Confinement stabilizes a bacterial suspension into a spiral vortex

Achieving designed texture and flows in bulk active nematics using optimal control theory

Being intrinsically nonequilibrium, active materials can potentially perform functions that would be thermodynamically forbidden in passive materials. However, active systems have diverse local attractors that correspond to distinct dynamical states, many of which exhibit chaotic turbulent-like dynamics and thus cannot perform work or useful functions. Designing such a system to choose a specific dynamical state is a formidable challenge. Motivated by recent advances enabling optogenetic control of experimental active materials, we describe an optimal control theory framework that identifies a spatiotemporal sequence of light-generated activity that drives an active nematic system toward a prescribed dynamical steady state. Active nematics are unstable to spontaneous defect proliferation and chaotic streaming dynamics in the absence of control. We demonstrate that optimal control theory can compute activity fields that redirect the dynamics into a variety of alternative dynamical programs and functions. This includes dynamically reconfiguring between states, selecting and stabilizing emergent behaviors that do not correspond to attractors, and are hence unstable in the uncontrolled system. Our results provide a roadmap to leverage optical control methods to rationally design structure, dynamics, and function in a wide variety of active materials.

Vortex reversal is a precursor of confined bacterial turbulence

Active turbulence, or chaotic self-organized collective motion, is often observed in concentrated suspensions of motile bacteria and other systems of self-propelled interacting agents. To date, there is no fundamental understanding of how geometrical confinement orchestrates active turbulence and alters its physical properties. Here, by combining large-scale experiments, computer modeling, and analytical theory, we have identified a generic sequence of transitions occurring in bacterial suspensions confined in cylindrical wells of varying radii. With increasing the well's radius, we observed that persistent vortex motion gives way to periodic vortex reversals, four-vortex pulsations, and then well-developed active turbulence. Using computational modeling and analytical theory, we have shown that vortex reversal results from the nonlinear interaction of the first three azimuthal modes that become unstable with the radius increase. The analytical results account for our key experimental findings. To further validate our approach, we reconstructed equations of motion from experimental data. Our findings shed light on the universal properties of confined bacterial active matter and can be applied to various biological and synthetic active systems.

Activity-Driven Emulsification of Phase-Separating Binary Mixtures

Active particles self-assemble into emergent structures that respond sensitively to external constraints. Consequently, their behavior under confinement is complex, especially in soft confined media, leading to diverse emergent morphologies. Through computer simulations, we investigate the dynamical interplay between active Brownian particles and a binary mixture. Our results show that active particles stabilize nonequilibrium morphologies, arresting coarsening by exerting active pressure that competes with surface tension. For moderate activities, particles stabilize an active emulsion with a well-defined droplet size. At higher activities, when particles can cross the liquid domains, a dynamic emulsion with large droplet dispersion is sustained. Furthermore, active particles drive phase-separated mixtures away from equilibrium configurations, demonstrating a rich coassembly behavior due to competing energy scales in the system.

Induced friction on a probe moving in a nonequilibrium medium

Using a powerful combination of projection-operator method and path-space response theory, we derive the fluctuation dynamics of a slow inertial probe coupled to a steady nonequilibrium medium under the assumption of time-scale separation. The nonequilibrium is realized by external nongradient driving on the medium particles or by their (athermal) active self-propulsion. The resulting friction on the probe is an explicit time correlation for medium observables and is decomposed into two terms: one entropic, proportional to the noise variance as in the Einstein relation for equilibrium media, and a frenetic term that can take both signs. As an illustration, we give the exact expressions for the linear friction coefficient and noise amplitude of a probe in a rotating run-and-tumble medium. We find a transition to absolute negative probe friction as the nonequilibrium medium exhibits sufficient and persistent rotational current. There, the run-away of the probe to high speeds realizes a nonequilibrium-induced acceleration. Simulations show that its speed finally saturates, yielding a symmetric stationary probe-momentum distribution with two peaks.

