Boundaries Control Collective Dynamics of Inertial Self-Propelled Robots

Effects of boundaries for high Reynolds number artificial swimmers

The spatial organization of active particles or swimmers may depend strongly on the nature of the interaction between the particles and the boundary. Here we use robotic fish of several centimeters dimensions that swim at high enough velocities to reach Reynolds numbers Re of order [Formula: see text] or [Formula: see text]. Under confinement in circular arenas filled with a shallow layer of water, these robots swim mostly near the walls and undergo a gradual transition from swirling motion near the boundaries to large cluster formation as the number of particles in the assembly is increased. This transition is highly dependent on the nature of the walls: for solid impermeable walls this transition occurs for small numbers of fish robots. For porous walls this transition is delayed and occurs at larger numbers. The main reason why the two boundaries affect the swimming differently is the alignment of the fish robots at the wall: for the impermeable boundary the fish robots align with a smaller angle to the wall while for the porous case, the fish robots align with a larger angle at the wall allowing the formation of linear clusters. We carry out numerical simulations of model fish in three dimensions to examine how such experimental results can be understood. The interest of these simulations is that they provide a direct and quantitative view of the properties of the flow engendered by the fish like objects. The interaction of this flow with other fish or with the boundaries is the crucial aspect behind the self organization. These simulations reproduce the main features of the behavior of the swimmers such as their swimming near the walls or their angle with respect to the boundary. By using flexible and free to move arenas in experiments and simulations, we show that the assembly of fish robots is capable of creating large deformations as well as induce mobility of the arenas through the self-organization of the robotic fish opening the possibility of making sub-aquatic flexible robots of robots.

Active magneto gyrator: Memory-induced trapped diamagnetism

We analytically explore the dynamics of a charged active particle coupled to two thermal baths kept at two different temperatures in two dimensions. The particle is confined to an asymmetric harmonic potential and a magnetic field of constant magnitude is applied perpendicular to the plane of motion of the particle. For such a system, as opposed to a Brownian gyrator, the potential asymmetry and temperature gradient are not the key factors for the gyration, as long as finite activity and magnetic field are present. The system shows only a paramagnetic behavior in the absence of either potential asymmetry or temperature gradient. However, by tuning the temperature gradient or potential asymmetry, the system as a function of the duration of activity can exhibit paramagnetic, diamagnetic, or coexistence of both the phases. Interestingly, the magnetic moment vanishes for parameters for which the system possesses a nonequilibrium steady state and hence, a magnetic transition is observed through these nonmagnetic points. Further, when the system is suspended in a viscoelastic medium characterized by a finite memory, it exhibits a magnetic transition in the activity-memory parameter space through a nonmagnetic line. This nonmagnetic line is sensitive to temperature gradient and potential asymmetry. It interestingly forms a closed loop with a diamagnetic phase inside the loop and the entire regime outside as paramagnetic. This results in the emergence of a trapped diamagnetic phase existing only within a finite regime of activity-memory parameter space. This phase eventually disappears as the temperature gradient increases (or decreases) depending on the sign of the potential asymmetry. Moreover, it is observed that by tuning the system parameters, one can obtain zero magnetic moment even for parameter ranges that defy the equilibrium condition of the system.

Experimental modeling of chiral active robots and a minimal model of non-Gaussian displacements

We design 3D-printed motor-driven active particles and find that their dynamics can be characterized using the model of overdamped chiral active Brownian particles (ABPs), as demonstrated by measured angular statistics and translational mean squared displacements (MSDs). Furthermore, we propose a minimal model that reproduces the double-peak velocity distributions and further predicts a transition from the single-peak to the double-peak displacement distributions in short-time regimes. The model provides a clear physics picture of these phenomena, originating from the competition between the active motion and the translational diffusion. Our experiments confirm such picture. The minimal model enhances our understanding of activity-driven non-Gaussian phenomena. The designed particles could be further applied in the study of collective chiral motions.

Controlled Locomotion of a Minimal Soft Structure by Stick-Slip Nonlinearity

We present a locomotion mechanism that uses the stick-slip transition of a soft passive structure with an internal mechanical resonance. The structure is harmonically driven by a global vertical shaking and, because of its resonance dephasing and the threshold response of stick-slip transition, it can either move forward or backward. We establish a relation for the motion acceleration threshold that we experimentally validate. We identify a nontrivial regime close to the resonance with a velocity inversion for a constant excitation frequency and an increasing driving amplitude. We finally show that we can achieve a controlled multimodal motion by combining multiple internal resonances.

Emergent behaviors of buckling-driven elasto-active structures

Active systems of self-propelled agents, e.g., birds, fish, and bacteria, can organize their collective motion into myriad autonomous behaviors. Ubiquitous in nature and across length scales, such phenomena are also amenable to artificial settings, e.g., where brainless self-propelled robots orchestrate their movements into spatial-temporal patterns via the application of external cues or when confined within flexible boundaries. Like their natural counterparts, these approaches typically require many units to initiate collective motion, so controlling the ensuing dynamics is challenging. Here, we demonstrate a simple mechanism that leverages nonlinear elasticity to tame near-diffusive motile particles in forming structures capable of directed motion and other emergent behaviors. Our elasto-active system comprises two centimeter-sized self-propelled microbots connected with elastic beams. These microbots exert forces that suffice to buckle the beam and set the structure in motion. We first rationalize the physics of the interaction between the beam and the microbots. Then we use reduced-order models to predict the interactions of our elasto-active structures with boundaries, e.g., walls and constrictions, and demonstrate how they can exhibit remarkable emergent behaviors such as maze navigation. These findings demonstrate that allowing and understanding changes in body morphology can enhance the capabilities of active matter systems and enable the design of robotic materials capable of space exploration, adaptation, and complex interactions with their surrounding environment.

