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

Direct measurement of self-diffusiophoretic force generated by active colloids of different patch coverage using optical tweezers

HYPOTHESIS

Synthetic micro/nanomotors are gaining extensive attention for various biomedical applications (especially in drug delivery) due to their ability to mimic the motion of biological micro/nanoscale swimmers. The feasibility of these applications relies on tight control of propulsion speed, direction, and type of motion (translation, circular, etc.) along with the exerted self-propulsive force. We propose to exploit the variation of both self-propulsion speed and force of active colloids with different patch coverages (with and without supporting layer) for engineering diffusiophoretic micro/nanomotors.

EXPERIMENTS

The microswimmers were designed at various patch coverages (10°, 30°, and 90°) with (Ti/Pt) and without (Pt) an adhesion layer for the catalytic patch through glancing angle metal deposition (GLAD) technique. Mean-square displacement (MSD) analysis was performed to obtain the self-propulsion parameters like speed and angular speed. Using optical tweezers (OT), the self-propulsive force was measured from the force power spectral density.

FINDINGS

The findings of our experiments suggest the non-requirement of any adhesion layer preceding the catalyst deposition since the Pt 10° colloidal batch had the maximal self-propulsion speed (4.61±0.3μm/s) and force (345±57fN) for 5% w/v H2O2 fuel concentration. Moreover, the self-propulsion speed and force decreased with increasing patch size, contrary to theoretical estimates. Also, the self-propulsive force obtained from MSD is 2 to 4 times lower in magnitude than the OT based force values. We believe that the self-propelling motion of the micromotors is possibly hindered due to interactions with the surface of the quartz cuvette during the optical microscopic analysis. Further, the MSD is limited to the self-propulsive motion in two dimensions. On the other hand, OT based force measurement involve trapping the particles in the bulk of the solution entirely avoiding the particle-substrate interactions. Hence, OT based force measurements are better than the propulsion velocity based stokes drag force estimates. We believe that this study can lay the foundation in designing efficient micro/nanomotors for translational biomedical applications.

Swirling Due to Misaligned Perception-Dependent Motility

A system of particles with motility variable in terms of a vision-type of perception is investigated by a combination of Langevin dynamics simulations in two-dimensional systems and an analytical approach based on conservation law principles. Persistent swirling with predetermined direction is here induced by differentiating the self-propulsion direction and the perception cone axis. Clusters can have a fluidlike center with a rotating outer layer or display a solidlike rotation driven by the outer layer activity. Discontinuous motility with misaligned perception might therefore serve as a powerful self-organization strategy in microrobots.

Phase separation, edge currents, and Hall effect for active matter with Magnus dynamics

We examine run-and-tumble disks in two-dimensional systems where the particles also have a Magnus component to their dynamics. For increased activity, we find that the system forms a motility-induced phase-separated (MIPS) state with chiral edge flow around the clusters, where the direction of the current is correlated with the sign of the Magnus term. The stability of the MIPS state is non-monotonic as a function of increasing Magnus term amplitude, with the MIPS region first extending down to lower activities followed by a break up of MIPS at large Magnus amplitudes into a gel-like state. We examine the dynamics in the presence of quenched disorder and a uniform drive and find that the bulk flow exhibits a drive-dependent Hall angle. This is a result of the side jump effect produced by scattering from the pinning sites and is similar to the behavior found for skyrmions in chiral magnets with quenched disorder.

Lane formation in gravitationally driven colloid mixtures consisting of up to three different particle sizes

Brownian dynamics simulations are utilized to study segregation phenomena far from thermodynamic equilibrium. In the present study, we expand upon the analysis of binary colloid mixtures and introduce a third particle species to further our understanding of colloidal systems. Gravitationally driven, spherical colloids immersed in an implicit solvent are confined in two-dimensional linear microchannels. The interaction between the colloids is modeled by the Weeks-Chandler-Andersen potential, and the confinement of the colloids is realized by hard walls based on the solution of the Smoluchowski equation in half space. In binary and ternary colloidal systems, a difference in the driving force is achieved by differing colloid sizes but fixed mass density. We observe for both the binary and ternary systems that a driving force difference induces a nonequilibrium phase transition to lanes. For ternary systems, we study the tendency of lane formation to depend on the diameter of the medium-sized colloids. Here we find a sweet spot for lane formation in ternary systems. Furthermore, we study the interaction of two differently sized colloids at the channel walls. Recently we observed that driven large colloids push smaller colloids to the walls. This results in small particle lanes at the walls at early simulation times. In this work we additionally find that thin lanes are unstable and dissolve over very long time frames. Furthermore, we observe a connection between lane formation and the nonuniform distribution of particles along the channel length. This nonuniform distribution occurs either alongside lane formation or in shared lanes (i.e., lanes consisting of two colloid types).

Swarm Autonomy: From Agent Functionalization to Machine Intelligence

Swarm behaviors are common in nature, where individual organisms collaborate via perception, communication, and adaptation. Emulating these dynamics, large groups of active agents can self-organize through localized interactions, giving rise to complex swarm behaviors, which exhibit potential for applications across various domains. This review presents a comprehensive summary and perspective of synthetic swarms, to bridge the gap between the microscale individual agents and potential applications of synthetic swarms. It is begun by examining active agents, the fundamental units of synthetic swarms, to understand the origins of their motility and functionality in the presence of external stimuli. Then inter-agent communications and agent-environment communications that contribute to the swarm generation are summarized. Furthermore, the swarm behaviors reported to date and the emergence of machine intelligence within these behaviors are reviewed. Eventually, the applications enabled by distinct synthetic swarms are summarized. By discussing the emergent machine intelligence in swarm behaviors, insights are offered into the design and deployment of autonomous synthetic swarms for real-world applications.