Spontaneous oscillation in collective microswimmers: Insights from a chiral self-propelled rod model

Active systems exhibit fascinating self-organized structures and rich motility patterns, yet the underlying mechanisms governing their emergence and characteristics remain elusive. Here, we develop a chiral self-propelled rod (CSPR) model with mechanical contact-induced quorum sensing to investigate the spatiotemporal dynamics of dense bacteria populations. Our findings show that the CSPR model showcases spontaneous nonequilibrium oscillatory clustering of active systems. The motion characteristics of these clusters depend on colony features (microswimmers' morphology and density) and mechanical contact-induced sensing mechanisms (polarization alignment and angular velocity alignment of CSPR). Interestingly, reinforced strength of polar alignment accelerates the formation of stable oscillations, while decreased density and angular velocity alignment strength modify their emergence pattern. Significantly, our study identifies three distinct oscillation patterns: global stable oscillation, bistable oscillation, and multistable oscillation, and reveals that their phase transitions are driven by variations in the spatial correlation of CSPR. These insights provide a new perspective on understanding the intricate evolution of active matter, opening possible avenues for emerging applications.

Topological orbital angular momentum extraction and twofold protection of vortex transport

Vortex phenomena are ubiquitous in nature. In optics, despite the availability of numerous techniques for vortex generation and detection, topological protection of vortex transport with desired orbital angular momentum (OAM) remains a challenge. Here, by use of topological disclination, we demonstrate a scheme to confine and guide vortices featuring arbitrary high-order charges. Such a scheme relies on twofold topological protection: a non-trivial winding in momentum space due to chiral symmetry, and a non-trivial winding in real space due to the complex coupling of OAM modes across the disclination structure. We unveil a vorticity-coordinated rotational symmetry, which sets up a universal relation between the vortex topological charge and the rotational symmetry order of the system. As an example, we construct photonic disclination lattices with a single core but different C n symmetries and achieve robust transport of an optical vortex with preserved OAM solely corresponding to one selected zero-energy vortex mode at the mid-gap. Furthermore, we show that such topological structures can be used for vortex filtering to extract a chosen OAM mode from mixed excitations. Our results illustrate the fundamental interplay of vorticity, disclination and higher-order topology, which may open a new pathway for the development of OAM-based photonic devices such as vortex guides, fibres and lasers.

Stochastic migrations of Marangoni surfers between two lobes of a dumbbell-shaped confinement

We report an experimental investigation on the stochastic migration dynamics of Marangoni surfers (camphor-infused paper disks) between the two lobes of a dumbbell-shaped chamber. We characterize the migration dynamics using survival analysis of a configuration, wherein a configuration represents a distinct distribution of disks between the lobes. We observe that a configuration's stability decreases with increasing pairwise interactions. Consequently, the configuration with equal partitioning of disks between the lobes-that is exactly one-half of disks in each lobe for even-numbered systems but with one extra disk in either of the lobes for odd-numbered systems-has the lowest pairwise interactions, thus is always the most stable configuration. Furthermore, all configurations exhibit a stretched exponential decay with time, which is ascribed to a disk's activity decay with time or "aging"-a phenomenon validated by modeling a camphor disk as a chiral active particle (CAP) as initially proposed by Cruz et al.

Strong Casimir-like Forces in Flocking Active Matter

Confining in space the equilibrium fluctuations of statistical systems with long-range correlations is known to result into effective forces on the boundaries. Here we demonstrate the occurrence of Casimir-like forces in the nonequilibrium context provided by flocking active matter. In particular, we consider a system of aligning self-propelled particles in two spatial dimensions that are transversally confined by reflecting or partially reflecting walls. We show that in the ordered flocking phase this confined active vectorial fluid is characterized by extensive boundary layers, as opposed to the finite ones usually observed in confined scalar active matter. Moreover, a finite-size, fluctuation-induced contribution to the pressure on the wall emerges, which decays slowly and algebraically upon increasing the distance between the walls. We explain our findings-which display a certain degree of universality-within a hydrodynamic description of the density and velocity fields.