Nature of barriers determines first passage times in heterogeneous media

Intuition suggests that passage times across a region increase with the number of barriers along the path. Can this fail depending on the nature of the barrier? To probe this fundamental question, we exactly solve for the first passage time in general d-dimensions for diffusive transport through a spatially patterned array of obstacles - either entropic or energetic, depending on the nature of the obstacles. For energetic barriers, we show that first passage times vary non-monotonically with the number of barriers, while for entropic barriers it increases monotonically. This non-monotonicity for energetic barriers is further reflected in the behaviour of effective diffusivity as well. We then design a simple experiment where a robotic bug navigates in a heterogeneous environment through a spatially patterned array of obstacles to validate our predictions. Finally, using numerical simulations, we show that this non-monotonic behaviour for energetic barriers is general and extends to even super-diffusive transport.

Deformation-induced phase separation of active vesicles

Many active materials, such as bacteria and cells, are deformable. Deformability significantly affects their collective behaviors and movements in complex environments. Here, we introduce a two-dimensional deformable active vesicle (DAV) model to emulate cell-like deformable active matter, wherein the deformability can be continuously adjusted. We find that changes in deformability can induce phase separation of DAVs. The system can transition between a homogeneous gas state, a coexistence of gas and liquid, and a coexistence of gas and solid. The occurrence of deformation-induced phase separation is accompanied by nonmonotonic changes in effective concentration, particle size and shape. Moreover, the degree of deformability also impacts the motility and stress within the dense phase following phase separation. Our results offer new insights into the role of deformability in the collective behavior of active matter.

Density and inertia effects on two-dimensional active semiflexible filament suspensions

We examine the influence of density on the transition between chain and spiral structures in planar assemblies of active semiflexible filaments, utilizing detailed numerical simulations. We focus on how increased density, and higher Péclet numbers, affect the activity-induced transition spiral state in a semiflexible, self-avoiding active chain. Our findings show that increasing the density causes the spiral state to break up, reverting to a motile chain-like shape. This results in a density-dependent reentrant phase transition from spirals back to open chains. We attribute this phenomenon to an inertial effect observed at the single polymer level, where increased persistence length due to inertia has been shown in recent three-dimensional studies to cause polymers to open up. Our two-dimensional simulations further reveal that a reduction in the damping coefficient leads to partial unwinding of the spirals, forming longer arms. In suspension, interactions among these extended arms can trigger a complete unwinding of the spirals, driven by the combined effects of density and inertia.

Shape-dependent motility of polar inclusions in active baths

Collections of persistently moving active particles are an example of a nonequilibrium heat bath. One way to study the nature of nonequilibrium fluctuations in such systems is to follow the dynamics of an embedded probe particle. With this aim, we study the dynamics of an anisotropic inclusion embedded in a bath of active particles. By studying various statistical correlation functions of the dynamics, we show that the emergent motility of this inclusion depends on its shape as well as the properties of the active bath. We demonstrate that both the decorrelation time of the net force on the inclusion and the dwell time of bath particles in a geometrical trap on the inclusion have a nonmonotonic dependence on its shape. We also find that the motility of the inclusion is optimal when the volume fraction of the active bath is close to the value for the onset of motility induced phase separation.

Collective dynamics of active dumbbells near a circular obstacle

In this article, we present the collective dynamics of active dumbbells in the presence of a static circular obstacle using Brownian dynamics simulation. The active dumbbells aggregate on the surface of a circular obstacle beyond a critical radius. The aggregation is non-uniform along the circumference, and the aggregate size increases with the activity (Pe) and the curvature radius (Ro). The dense aggregate of active dumbbells displays persistent rotational motion with a certain angular speed, which linearly increases with activity. Furthermore, we show a strong polar ordering of the active dumbbells within the aggregate. The polar ordering exhibits long-range correlation, with the correlation length corresponding to the aggregate size. Additionally, we show that the residence time of an active dumbbell on the obstacle surface increases rapidly with area fraction due to many-body interactions that lead to a slowdown of the rotational diffusion. This article further considers the dynamical behavior of a tracer particle in the solution of active dumbbells. Interestingly, the speed of the passive tracer particle displays a crossover from monotonically decreasing to increasing with the size of the tracer particle upon increasing the dumbbells' speed. Furthermore, the effective diffusion of the tracer particle displays non-monotonic behavior with the area fraction; the initial increase in diffusivity is followed by a decrease for a larger area fraction.

Programming tunable active dynamics in a self-propelled robot

We present a scheme for producing tunable active dynamics in a self-propelled robotic device. The robot moves using the differential drive mechanism where two wheels can vary their instantaneous velocities independently. These velocities are calculated by equating robot's equations of motion in two dimensions with well-established active particle models and encoded into the robot's microcontroller. We demonstrate that the robot can depict active Brownian, run and tumble, and Brownian dynamics with a wide range of parameters. The resulting motion analyzed using particle tracking shows excellent agreement with the theoretically predicted trajectories. Later, we show that its motion can be switched between different dynamics using light intensity as an external parameter. Intriguingly, we demonstrate that the robot can efficiently navigate through many obstacles by performing stochastic reorientations driven by the gradient in light intensity towards a desired location, namely the target. This work opens an avenue for designing tunable active systems with the potential of revealing the physics of active matter and its application for bio- and nature-inspired robotics.