Smart active particles learn and transcend bacterial foraging strategies

Throughout evolution, bacteria and other microorganisms have learned efficient foraging strategies that exploit characteristic properties of their unknown environment. While much research has been devoted to the exploration of statistical models describing the dynamics of foraging bacteria and other (micro-) organisms, little is known, regarding the question of how good the learned strategies actually are. This knowledge gap is largely caused by the absence of methods allowing to systematically develop alternative foraging strategies to compare with. In the present work, we use deep reinforcement learning to show that a smart run-and-tumble agent, which strives to find nutrients for its survival, learns motion patterns that are remarkably similar to the trajectories of chemotactic bacteria. Strikingly, despite this similarity, we also find interesting differences between the learned tumble rate distribution and the one that is commonly assumed for the run and tumble model. We find that these differences equip the agent with significant advantages regarding its foraging and survival capabilities. Our results uncover a generic route to use deep reinforcement learning for discovering search and collection strategies that exploit characteristic but initially unknown features of the environment. These results can be used, e.g., to program future microswimmers, nanorobots, and smart active particles for tasks like searching for cancer cells, micro-waste collection, or environmental remediation.

Persistent and responsive collective motion with adaptive time delay

It is beneficial for collective structures to simultaneously have high persistence to environmental noise and high responsivity to nontrivial external stimuli. However, without the ability to differentiate useful information from noise, there is always a tradeoff between persistence and responsivity within the collective structures. To address this, we propose adaptive time delay inspired by the adaptive behavior observed in the school of fish. This strategy is tested using particles powered by optothermal fields coupled with an optical feedback-control system. By applying the adaptive time delay with a proper threshold, we experimentally observe the responsivity of the collective structures enhanced by approximately 1.6 times without sacrificing persistence. Furthermore, we integrate adaptive time delay with long-distance transportation and obstacle-avoidance capabilities to prototype adaptive swarm microrobots. This research demonstrates the potential of adaptive time delay to address the persistence-responsivity tradeoff and lays the foundation for intelligent swarm micro/nanorobots operating in complex environments.

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.

Quorum sensing-induced transition from colloidal waves to Turing-like patterns in chemorepulsive active colloids

The study of active systems, especially in the presence of a chemical background field, is garnering significant attention. Traditionally, the self-propelled velocity of active colloids was assumed to be constant, independent of the local density of colloids. In this work, we introduce a chemotactic active system that features quorum sensing (QS), wherein particles act as chemorepellents. Interestingly, these particles lose their activity in regions of high local particle density. Our findings reveal that QS leads to a transition from an oscillatory colloidal wave to a Turing-like pattern, with the observation of an intermediate state. With the variation of the sensing threshold, both the mean oscillation frequency of the system and the number of clusters exhibit non-monotonic dependence. Furthermore, the QS-induced pattern differs markedly from systems without QS, primarily due to the competitive interplay between diffusion and chemotaxis. The dynamics of this phenomenon are explained using a coarse-grained mean field model.

Motility-induced phase separation and frustration in active matter swarmalators

We introduce a two dimensional system of active matter swarmalators composed of elastically interacting run-and-tumble active disks with an internal parameter ϕ_{i}. The disks experience an additional attractive or repulsive force with neighboring disks depending upon their relative difference in ϕ_{i}, making them similar to swarmalators used in robotic systems. In the absence of the internal parameter, the system forms a motility-induced phase separated (MIPS) state, but when the swarmalator interactions are present, a wide variety of other active phases appear depending upon whether the interaction is attractive or repulsive and whether the particles act to synchronize or ant-synchronize their internal parameter values. These phases include a gas-free gel regime, arrested clusters, a labyrinthine state, a regular MIPS state, a frustrated MIPS state for attractive antisynchronization, and a superlattice MIPS state for attractive synchronization.

Synchronous and Fully Steerable Active Particle Systems for Enhanced Mimicking of Collective Motion in Nature

The collective motion observed in living active matter, such as fish schools and bird flocks, is characterized by its dynamic and complex nature, involving various moving states and transitions. By tailoring physical interactions or incorporating information exchange capabilities, inanimate active particles can exhibit similar behavior. However, the lack of synchronous and arbitrary control over individual particles hinders their use as a test system for the study of more intricate collective motions in living species. Herein, a novel optical feedback control system that enables the mimicry of collective motion observed in living objects using active particles is proposed. This system allows for the experimental investigation of the velocity alignment, a seminal model of collective motion (known as the Vicsek model), in a microscale perturbed environment with controllable and realistic conditions. The spontaneous formation of different moving states and dynamic transitions between these states is observed. Additionally, the high robustness of the active-particle group at the critical density under the influence of different perturbations is quantitatively validated. These findings support the effectiveness of velocity alignment in real perturbed environments, thereby providing a versatile platform for fundamental studies on collective motion and the development of innovative swarm microrobotics.

Harnessing synthetic active particles for physical reservoir computing

The processing of information is an indispensable property of living systems realized by networks of active processes with enormous complexity. They have inspired many variants of modern machine learning, one of them being reservoir computing, in which stimulating a network of nodes with fading memory enables computations and complex predictions. Reservoirs are implemented on computer hardware, but also on unconventional physical substrates such as mechanical oscillators, spins, or bacteria often summarized as physical reservoir computing. Here we demonstrate physical reservoir computing with a synthetic active microparticle system that self-organizes from an active and passive component into inherently noisy nonlinear dynamical units. The self-organization and dynamical response of the unit are the results of a delayed propulsion of the microswimmer to a passive target. A reservoir of such units with a self-coupling via the delayed response can perform predictive tasks despite the strong noise resulting from the Brownian motion of the microswimmers. To achieve efficient noise suppression, we introduce a special architecture that uses historical reservoir states for output. Our results pave the way for the study of information processing in synthetic self-organized active particle systems.

