Turbulent flows are observed in low-Reynolds active fluids, which display similar phenomenology to the classical inertial turbulence but are of a different nature. Understanding the dependence of this new type of turbulence on dimensionality is a fundamental challenge in non-equilibrium physics. Real-space structures and kinetic energy spectra of bacterial turbulence are experimentally measured from two to three dimensions. The turbulence shows three regimes separated by two critical confinement heights, resulting from the competition of bacterial length, vortex size and confinement height. Meanwhile, the kinetic energy spectra display distinct universal scaling laws in quasi-2D and 3D regimes, independent of bacterial activity, length, and confinement height, whereas scaling exponents transition in two steps around the critical heights. The scaling behaviors are well captured by the hydrodynamic model we develop, which employs image systems to represent the effects of confining boundaries. The study suggests a framework for investigating the effect of dimensionality on non-equilibrium self-organized systems.

Regulation of cell proliferation is a crucial aspect of tissue development and homeostasis and plays a major role in morphogenesis, wound healing, and tumor invasion. A phenomenon of such regulation is contact inhibition, which describes the dramatic slowing of proliferation, cell migration and individual cell growth when multiple cells are in contact with each other. While many physiological, molecular and genetic factors are known, the mechanism of contact inhibition is still not fully understood. In particular, the relevance of cellular signaling due to interfacial contact for contact inhibition is still debated. Cellular automata (CA) have been employed in the past as numerically efficient mathematical models to study the dynamics of cell ensembles, but they are not suitable to explore the origins of contact inhibition as such agent-based models assume fixed cell sizes. We develop a minimal, data-driven model to simulate the dynamics of planar cell cultures by extending a probabilistic CA to incorporate size changes of individual cells during growth and cell division. We successfully apply this model to previous in-vitro experiments on contact inhibition in epithelial tissue: After a systematic calibration of the model parameters to measurements of single-cell dynamics, our CA model quantitatively reproduces independent measurements of emergent, culture-wide features, like colony size, cell density and collective cell migration. In particular, the dynamics of the CA model also exhibit the transition from a low-density confluent regime to a stationary postconfluent regime with a rapid decrease in cell size and motion. This implies that the volume exclusion principle, a mechanical constraint which is the only inter-cellular interaction incorporated in the model, paired with a size-dependent proliferation rate is sufficient to generate the observed contact inhibition. We discuss how our approach enables the introduction of effective bio-mechanical interactions in a CA framework for future studies.

Cellular collective motion in confluent epithelial monolayers is involved in many processes such as embryo development, carcinoma invasion, and wound healing. The development of new chemical strategies to achieve large-scale control of cells\' collective motion is essential for biomedical applications. Here a series of DNA nanostructures with different dimensions were synthesized and their influences on cells\' collective migration and packing behaviors in epithelial monolayers were investigated. We found that the framed DNA nanoassemblies effectively reduced the cells\' speed by increasing the rigidity of cells, while the lipid-DNA micelles had a more pronounced effect on cells\' projection area and shape factor. These DNA nanostructures all significantly enhanced the dependence of cells\' speed on their shape factor. Our results indicate that cells\' mobility in monolayers can be manipulated by chemical intercellular interactions without any genetic intervention. This may provide a new chemical strategy for tissue engineering and tumor therapy.

The phenomenon of group motion is common in nature, ranging from the schools of fish, birds and insects, to avalanches, landslides and sand drift. If we treat objects as collectively moving particles, such phenomena can be studied from a physical point of view, and the research on many-body systems has proved that marvelous effects can arise from the simplest individuals. The motion of numerous individuals presents different dynamic phases related to the ordering of the system. However, it is usually difficult to study the dynamic ordering and its transitions through experiments. Electron bubble states formed in a two-dimensional electron gas, as a type of electron solids, can be driven by an external electric field and provide a platform to study the dynamic collective behaviors. Here, we demonstrate that the noise spectrum is a powerful method to investigate the dynamics of bubble states. We observed not only the phenomena of dynamically ordered and disordered structures, but also unexpected alternations between them. Our results show that a dissipative system can convert between chaotic structures and ordered structures when tuning global parameters, which is concealed in conventional transport measurements of resistance or conductance. Moreover, charging the objects to study the electrical noise spectrum in collective motions can be an additional approach to revealing dynamic ordering transitions.

Collective motion is common across all animal taxa, from swarming insects to schools of fish. The collective motion requires intricate behavioral integration among individuals, yet little is known about how evolutionary changes in brain morphology influence the ability for individuals to coordinate behavior in groups. In this study, we utilized guppies that were selectively bred for relative telencephalon size, an aspect of brain morphology that is normally associated with advanced cognitive functions, to examine its role in collective motion using an open-field assay. We analyzed high-resolution tracking data of same-sex shoals consisting of 8 individuals to assess different aspects of collective motion, such as alignment, attraction to nearby shoal members, and swimming speed. Our findings indicate that variation in collective motion in guppy shoals might not be strongly affected by variation in relative telencephalon size. Our study suggests that group dynamics in collectively moving animals are likely not driven by advanced cognitive functions but rather by fundamental cognitive processes stemming from relatively simple rules among neighboring individuals.