Confined run-and-tumble particles with non-Markovian tumbling statistics

Confined active particles constitute simple, yet realistic, examples of systems that converge into a nonequilibrium steady state. We investigate a run-and-tumble particle in one spatial dimension, trapped by an external potential, with a given distribution g(t) of waiting times between tumbling events whose mean value is equal to τ. Unless g(t) is an exponential distribution (corresponding to a constant tumbling rate), the process is non-Markovian, which makes the analysis of the model particularly challenging. We use an analytical framework involving effective position-dependent tumbling rates to develop a numerical method that yields the full steady-state distribution (SSD) of the particle's position. The method is very efficient and requires modest computing resources, including in the large-deviation and/or small-τ regime, where the SSD can be related to the the large-deviation function, s(x), via the scaling relation P_{st}(x)∼e^{-s(x)/τ}.

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.

Polar order, shear banding, and clustering in confined active matter

We investigate the collective behavior of sterically interacting self-propelled particles confined in a harmonic potential. Our theoretical and numerical study unveils the emergence of distinctive collective polar organizations, revealing how different levels of interparticle torques and noise influence the system. The observed phases include the shear-banded vortex, where the system self organizes in two concentric bands rotating in opposite directions around the potential center; the uniform vortex, where the two bands merge into a close packed configuration rotating uniformly as a quasi-rigid body; and the orbiting polar state, characterized by parallel orientation vectors and the cluster revolving around the potential center, without rotation, as a rigid body. Intriguingly, at lower filling fractions, the vortex and polar phases merge into a single phase where the trapped cluster breaks into smaller polarized clusters, each one orbiting the potential center as a rigid body.

Nematic Torques in Scalar Active Matter: When Fluctuations Favor Polar Order and Persistence

We study the impact of nematic alignment on scalar active matter in the disordered phase. We show that nematic torques control the emergent physics of particles interacting via pairwise forces and can either induce or prevent phase separation. The underlying mechanism is a fluctuation-induced renormalization of the mass of the polar field that generically arises from nematic torques. The correlations between the fluctuations of the polar and nematic fields indeed conspire to increase the particle persistence length, contrary to what phenomenological computations predict. This effect is generic and our theory also quantitatively accounts for how nematic torques enhance particle accumulation along confining boundaries and opposes demixing in mixtures of active and passive particles.

Active chiral dynamics and boundary accumulation phenomenon in confined camphor particles

In this work, we perform experimental and numerical investigations on the dynamics of camphor-infused discs, well-established as active particles in their behavior. Our analysis focuses on examining the individual dynamics of these discs within a confined circular domain, revealing that they exhibit characteristics akin to active chiral particles. To characterize this behavior effectively, we introduce a methodology for estimating key model parameter values from our experiments, including linear velocity, angular velocity, and angular noise intensity. To validate our findings, we compare our experimental results with numerical simulations of the model. Our results demonstrate a striking phenomenon associated with camphor-infused discs: a pronounced accumulation of particles along the boundary. This intriguing observation suggests the occurrence of an attractive interaction between the active particles and the boundary, resulting in a kind of adsorption effect. The latter results in the confinement of the camphor disc along the Petri dish wall, which we refer to as sliding dynamics. We empirically determine the velocity of the particle along the Petri dish wall as well as its fluctuations, properties whose behavior notably deviates from the bulk dynamics.

When an active bath behaves as an equilibrium one

Active scalar baths consisting of active Brownian particles are characterized by a non-Gaussian velocity distribution, a kinetic temperature, and a diffusion coefficient that scale with the square of the active velocity v_{0}. While these results hold in overdamped active systems, inertial effects lead to normal velocity distributions, with kinetic temperature and diffusion coefficient increasing as ∼v_{0}^{α} with 1<α<2. Remarkably, the late-time diffusivity and mobility decrease with mass. Moreover, we show that the equilibrium Einstein relation is asymptotically recovered with inertia. In summary, the inertial mass restores an equilibriumlike behavior.

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.

Controlling the transport of the mixture involving active and passive rods in confined channel

The transport of the binary mixture of self-propelled rods (SPRs) and passive rods in the asymmetric conjugate periodic channel is studied by dissipative particle dynamics (DPD) simulations. It is found that the autonomous pumping of the binary mixture of active and passive rods can be achieved by either the individual or collective behaviour of SPRs. More specifically, the transport of passive rods can be driven through the individual, collective jostlement of the active rods, and crowding out effect. The strength of self-propulsion, rod length, rod concentration, and geometric feature of the channel determines the mechanism of pumping. In addition, the drift of the binary mixture can be in the positive and negative directions of the channel or the currents of SPRs and passive rods in opposite directions and relies on the geometric feature of the channel and concentration of the two species. Overall, our simulation study offers an efficient approach of flow control for both species.

Nonequilibrium steady state of trapped active particles

We consider an overdamped particle with a general physical mechanism that creates noisy active movement (e.g., a run-and-tumble particle or active Brownian particle, etc.), that is confined by an external potential. Focusing on the limit in which the correlation time τ of the active noise is small, we find the nonequilibrium steady-state distribution P_{st}(X) of the particle's position X. While typical fluctuations of X follow a Boltzmann distribution with an effective temperature that is not difficult to find, the tails of P_{st}(X) deviate from a Boltzmann behavior: In the limit τ→0, they scale as P_{st}(X)∼e^{-s(X)/τ}. We calculate the large-deviation function s(X) exactly for arbitrary trapping potential and active noise in dimension d=1, by relating it to the rate function that describes large deviations of the position of the same active particle in absence of an external potential at long times. We then extend our results to d>1 assuming rotational symmetry.