Irreversibility across a Nonreciprocal PT-Symmetry-Breaking Phase Transition

Nonreciprocal interactions are commonplace in continuum-level descriptions of both biological and synthetic active matter, yet studies addressing their implications for time reversibility have so far been limited to microscopic models. Here, we derive a general expression for the average rate of informational entropy production in the most generic mixture of conserved phase fields with nonreciprocal couplings and additive conservative noise. For the particular case of a binary system with Cahn-Hilliard dynamics augmented by nonreciprocal cross-diffusion terms, we observe a nontrivial scaling of the entropy production rate across a parity-time symmetry breaking phase transition. We derive a closed-form analytic expression in the weak-noise regime for the entropy production rate due to the emergence of a macroscopic dynamic phase, showing it can be written in terms of the global polar order parameter, a measure of parity-time symmetry breaking.

Complex motion of steerable vesicular robots filled with active colloidal rods

While the collective motion of active particles has been studied extensively, effective strategies to navigate particle swarms without external guidance remain elusive. We introduce a method to control the trajectories of two-dimensional swarms of active rod-like particles by confining the particles to rigid bounding membranes (vesicles) with non-uniform curvature. We show that the propelling agents spontaneously form clusters at the membrane wall and collectively propel the vesicle, turning it into an active superstructure. To further guide the motion of the superstructure, we add discontinuous features to the rigid membrane boundary in the form of a kinked tip, which acts as a steering component to direct the motion of the vesicle. We report that the system's geometrical and material properties, such as the aspect ratio and Péclet number of the active rods as well as the kink angle and flexibility of the membrane, determine the stacking of active particles close to the kinked confinement and induce a diverse set of dynamical behaviors of the superstructure, including linear and circular motion both in the direction of, and opposite to, the kink. From a systematic study of these various behaviors, we design vesicles with switchable and reversible locomotions by tuning the confinement parameters. The observed phenomena suggest a promising mechanism for particle transportation and could be used as a basic element to navigate active matter through complex and tortuous environments.

Entropy production in the nonreciprocal Cahn-Hilliard model

We study the nonreciprocal Cahn-Hilliard model with thermal noise as a prototypical example of a generic class of non-Hermitian stochastic field theories, analyzed in two companion papers [Suchanek, Kroy, and Loos, Phys. Rev. Lett. 131, 258302 (2023)10.1103/PhysRevLett.131.258302; Phys. Rev. E 108, 064123 (2023)10.1103/PhysRevE.108.064123]. Due to the nonreciprocal coupling between two field components, the model is inherently out of equilibrium and can be regarded as an active field theory. Beyond the conventional homogeneous and static-demixed phases, it exhibits a traveling-wave phase, which can be entered via either an oscillatory instability or a critical exceptional point. By means of a Fourier decomposition of the entropy production rate, we quantify the associated scale-resolved time-reversal symmetry breaking, in all phases and across the transitions, in the low-noise regime. Our perturbative calculation reveals its dependence on the strength of the nonreciprocal coupling. Surging entropy production near the static-dynamic transitions can be attributed to entropy-generating fluctuations in the longest wavelength Fourier mode and heralds the emerging traveling wave. Its translational dynamics can be mapped on the dissipative ballistic motion of an active (quasi)particle.

Hierarchical defect-induced condensation in active nematics

Topological defects play a central role in the formation and organization of various biological systems. Historically, such nonequilibrium defects have been mainly studied in the context of homogeneous active nematics. Phase-separated systems, in turn, are known to form dense and dynamic nematic bands, but typically lack topological defects. In this paper, we use agent-based simulations of weakly aligning, self-propelled polymers and demonstrate that contrary to the existing paradigm phase-separated active nematics form -1/2 defects. Moreover, these defects, emerging due to interactions among dense nematic bands, constitute a novel second-order collective state. We investigate the morphology of defects in detail and find that their cores correspond to a strong increase in density, associated with a condensation of nematic fluxes. Unlike their analogs in homogeneous systems, such condensed defects form and decay in a different way and do not involve positively charged partners. We additionally observe and characterize lateral arc-like structures that separate from a band's bulk and move in transverse direction. We show that the key control parameters defining the route from stable bands to the coexistence of dynamic lanes and defects are the total density of particles and their path persistence length. We introduce a hydrodynamic theory that qualitatively recapitulates all the main features of the agent-based model, and use it to show that the emergence of both defects and arcs can be attributed to the same anisotropic active fluxes. Finally, we present a way to artificially engineer and position defects, and speculate about experimental verification of the provided model.

Environmental memory boosts group formation of clueless individuals

The formation of groups of interacting individuals improves performance and fitness in many decentralised systems, from micro-organisms to social insects, from robotic swarms to artificial intelligence algorithms. Often, group formation and high-level coordination in these systems emerge from individuals with limited information-processing capabilities implementing low-level rules of communication to signal to each other. Here, we show that, even in a community of clueless individuals incapable of processing information and communicating, a dynamic environment can coordinate group formation by transiently storing memory of the earlier passage of individuals. Our results identify a new mechanism of indirect coordination via shared memory that is primarily promoted and reinforced by dynamic environmental factors, thus overshadowing the need for any form of explicit signalling between individuals. We expect this pathway to group formation to be relevant for understanding and controlling self-organisation and collective decision making in both living and artificial active matter in real-life environments.

