Group formation and cohesion of active particles with visual perception-dependent motility

Rectification and confinement of photokinetic bacteria in an optical feedback loop

Active particles can self-propel by exploiting locally available energy resources. When powered by light, these resources can be distributed with high resolution allowing spatio-temporal modulation of motility. Here we show that the random walks of light-driven bacteria are rectified when they swim in a structured light field that is obtained by a simple geometric transformation of a previous system snapshot. The obtained currents achieve an optimal value that we establish by general theoretical arguments. This optical feedback is used to gather and confine bacteria in high-density and high-activity regions that can be dynamically relocated and reconfigured. Moving away from the boundaries of these optically confined states, the density decays to zero in a few tens of micrometers, exhibiting steep exponential tails that suppress cell escape and ensure long-term stability. Our method is general and scalable, providing a versatile tool to produce localized and tunable active baths for microengineering applications and systematic studies of non-equilibrium phenomena in active systems.

 Light can be used to precisely modulate the speed of active particles in space and time. Here, the authors rectify and confine bacteria using an optical feedback loop that couples bacteria topast configurations.

Microrobot collectives with reconfigurable morphologies, behaviors, and functions

Mobile microrobots, which can navigate, sense, and interact with their environment, could potentially revolutionize biomedicine and environmental remediation. Many self-organizing microrobotic collectives have been developed to overcome inherent limits in actuation, sensing, and manipulation of individual microrobots; however, reconfigurable collectives with robust transitions between behaviors are rare. Such systems that perform multiple functions are advantageous to operate in complex environments. Here, we present a versatile microrobotic collective system capable of on-demand reconfiguration to adapt to and utilize their environments to perform various functions at the air-water interface. Our system exhibits diverse modes ranging from isotropic to anisotrpic behaviors and transitions between a globally driven and a novel self-propelling behavior. We show the transition between different modes in experiments and simulations, and demonstrate various functions, using the reconfigurability of our system to navigate, explore, and interact with the environment. Such versatile microrobot collectives with globally driven and self-propelled behaviors have great potential in future medical and environmental applications.

Aggregation of self-propelled particles with sensitivity to local order

We study a system of self-propelled particles (SPPs) in which individual particles are allowed to switch between a fast aligning and a slow nonaligning state depending upon the degree of the alignment in the neighborhood. The switching is modeled using a threshold for the local order parameter. This additional attribute gives rise to a mixed phase, in contrast to the ordered phases found in clean SPP systems. As the threshold is increased from zero, we find the sudden appearance of clusters of nonaligners. Clusters of nonaligners coexist with moving clusters of aligners with continual coalescence and fragmentation. The behavior of the system with respect to the clustering of nonaligners appears to be very different for values of low and high global densities. In the low density regime, for an optimal value of the threshold, the largest cluster of nonaligners grows in size up to a maximum that varies logarithmically with the total number of particles. However, on further increasing the threshold the size decreases. In contrast, for the high density regime, an initial abrupt rise is followed by the appearance of a giant cluster of nonaligners. The latter growth can be characterized as a continuous percolation transition. In addition, we find that the speed differences between aligners and nonaligners is necessary for the segregation of aligners and nonaligners.

Modes of information flow in collective cohesion

Pairwise interactions are fundamental drivers of collective behavior-responsible for group cohesion. The abiding question is how each individual influences the collective. However, time-delayed mutual information and transfer entropy, commonly used to quantify mutual influence in aggregated individuals, can result in misleading interpretations. Here, we show that these information measures have substantial pitfalls in measuring information flow between agents from their trajectories. We decompose the information measures into three distinct modes of information flow to expose the role of individual and group memory in collective behavior. It is found that decomposed information modes between a single pair of agents reveal the nature of mutual influence involving many-body nonadditive interactions without conditioning on additional agents. The pairwise decomposed modes of information flow facilitate an improved diagnosis of mutual influence in collectives.

Heat-Mediated Optical Manipulation

Progress in optical manipulation has stimulated remarkable advances in a wide range of fields, including materials science, robotics, medical engineering, and nanotechnology. This Review focuses on an emerging class of optical manipulation techniques, termed heat-mediated optical manipulation. In comparison to conventional optical tweezers that rely on a tightly focused laser beam to trap objects, heat-mediated optical manipulation techniques exploit tailorable optothermo-matter interactions and rich mass transport dynamics to enable versatile control of matter of various compositions, shapes, and sizes. In addition to conventional tweezing, more distinct manipulation modes, including optothermal pulling, nudging, rotating, swimming, oscillating, and walking, have been demonstrated to enhance the functionalities using simple and low-power optics. We start with an introduction to basic physics involved in heat-mediated optical manipulation, highlighting major working mechanisms underpinning a variety of manipulation techniques. Next, we categorize the heat-mediated optical manipulation techniques based on different working mechanisms and discuss working modes, capabilities, and applications for each technique. We conclude this Review with our outlook on current challenges and future opportunities in this rapidly evolving field of heat-mediated optical manipulation.