The forefront of micro- and nanorobot research involves the development of smart swimming micromachines emulating the complexity of natural systems, such as the swarming and collective behaviors typically observed in animals and microorganisms, for efficient task execution. This study introduces magnetically controlled microrobots that possess polymeric sequestrant \"hands\" decorating a magnetic core. Under the influence of external magnetic fields, the functionalized magnetic beads dynamically self-assemble from individual microparticles into well-defined rotating planes of diverse dimensions, allowing modulation of their propulsion speed, and exhibiting a collective motion. These mobile microrobotic swarms can actively capture free-swimming bacteria and dispersed microplastics \"on-the-fly\", thereby cleaning aquatic environments. Unlike conventional methods, these microrobots can be collected from the complex media and can release the captured contaminants in a second vessel in a controllable manner, that is, using ultrasound, offering a sustainable solution for repeated use in decontamination processes. Additionally, the residual water is subjected to UV irradiation to eliminate any remaining bacteria, providing a comprehensive cleaning solution. In summary, this study shows a swarming microrobot design for water decontamination processes.

Collective motion is ubiquitous in nature; groups of animals, such as fish, birds, and ungulates appear to move as a whole, exhibiting a rich behavioral repertoire that ranges from directed movement to milling to disordered swarming. Typically, such macroscopic patterns arise from decentralized, local interactions among constituent components (e.g., individual fish in a school). Preeminent models of this process describe individuals as self-propelled particles, subject to self-generated motion and \"social forces\" such as short-range repulsion and long-range attraction or alignment. However, organisms are not particles; they are probabilistic decision-makers. Here, we introduce an approach to modeling collective behavior based on active inference. This cognitive framework casts behavior as the consequence of a single imperative: to minimize surprise. We demonstrate that many empirically observed collective phenomena, including cohesion, milling, and directed motion, emerge naturally when considering behavior as driven by active Bayesian inference-without explicitly building behavioral rules or goals into individual agents. Furthermore, we show that active inference can recover and generalize the classical notion of social forces as agents attempt to suppress prediction errors that conflict with their expectations. By exploring the parameter space of the belief-based model, we reveal nontrivial relationships between the individual beliefs and group properties like polarization and the tendency to visit different collective states. We also explore how individual beliefs about uncertainty determine collective decision-making accuracy. Finally, we show how agents can update their generative model over time, resulting in groups that are collectively more sensitive to external fluctuations and encode information more robustly.

Studies of collective motion have heretofore been dominated by a thermodynamic perspective in which the emergent \"flocked\" phases are analyzed in terms of their time-averaged orientational and spatial properties. Studies that attempt to scrutinize the dynamical processes that spontaneously drive the formation of these flocks from initially random configurations are far more rare, perhaps owing to the fact that said processes occur far from the eventual long-time steady state of the system and thus lie outside the scope of traditional statistical mechanics. For systems whose dynamics are simulated numerically, the nonstationary distribution of system configurations can be sampled at different time points, and the time evolution of the average structural properties of the system can be quantified. In this paper, we employ this strategy to characterize the spatial dynamics of the standard Vicsek flocking model using two correlation functions common to condensed matter physics. We demonstrate, for modest system sizes with 800 to 2000 agents, that the self-assembly dynamics can be characterized by three distinct and disparate time scales that we associate with the corresponding physical processes of clustering (compaction), relaxing (expansion), and mixing (rearrangement). We further show that the behavior of these correlation functions can be used to reliably distinguish between phenomenologically similar models with different underlying interactions and, in some cases, even provide a direct measurement of key model parameters.

Intermittent motion is prevalent in animal locomotion. Of special interest is the case of collective motion, in which social and environmental information must be processed in order to establish coordinated movement. We explored this nexus in locust, focusing on how intermittent motion interacts with swarming-related visual-based decision-making. Using a novel approach, we compared individual locust behaviour in response to continuously moving stimuli, with their response in semi-closed-loop conditions, in which the stimuli moved either in phase with the locust walking, or out of phase, i.e. only during the locust\'s pauses. Our findings clearly indicate the greater tendency of a locust to respond and \'join the swarming motion\' when the visual stimuli were presented during its pauses. Hence, the current study strongly confirms previous indications of the dominant role of pauses in the collective motion-related decision-making of locusts. The presented insights contribute to a deeper general understanding of how intermittent motion contributes to group cohesion and coordination in animal swarms.

A fundamental question in complex systems is how to relate interactions between individual components (\'microscopic description\') to the global properties of the system (\'macroscopic description\'). Furthermore, it is unclear whether such a macroscopic description exists and if such a description can capture large-scale properties. Here, we address the validity of a macroscopic description of a complex biological system using the collective motion of desert locusts as a canonical example. One of the world\'s most devastating insect plagues begins when flightless juvenile locusts form \'marching bands\'. These bands display remarkable coordinated motion, moving through semiarid habitats in search of food. We investigated how well macroscopic physical models can describe the flow of locusts within a band. For this, we filmed locusts within marching bands during an outbreak in Kenya and automatically tracked all individuals passing through the camera frame. We first analyzed the spatial topology of nearest neighbors and found individuals to be isotropically distributed. Despite this apparent randomness, a local order was observed in regions of high density in the radial distribution function, akin to an ordered fluid. Furthermore, reconstructing individual locust trajectories revealed a highly aligned movement, consistent with the one-dimensional version of the Toner-Tu equations, a generalization of the Navier-Stokes equations for fluids, used to describe the equivalent macroscopic fluid properties of active particles. Using this effective Toner-Tu equation, which relates the gradient of the pressure to the acceleration, we show that the effective \'pressure\' of locusts increases as a linear function of density in segments with the highest polarization (for which the one-dimensional approximation is most appropriate). Our study thus demonstrates an effective hydrodynamic description of flow dynamics in plague locust swarms.