Inertial and geometrical effects of self-propelled elliptical Brownian particles

Active particles that self-propel by transforming energy into mechanical motion represent a growing area of research in mathematics, physics, and chemistry. Here we investigate the dynamics of nonspherical inertial active particles moving in a harmonic potential, introducing geometric parameters which take into account the role of eccentricity for nonspherical particles. A comparison between the overdamped and underdamped models for elliptical particles is performed. The model of overdamped active Brownian motion has been used to describe most of the basic aspects of micrometer-sized particles moving in a liquid ("microswimmers"). We consider active particles by extending the active Brownian motion model to incorporate translation and rotation inertia and account for the role of eccentricity. We show how the overdamped and the underdamped models behave in the same way for small values of activity (Brownian case) if eccentricity is equal to zero, but increasing eccentricity leads the two dynamics to substantially depart from each other-in particular, the action of a torque induced by external forces, induced a marked difference close to the walls of the domain if eccentricity is high. Effects induced by inertia include an inertial delay time of the self-propulsion direction from the particle velocity, and the differences between the overdamped and underdamped systems are particularly evident in the first and second moments of the particle velocities. Comparison with the experimental results of vibrated granular particles shows good agreement and corroborates the notion that self-propelling massive particles moving in gaseous media are dominated by inertial effects.

Directional switches in network-organized swarming systems with delay

Coordinated directional switches can emerge between members of moving biological groups. Previous studies have shown that the self-propelled particles model can well reproduce directional switching behaviors, but it neglects the impact of social interactions. Thus, we focus on the influence of social interactions on the ordered directional switching motion of swarming systems, in which homogeneous Erdös-Rényi networks, heterogeneous scale-free networks, networks with community structures, and real-world animal social networks have been considered. The theoretical estimation of mean switching time is obtained, and the results show that the interplay between social and delayed interactions plays an important role in regulating directional switching behavior. To be specific, for homogeneous Erdös-Rényi networks, the increase in mean degree may suppress the directional switching behaviors if the delay is sufficiently small. However, when the delay is large, the large mean degree may promote the directional switching behavior. For heterogeneous scale-free networks, the increase of degree heterogeneity can reduce the mean switching time if the delay is sufficiently small, while the increasing degree heterogeneity may suppress the ordered directional switches if the delay is large. For networks with community structures, higher communities can promote directional switches for small delays, while for large delays, it may inhibit directional switching behavior. For dolphin social networks, delay can promote the directional switching behavior. Our results bring to light the role of social and delayed interactions in the ordered directional switching motion.

Morphological computation and decentralized learning in a swarm of sterically interacting robots

Whereas naturally occurring swarms thrive when crowded, physical interactions in robotic swarms are either avoided or carefully controlled, thus limiting their operational density. Here, we present a mechanical design rule that allows robots to act in a collision-dominated environment. We introduce Morphobots, a robotic swarm platform developed to implement embodied computation through a morpho-functional design. By engineering a three-dimensional printed exoskeleton, we encode a reorientation response to an external body force (such as gravity) or a surface force (such as a collision). We show that the force orientation response is generic and can augment existing swarm robotic platforms (e.g., Kilobots) as well as custom robots even 10 times larger. At the individual level, the exoskeleton improves motility and stability and also allows encoding of two contrasting dynamical behaviors in response to an external force or a collision (including collision with a wall or a movable obstacle and on a dynamically tilting plane). This force orientation response adds a mechanical layer to the robot's sense-act cycle at the swarm level, leveraging steric interactions for collective phototaxis when crowded. Enabling collisions also promotes information flow, facilitating online distributed learning. Each robot runs an embedded algorithm that ultimately optimizes collective performance. We identify an effective parameter that controls the force orientation response and explore its implications in swarms that transition from dilute to crowded. Experimenting with physical swarms (of up to 64 robots) and simulated swarms (of up to 8192 agents) shows that the effect of morphological computation increases with growing swarm size.

Bouncing dynamics of inertial self-propelled particles reveals directional asymmetry

This study aims to examine experimental conditions in which active particles are forced by their surroundings to move forward and backward in a continuous oscillatory manner. The experimental design is based on using a vibrating self-propelled toyrobot called hexbug, which is placed inside a narrow channel closed on one end by a rigid moving wall. Using the end-wall velocity as a controlling factor, the main forward mode of the hexbug movement can be turned to mostly rearward mode. We investigate the bouncing hexbug motion on both experimental and theoretical grounds. The Brownian model of active particles with inertia is employed in the theoretical framework. The model itself uses a pulsed Langevin equation in order to simulate abrupt changes in velocity that mimic hexbug propulsion in the moments when its legs make contact with the base plate. Significant directional asymmetry is caused by the legs bending backward. We demonstrate that the simulation successfully reproduces the experimental characteristics of hexbug motion after regressing the spatial and temporal statistical characteristics, especially when directional asymmetry is under consideration.

