Collective decision-making in biological systems requires all individuals in the group to go through a behavioural change of state. During this transition fast and robust transfer of information is essential to prevent cohesion loss. The mechanism by which natural groups achieve such robustness, though, is not clear. Here we present an experimental study of starling flocks performing collective turns. We find that information about direction changes propagates across the flock with a linear dispersion law and negligible attenuation, hence minimizing group decoherence. These results contrast starkly with current models of collective motion, which predict diffusive transport of information. Building on spontaneous symmetry breaking and conservation laws arguments, we formulate a new theory that correctly reproduces linear and undamped propagation. Essential to the new framework is the inclusion of the birds’ behavioural inertia. The new theory not only explains the data, but also predicts that information transfer must be faster the stronger the group’s orientational order, a prediction accurately verified by the data. Our results suggest that swift decision-making may be the adaptive drive for the strong behavioural polarization observed in many living groups.

Collective behaviour is a widespread phenomenon in biology, cutting through a huge span of scales, from cell colonies up to bird flocks and fish schools. The most prominent trait of collective behaviour is the emergence of global order: individuals synchronize their states, giving the stunning impression that the group behaves as one. In many biological systems, though, it is unclear whether global order is present. A paradigmatic case is that of insect swarms, whose erratic movements seem to suggest that group formation is a mere epiphenomenon of the independent interaction of each individual with an external landmark. In these cases, whether or not the group behaves truly collectively is debated. Here, we experimentally study swarms of midges in the field and measure how much the change of direction of one midge affects that of other individuals. We discover that, despite the lack of collective order, swarms display very strong correlations, totally incompatible with models of non-interacting particles. We find that correlation increases sharply with the swarm's density, indicating that the interaction between midges is based on a metric perception mechanism. By means of numerical simulations we demonstrate that such growing correlation is typical of a system close to an ordering transition. Our findings suggest that correlation, rather than order, is the true hallmark of collective behaviour in biological systems.

Recent experiments with self-phoretic particles at low concentrations show a pronounced dynamic clustering [I. Theurkauff et al., Phys. Rev. Lett. 108, 268303 (2012)]. We model this situation by taking into account the translational and rotational diffusiophoretic motion, which the active particles perform in their self-generated chemical field. Our Brownian dynamics simulations show pronounced dynamic clustering only when these two phoretic contributions give rise to competing attractive and repulsive interactions, respectively. We identify two dynamic clustering states and characterize them by power-law-exponential distributions. In case of mere attraction a chemotactic collaps occurs directly from the gas-like into the collapsed state, which we also predict by mapping our Langevin dynamics on the Keller-Segel model for bacterial chemotaxis.The collective motion of self-propelling objects is a most fascinating subject which has been studied in a variety of systems [1,2]. At the macroscale, collective patterns occur, for example, in flocks of birds or fish schooles [3][4][5] while at the microscopic scale bacterical cells in an aqueous environment generate intricate motional patterns [6][7][8]. To understand basic features of structure formation in non-equilibrium, systems with spherical or circular microswimmers are investigated. A number of theoretical and experimental studies have demonstrated that activity of microswimmers alone can result in clustering and phase separation [9-17] due to reduced motility in dense aggregates [9,15]. However, the colloidal density has to be large enough that the characteristic time for a particle to join a cluster becomes comparable to its rotational diffusion time needed to dissolve from it [13]. Other investigations explore the influence of hydrodynamics on collective motion [18][19][20][21][22][23][24].In experiments with dilute suspensions of self-phoretic active Janus colloids, dynamic clustering has been observed [25,26]. In this novel non-equilibrium phenomenon, particles constantly join and leave clusters which exhibit a very dynamic shape. [7,29,30,32].Recent theoretical and experimental studies included short-range attraction between active colloids and observed clustering at low colloidal densities [26,[33][34][35].Ref.[36] implements diffusiophoresis for concrete surface properties of self-phoretic colloids and indentifies various states such as clumping and asters.The work presented here has very much been inspired by the experiments of the Lyon group [25]. The diffusiophoretic interaction has a translational and orientational contribution. Using Brownian dynamics simulations, we demonstrate that pronounced dynamic clustering occurs only when these two contributions give rise to competing attractive and repulsive interactions, respectively. We identify two dynamic clustering states and characterize them. Otherwise, in case of mere attraction a chemotactic collaps occurs directly from the gas-like state before pronounced clusters are able to form. We support this...

Collective behavior in biological systems is often accompanied by strong correlations. The question has therefore arisen of whether correlation is amplified by the vicinity to some critical point in the parameters space. Biological systems, though, are typically quite far from the thermodynamic limit, so that the value of the control parameter at which correlation and susceptibility peak depend on size. Hence, a system would need to readjust its control parameter according to its size in order to be maximally correlated. This readjustment, though, has never been observed experimentally. By gathering three-dimensional data on swarms of midges in the field we find that swarms tune their control parameter and size so as to maintain a scaling behavior of the correlation function. As a consequence, correlation length and susceptibility scale with the system's size and swarms exhibit a near-maximal degree of correlation at all sizes.