Scaling Transition of Active Turbulence from Two to Three Dimensions

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

Surface-directed dynamics in living liquid crystals

We study living liquid crystals (LLCs), which are an amalgam of nematic liquid crystals (LCs) and active matter (AM). These LLCs are placed in contact with surfaces which impose planar/homeotropic boundary conditions on the director field of the LC and the polarization field of the AM. The interplay of LC-AM interactions and the surface-directed conditions yield controlled pattern dynamics in the LLC, which has important technological implications. We discuss two representative examples of this pattern dynamics.

Light-regulated soliton dynamics in liquid crystals

Electrically powered solitons are particle-like field configurations in out-of-equilibrium nematics that have garnered significant interest. However, their random generation and lack of controllable motion have limited their application. Here, we present a reconfigurable optoelectronic approach capable of regulating the entire lifecycle of solitons by utilizing multi-strategy digital light projection to construct delicate patterning of virtual electrode. We demonstrate that optically actuated domains with diverse geometry enable the generation of multiple solitons and further allow in-situ formation of individual soliton by matching the light pattern to its dimension. Exquisitely engineered light intensity of patterns facilitates modulation of soliton velocity and transformation of propagating direction. The utilization of a light-guided channel enables the on-demand control of soliton trajectories along customized paths. Furthermore, dynamic light patterns that vary in space and time allow for collective motion such as migration, mimicking phototaxis in biological systems. This reconfigurable manipulation strategy, grounded in the photoconductive effect, proves highly versatile and effective in directing soliton dynamics, heralding the potential for their programmable control and offering a significant advantage in multitasking scenarios.

Collective behavior of squirmers in thin films

Bacteria in biofilms form complex structures and can collectively migrate within mobile aggregates, which is referred to as swarming. This behavior is influenced by a combination of various factors, including morphological characteristics and propulsive forces of swimmers, their volume fraction within a confined environment, and hydrodynamic and steric interactions between them. In our study, we employ the squirmer model for microswimmers and the dissipative particle dynamics method for fluid modeling to investigate the collective motion of swimmers in thin films. The film thickness permits a free orientation of non-spherical squirmers, but constraints them to form a two-layered structure at maximum. Structural and dynamic properties of squirmer suspensions confined within the slit are analyzed for different volume fractions of swimmers, motility types (e.g., pusher, neutral squirmer, puller), and the presence of a rotlet dipolar flow field, which mimics the counter-rotating flow generated by flagellated bacteria. Different states are characterized, including a gas-like phase, swarming, and motility-induced phase separation, as a function of increasing volume fraction. Our study highlights the importance of an anisotropic swimmer shape, hydrodynamic interactions between squirmers, and their interaction with the walls for the emergence of different collective behaviors. Interestingly, the formation of collective structures may not be symmetric with respect to the two walls. Furthermore, the presence of a rotlet dipole significantly mitigates differences in the collective behavior between various swimmer types. These results contribute to a better understanding of the formation of bacterial biofilms and the emergence of collective states in confined active matter.

Spontaneous stable rotation of flocking flexible active matter

In this paper we present an n-node flexible active matter model to study the collective motion due to the flocking of individual achiral agents on a two-dimensional surface. By introducing a measure of the direction detectability of the agents to tune their body direction towards the food source, we find that a spontaneous stable cluster rotation emerges with increasing direction detectability. The spontaneous rotation is synchronized with the chirality produced by the alignment of their bodies under the impetus of the active force. A linear relationship between the normalized angular velocity and chirality is observed and the numerical simulation agrees well with the analytical derivation. The conclusions explain well the spontaneous stable rotation of clusters that exists in many flexible active matter systems, like worms or dogs, when they flock to the same single source.