Mode-coupling theory for the dynamics of dense underdamped active Brownian particle system

We present a theory to study the inertial effect on glassy dynamics of the underdamped active Brownian particle (UABP) system. Using the assumption of the nonequilibrium steady-state, we obtain an effective Fokker-Planck equation for the probability distribution function (PDF) as a function of positions and momentums. With this equation, we achieve the evolution equation of the intermediate scattering function through the Zwanzig-Mori projection operator method and the mode-coupling theory (MCT). Theoretical analysis shows that the inertia of the particle affects the memory function and corresponding glass transition by influencing the structure factor and a velocity correlation function. The theory provides theoretical support and guidance for subsequent simulation work.

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.

Exact position distribution of a harmonically confined run-and-tumble particle in two dimensions

We consider an overdamped run-and-tumble particle in two dimensions, with self-propulsion in an orientation that stochastically rotates by 90^{∘} at a constant rate, clockwise or counterclockwise with equal probabilities. In addition, the particle is confined by an external harmonic potential of stiffness μ, and possibly diffuses. We find the exact time-dependent distribution P(x,y,t) of the particle's position, and in particular, the steady-state distribution P_{st}(x,y) that is reached in the long-time limit. We also find P(x,y,t) for a "free" particle, μ=0. We achieve this by showing that, under a proper change of coordinates, the problem decomposes into two statistically independent one-dimensional problems, whose exact solution has recently been obtained. We then extend these results in several directions, to two such run-and-tumble particles with a harmonic interaction, to analogous systems of dimension three or higher, and by allowing stochastic resetting.

Active Refrigerators Powered by Inertia

We present the operational principle for a refrigerator that uses inertial effects in active Brownian particles to locally reduce their (kinetic) temperature by 2 orders of magnitude below the environmental temperature. This principle exploits the peculiar but so-far unknown shape of the phase diagram of inertial active Brownian particles to initiate motility-induced phase separation in the targeted cooling regime only. Remarkably, active refrigerators operate without requiring isolating walls opening the route toward using them to systematically absorb and trap, e.g., toxic substances from the environment.

Cell clusters adopt a collective amoeboid mode of migration in confined nonadhesive environments

Cell migration is essential to living organisms and deregulated in cancer. Single cell's migration ranges from traction-dependent mesenchymal motility to contractility-driven propulsive amoeboid locomotion, but collective cell migration has only been described as a focal adhesion-dependent and traction-dependent process. Here, we show that cancer cell clusters, from patients and cell lines, migrate without focal adhesions when confined into nonadhesive microfabricated channels. Clusters coordinate and behave like giant super cells, mobilizing their actomyosin contractility at the rear to power their migration. This polarized cortex does not sustain persistent retrograde flows, of cells or actin, like in the other modes of migration but rather harnesses fluctuating cell deformations, or jiggling. Theoretical physical modeling shows this is sufficient to create a gradient of friction forces and trigger directed cluster motion. This collective amoeboid mode of migration could foster metastatic spread by enabling cells to cross a wide spectrum of environments.

Activity Induced Rigidity of Liquid Droplets

Here we show that encapsulating active Janus particles within a drop renders it more resistant to deformation. This drop is deformed under the action of an extensional flow. Such deformation is primarily resisted by the drop interfacial tension. When the particles are active under the action of laser illumination, the deformation decreases signaling an increase in effective tension or Laplace pressure. This increase is attributed to the activity of the particles. Our results using numerous drop sizes, particle number densities, and active velocities show that the obtained increase agrees surprisingly well, over an extended range, with a standard expression for the pressure engendered by an ensemble of active particles, proposed years ago but not tested yet in three dimensions.

Non-equilibrium shapes and dynamics of active vesicles

Active vesicles, constructed through the confinement of self-propelled particles (SPPs) inside a lipid membrane shell, exhibit a large variety of non-equilibrium shapes, ranging from the formation of local tethers and dendritic conformations, to prolate and bola-like structures. To better understand the behavior of active vesicles, we perform simulations of membranes modelled as dynamically triangulated surfaces enclosing active Brownian particles. A systematic analysis of membrane deformations and SPP clustering, as a function of SPP activity and volume fraction inside the vesicle is carried out. Distributions of membrane local curvature, and the clustering and mobility of SPPs obtained from simulations of active vesicles are analysed. There exists a feedback mechanism between the enhancement of membrane curvature, the formation of clusters of active particles, and local or global changes in vesicle shape. The emergence of active tension due to the activity of SPPs can well be captured by the Young-Laplace equation. Furthermore, a simple numerical method for tether detection is presented and used to determine correlations between the number of tethers, their length, and local curvature. We also provide several geometrical arguments to explain different tether characteristics for various conditions. These results contribute to the future development of steerable active vesicles or soft micro-robots whose behaviour can be controlled and used for potential applications.

Inertial dynamics of an active Brownian particle

Active Brownian motion commonly assumes spherical overdamped particles. However, self-propelled particles are often neither symmetric nor overdamped yet underlie random fluctuations from their surroundings. Active Brownian motion has already been generalized to include asymmetric particles. Separately, recent findings have shown the importance of inertial effects for particles of macroscopic size or in low-friction environments. We aim to consolidate the previous findings into the general description of a self-propelled asymmetric particle with inertia. We derive the Langevin equation of such a particle as well as the corresponding Fokker-Planck equation. Furthermore, a formula is presented that allows reconstructing the hydrodynamic resistance matrix of the particle by measuring its trajectory. Numerical solutions of the Langevin equation show that, independently of the particle's shape, the noise-free trajectory at zero temperature starts with an inertial transition phase and converges to a circular helix. We discuss this universal convergence with respect to the helical motion that many microorganisms exhibit.