When Soft Crystals Defy Newton's Third Law: Nonreciprocal Mechanics and Dislocation Motility

The effective interactions between the constituents of driven soft matter generically defy Newton's third law. Combining theory and numerical simulations, we establish that six classes of mechanics with no counterparts in equilibrium systems emerge in elastic crystals challenged by nonreciprocal interactions. Going beyond linear deformations, we reveal that interactions violating Newton's third law generically turn otherwise quiescent dislocations into motile singularities which steadily glide though periodic lattices.

Order and information in the patterns of spinning magnetic micro-disks at the air-water interface

The application of the Shannon entropy to study the relationship between information and structures has yielded insights into molecular and material systems. However, the difficulty in directly observing and manipulating atoms and molecules hampers the ability of these systems to serve as model systems for further exploring the links between information and structures. Here, we use, as a model experimental system, hundreds of spinning magnetic micro-disks self-organizing at the air-water interface to generate various spatiotemporal patterns with varying degrees of order. Using the neighbor distance as the information-bearing variable, we demonstrate the links among information, structure, and interactions. We establish a direct link between information and structure without using explicit knowledge of interactions. Last, we show that the Shannon entropy by neighbor distances is a powerful observable in characterizing structural changes. Our findings are relevant for analyzing natural self-organizing systems and for designing collective robots.

Guiding Self-Assembly of Active Colloids by Temporal Modulation of Activity

Self-organization phenomena in ensembles of self-propelled particles open pathways to the synthesis of new dynamic states not accessible by traditional equilibrium processes. The challenge is to develop a set of principles that facilitate the control and manipulation of emergent active states. Here, we report that dielectric rolling colloids energized by a pulsating electric field self-organize into alternating square lattices with a lattice constant controlled by the parameters of the field. We combine experiments and simulations to examine spatiotemporal properties of the emergent collective patterns and investigate the underlying dynamics of the self-organization.We reveal the resistance of the dynamic lattices to compression and expansion stresses leading to a hysteretic behavior of the lattice constant. The general mechanism of pattern synthesis and control in active ensembles via temporal modulation of activity can be applied to other active colloidal systems.

Hunting active Brownian particles: Learning optimal behavior

We numerically study active Brownian particles that can respond to environmental cues through a small set of actions (switching their motility and turning left or right with respect to some direction) which are motivated by recent experiments with colloidal self-propelled Janus particles. We employ reinforcement learning to find optimal mappings between the state of particles and these actions. Specifically, we first consider a predator-prey situation in which prey particles try to avoid a predator. Using as reward the squared distance from the predator, we discuss the merits of three state-action sets and show that turning away from the predator is the most successful strategy. We then remove the predator and employ as collective reward the local concentration of signaling molecules exuded by all particles and show that aligning with the concentration gradient leads to chemotactic collapse into a single cluster. Our results illustrate a promising route to obtain local interaction rules and design collective states in active matter.

Finite-Size Scaling at the Edge of Disorder in a Time-Delay Vicsek Model

Living many-body systems often exhibit scale-free collective behavior reminiscent of thermal critical phenomena. But their mutual interactions are inevitably retarded due to information processing and delayed actuation. We numerically investigate the consequences for the finite-size scaling in the Vicsek model of motile active matter. A growing delay time initially facilitates but ultimately impedes collective ordering and turns the dynamical scaling from diffusive to ballistic. It provides an alternative explanation of swarm traits previously attributed to inertia.

Phases and homogeneous ordered states in alignment-based self-propelled particle models

We study a set of models of self-propelled particles that achieve collective motion through similar alignment-based dynamics, considering versions with and without repulsive interactions that do not affect the heading directions. We explore their phase space within a broad range of values of two nondimensional parameters (coupling strength and Peclet number), characterizing their polarization and degree of clustering. The resulting phase diagrams display equivalent, similarly distributed regions for all models with repulsion. The diagrams without repulsion exhibit differences, in particular for high coupling strengths. We compare the boundaries and representative states of all regions, identifying various regimes that had not been previously characterized. We analyze in detail three types of homogeneous polarized states, comparing them to existing theoretical and numerical results by computing their velocity and density correlations, giant number fluctuations, and local order-density coupling. We find that they all deviate in one way or another from the theoretical predictions, attributing these differences either to the remaining inhomogeneities or to finite-size effects. We discuss our results in terms of the generic or specific features of each model, their thermodynamic limit, and the high mixing and low mixing regimes. Our study provides a broad, overarching perspective on the multiple phases and states found in alignment-based self-propelled particle models.

Precise visuomotor transformations underlying collective behavior in larval zebrafish

Complex schooling behaviors result from local interactions among individuals. Yet, how sensory signals from neighbors are analyzed in the visuomotor stream of animals is poorly understood. Here, we studied aggregation behavior in larval zebrafish and found that over development larvae transition from overdispersed groups to tight shoals. Using a virtual reality assay, we characterized the algorithms fish use to transform visual inputs from neighbors into movement decisions. We found that young larvae turn away from virtual neighbors by integrating and averaging retina-wide visual occupancy within each eye, and by using a winner-take-all strategy for binocular integration. As fish mature, their responses expand to include attraction to virtual neighbors, which is based on similar algorithms of visual integration. Using model simulations, we show that the observed algorithms accurately predict group structure over development. These findings allow us to make testable predictions regarding the neuronal circuits underlying collective behavior in zebrafish.