Self-organized vortex phases and hydrodynamic interactions in Bos taurus sperm cells

Flocking behavior is observed in biological systems from the cellular to superorganismal length scales, and the mechanisms and purposes of this behavior are objects of intense interest. In this paper, we study the collective dynamics of bovine sperm cells in a viscoelastic fluid. These cells appear not to spontaneously flock, but transition into a long-lived flocking phase after being exposed to a transient ordering pulse of fluid flow. Surprisingly, this induced flocking phase has many qualitative similarities with the spontaneous polar flocking phases predicted by Toner-Tu theory, such as anisotropic giant number fluctuations and nontrivial transverse density correlations, despite the induced nature of the phase and the clearly important role of momentum conservation between the swimmers and the surrounding fluid in these experiments. We also find a self-organized global vortex state of the sperm cells, and map out an experimental phase diagram of states of collective motion as a function of cell density and motility statistics. We compare our experiments with a parameter-matched computational model of persistently turning active particles and find that the experimental order-disorder phase boundary as a function of cell density and persistence time can be approximately predicted from measures of single-cell properties. Our results may have implications for the evaluation of sample fertility by studying the collective phase behavior of dense groups of swimming sperm.

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.

Hydrodynamically induced aggregation of two dimensional oriented active particles

We investigate a system of co-oriented active particles interacting only via hydrodynamic and steric interactions in a two-dimensional fluid. We offer a new method of calculating the flow created by any active particle in such a fluid, focusing on the dynamics of flow fields with a high-order spatial decay, which we analyze using a geometric Hamiltonian. We show that when the particles are oriented and the flow has a single, odd power decay, such systems lead to stable, fractal-like aggregation, with the only exception being the force dipole. We discuss how our results can easily be generalized to more complicated force distributions and to other effective two-dimensional systems.

Active Darcy's Law

While bacterial swarms can exhibit active turbulence in vacant spaces, they naturally inhabit crowded environments. We numerically show that driving disorderly active fluids through porous media enhances Darcy's law. While purely active flows average to zero flux, hybrid active/driven flows display greater drift than purely pressure-driven flows. This enhancement is nonmonotonic with activity, leading to an optimal activity to maximize flow rate. We incorporate the active contribution into an active Darcy's law, which may serve to help understand anomalous transport of swarming in porous media.

Oscillating edge current in polar active fluid

Dense bacterial suspensions exhibit turbulent behavior called bacterial turbulence. The behavior of the bulk unconstrained bacterial turbulence is described well by the Toner-Tu-Swift-Hohenberg (TTSH) equation for the velocity field. However, it remains unclear how we should treat boundary conditions on bacterial turbulence in contact with some boundaries (e.g., solid walls). To be more specific, although the importance of the edge current, the flow along the boundary, has been demonstrated in several experimental studies on confined bacterial suspensions, previous numerical studies based on the TTSH equation employ nonslip boundary conditions and do not seem to properly describe the behavior of bacteria near the boundaries. In this paper, we impose a slip boundary condition on the TTSH equation to describe the bacterial motion at boundaries. We develop a method to implement the slip boundary condition. Using this method, we have successfully produced edge current and discovered that the direction of the edge current temporally oscillates. The oscillation can be attributable to the advection term in the TTSH equation. Our paper demonstrates that boundary conditions could play an important role in the collective dynamics of active systems.

Experimental and numerical study of a second-order transition in the behavior of confined self-propelled particles

In this paper, we conduct experimental investigations on the behavior of confined self-propelled particles within a circular arena, employing small commercial robots capable of locomotion, communication, and information processing. These robots execute circular trajectories, which can be clockwise or counterclockwise, based on two internal states. Using a majority-based stochastic decision algorithm, each robot can reverse its direction based on the states of two neighboring robots. By manipulating a control parameter governing the interaction, the system exhibits a transition from a state where all robots rotate randomly to one where they rotate uniformly in the same direction. Moreover, this transition significantly impacts the trajectories of the robots. To extend our findings to larger systems, we introduce a mathematical model enabling characterization of the order transition type and the resulting trajectories. Our results reveal a second-order transition from active Brownian to chiral motion.