Effect of anisotropy on the formation of active particle films

Active colloids belong to a class of nonequilibrium systems where energy uptake, conversion, and dissipation occur at the level of individual colloidal particles, which can lead to particles' self-propelled motion and surprising collective behavior. Examples include coexistence of vapor- and liquid-like steady states for active particles with repulsive interactions only, phenomena known as motility-induced phase transitions. Similarly to motile unicellular organisms, active colloids tend to accumulate at confining surfaces forming dense adsorbed films. In this work, we study the structure and dynamics of aggregates of self-propelled particles near confining solid surfaces, focusing on the effects of the particle anisotropic interactions. We performed Langevin dynamics simulations of two complementary models for active particles: ellipsoidal particles interacting through the Gay-Berne potential and rodlike particles composed of several repulsive Lennard-Jones beads. We observe a nonmonotonic behavior of the structure of clusters formed along the confining surface as a function of the particle aspect ratio, with a film spreading when particles are near-spherical, compact clusters with hedgehog-like particle orientation for more elongated active particles, and a complex dynamical behavior for an intermediate aspect ratio. The stabilization time of cluster formation along the confining surface also displays a nonmonotonic dependence on the aspect ratio, with a local minimum at intermediate values. Additionally, we demonstrate that the hedgehog-like aggregates formed by Gay-Berne ellipsoids exhibit higher structural stability as compared to the ones formed by purely repulsive active rods, which are stable due to the particle activity only.

Bistability in orbital trajectories of a chiral self-propelled particle interacting with an external field

In this paper, the dynamics of a self-propelled stochastic particle under the influence of an axisymmetric light field is experimentally studied. The particle under consideration has the main characteristic of carrying a light sensor in an eccentric location. For the chosen experimental conditions, the emerging trajectories are orbital, and, more interestingly, they suggest the existence of bistability. A mathematical model incorporating the key experimental components is introduced. By means of numerical simulations and theoretical analysis, it is found that, in addition to the orbiting behavior, the sensor location could produce trapped or diffusive behaviors. Furthermore, the study reveals that stochastic perturbation and the eccentric location of the sensor are responsible for inducing bistability in the orbital trajectories, supporting experimental observations.

Chromatographic separation of active polymer-like worm mixtures by contour length and activity

The convective transport rate of polymers through confined geometries depends on their size, allowing for size-based separation of polymer mixtures (chromatography). Here, we investigate whether mixtures of active polymers can be separated in a similar manner based on their activity. We use thin, living Tubifex tubifex worms as a model system for active polymers and study the transport of these worms by an imposed flow through a channel filled with a hexagonal pillar array. The transport rate through the channel depends strongly on the degree of activity, an effect that we assign to the different distribution of conformations sampled by the worms depending on their activity. Our results demonstrate a unique way to sort mixtures of active polymers based on their activity and provide a versatile and convenient experimental system to investigate the hydrodynamics of active polymers.

Coexisting orbits and chaotic dynamics of a confined self-propelled particle

We investigate theoretically the dynamics of a confined active swimmer with velocity and orientation axis coupled to each other via a self-alignment torque. For an isotropic harmonic potential, this system is known to exhibit two distinct dynamical phases: a climbing one, where the particle is oriented radially and undergoes angular Brownian motion, and a circularly orbiting phase. Here we show that for nonradially symmetric confinement an assortment of complex phenomena emerge. For an elliptic harmonic potential the orbiting phase splits into several periodic orbits with a diversity of shapes: ovals, lemniscates, and generalized lemniscates with multiple lobes. These orbits can coexist in the parameter space and decay into one another induced by noise. For anharmonic confining potentials, we report transitions from periodic to chaotic dynamics, as one changes the intensity of the self-alignment torque and noise-induced complex orbits. These results demonstrate that the combination of the shape of the trapping potential and self-alignment torque can induce a rich variety of nontrivial dynamical states of a confined active particle.

Motion of a self-propelled particle with rotational inertia

Overdamped active Brownian motion of self-propelled particles in a liquid has been fairly well studied. However, there are a variety of situations in which the overdamped approximation is not justified, for instance, when self-propelled particles move in a low-viscosity medium or when their rotational diffusivity is enhanced by internal active processes or external control. Examples of various origins include biofilaments driven by molecular motors, living and artificial microflyers and interfacial surfers, field-controlled and superfluid microswimmers, vibration-driven granular particles and autonomous mini-robots with sensorial delays, etc. All of them extend active Brownian motion to the underdamped case, i.e., to active Langevin motion, which takes into account inertia. Despite a rich experimental background, there is a gap in the theory in the field where rotational inertia significantly affects the random walk of active particles on all time scales. In particular, although the well-known models of active Brownian and Ornstein-Uhlenbeck particles include a memory effect of the direction of motion, they are not applicable in the underdamped case, because the rotational inertia, which they do not account for, can partially prevent "memory loss" with increasing rotational diffusion. We describe the two-dimensional motion of a self-propelled particle with both translational and rotational inertia and velocity fluctuations. The proposed generalized analytical equations for the mean kinetic energy, mean-square displacement and noise-averaged trajectory of the self-propelled particle are confirmed by numerical simulations in a wide range of self-propulsion velocities, moments of inertia, rotational diffusivities, medium viscosities and observation times.