Active droploids

Active matter comprises self-driven units, such as bacteria and synthetic microswimmers, that can spontaneously form complex patterns and assemble into functional microdevices. These processes are possible thanks to the out-of-equilibrium nature of active-matter systems, fueled by a one-way free-energy flow from the environment into the system. Here, we take the next step in the evolution of active matter by realizing a two-way coupling between active particles and their environment, where active particles act back on the environment giving rise to the formation of superstructures. In experiments and simulations we observe that, under light-illumination, colloidal particles and their near-critical environment create mutually-coupled co-evolving structures. These structures unify in the form of active superstructures featuring a droplet shape and a colloidal engine inducing self-propulsion. We call them active droploids-a portmanteau of droplet and colloids. Our results provide a pathway to create active superstructures through environmental feedback.

Asymmetry-induced order in multilayer networks

Symmetries naturally occur in real-world networks and can significantly influence the observed dynamics. For instance, many synchronization patterns result from the underlying network symmetries, and high symmetries are known to increase the stability of synchronization. Yet here we find that general macroscopic features of network solutions such as regularity can be induced by breaking their symmetry of interactions. We demonstrate this effect in an ecological multilayer network where the topological asymmetries occur naturally. These asymmetries rescue the system from chaotic oscillations by establishing stable periodic orbits and equilibria. We call this phenomenon asymmetry-induced order and uncover its mechanism by analyzing both analytically and numerically the absence of dynamics on the system's synchronization manifold. Moreover, the bifurcation scenario describing the route from chaos to order is also disclosed. We demonstrate that this result also holds for generic node dynamics by analyzing coupled paradigmatic Rössler and Lorenz systems.

Reconfigurable artificial microswimmers with internal feedback

Self-propelling microparticles are often proposed as synthetic models for biological microswimmers, yet they lack the internally regulated adaptation of their biological counterparts. Conversely, adaptation can be encoded in larger-scale soft-robotic devices but remains elusive to transfer to the colloidal scale. Here, we create responsive microswimmers, powered by electro-hydrodynamic flows, which can adapt their motility via internal reconfiguration. Using sequential capillary assembly, we fabricate deterministic colloidal clusters comprising soft thermo-responsive microgels and light-absorbing particles. Light absorption induces preferential local heating and triggers the volume phase transition of the microgels, leading to an adaptation of the clusters' motility, which is orthogonal to their propulsion scheme. We rationalize this response via the coupling between self-propulsion and variations of particle shape and dielectric properties upon heating. Harnessing such coupling allows for strategies to achieve local dynamical control with simple illumination patterns, revealing exciting opportunities for developing tactic active materials.

The role of dimensionality and geometry in quench-induced nonequilibrium forces

We present an analytical formalism, supported by numerical simulations, for studying forces that act on curved walls following temperature quenches of the surrounding ideal Brownian fluid. We show that, for curved surfaces, the post-quench forces initially evolve rapidly to an extremal value, whereafter they approach their steady state value algebraically in time. In contrast to the previously-studied case of flat boundaries (lines or planes), the algebraic decay for curved geometries depends on the dimension of the system. Specifically, steady-state values of the force are approached in time ast^-d/2ind-dimensional spherical (curved) geometries. For systems consisting of concentric circles or spheres, the exponent does not change for the force on the outer circle or sphere. However, the force exerted on the inner circles or sphere experiences an overshoot and, as a result, does not evolve to the steady state in a simple algebraic manner. The extremal value of the force also depends on the dimension of the system, and originates from curved boundaries and the fact that particles inside a sphere or circle are locally more confined, and diffuse less freely than particles outside the circle or sphere.

Programmable Dynamic Shapes with a Swarm of Light-Powered Colloidal Motors

We report robust control over the dynamic assembly, disassembly, and reconfiguration of light-activated molybdenum disulfide (MoS₂ ) colloidal motor swarms with features not possible in equilibrium systems. A photochemical reaction produces chemical gradients across the MoS₂ colloidal motors to drive them to move. Under illumination of a gradient light, these colloidal motors display a positive phototactic motion. Mesoscale simulations prove that the self-diffusiophoresis induced by the locally consumed oxygen gradient across MoS₂ colloidal motors dominates the phototactic process. By programming the structured illumination, the collective migration and well-defined shapes of colloidal motor swarms can be externally regulated. The successful realization of programmable swarm transformation of colloidal motors like the emergent behaviors of living systems in nature provides a direct proof-of-concept for active soft materials and systems, with adaptive and interactive functions.