Vortex Pattern Stabilization in Thin Films Resulting from Shear Thickening of Active Suspensions

The need for structuring on micrometer scales is abundant, for example, in view of phononic applications. We here outline a novel approach based on the phenomenon of active turbulence on the mesoscale. As we demonstrate, a shear-thickening carrier fluid of active microswimmers intrinsically stabilizes regular vortex patterns of otherwise turbulent active suspensions. The fluid self-organizes into a periodically structured nonequilibrium state. Introducing additional passive particles of intermediate size leads to regular spatial organization of these objects. Our approach opens a new path toward functionalization through patterning of thin films and membranes.

Controlling Confined Collective Organization with Taxis

Biased locomotion is a common feature of microorganisms, but little is known about its impact on self-organization. Inspired by recent experiments showing a transition to large-scale flows, we study theoretically the dynamics of magnetotactic bacteria confined to a drop. We reveal two symmetry-breaking mechanisms (one local chiral and one global achiral) leading to self-organization into global vortices and a net torque exerted on the drop. The collective behavior is ultimately controlled by the swimmers' microscopic chirality and, strikingly, the system can exhibit oscillations and memorylike features.

The narrow escape problem of a chiral active particle (CAP): an optimal scheme

We report a simulation study on the narrow escape kinetics of a chiral active particle (CAP) confined to a circular domain with a narrow escape opening. The study's main objective is to optimize the CAP's escape chances as a function of the relevant parameters, such as translational and rotational speeds of the CAP, domain size, etc. We identified three regimes in the escape kinetics, namely the noise-dominated regime, the optimal regime, and the chiral activity-dominated regime. In particular, the optimal regime is characterized by an escape scheme that involves a direct passage to the domain boundary at first and then a unidirectional drift along the boundary towards the exit. Furthermore, we propose a non-dimensionalization approach to optimize the escape performance across microorganisms with varying motile characteristics. Additionally, we explore the influence of the translational and rotational noise on the CAP's escape kinetics.

Soft confinement of self-propelled rods: simulation and theory

We present an analytical framework for evolving the dynamics of active rods under any periodic external potential, including confining channels and arrays of harmonic traps. As a proof of concept, we analyze the structure and dispersion of self-propelled rods under a soft, periodic one-dimensional (1D) confinement potential and under a two-dimensional (2D) periodic radial harmonic trap. While passive rods and polymers nematically order under 1D confinement, their diffusive transport along the director is limited by thermal diffusion. In contrast, self-propelled rods can generate large convective fluxes when combined with nematic ordering, producing a strong dispersion along the director. Combining theory and simulation, we demonstrate that nematic alignment and self-propulsion generates an exponential enhancement in active diffusivity along the director, in contrast to passive rods that experience at most a 2-fold increase.

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.

Self-enhanced mobility enables vortex pattern formation in living matter

Ranging from subcellular organelle biogenesis to embryo development, the formation of self-organized structures is a hallmark of living systems. Whereas the emergence of ordered spatial patterns in biology is often driven by intricate chemical signalling that coordinates cellular behaviour and differentiation1-4, purely physical interactions can drive the formation of regular biological patterns such as crystalline vortex arrays in suspensions of spermatozoa5 and bacteria6. Here we discovered a new route to self-organized pattern formation driven by physical interactions, which creates large-scale regular spatial structures with multiscale ordering. Specifically we found that dense bacterial living matter spontaneously developed a lattice of mesoscale, fast-spinning vortices; these vortices each consisted of around 104-105 motile bacterial cells and were arranged in space at greater than centimetre scale and with apparent hexagonal order, whereas individual cells in the vortices moved in coordinated directions with strong polar and vortical order. Single-cell tracking and numerical simulations suggest that the phenomenon is enabled by self-enhanced mobility in the system-that is, the speed of individual cells increasing with cell-generated collective stresses at a given cell density. Stress-induced mobility enhancement and fluidization is prevalent in dense living matter at various scales of length7-9. Our findings demonstrate that self-enhanced mobility offers a simple physical mechanism for pattern formation in living systems and, more generally, in other active matter systems10 near the boundary of fluid- and solid-like behaviours11-17.