Evolution of Brains and Computers: The Roads Not Taken

When computers started to become a dominant part of technology around the 1950s, fundamental questions about reliable designs and robustness were of great relevance. Their development gave rise to the exploration of new questions, such as what made brains reliable (since neurons can die) and how computers could get inspiration from neural systems. In parallel, the first artificial neural networks came to life. Since then, the comparative view between brains and computers has been developed in new, sometimes unexpected directions. With the rise of deep learning and the development of connectomics, an evolutionary look at how both hardware and neural complexity have evolved or designed is required. In this paper, we argue that important similarities have resulted both from convergent evolution (the inevitable outcome of architectural constraints) and inspiration of hardware and software principles guided by toy pictures of neurobiology. Moreover, dissimilarities and gaps originate from the lack of major innovations that have paved the way to biological computing (including brains) that are completely absent within the artificial domain. As it occurs within synthetic biocomputation, we can also ask whether alternative minds can emerge from A.I. designs. Here, we take an evolutionary view of the problem and discuss the remarkable convergences between living and artificial designs and what are the pre-conditions to achieve artificial intelligence.

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.

Migration of an active colloidal cell in inhomogeneous environments

Living cells on a substrate with mechanical inhomogeneities often migrate along or against the mechanical gradient, i.e., mechanotaxis, which inspires us to ask how biomimetic cells without biochemical signaling processes respond to environmental inhomogeneity. Here, we perform computer simulations to study the migration of a 2D active colloidal cell (ACC), which consists of active particles enclosed by a passive vesicle, in a heterogeneous environment composed of two adjoining uniform regions with different attributes (influencing the persistent length of the active particle). We find that the ACC can migrate unidirectionally across the interface separating the heterogeneous region and behave tactically. Interestingly, the tactic motion of the ACC is qualitatively different from that of the constituent active particles themselves. In addition, the ACC may also experience a directed drift along the interface of the heterogeneous environment. The tactic behavior of the ACC can be explained by analyzing the pressure distribution on the cell membrane exerted by the enclosed active particles. The findings provide insights into understanding the taxis of biological cells and designing biomimetic cells with environment-sensitive capabilities.

Collective behavior of composite active particles

We describe simulations of active Brownian particles carried out to explore how dynamics and clustering are influenced by particle shape. Our particles are composed of four disks, held together by springs, whose relative size can be varied. These composite objects can be tuned smoothly from having a predominantly concave to a convex surface. We show that even two of these composite particles can exhibit collective motion which modifies the effective Peclet number. We then investigate how particle geometry can be used to explain the phase behavior of many such particles.

Spontaneous emergence of counterclockwise vortex motion in assemblies of pedestrians roaming within an enclosure

The emergence of coherent vortices has been observed in a wide variety of many-body systems such as animal flocks, bacteria, colloids, vibrated granular materials or human crowds. Here, we experimentally demonstrate that pedestrians roaming within an enclosure also form vortex-like patterns which, intriguingly, only rotate counterclockwise. By implementing simple numerical simulations, we evidence that the development of swirls in many-particle systems can be described as a phase transition in which both the density of agents and their dissipative interactions with the boundaries play a determinant role. Also, for the specific case of pedestrians, we show that the preference of right-handed people (the majority in our experiments) to turn leftwards when facing a wall is the symmetry breaking mechanism needed to trigger the global counterclockwise rotation observed.

Active Ornstein-Uhlenbeck model for self-propelled particles with inertia

Self-propelled particles, which convert energy into mechanical motion, exhibit inertia if they have a macroscopic size or move inside a gaseous medium, in contrast to micron-sized overdamped particles immersed in a viscous fluid. Here we study an extension of the active Ornstein-Uhlenbeck model, in which self-propulsion is described by colored noise, to access these inertial effects. We summarize and discuss analytical solutions of the particle's mean-squared displacement and velocity autocorrelation function for several settings ranging from a free particle to various external influences, like a linear or harmonic potential and coupling to another particle via a harmonic spring. Taking into account the particular role of the initial particle velocity in a nonstationary setup, we observe all dynamical exponents between zero and four. After the typical inertial time, determined by the particle's mass, the results inherently revert to the behavior of an overdamped particle with the exception of the harmonically confined systems, in which the overall displacement is enhanced by inertia. We further consider an underdamped model for an active particle with a time-dependent mass, which critically affects the displacement in the intermediate time-regime. Most strikingly, for a sufficiently large rate of mass accumulation, the particle's motion is completely governed by inertial effects as it remains superdiffusive for all times.

Orbital magnetism of an active particle in viscoelastic suspension

We consider an active (self-propelling) particle in a viscoelastic fluid. The particle is charged and constrained to move in a two-dimensional harmonic trap. Its dynamics is coupled to a constant magnetic field applied perpendicular to its plane of motion via Lorentz force. Due to the finite activity, the generalized fluctuation-dissipation relation (GFDR) breaks down, driving the system away from equilibrium. While breaking GFDR, we have shown that the system can have finite classical orbital magnetism only when the dynamics of the system contains finite inertia. The orbital magnetic moment has been calculated exactly. Remarkably, we find that when the elastic dissipation timescale of the medium is larger (smaller) than the persistence timescale of the self-propelling particle, it is diamagnetic (paramagnetic). Therefore, for a given strength of the magnetic field, the system undergoes a transition from diamagnetic to paramagnetic state (and vice versa) simply by tuning the timescales of underlying physical processes, such as active fluctuations and viscoelastic dissipation. Interestingly, we also find that the magnetic moment, which vanishes at equilibrium, behaves nonmonotonically with respect to increasing persistence of self-propulsion, which drives the system out of equilibrium.