Non-reciprocity across scales in active mixtures

In active matter, particles typically experience mediated interactions, which are not constrained by Newton's third law and are therefore generically non-reciprocal. Non-reciprocity leads to a rich set of emerging behaviors that are hard to account for starting from the microscopic scale, due to the absence of a generic theoretical framework out of equilibrium. Here we consider bacterial mixtures that interact via mediated, non-reciprocal interactions (NRI) like quorum-sensing and chemotaxis. By explicitly relating microscopic and macroscopic dynamics, we show that, under conditions that we derive explicitly, non-reciprocity may fade upon coarse-graining, leading to large-scale equilibrium descriptions. In turn, this allows us to account quantitatively, and without fitting parameters, for the rich behaviors observed in microscopic simulations including phase separation, demixing, and multi-phase coexistence. We also derive the condition under which non-reciprocity survives coarse-graining, leading to a wealth of dynamical patterns. Again, our analytical approach allows us to predict the phase diagram of the system starting from its microscopic description. All in all, our work demonstrates that the fate of non-reciprocity across scales is a subtle and important question.

Method of spectral response to stochastic processes for measuring the nonreciprocal effective interactions

The theoretical background of the nonperturbative method of spectral response to stochastic processes (SRSP) for measuring the nonreciprocal interparticle effective interactions in strongly coupled underdamped systems is described. Analytical expressions for vibrational spectral density of confined Brownian particles with a nonreciprocal effective interaction are presented. The changes in the vibrational spectral density with varying different parameters of the system (nonreciprocity, viscosity, ratios of particle sizes, and intensities of random processes acting on each particle) are discussed using the example of a pair of nonidentical particles in a harmonic trap. The SRSP method is compared to three other nonperturbative methods. The SRSP method demonstrates an undeniable advantage when processing particle trajectories with errors in particle tracking.

Dynamical Pattern Formation without Self-Attraction in Quorum-Sensing Active Matter: The Interplay between Nonreciprocity and Motility

We study a minimal model involving two species of particles interacting via quorum-sensing rules. Combining simulations of the microscopic model and linear stability analysis of the associated coarse-grained field theory, we identify a mechanism for dynamical pattern formation that does not rely on the standard route of intraspecies effective attractive interactions. Instead, our results reveal a highly dynamical phase of chasing bands induced only by the combined effects of self-propulsion and nonreciprocity in the interspecies couplings. Turning on self-attraction, we find that the system may phase separate into a macroscopic domain of such chaotic chasing bands coexisting with a dilute gas. We show that the chaotic dynamics of bands at the interfaces of this phase-separated phase results in anomalously slow coarsening.

Pattern formation by bacteria-phage interactions

The interactions between bacteria and phages-viruses that infect bacteria-play critical roles in agriculture, ecology, and medicine; however, how these interactions influence the spatial organization of both bacteria and phages remain largely unexplored. Here, we address this gap in knowledge by developing a theoretical model of motile, proliferating bacteria that aggregate via motility-induced phase separation (MIPS) and encounter phage that infect and lyse the cells. We find that the non-reciprocal predator-prey interactions between phage and bacteria strongly alter spatial organization, in some cases giving rise to a rich array of finite-scale stationary and dynamic patterns in which bacteria and phage coexist. We establish principles describing the onset and characteristics of these diverse behaviors, thereby helping to provide a biophysical basis for understanding pattern formation in bacteria-phage systems, as well as in a broader range of active and living systems with similar predator-prey or other non-reciprocal interactions.

Nonreciprocal Dicke Model

We investigate the physics of an open two-component Dicke model, where the light field mediates nonreciprocal interactions between two spin species. We show that the model, which we dub nonreciprocal Dicke model, exhibits a discrete parity-time (PT) symmetry and we characterize the emergence of a nonstationary phase, so far explained in terms of dissipation-induced instability, as spontaneous breaking of PT symmetry. We further show that such PT symmetry breaking embodies an instance of a nonreciprocal phase transition, a concept recently introduced by Fruchart et al. [Nature (London) 592, 363 (2021)NATUAS0028-083610.1038/s41586-021-03375-9]. Remarkably, the phase transition in our model does not necessitate the presence of any underlying broken symmetry or exceptional points in the spectrum, both believed to be essential requirements for nonreciprocal phase transitions. Our results establish driven-dissipative light-matter systems as a new avenue for exploring nonreciprocal phase transitions and contribute to the theory of nonreciprocal collective phenomena.

Capture and transport of rod-shaped cargo via programmable active particles

We study the influence of the cargo shape on the capture and transport process of colloidal rods via swarms of active particles using Brownian dynamics simulations. Starting at random initial conditions, active particles that interact via the Lennard-Jones potential and possess a tuneable speed are utilised to capture passive rods inside a hexagonal cage of individually addressable units. By adjusting the velocity of the individual active particles, the rod can then be transported. To guarantee a successful capture process (with a strong localisation), we find that specific geometric and energetic constraints have to be met; i.e., the length of the rod must approximately be in the vicinity of an odd multiple of the lattice constant of the hexagonal cage, and the Lennard-Jones interaction strength must be in the range of [Formula: see text] to [Formula: see text]. If the cargo aspect ratio gets too large, the subsequent transport of successfully captured rods can fail. For systems where transport is possible, an increase in the cargo aspect ratio decreases the achievable transport velocity. Our work shows that the particle shape must be considered while designing interaction rules to accomplish specific tasks via groups of controllable units.