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.

Vortex Lattices in Active Nematics with Periodic Obstacle Arrays

We numerically model a two-dimensional active nematic confined by a periodic array of fixed obstacles. Even in the passive nematic, the appearance of topological defects is unavoidable due to planar anchoring by the obstacle surfaces. We show that a vortex lattice state emerges as activity is increased, and that this lattice may be tuned from "ferromagnetic" to "antiferromagnetic" by varying the gap size between obstacles. We map the rich variety of states exhibited by the system as a function of distance between obstacles and activity, including a pinned defect state, motile defects, the vortex lattice, and active turbulence. We demonstrate that the flows in the active turbulent phase can be tuned by the presence of obstacles, and explore the effects of a frustrated lattice geometry on the vortex lattice phase.

Emergent structures in active block copolymer composites

Block copolymer melts offer unique templates to control the position and alignment of nanoparticles due to their ability to self-assemble into periodic ordered structures. Active particles are shown to coassemble with block copolymers leading to emergent organized structures. The block copolymer acts as a soft template that can control the self-propulsion of active particles, both for interface-segregated and selective nanoparticles. At moderate activities, active particles can form organized structures such as polarized trains or rotating vortices. At high activity, the contrast in the polymeric and colloidal timescales can lead to particle swarms with distorted block copolymer morphology, due to the competition between polymeric self-assembly and active Brownian self-propulsion.

Hydrodynamics-Induced Long-Range Attraction between Plates in Bacterial Suspensions

We perform optical-tweezers experiments and mesoscale fluid simulations to study the effective interactions between two parallel plates immersed in bacterial suspensions. The plates are found to experience a long-range attraction, which increases linearly with bacterial density and decreases with plate separation. The higher bacterial density and orientation order between plates observed in the experiments imply that the long-range effective attraction mainly arises from the bacterial flow field, instead of the direct bacterium-plate collisions, which is confirmed by the simulations. Furthermore, the hydrodynamic contribution is inversely proportional to the squared interplate separation in the far field. Our findings highlight the importance of hydrodynamics on the effective forces between passive objects in active baths, providing new possibilities to control activity-directed assembly.

Geometrical control of interface patterning underlies active matter invasion

Interaction between active materials and the boundaries of geometrical confinement is key to many emergent phenomena in active systems. For living active matter consisting of animal cells or motile bacteria, the confinement boundary is often a deformable interface, and it has been unclear how activity-induced interface dynamics might lead to morphogenesis and pattern formation. Here, we studied the evolution of bacterial active matter confined by a deformable boundary. We found that an ordered morphological pattern emerged at the interface characterized by periodically spaced interfacial protrusions; behind the interfacial protrusions, bacterial swimmers self-organized into multicellular clusters displaying +1/2 nematic defects. Subsequently, a hierarchical sequence of transitions from interfacial protrusions to creeping branches allowed the bacterial active drop to rapidly invade surrounding space with a striking self-similar branch pattern. We found that this interface patterning is geometrically controlled by the local curvature of the interface, a phenomenon we denote as collective curvature sensing. Using a continuum active model, we revealed that the collective curvature sensing arises from enhanced active stresses near high-curvature regions, with the active length scale setting the characteristic distance between the interfacial protrusions. Our findings reveal a protrusion-to-branch transition as a unique mode of active matter invasion and suggest a strategy to engineer pattern formation of active materials.

Friction-mediated phase transition in confined active nematics

Using a minimal continuum model, we investigate the interplay between circular confinement and substrate friction in active nematics. Upon increasing the friction from low to high, we observe a dynamical phase transition from a circulating flow phase to an anisotropic flow phase in which the flow tends to align perpendicular to the nematic director at the boundary. We demonstrate that both the flow structure and dynamic correlations in the latter phase differ from those of an unconfined, active turbulent system and may be controlled by the prescribed nematic boundary conditions. Our results show that substrate friction and geometric confinement act as valuable control parameters in active nematics.