Medium Entropy Reduction and Instability in Stochastic Systems with Distributed Delay

Many natural and artificial systems are subject to some sort of delay, which can be in the form of a single discrete delay or distributed over a range of times. Here, we discuss the impact of this distribution on (thermo-)dynamical properties of time-delayed stochastic systems. To this end, we study a simple classical model with white and colored noise, and focus on the class of Gamma-distributed delays which includes a variety of distinct delay distributions typical for feedback experiments and biological systems. A physical application is a colloid subject to time-delayed feedback control, which is, in principle, experimentally realizable by co-moving optical traps. We uncover several unexpected phenomena in regard to the system's linear stability and its thermodynamic properties. First, increasing the mean delay time can destabilize or stabilize the process, depending on the distribution of the delay. Second, for all considered distributions, the heat dissipated by the controlled system (e.g., the colloidal particle) can become negative, which implies that the delay force extracts energy and entropy of the bath. As we show here, this refrigerating effect is particularly pronounced for exponential delay. For a specific non-reciprocal realization of a control device, we find that the entropic costs, measured by the total entropy production of the system plus controller, are the lowest for exponential delay. The exponential delay further yields the largest stable parameter regions. In this sense, exponential delay represents the most effective and robust type of delayed feedback.

Non-reciprocal phase transitions

Out of equilibrium, a lack of reciprocity is the rule rather than the exception. Non-reciprocity occurs, for instance, in active matter^1-6, non-equilibrium systems^7-9, networks of neurons^10,11, social groups with conformist and contrarian members¹², directional interface growth phenomena^13-15 and metamaterials^16-20. Although wave propagation in non-reciprocal media has recently been closely studied^1,16-20, less is known about the consequences of non-reciprocity on the collective behaviour of many-body systems. Here we show that non-reciprocity leads to time-dependent phases in which spontaneously broken continuous symmetries are dynamically restored. We illustrate this mechanism with simple robotic demonstrations. The resulting phase transitions are controlled by spectral singularities called exceptional points²¹. We describe the emergence of these phases using insights from bifurcation theory^22,23 and non-Hermitian quantum mechanics^24,25. Our approach captures non-reciprocal generalizations of three archetypal classes of self-organization out of equilibrium: synchronization, flocking and pattern formation. Collective phenomena in these systems range from active time-(quasi)crystals to exceptional-point-enforced pattern formation and hysteresis. Our work lays the foundation for a general theory of critical phenomena in systems whose dynamics is not governed by an optimization principle.

Fluctuation-Induced Phase Separation in Metric and Topological Models of Collective Motion

We study the role of noise on the nature of the transition to collective motion in dry active matter. Starting from field theories that predict a continuous transition at the deterministic level, we show that fluctuations induce a density-dependent shift of the onset of order, which in turn changes the nature of the transition into a phase-separation scenario. Our results apply to a range of systems, including models in which particles interact with their "topological" neighbors that have been believed so far to exhibit a continuous onset of order. Our analytical predictions are confirmed by numerical simulations of fluctuating hydrodynamics and microscopic models.

Reinforcement learning with artificial microswimmers

Artificial microswimmers that can replicate the complex behavior of active matter are often designed to mimic the self-propulsion of microscopic living organisms. However, compared with their living counterparts, artificial microswimmers have a limited ability to adapt to environmental signals or to retain a physical memory to yield optimized emergent behavior. Different from macroscopic living systems and robots, both microscopic living organisms and artificial microswimmers are subject to Brownian motion, which randomizes their position and propulsion direction. Here, we combine real-world artificial active particles with machine learning algorithms to explore their adaptive behavior in a noisy environment with reinforcement learning. We use a real-time control of self-thermophoretic active particles to demonstrate the solution of a simple standard navigation problem under the inevitable influence of Brownian motion at these length scales. We show that, with external control, collective learning is possible. Concerning the learning under noise, we find that noise decreases the learning speed, modifies the optimal behavior, and also increases the strength of the decisions made. As a consequence of time delay in the feedback loop controlling the particles, an optimum velocity, reminiscent of optimal run-and-tumble times of bacteria, is found for the system, which is conjectured to be a universal property of systems exhibiting delayed response in a noisy environment.

Shaping the gradients driving phoretic micro-swimmers: influence of swimming speed, budget of carbonic acid and environment

pH gradient-driven modular micro-swimmers are investigated as a model for a large variety of quasi-two-dimensional chemi-phoretic self-propelled entities. Using three-channel micro-photometry, we obtain a precise large field mapping of pH at a spatial resolution of a few microns and a pH resolution of [Formula: see text] units for swimmers of different velocities propelling on two differently charged substrates. We model our results in terms of solutions of the three-dimensional advection-diffusion equation for a 1:1 electrolyte, i.e. carbonic acid, which is produced by ion exchange and consumed by equilibration with dissolved [Formula: see text]. We demonstrate the dependence of gradient shape and steepness on swimmer speed, diffusivity of chemicals, as well as the fuel budget. Moreover, we experimentally observe a subtle, but significant feedback of the swimmer's immediate environment in terms of a substrate charge-mediated solvent convection. We discuss our findings in view of different recent results from other micro-fluidic or active matter investigations. We anticipate that they are relevant for quantitative modelling and targeted applications of diffusio-phoretic flows in general and artificial micro-swimmers in particular.