Pair Interaction between Two Catalytically Active Colloids

Due to the intrinsically complex non-equilibrium behavior of the constituents of active matter systems, a comprehensive understanding of their collective properties is a challenge that requires systematic bottom-up characterization of the individual components and their interactions. For self-propelled particles, intrinsic complexity stems from the fact that the polar nature of the colloids necessitates that the interactions depend on positions and orientations of the particles, leading to a 2d - 1 dimensional configuration space for each particle, in d dimensions. Moreover, the interactions between such non-equilibrium colloids are generically non-reciprocal, which makes the characterization even more complex. Therefore, derivation of generic rules that enable us to predict the outcomes of individual encounters as well as the ensuing collective behavior will be an important step forward. While significant advances have been made on the theoretical front, such systematic experimental characterizations using simple artificial systems with measurable parameters are scarce. Here, two different contrasting types of colloidal microswimmers are studied, which move in opposite directions and show distinctly different interactions. To facilitate the extraction of parameters, an experimental platform is introduced in which these parameters are confined on a 1D track. Furthermore, a theoretical model for interparticle interactions near a substrate is developed, including both phoretic and hydrodynamic effects, which reproduces their behavior. For subsequent validation, the degrees of freedom are increased to 2D motion and resulting trajectories are predicted, finding remarkable agreement. These results may prove useful in characterizing the overall alignment behavior of interacting self-propelling active swimmer and may find direct applications in guiding the design of active-matter systems involving phoretic and hydrodynamic interactions.

On-Demand Breaking of Action-Reaction Reciprocity between Magnetic Microdisks Using Global Stimuli

Coupled physical interactions induce emergent collective behaviors of many interacting objects. Nonreciprocity in the interactions generates unexpected behaviors. There is a lack of experimental model system that switches between the reciprocal and nonreciprocal regime on demand. Here, we study a system of magnetic microdisks that breaks action-reaction reciprocity via fluid-mediated hydrodynamic interactions, on demand. Via experiments and simulations, we demonstrate that nonreciprocal interactions generate self-propulsion-like behaviors of a pair of disks; group separation in collective of magnetically nonidentical disks; and decouples a part of the group from the rest. Our results could help in developing controllable microrobot collectives. Our approach highlights the effect of global stimuli in generating nonreciprocal interactions.

Inverted Sedimentation of Active Particles in Unbiased ac Fields

Gaining control over the motion of active particles is crucial for applications ranging from targeted cargo delivery to nanomedicine. While much progress has been made recently to control active motion based on external forces, flows, or gradients in concentration or light intensity, which all have a well-defined direction or bias, little is known about how to steer active particles in situations where no permanent bias can be realized. Here, we show that ac fields with a vanishing time average provide an alternative route to steering active particles. We exemplify this route for inertial active particles in a gravitational field, observing that a substantial fraction of them persistently travels in the upward direction upon switching on the ac field, resulting in an inverted sedimentation profile at the top wall of a confining container. Our results offer a generic control principle that could be used in the future to steer active motion, direct collective behaviors, and purify mixtures.

Perspectives on adaptive dynamical systems

Adaptivity is a dynamical feature that is omnipresent in nature, socio-economics, and technology. For example, adaptive couplings appear in various real-world systems, such as the power grid, social, and neural networks, and they form the backbone of closed-loop control strategies and machine learning algorithms. In this article, we provide an interdisciplinary perspective on adaptive systems. We reflect on the notion and terminology of adaptivity in different disciplines and discuss which role adaptivity plays for various fields. We highlight common open challenges and give perspectives on future research directions, looking to inspire interdisciplinary approaches.

Dynamics and interactions of Quincke roller clusters: From orbits and flips to excited states

Active matter systems may be characterized by the conversion of energy into active motion, e.g., the self-propulsion of microorganisms. Artificial active colloids form models that exhibit essential properties of more complex biological systems but are amenable to laboratory experiments. While most experimental models consist of spheres, active particles of different shapes are less understood. Furthermore, interactions between these anisotropic active colloids are even less explored. Here, we investigate the motion of active colloidal clusters and the interactions between them. We focus on self-assembled dumbbells and trimers powered by an external dc electric field. For dumbbells, we observe an activity-dependent behavior of spinning, circular, and orbital motions. Moreover, collisions between dumbbells lead to the hierarchical self-assembly of tetramers and hexamers, both of which form rotational excited states. On the other hand, trimers exhibit flipping motion that leads to trajectories reminiscent of a honeycomb lattice.

Light, Matter, Action: Shining Light on Active Matter

Light carries energy and momentum. It can therefore alter the motion of objects on the atomic to astronomical scales. Being widely available, readily controllable, and broadly biocompatible, light is also an ideal tool to propel microscopic particles, drive them out of thermodynamic equilibrium, and make them active. Thus, light-driven particles have become a recent focus of research in the field of soft active matter. In this Perspective, we discuss recent advances in the control of soft active matter with light, which has mainly been achieved using light intensity. We also highlight some first attempts to utilize light's additional properties, such as its wavelength, polarization, and momentum. We then argue that fully exploiting light with all of its properties will play a critical role in increasing the level of control over the actuation of active matter as well as the flow of light itself through it. This enabling step will advance the design of soft active matter systems, their functionalities, and their transfer toward technological applications.

Long-Range Order and Directional Defect Propagation in the Nonreciprocal XY Model with Vision Cone Interactions

We study a two-dimensional, nonreciprocal XY model, where each spin interacts only with its nearest neighbors in a certain angle around its current orientation, i.e., its "vision cone." Using energetic arguments and Monte Carlo simulations, we show that a true long-range ordered phase emerges. A necessary ingredient is a configuration-dependent bond dilution entailed by the vision cones. Strikingly, defects propagate in a directional manner, thereby breaking the parity and time-reversal symmetry of the spin dynamics. This is detectable by a nonzero entropy production rate.