Flocks of birds exhibit a remarkable degree of coordination and collective response. It is not just that thousands of individuals fly, on average, in the same direction and at the same speed, but that even the fluctuations around the mean velocity are correlated over long distances. Quantitative measurements on flocks of starlings, in particular, show that these fluctuations are scale-free, with effective correlation lengths proportional to the linear size of the flock. Here we construct models for the joint distribution of velocities in the flock that reproduce the observed local correlations between individuals and their neighbors, as well as the variance of flight speeds across individuals, but otherwise have as little structure as possible. These minimally structured or maximum entropy models provide quantitative, parameter-free predictions for the spread of correlations throughout the flock, and these are in excellent agreement with the data. These models are mathematically equivalent to statistical physics models for ordering in magnets, and the correct prediction of scale-free correlations arises because the parameterscompletely determined by the data-are in the critical regime. In biological terms, criticality allows the flock to achieve maximal correlation across long distances with limited speed fluctuations.collective behavior | statistical mechanics I n a flock of birds, thousands of individuals will fly in the same direction and at the same speed, for long periods of time. However, this average behavior is not enough for flocking to be advantageous. The entire flock must respond to dangers that may be visible only to a small fraction of individuals, requiring information to propagate over long distances. Although it is difficult to measure this information flow directly (1), we know that attacks by predators on a flock have very low success rates (2-4), and that the evasion of predators by starling flocks is associated with the triggering and propagation of waves through the flock (5). Even in the absence of predators, we can see deviations of individual behavior from the average behavior of the flock, and correlations in these fluctuations provide a signature of information flow through the flock. Strikingly, observations on flocks of starlings show that these correlations extend over very long distances, comparable to the size of the flock itself (6).It is generally believed that the interactions among birds in a flock are local-each bird aligns its flight direction and speed to those of its near neighbors (7). If this is correct, then we have to understand how local interactions can generate correlations over much longer distances. In physics, we have two very different mechanisms for local interactions to produce long-ranged correlations. If the system spontaneously breaks a continuous symmetry, for example when all of the spins in a magnet select a particular direction in space along which the macroscopic magnetization will point, then the fluctuations in the system are dominated by Goldstone m...

The rapid growth, demand, and production of batteries to meet various emerging applications, such as electric vehicles and energy storage systems, will result in waste and disposal problems in the next few years as these batteries reach end-of-life. Battery reuse and recycling are becoming urgent worldwide priorities to protect the environment and address the increasing need for critical metals. As a review article, this paper reveals the current global battery market and global battery waste status from which the main battery chemistry types and their management, including reuse and recycling status, are discussed. This review then presents details of the challenges, opportunities, and arguments on battery second-life and recycling. The recent research and industrial activities in the battery reuse domain are summarized to provide a landscape picture and valuable insight into battery reuse and recycling for industries, scientific research, and waste management.

Self-phoretic active colloids move and orient along self-generated chemical gradients by diffusiophoresis, a mechanism reminiscent of bacterial chemotaxis. In combination with the activity of the colloids, this creates effective repulsive and attractive interactions between particles depending on the sign of the translational and rotational diffusiophoretic parameters. A delicate balance of these interactions causes dynamic clustering and for overall strong effective attraction the particles collapse to one single cluster. Using Langevin dynamics simulations, we extend the state diagram of our earlier work (Phys. Rev. Lett. 112, 238303 (2014)) to regions with translational phoretic repulsion. With increasing repulsive strength, the collapsed cluster first starts to fluctuate strongly, then oscillates between a compact form and a colloidal cloud, and ultimately the colloidal cloud becomes static. The oscillations disappear if the phoretic interactions within compact clusters are not screened. We also study dynamic clustering at larger area fractions by exploiting cluster size distributions and mean cluster sizes. In particular, we identify the dynamic clustering 2 state as a signature of phoretic interactions. We analyze fusion and fission rate functions to quantify the kinetics of cluster formation and identify them as local signatures of phoretic interactions, since they can be measured on single clusters.

One of the most impressive features of moving animal groups is their ability to perform sudden coherent changes in travel direction. While this collective decision can be a response to an external alarm cue, directional switching can also emerge from the intrinsic fluctuations in individual behaviour. However, the cause and the mechanism by which such collective changes of direction occur are not fully understood yet. Here, we present an experimental study of spontaneous collective turns in natural flocks of starlings. We employ a recently developed tracking algorithm to reconstruct threedimensional trajectories of each individual bird in the flock for the whole duration of a turning event. Our approach enables us to analyse changes in the individual behaviour of every group member and reveal the emergent dynamics of turning. We show that spontaneous turns start from individuals located at the elongated tips of the flocks, and then propagate through the group. We find that birds on the tips deviate from the mean direction of motion much more frequently than other individuals, indicating that persistent localized fluctuations are the crucial ingredient for triggering a collective directional change. Finally, we quantitatively verify that birds follow equalradius paths during turning, the effects of which are a change of the flock's orientation and a redistribution of individual locations in the group.