Controlling Cell Motion and Microscale Flow with Polarized Light Fields

We investigate how light polarization affects the motion of photoresponsive algae, Euglena gracilis. In a uniformly polarized field, cells swim approximately perpendicular to the polarization direction and form a nematic state with zero mean velocity. When light polarization varies spatially, cell motion is modulated by local polarization. In such light fields, cells exhibit complex spatial distribution and motion patterns which are controlled by topological properties of the underlying fields; we further show that ordered cell swimming can generate directed transporting fluid flow. Experimental results are quantitatively reproduced by an active Brownian particle model in which particle motion direction is nematically coupled to local light polarization.

Zebrafish Neighbor Distance Changes Relative to Conspecific Size, Position in the Water Column, and the Horizon: A Video-Playback Experiment

Many fish form schools and maintain visual contact with their neighbors in a three-dimensional environment. In this study, we assessed whether zebrafish modified their spacing and interaction time in an additive or multiplicative way relative to multiple sources of social information using computer animations. We simultaneously manipulated: (a) the size of the virtual conspecific (as a proxy of social cue magnitude), (b) the position of the virtual conspecific in the water column (as a proxy of the level of perceived risk), and (c) the absence/presence of the visual horizon (as a proxy of depth perception). We found that the size of the virtual conspecific independently affected spacing behavior (zebrafish increased their separation distance as conspecific size increased). However, some of these factors interacted significantly, such that their effects on social behavior depended on each other. For instance, zebrafish increased their separation distance under high risk conditions when the virtual conspecific was larger, but this risk effect disappeared when the conspecific was the same size or smaller, likely to avoid aggression. Also, zebrafish increased their separation distance when depth perception was enhanced under low risk conditions, but the effect of depth perception disappeared under high risk conditions. Overall, we found that certain dimensions of the visual social environment affected zebrafish spacing behavior in different ways, but they did not affect social interaction time. We discuss the implications of these findings for the spatial organization of fish schools.

Self-Motility of an Active Particle Induced by Correlations in the Surrounding Solution

Current models of phoretic transport rely on molecular forces creating a "diffuse" particle-fluid interface. We investigate theoretically an alternative mechanism, in which a diffuse interface emerges solely due to a nonvanishing correlation length of the surrounding solution. This mechanism can drive self-motility of a chemically active particle. Numerical estimates indicate that the velocity can reach micrometers per second. The predicted phenomenology includes a bilinear dependence of the velocity on the activity and a possible double velocity reversal upon varying the correlation length.

Dynamical Crystallites of Active Chiral Particles

One of the intrinsic characteristics of far-from-equilibrium systems is the nonrelaxational nature of the system dynamics, which leads to novel properties that cannot be understood and described by conventional pathways based on thermodynamic potentials. Of particular interest are the formation and evolution of ordered patterns composed of active particles that exhibit collective behavior. Here we examine such a type of nonpotential active system, focusing on effects of coupling and competition between chiral particle self-propulsion and self-spinning. It leads to the transition between three bulk dynamical regimes dominated by collective translative motion, spinning-induced structural arrest, and dynamical frustration. In addition, a persistently dynamical state of self-rotating crystallites is identified as a result of a localized-delocalized transition induced by the crystal-melt interface. The mechanism for the breaking of localized bulk states can also be utilized to achieve self-shearing or self-flow of active crystalline layers.

Lamellar to Micellar Phases and Beyond: When Tactic Active Systems Admit Free Energy Functionals

We consider microscopic models of active particles whose velocities, rotational diffusivities, and tumbling rates depend on the gradient of a local field that is either externally imposed or depends on all particle positions. Despite the fundamental differences between active and passive dynamics at the microscopic scale, we show that a large class of such tactic active systems admit fluctuating hydrodynamics equivalent to those of interacting Brownian colloids in equilibrium. We exploit this mapping to show how taxis may lead to the lamellar and micellar phases observed for soft repulsive colloids. In the context of chemotaxis, we show how the competition between chemoattractant and chemorepellent may lead to a bona fide equilibrium liquid-gas phase separation in which a loss of thermodynamic stability of the fluid signals the onset of a chemotactic collapse.

Leveraging synthetic particles for communication: from passive to active systems

Communication is one of the most remarkable behaviors in the living world. It is an important prerequisite for building an artificial cell which can be considered as alive. Achieving complex communicative behaviors leveraging synthetic particles will likely fill the gap between artificial vesicles and natural counterpart of cells and allow for the discovery of new therapies in medicine. In this review, we highlight recent endeavors for constructing communication with synthetic particles by revealing the principles underlying the communicative behaviors. Emergent progress using active particles to achieve communication is also discussed, which resembles the dynamic and out-of-equilibrium properties of communication in nature.