Photochromism from wavelength-selective colloidal phase segregation

Phase segregation is ubiquitously observed in immiscible mixtures, such as oil and water, in which the mixing entropy is overcome by the segregation enthalpy1-3. In monodispersed colloidal systems, however, the colloidal-colloidal interactions are usually non-specific and short-ranged, which leads to negligible segregation enthalpy4. The recently developed photoactive colloidal particles show long-range phoretic interactions, which can be readily tuned with incident light, suggesting an ideal model for studying phase behaviour and structure evolution kinetics5,6. In this work, we design a simple spectral selective active colloidal system, in which TiO2 colloidal species were coded with spectral distinctive dyes to form a photochromic colloidal swarm. In this system, the particle-particle interactions can be programmed by combining incident light with various wavelengths and intensities to enable controllable colloidal gelation and segregation. Furthermore, by mixing the cyan, magenta and yellow colloids, a dynamic photochromic colloidal swarm is formulated. On illumination of coloured light, the colloidal swarm adapts the appearance of incident light due to layered phase segregation, presenting a facile approach towards coloured electronic paper and self-powered optical camouflage.

Three-Dimensionally Complex Phase Behavior and Collective Phenomena in Mixtures of Acoustically Powered Chiral Microspinners

The process of dynamic self-organization of small building blocks is fundamental to the emergent function of living systems and is characteristic of their out-of-equilibrium homeostasis. The ability to control the interactions of synthetic particles in large groups could lead to the realization of analogous macroscopic robotic systems with microscopic complexity. Rotationally induced self-organization has been observed in biological systems and modeled theoretically, but studies of fast, autonomously moving synthetic rotors remain rare. Here, we report switchable, out-of-equilibrium hydrodynamic assembly and phase separation in suspensions of acoustically powered chiral microspinners. Semiquantitative modeling suggests that three-dimensionally (3D) complex spinners interact through viscous and weakly inertial (streaming) flows. The interactions between spinners were studied over a range of densities to construct a phase diagram, which included gaseous dimer pairing at low density, collective rotation and multiphase separation at intermediate densities, and ultimately jamming at high density. The 3D chirality of the spinners leads to self-organization in parallel planes, forming a three-dimensionally hierarchical system that goes beyond the 2D systems that have so far been modeled computationally. Dense mixtures of spinners and passive tracer particles also show active-passive phase separation. These observations are consistent with recent theoretical predictions of the hydrodynamic coupling between rotlets generated by autonomous spinners and provide an exciting experimental window to the study of colloidal active matter and microrobotic systems.

Optical Manipulation Heats up: Present and Future of Optothermal Manipulation

Optothermal manipulation is a versatile technique that combines optical and thermal forces to control synthetic micro-/nanoparticles and biological entities. This emerging technique overcomes the limitations of traditional optical tweezers, including high laser power, photon and thermal damage to fragile objects, and the requirement of refractive-index contrast between target objects and the surrounding solvents. In this perspective, we discuss how the rich opto-thermo-fluidic multiphysics leads to a variety of working mechanisms and modes of optothermal manipulation in both liquid and solid media, underpinning a broad range of applications in biology, nanotechnology, and robotics. Moreover, we highlight current experimental and modeling challenges in the pursuit of optothermal manipulation and propose future directions and solutions to the challenges.

Nonreciprocal forces enable cold-to-hot heat transfer between nanoparticles

We study the heat transfer between two nanoparticles held at different temperatures that interact through nonreciprocal forces, by combining molecular dynamics simulations with stochastic thermodynamics. Our simulations reveal that it is possible to construct nano refrigerators that generate a net heat transfer from a cold to a hot reservoir at the expense of power exerted by the nonreciprocal forces. Applying concepts from stochastic thermodynamics to a minimal underdamped Langevin model, we derive exact analytical expressions predictions for the fluctuations of work, heat, and efficiency, which reproduce thermodynamic quantities extracted from the molecular dynamics simulations. The theory only involves a single unknown parameter, namely an effective friction coefficient, which we estimate fitting the results of the molecular dynamics simulation to our theoretical predictions. Using this framework, we also establish design principles which identify the minimal amount of entropy production that is needed to achieve a certain amount of uncertainty in the power fluctuations of our nano refrigerator. Taken together, our results shed light on how the direction and fluctuations of heat flows in natural and artificial nano machines can be accurately quantified and controlled by using nonreciprocal forces.

Active control of equilibrium, near-equilibrium, and far-from-equilibrium colloidal systems

The development of top-down active control over bottom-up colloidal assembly processes has the potential to produce materials, surfaces, and objects with applications in a wide range of fields spanning from computing to materials science to biomedical engineering. In this review, we summarize recent progress in the field using a taxonomy based on how active control is used to guide assembly. We find there are three distinct scenarios: (1) navigating kinetic pathways to reach a desirable equilibrium state, (2) the creation of a desirable metastable, kinetically trapped, or kinetically arrested state, and (3) the creation of a desirable far-from-equilibrium state through continuous energy input. We review seminal works within this framework, provide a summary of important application areas, and present a brief introduction to the fundamental concepts of control theory that are necessary for the soft materials community to understand this literature. In addition, we outline current and potential future applications of actively-controlled colloidal systems, and we highlight important open questions and future directions.