Enhancing directed collective motion of self-propelled particles in confined channel

The collective transport of the self-propelled rods (SPRs) is studied by dissipative particle dynamics simulations. Two types of channels (channel I and channel II) are taken into account for various rod concentrations. It is found that in channel I-the asymmetric corrugated channel with periodically varying width, some SPRs are trapped at the corners and form the hedgehog clusters. Other SPRs aggregate at the bottleneck and lead to a traffic jam. Consequently, channel I is inefficient for the directional SPR transport in the case of finite concentration. To achieve efficient collective particle transport, channel II-the channel with constant width and arrays of asymmetric obstacles within it, which can avoid the traffic clogging and hedgehog aggregate is suggested. It is found that the swimmer-obstacle interaction gives rise to the directional motion, the spacing between obstacles can avoid the formation of the hedgehog clusters. The high-efficiency directional collective motion of the SPRs is acquired in channel II. Overall, our simulation study offers an efficient approach for directional collective motion of SPRs.

From collections of independent, mindless robots to flexible, mobile, and directional superstructures

A swarm of simple active particles confined in a flexible scaffold is a promising system to make mobile and deformable superstructures. These soft structures can perform tasks that are difficult to carry out for monolithic robots because they can infiltrate narrow spaces, smaller than their size, and move around obstacles. To achieve such tasks, the origin of the forces the superstructures develop, how they can be guided, and the effects of external environment, especially geometry and the presence of obstacles, need to be understood. Here, we report measurements of the forces developed by such superstructures, enclosing a number of mindless active rod-like robots, as well as the forces exerted by these structures to achieve a simple function, crossing a constriction. We relate these forces to the self-organization of the individual entities. Furthermore, and based on a physical understanding of what controls the mobility of these superstructures and the role of geometry in such a process, we devise a simple strategy where the environment can be designed to bias the mobility of the superstructure, giving rise to directional motion. Simple tasks-such as pulling a load, moving through an obstacle course, or cleaning up an arena-are demonstrated. Rudimentary control of the superstructures using light is also proposed. The results are of relevance to the making of robust flexible superstructures with nontrivial space exploration properties out of a swarm of simpler and cheaper robots.

A single active ring model with velocity self-alignment

Cellular tissue behavior is a multiscale problem. At the cell level, out of equilibrium, biochemical reactions drive physical cell-cell interactions in a typical active matter process. Cell modeling computer simulations are a robust tool to explore countless possibilities and test hypotheses. Here, we introduce a two-dimensional, extended active matter model for biological cells. A ring of interconnected self-propelled particles represents the cell. Neighboring particles are subject to harmonic and bending potentials. Within a characteristic time, each particle's self-velocity tends to align with its scattering velocity after an interaction. Translational modes, rotational modes, and mixtures of these appear as collective states. Using analytical results derived from active Brownian particles, we identify effective characteristic time scales for ballistic and diffusive movements. Finite-size scale investigation shows that the ring diffusion increases linearly with its size when in collective movement. A study on the ring shape reveals that all collective states are present even when bending forces are weak. In that case, when in a translational mode, the collective velocity aligns with the largest ring's direction in a spontaneous polarization emergence.

Whirligig beetles as corralled active Brownian particles

We study the collective dynamics of groups of whirligig beetles Dineutus discolor (Coleoptera: Gyrinidae) swimming freely on the surface of water. We extract individual trajectories for each beetle, including positions and orientations, and use this to discover (i) a density-dependent speed scaling like v ∼ ρ^-ν with ν ≈ 0.4 over two orders of magnitude in density (ii) an inertial delay for velocity alignment of approximately 13 ms and (iii) coexisting high and low-density phases, consistent with motility-induced phase separation (MIPS). We modify a standard active Brownian particle (ABP) model to a corralled ABP (CABP) model that functions in open space by incorporating a density-dependent reorientation of the beetles, towards the cluster. We use our new model to test our hypothesis that an motility-induced phase separation (MIPS) (or a MIPS like effect) can explain the co-occurrence of high- and low-density phases we see in our data. The fitted model then successfully recovers a MIPS-like condensed phase for N = 200 and the absence of such a phase for smaller group sizes N = 50, 100.

Time-dependent inertia of self-propelled particles: The Langevin rocket

Many self-propelled objects are large enough to exhibit inertial effects but still suffer from environmental fluctuations. The corresponding basic equations of motion are governed by active Langevin dynamics, which involve inertia, friction, and stochastic noise for both the translational and orientational degrees of freedom coupled via the self-propulsion along the particle orientation. In this paper, we generalize the active Langevin model to time-dependent parameters and explicitly discuss the effect of time-dependent inertia for achiral and chiral particles. Realizations of this situation are manifold, ranging from minirockets (which are self-propelled by burning their own mass), to dust particles in plasma (which lose mass by evaporating material), to walkers with expiring activity. Here we present analytical solutions for several dynamical correlation functions, such as mean-square displacement and orientational and velocity autocorrelation functions. If the parameters exhibit a slow power law in time, we obtain anomalous superdiffusion with a nontrivial dynamical exponent. Finally, we constitute the "Langevin rocket" model by including orientational fluctuations in the traditional Tsiolkovsky rocket equation. We calculate the mean reach of the Langevin rocket and discuss different mass ejection strategies to maximize it. Our results can be tested in experiments on macroscopic robotic or living particles or in self-propelled mesoscopic objects moving in media of low viscosity, such as complex plasma.