Pair formation in insect swarms driven by adaptive long-range interactions

In swarms of flying insects, the motions of individuals are largely uncoordinated with those of their neighbours, unlike the highly ordered motion of bird flocks. However, it has been observed that insects may transiently form pairs with synchronized relative motion while moving through the swarm. The origin of this phenomenon remains an open question. In particular, it is not known if pairing is a new behavioural process or whether it is a natural by-product of typical swarming behaviour. Here, using an 'adaptive-gravity' model that proposes that insects interact via long-range gravity-like acoustic attractions that are modulated by the total background sound (via 'adaptivity' or fold-change detection) and that reproduces measured features of real swarms, we show that pair formation can indeed occur without the introduction of additional behavioural rules. In the model, pairs form robustly whenever two insects happen to move together from the centre of the swarm (where the background sound is high) towards the swarm periphery (where the background sound is low). Due to adaptivity, the attraction between the pair increases as the background sound decreases, thereby forming a bound state since their relative kinetic energy is smaller than their pair-potential energy. When the pair moves into regions of high background sound, however, the process is reversed and the pair may break up. Our results suggest that pairing should appear generally in biological systems with long-range attraction and adaptive sensing, such as during chemotaxis-driven cellular swarming.

Straightforward preparation of supramolecular Janus nanorods by hydrogen bonding of end-functionalized polymers

Janus cylinders are one-dimensional colloids that have two faces with different compositions and functionalities, and are useful as building blocks for advanced functional materials. Such anisotropic objects are difficult to prepare with nanometric dimensions. Here we describe a robust and versatile strategy to form micrometer long Janus nanorods with diameters in the 10-nanometer range, by self-assembly in water of end-functionalized polymers. The Janus topology is not a result of the phase segregation of incompatible polymer arms, but is driven by the interactions between unsymmetrical and complementary hydrogen bonded stickers. Therefore, even compatible polymers can be used to form these Janus objects. In fact, any polymers should qualify, as long as they do not prevent co-assembly of the stickers. To illustrate their applicative potential, we show that these Janus nanorods can efficiently stabilize oil-in-water emulsions.

Feedback-controlled active brownian colloids with space-dependent rotational dynamics

The non-thermal nature of self-propelling colloids offers new insights into non-equilibrium physics. The central mathematical model to describe their trajectories is active Brownian motion, where a particle moves with a constant speed, while randomly changing direction due to rotational diffusion. While several feedback strategies exist to achieve position-dependent velocity, the possibility of spatial and temporal control over rotational diffusion, which is inherently dictated by thermal fluctuations, remains untapped. Here, we decouple rotational diffusion from thermal fluctuations. Using external magnetic fields and discrete-time feedback loops, we tune the rotational diffusivity of active colloids above and below its thermal value at will and explore a rich range of phenomena including anomalous diffusion, directed transport, and localization. These findings add a new dimension to the control of active matter, with implications for a broad range of disciplines, from optimal transport to smart materials.

Active colloidal systems can serve as an enabling platform to study complex out-of-equilibrium physical phenomena. Using a magnetic control with a feedback loop, here the authors program the dynamics of active Brownian particles by updating their rotational diffusion coefficient depending on their locations.

Otherwise identical particles with differing, fixed speeds demix under time-reversible dynamics

In recent years situations where elsewise identical particles demix when different degrees of freedom do not thermalize have become a research focus in nonequilibrium statistical mechanics. The majority of these models are formulated in the context of active particles, but the phenomenon also occurs for particles without driving. All the models studied so far share the property that they do not obey microscopic reversibility, and it may be thought that this is a necessary condition for such demixing to occur. We show here that such a demixing transition also occurs in a mixture of otherwise identical particles moving at two fixed but different speeds according to a time-reversible quasi-Newtonian dynamics. The mechanical instability underlying this behavior is generated by the lack of thermalization between the two subsystems, which is shared by all systems showing this behavior.

Chemically Active Particles: From One to Few on the Way to Many

Chemically active particles suspended in a liquid solution can achieve self-motility by locally changing the chemical composition of the solution via catalytic reactions at their surfaces. They operate intrinsically out of equilibrium, continuously extracting free energy from the environment to power the dissipative self-motility. The effective interactions involving active particles are, in general, nonreciprocal and anisotropic, even if the particles have simple shapes (e.g., Janus spheres). Accordingly, for chemically active particles a very rich behavior of collective motion and self-assembly may be expected to emerge, including phenomena such as microphase separation in the form of kinetically stable, finite-sized aggregates. Here, I succinctly review a number of recent experimental studies that demonstrate the self-assembly of structures, involving chemically active Janus particles, which exhibit various patterns of motion. These examples illustrate concepts such as "motors made out of motors" (as suggestively named by Fischer [Fischer, P. Nat. Phys. 2018, 14, 1072]). The dynamics of assembly and structure formation observed in these systems can provide benchmark, in-depth testing of the current understanding of motion and effective interactions produced by chemical activity. Finally, one notes that these significant achievements are likely just the beginning of the field. Recently reported particles endowed with time-dependent chemical activity or switchable reaction mechanisms open the way for exciting developments, such as periodic reshaping of self-assembled structures based on man-made internal clocks.