Steering self-organisation through confinement

Self-organisation is the spontaneous emergence of spatio-temporal structures and patterns from the interaction of smaller individual units. Examples are found across many scales in very different systems and scientific disciplines, from physics, materials science and robotics to biology, geophysics and astronomy. Recent research has highlighted how self-organisation can be both mediated and controlled by confinement. Confinement is an action over a system that limits its units' translational and rotational degrees of freedom, thus also influencing the system's phase space probability density; it can function as either a catalyst or inhibitor of self-organisation. Confinement can then become a means to actively steer the emergence or suppression of collective phenomena in space and time. Here, to provide a common framework and perspective for future research, we examine the role of confinement in the self-organisation of soft-matter systems and identify overarching scientific challenges that need to be addressed to harness its full scientific and technological potential in soft matter and related fields. By drawing analogies with other disciplines, this framework will accelerate a common deeper understanding of self-organisation and trigger the development of innovative strategies to steer it using confinement, with impact on, e.g., the design of smarter materials, tissue engineering for biomedicine and in guiding active matter.

Flocking of two unfriendly species: The two-species Vicsek model

We consider the two-species Vicsek model (TSVM) consisting of two kinds of self-propelled particles, A and B, that tend to align with particles from the same species and to antialign with the other. The model shows a flocking transition that is reminiscent of the original Vicsek model: it has a liquid-gas phase transition and displays micro-phase-separation in the coexistence region where multiple dense liquid bands propagate in a gaseous background. The interesting features of the TSVM are the existence of two kinds of bands, one composed of mainly A particles and one mainly of B particles, the appearance of two dynamical states in the coexistence region: the PF (parallel flocking) state in which all bands of the two species propagate in the same direction, and the APF (antiparallel flocking) state in which the bands of species A and species B move in opposite directions. When PF and APF states exist in the low-density part of the coexistence region they perform stochastic transitions from one to the other. The system size dependence of the transition frequency and dwell times show a pronounced crossover that is determined by the ratio of the band width and the longitudinal system size. Our work paves the way for studying multispecies flocking models with heterogeneous alignment interactions.

Persistent motion of a Brownian particle subject to repulsive feedback with time delay

Based on analytical and numerical calculations we study the dynamics of an overdamped colloidal particle moving in two dimensions under time-delayed, nonlinear feedback control. Specifically, the particle is subject to a force derived from a repulsive Gaussian potential depending on the difference between its instantaneous position, r(t), and its earlier position r(t-τ), where τ is the delay time. Considering first the deterministic case, we provide analytical results for both the case of small displacements and the dynamics at long times. In particular, at appropriate values of the feedback parameters, the particle approaches a steady state with a constant, nonzero velocity whose direction is constant as well. In the presence of noise, the direction of motion becomes randomized at long times, but the (numerically obtained) velocity autocorrelation still reveals some persistence of motion. Moreover, the mean-squared displacement (MSD) reveals a mixed regime at intermediate times with contributions of both ballistic motion and diffusive translational motion, allowing us to extract an estimate for the effective propulsion velocity in presence of noise. We then analyze the data in terms of exact, known results for the MSD of active Brownian particles. The comparison indeed indicates a strong similarity between the dynamics of the particle under repulsive delayed feedback and active motion. This relation carries over to the behavior of the long-time diffusion coefficient D_{eff} which, similarly to active motion, is strongly enhanced compared to the free case. Finally, we show that, for small delays, D_{eff} can be estimated analytically.

Transition from susceptible-infected to susceptible-infected-recovered dynamics in a susceptible-cleric-zombie-recovered active matter model

The susceptible-infected (SI) and susceptible-infected-recovered (SIR) models provide two distinct representations of epidemic evolution, distinguished by whether or not the number of susceptibles always drops to zero at long times. Here we introduce a new active matter epidemic model, the "susceptible-cleric-zombie-recovered" (SCZR) model, in which spontaneous recovery is absent but zombies can recover with probability γ via interaction with a cleric. Upon colliding with a zombie, both susceptibles and clerics enter the zombie state with probability β and α, respectively. By changing the initial fraction of clerics or their healing ability rate γ, we can tune the SCZR model between SI dynamics, in which no susceptibles or clerics remain at long times, and SIR dynamics, in which a finite number of clerics and susceptibles survive at long times. The model is relevant to certain real world diseases such as HIV where spontaneous recovery is impossible but where medical interventions by a limited number of caregivers can reduce or eliminate the spread of infection.

Controlled propulsion of micro/nanomotors: operational mechanisms, motion manipulation and potential biomedical applications

Inspired by natural mobile microorganisms, researchers have developed micro/nanomotors (MNMs) that can autonomously move by transducing different kinds of energies into kinetic energy. The rapid development of MNMs has created tremendous opportunities for biomedical fields including diagnostics, therapeutics, and theranostics. Although the great progress has been made in MNM research, at a fundamental level, the accepted propulsion mechanisms are still a controversial matter. In practical applications such as precision nanomedicine, the precise control of the motion, including the speed and directionality, of MNMs is also important, which makes advanced motion manipulation desirable. Very recently, diverse MNMs with different propulsion strategies, morphologies, sizes, porosities and chemical structures have been fabricated and applied for various uses. Herein, we thoroughly summarize the physical principles behind propulsion strategies, as well as the recent advances in motion manipulation methods and relevant biomedical applications of these MNMs. The current challenges in MNM research are also discussed. We hope this review can provide a bird's eye overview of the MNM research and inspire researchers to create novel and more powerful MNMs.