Rectified Rotational Dynamics of Mobile Inclusions in Two-Dimensional Active Nematics

We investigate the dynamics of mobile inclusions embedded in 2D active nematics. The interplay between the inclusion shape, boundary-induced nematic order, and autonomous flows powers the inclusion motion. Disks and achiral gears exhibit unbiased rotational motion, but with distinct dynamics. In comparison, chiral gear-shaped inclusions exhibit long-term rectified rotation, which is correlated with dynamics and polarization of nearby +1/2 topological defects. The chirality of defect polarities and the active nematic texture around the inclusion correlate with the inclusion's instantaneous rotation rate. Inclusions provide a promising tool for probing the rheological properties of active nematics and extracting ordered motion from their inherently chaotic motion.

Phase behavior and dynamics in a colloid-polymer mixture under spherical confinement

From studies via molecular dynamics simulations, we report results on structure and dynamics in mixtures of active colloids and passive polymers that are confined inside a spherical container with a repulsive boundary. All interactions in the fully passive limit are chosen in such a way that in equilibrium coexistence between colloid-rich and polymer-rich phases occurs. For most part of the studies the chosen compositions give rise to Janus-like structure: nearly one side of the sphere is occupied by the colloids and the rest by the polymers. This partially wet situation mimics approximately a neutral wall in the fully passive scenario. Following the introduction of a velocity-aligning activity to the colloids, the shape of the polymer-rich domain changes to that of an ellipsoid, around the long axis of which the colloid-rich domain attains a macroscopic angular momentum. In the steady state, the orientation of this axis evolves via diffusion, magnitude of which depends upon the strength of activity, but only weakly.

Spatio-temporal patterning of extensile active stresses in microtubule-based active fluids

Microtubule-based active fluids exhibit turbulent-like autonomous flows, which are driven by the molecular motor powered motion of filamentous constituents. Controlling active stresses in space and time is an essential prerequisite for controlling the intrinsically chaotic dynamics of extensile active fluids. We design single-headed kinesin molecular motors that exhibit optically enhanced clustering and thus enable precise and repeatable spatial and temporal control of extensile active stresses. Such motors enable rapid, reversible switching between flowing and quiescent states. In turn, spatio-temporal patterning of the active stress controls the evolution of the ubiquitous bend instability of extensile active fluids and determines its critical length dependence. Combining optically controlled clusters with conventional kinesin motors enables one-time switching from contractile to extensile active stresses. These results open a path towards real-time control of the autonomous flows generated by active fluids.

Flocking turbulence of microswimmers in confined domains

We extensively study the Toner-Tu-Swift-Hohenberg model of motile active matter by means of direct numerical simulations in a two-dimensional confined domain. By exploring the space of parameters of the model we investigate the emergence of a new state of active turbulence which occurs when the aligning interactions and the self-propulsion of the swimmers are strong. This regime of flocking turbulence is characterized by a population of few strong vortices, each surrounded by an island of coherent flocking motion. The energy spectrum of flocking turbulence displays a power-law scaling with an exponent which depends weakly on the model parameters. By increasing the confinement we observe that the system, after a long transient characterized by power-law-distributed transition times, switches to the ordered state of a single giant vortex.