Colloidal Dynamics on a Choreographic Time Crystal

A choreographic time crystal is a dynamic lattice structure in which the points comprising the lattice move in a coordinated fashion. These structures were initially proposed for understanding the motion of synchronized satellite swarms. Using simulations, we examine colloids interacting with a choreographic crystal consisting of traps that could be created optically. As a function of the trap strength, speed, and colloidal filling fraction, we identify a series of phases including states where the colloids organize into a dynamic chiral loop lattice as well as a frustrated induced liquid state and a choreographic lattice state. We show that transitions between these states can be understood in terms of vertex frustration effects that occur during a certain portion of the choreographic cycle. Our results can be generalized to a broader class of systems of particles coupled to choreographic structures, such as vortices, ions, cold atoms, and soft matter systems.

Formation of stable and responsive collective states in suspensions of active colloids

Many animal species organise into disordered swarms, polarised flocks or swirls to protect from predators or optimise foraging. Previous studies suggest that such collective states are related to a critical point, which could explain their balance between robustness to noise and high responsiveness regarding external perturbations. Here we provide experimental evidence for this idea by investigating the stability of swirls formed by light-responsive active colloids which adjust their individual motion to positions and orientations of neighbours. Because their behaviour can be precisely tuned, controlled changes between different collective states can be achieved. During the transition between stable swirls and swarms we observe a maximum of the group's susceptibility indicating the vicinity of a critical point. Our results support the idea of system-independent organisation principles of collective states and provide useful strategies for the realisation of responsive yet stable ensembles in microrobotic systems.

Predictive local field theory for interacting active Brownian spheres in two spatial dimensions

We present a predictive local field theory for the nonequilibrium dynamics of interacting active Brownian particles with a spherical shape in two spatial dimensions. The theory is derived by a rigorous coarse-graining starting from the Langevin equations that describe the trajectories of the individual particles. For high accuracy and generality of the theory, it includes configurational order parameters and derivatives up to infinite order. In addition, we discuss possible approximations of the theory and present reduced models that are easier to apply. We show that our theory contains popular models such as Active Model B+  as special cases and that it provides explicit expressions for the coefficients occurring in these and other, often phenomenological, models. As a further outcome, the theory yields an analytical expression for the density-dependent mean swimming speed of the particles. To demonstrate an application of the new theory, we analyze a simple reduced model of the lowest nontrivial order in derivatives, which is able to predict the onset of motility-induced phase separation of the particles. By a linear stability analysis, an analytical expression for the spinodal corresponding to motility-induced phase separation is obtained. This expression is evaluated for the case of particles interacting repulsively by a Weeks-Chandler-Andersen potential. The analytical predictions for the spinodal associated with these particles are found to be in very good agreement with the results of Brownian dynamics simulations that are based on the same Langevin equations as our theory. Furthermore, the critical point predicted by our analytical results agrees excellently with recent computational results from the literature.

Effect of structure: A new insight into nanoparticle assemblies from inanimate to animate

Nanoparticle (NP) assemblies are among the foremost achievements of nanoscience and nanotechnology because their interparticle interactions overcome the weaknesses displayed by individual NPs. However, previous studies have considered NP assemblies as inanimate, which had led to their dynamic properties being overlooked. Animate properties, i.e., those mimicking biological properties, endow NP ensembles with unique and unexpected functionalities for practical applications. In this critical review, we highlight recent advances in our understanding of the properties of NP assemblies, particularly their animate properties. Key examples are used to illustrate critical concepts, and special emphasis is placed on animate property-dependent applications. Last, we discuss the barriers to further advances in this field.

A practical guide to active colloids: choosing synthetic model systems for soft matter physics research

Synthetic active colloids that harvest energy stored in the environment and swim autonomously are a popular model system for active matter. This emerging field of research sits at the intersection of materials chemistry, soft matter physics, and engineering, and thus cross-talk among researchers from different backgrounds becomes critical yet difficult. To facilitate this interdisciplinary communication, and to help soft matter physicists with choosing the best model system for their research, we here present a tutorial review article that describes, in appropriate detail, six experimental systems of active colloids commonly found in the physics literature. For each type, we introduce their background, material synthesis and operating mechanisms and notable studies from the soft matter community, and comment on their respective advantages and limitations. In addition, the main features of each type of active colloid are summarized into two useful tables. As materials chemists and engineers, we intend for this article to serve as a practical guide, so those who are not familiar with the experimental aspects of active colloids can make more informed decisions and maximize their creativity.

