic oscillators. The phase relationship in the majority of cases can be quantitatively modeled. Moreover, by incorporating a reactive coupling term, the model is able to reproduce the frequency shift observed experimentally. This study demonstrates the feasibility of using a simple low-order model to reproduce collective dynamics in complex turbulent combustion systems. This suggests that this model could be used (i) to facilitate the interpretation of experimental data within the synchronization framework, (ii) to identify potential parameter regimes leading to amplitude death, and (iii) to serve as a basis for modeling the collective dynamics observed in more complicated multi-combustors.