Pattern formation and flocking for particles near the jamming transition on resource gradient substrates

We numerically examine a bidisperse system of active and passive particles coupled to a resource substrate. The active particles deplete the resource at a fixed rate and move toward regions with higher resources, while all of the particles interact sterically with each other. We show that at high densities, this system exhibits a rich variety of pattern-forming phases along with directed motion or flocking as a function of the relative rates of resource absorption and consumption as well as the active to passive particle ratio. These include partial phase separation into rivers of active particles flowing through passive clusters, strongly phase separated states where the active particles induce crystallization of the passive particles, mixed jammed states, and fluctuating mixed fluid phases. For higher resource recovery rates, we demonstrate that the active particles can undergo motility-induced phase separation, while at high densities, there can be a coherent flock containing only active particles or a solid mixture of active and passive particles. The directed flocking motion typically shows a transient in which the flow switches among different directions before settling into one direction, and there is a critical density below which flocking does not occur. We map out the different phases as function of system density, resource absorption and recovery rates, and the ratio of active to passive particles.

Circular motion subject to external alignment under active driving: Nonlinear dynamics and the circle map

Hardly any real self-propelling or actively driven object is perfect. Thus, undisturbed motion will generally not follow straight lines but rather bent or circular trajectories. We here address self-propelled or actively driven objects that move in discrete steps and additionally tend to migrate towards a certain direction by discrete angular adjustment. Overreaction in the angular alignment is possible. This competition implies pronounced nonlinear dynamics including period doubling and chaotic behavior in a broad parameter regime. Such behavior directly affects the appearance of the trajectories. Furthermore, we address collective motion and effects of spatial self-concentration.

Active matter in space

In the last 20 years, active matter has been a highly dynamic field of research, bridging fundamental aspects of non-equilibrium thermodynamics with applications to biology, robotics, and nano-medicine. Active matter systems are composed of units that can harvest and harness energy and information from their environment to generate complex collective behaviours and forms of self-organisation. On Earth, gravity-driven phenomena (such as sedimentation and convection) often dominate or conceal the emergence of these dynamics, especially for soft active matter systems where typical interactions are of the order of the thermal energy. In this review, we explore the ongoing and future efforts to study active matter in space, where low-gravity and microgravity conditions can lift some of these limitations. We envision that these studies will help unify our understanding of active matter systems and, more generally, of far-from-equilibrium physics both on Earth and in space. Furthermore, they will also provide guidance on how to use, process and manufacture active materials for space exploration and colonisation.

Collective motion of active particles exhibiting non-reciprocal orientational interactions

We present a Brownian dynamics study of a 2D bath of active particles interacting among each other through usual steric interactions and, additionally, via non-reciprocal avoidant orientational interactions. We motivate them by the fact that the two flagella of the alga Chlamydomonas interact sterically with nearby surfaces such that a torque acts on the alga. As expected, in most cases such interactions disrupt the motility-induced particle clustering in active baths. Surprisingly, however, we find that the active particles can self-organize into collectively moving flocks if the range of non-reciprocal interactions is close to that of steric interactions. We observe that the flocking motion can manifest itself through a variety of structural forms, spanning from single dense bands to multiple moderately-dense stripes, which are highly dynamic. The flocking order parameter is found to be only weakly dependent on the underlying flock structure. Together with the variance of the local-density distribution, one can clearly group the flocking motion into the two separate band and dynamic-stripes states.

Critical behavior of quorum-sensing active particles

It is still a debated issue whether all critical active particles belong to the same universality class. Here we numerically study the critical behavior of quorum sensing active particles that represents the archetypal model for interpreting motility-induced phase separation. Mean-field theory predicts that this model should undergo a full phase separation if particles slow-down enough when sensing the presence of their neighbors and that the coexistence line terminates in a critical point. By performing large-scale numerical simulations, we confirm this scenario, locate the critical point and use finite-size scaling analysis to show that the static and dynamic critical exponents of this active system substantially agree with those of the Ising universality class.

Using active matter to introduce spatial heterogeneity to the susceptible infected recovered model of epidemic spreading

The widely used susceptible-infected-recovered (S-I-R) epidemic model assumes a uniform, well-mixed population, and incorporation of spatial heterogeneities remains a major challenge. Understanding failures of the mixing assumption is important for designing effective disease mitigation approaches. We combine a run-and-tumble self-propelled active matter system with an S-I-R model to capture the effects of spatial disorder. Working in the motility-induced phase separation regime both with and without quenched disorder, we find two epidemic regimes. For low transmissibility, quenched disorder lowers the frequency of epidemics and increases their average duration. For high transmissibility, the epidemic spreads as a front and the epidemic curves are less sensitive to quenched disorder; however, within this regime it is possible for quenched disorder to enhance the contagion by creating regions of higher particle densities. We discuss how this system could be realized using artificial swimmers with mobile optical traps operated on a feedback loop.

Group formation and collective motion of colloidal rods with an activity triggered by visual perception

We investigate the formation of cohesive groups and the collective diffusion of colloidal spherocylinders with a motility driven by a simple visual perception model. For this, we perform Brownian dynamics simulations without hydrodynamic interactions. The visual perception is based on sight cones attached to the spherocylinders and perception functions quantifying the visual stimuli. If the perception function of a particle reaches a predefined threshold, an active component is added to its motion. We find that, in addition to the opening angle of the cone of sight, the aspect ratio of the particles plays an important role for the formation of cohesive groups. If the elongation of the particles is increased, the maximum angle for which the rods organize themselves into such groups decreases distinctly. After a system forms a cohesive group, it performs a diffusive motion, which can be quantified by an effective diffusion coefficient. For increasing aspect ratios, the spatial expansion of the cohesive groups and the effective diffusion coefficient of the collective motion increase, while the number of active group members decreases. We also find that a larger particle number, a smaller propulsion velocity of the group members, and a smaller threshold for the visual stimulus increase the maximum opening angle for which cohesive groups form. Based on our results, we expect anisotropic particles to be of great relevance for the adjustability of visual perception-dependent motility.