Controlled Group Motion of Anisotropic Janus Droplets Prepared by One-Step Vortex Mixing

In living systems, highly efficient biological micromotors are fascinating and crucial to the maintenance and regulation of normal functions. Inspired by this, solid colloid motors with controlled movements were recently developed for diverse applications. However, to meet the requirements of more elaborate functionalities, the development of droplet-based micromotors, which feature with appealing advantages such as deformability, encapsulation capability, and biocompatibility, is demanding. Herein, responsive Janus droplets with intrinsic magnetic anisotropy were fabricated, taking advantage of the traditional one-step vortex mixing that guarantees large-scale production. Furthermore, the size range of the droplets can be easily extended continuously from hundreds of micrometers down to tens of nanometers. What is more appealing, directed in situ group motions that include alignment, rotation, and transfer of the Janus droplets prepared were successfully realized and precisely controlled by using an external magnetic field. These collective motions induced excellent performances in pollutant adsorption and separation, switchable conductivities, and the size grading. Such scalable, simple, and controllable strategy can expand the application of Janus emulsions to complicated fields of microreactors, microsensors, and environmental regulation.

Self-Propulsion of Active Colloids via Ion Release: Theory and Experiments

We study the self-propulsion of a charged colloidal particle that releases ionic species using theory and experiments. We relax the assumptions of thin Debye length and weak nonequilibrium effects assumed in classical phoretic models. This leads to a number of unexpected features that cannot be rationalized considering the classic phoretic framework: an active particle can reverse the direction of motion by increasing the rate of ion release and can propel even with zero surface charge. Our theory predicts that there are optimal conditions for self-propulsion and a novel regime in which the velocity is insensitive to the background electrolyte concentration. The theoretical results quantitatively capture the salt-dependent velocity measured in our experiments using active colloids that propel by decomposing urea via a surface enzymatic reaction.

Conformation and dynamics of a self-avoiding active flexible polymer

We investigate conformations and dynamics of a polymer considering its monomers to be active Brownian particles. This active polymer shows very intriguing physical behavior which is absent in an active Rouse chain. The chain initially shrinks with active force, which starts swelling on further increase in force. The shrinkage followed by swelling is attributed purely to excluded-volume interactions among the monomers. In the swelling regime, the chain shows a crossover from the self-avoiding behavior to the Rouse behavior with scaling exponent ν_{a}≈1/2 for end-to-end distance. The nonmonotonicity in the structure is analyzed through various physical quantities; specifically, radial distribution function of monomers, scattering time, as well as various energy calculations. The chain relaxes faster than the Rouse chain in the intermediate force regime, with a crossover in variation of relaxation time at large active force as given by a power law τ_{r}∼Pe^{-4/3} (Pe is Péclet number).

Cohesive self-organization of mobile microrobotic swarms

Mobile microrobots are envisioned to be useful in a wide range of high-impact applications, many of which require cohesive group formation to maintain self-bounded swarms in the absence of confining boundaries. Cohesive group formation relies on a balance between attractive and repulsive interactions between agents. We found that a balance of magnetic dipolar attraction and multipolar repulsion between self-assembled particle chain microrobots enables their self-organization into cohesive clusters. Self-organized microrobotic clusters move above a solid substrate via a hydrodynamic self-propulsion mechanism. Cluster velocity increases with cluster size, resulting from collective hydrodynamic effects. Clustering is promoted by the strength of cohesive interactions and is hindered by the heterogeneities of individual microrobots. The scalability of cohesive interactions allows the formation of larger groups, whose internal spatiotemporal organization undergoes a transition from solid-like ordering to a liquid-like behavior with increasing cluster size. Our work elucidates the dynamics of clustering under cohesive interactions, and presents an approach for addressing the operation of microrobots as localized collectives.

A model of collective behavior based purely on vision

Classical models of collective behavior often take a "bird's-eye perspective," assuming that individuals have access to social information that is not directly available (e.g., the behavior of individuals outside of their field of view). Despite the explanatory success of those models, it is now thought that a better understanding needs to incorporate the perception of the individual, i.e., how internal and external information are acquired and processed. In particular, vision has appeared to be a central feature to gather external information and influence the collective organization of the group. Here, we show that a vision-based model of collective behavior is sufficient to generate organized collective behavior in the absence of spatial representation and collision. Our work suggests a different approach for the development of purely vision-based autonomous swarm robotic systems and formulates a mathematical framework for exploration of perception-based interactions and how they differ from physical ones.

Cargo capture and transport by colloidal swarms

Controlling active colloidal particle swarms could enable useful microscopic functions in emerging applications at the interface of nanotechnology and robotics. Here, we present a computational study of controlling self-propelled colloidal particle propulsion speeds to cooperatively capture and transport cargo particles, which otherwise produce random dispersions. By sensing swarm and cargo coordinates, each particle's speed is actuated according to a control policy based on multiagent assignment and path planning strategies that navigate stochastic particle trajectories to targets around cargo. Colloidal swarms are shown to dynamically cage cargo at their center via inward radial forces while simultaneously translating via directional forces. Speed, power, and efficiency of swarm tasks display emergent coupled dependences on swarm size and pair interactions and approach asymptotic limits indicating near-optimal performance. This scheme exploits unique interactions and stochastic dynamics in colloidal swarms to capture and transport microscopic cargo in a robust, stable, error-tolerant, and dynamic manner.