Collective behavior of chiral active particles with anisotropic interactions in a confined space

Extensive studies so far have indicated that chirality, anisotropic interactions and spatial confinement play important roles in collective dynamics in active matter systems. However, how the overall interplay of these crucial factors affects the novel phases and macroscopic properties remains less explored. Here, using Langevin dynamics simulations, we investigate the self-organization of a chiral active system composed of amphiphilic Janus particles, where the embedded anisotropic interaction orientation is assumed to be either the same or just opposite to the direction of active force. A wealth of dynamic phases are observed including formation of phase separation, clustering state, homogeneous state, spiral vortex flow, swarm and spatiotemporal oscillation. By tuning self-propelled angular speed and anisotropic interaction strength, we identify the non-equilibrium phase diagrams, and reveal the very non-trivial modulation of both vortex and swarm patterns. Intriguingly, we find that strong chirality-alignment-confinement coupling yields a self-driven spatial and temporal organization periodically oscillating between a counterclockwise vortex and a clockwise one. Our work provides a new understanding of the novel self-assembly arising in such a confined system and enables new strategies for achieving ordered dynamic structures.

Collective vortical motion and vorticity reversals of self-propelled particles on circularly patterned substrates

The collective behavior of self-propelled particles (SPPs) under the combined effects of a circularly patterned substrate and circular confinement is investigated through coarse-grained molecular dynamics simulations of polarized and disjoint ring polymers. The study is performed over a wide range of values of the SPPs packing fraction ϕ[over ¯], motility force F_{D}, and area fraction of the patterned region. At low packing fractions, the SPPs are excluded from the system's center and exhibit a vortical motion that is dominated by the substrate at intermediate values of F_{D}. This exclusion zone is due to the coupling between the driving force and torque induced by the substrate, which induces an outward spiral motion of the SPPs. For high values of F_{D}, the SPPs exclusion from the center is dominated by the confining boundary. At high values of ϕ[over ¯], the substrate pattern leads to reversals in the vorticity, which become quasiperiodic with increasing ϕ[over ¯]. We also found that the substrate pattern is able to separate SPPs based on their motilities.

Polarity and chirality control of an active fluid by passive nematic defects

Much like passive materials, active systems can be affected by the presence of imperfections in their microscopic order, called defects, that influence macroscopic properties. This suggests the possibility to steer collective patterns by introducing and controlling defects in an active system. Here we show that a self-assembled, passive nematic is ideally suited to control the pattern formation process of an active fluid. To this end, we force microtubules to glide inside a passive nematic material made from actin filaments. The actin nematic features self-assembled half-integer defects that steer the active microtubules and lead to the formation of macroscopic polar patterns. Moreover, by confining the nematic in circular geometries, chiral loops form. We find that the exact positioning of nematic defects in the passive material deterministically controls the formation and the polarity of the active flow, opening the possibility of efficiently shaping an active material using passive defects.

Alignment rule and geometric confinement lead to stability of a vortex in active flow

Vortices are hallmarks of a wide range of nonequilibrium phenomena in fluids at multiple length scales. In this work, we numerically study the whirling motion of self-propelled soft point particles confined in circular domain, and aim at addressing the stability issue of the coherent vortex structure. By the combination of dynamical and statistical analysis at the individual particle level, we reveal the persistence of the whirling motion resulting from the subtle competition of activity and geometric confinement. In the stable whirling motion, the scenario of the coexistence of the irregular microscopic motions of individual particles and the regular global whirling motion is fundamentally different from the motion of a vortex in passive fluid. Possible orientational order coexisting with the whirling are further explored. This work shows the stability mechanism of vortical dynamics in active media under the alignment rule in confined space and may have implications in creating and harnessing macroscale coherent dynamical states by tuning the confining geometry.

Active turbulence and spontaneous phase separation in inhomogeneous extensile active gels

We report numerical results for the hydrodynamics of inhomogeneous lyotropic and extensile active nematic gels. By simulating the coupled Cahn-Hilliard, Navier-Stokes, and Beris-Edwards equation for the evolution of the composition, flow and orientational order of an active nematic, we ask whether composition variations are important to determine its emergent physics. As in active gels of uniform composition, we find that increasing either activity or nematic tendency (e.g., overall active matter concentration) triggers a transition between an isotropic passive phase and an active nematic one. We show that composition inhomogeneities are important in the latter phase, where we find three types of possible dynamical regimes. First, we observe regular patterns with defects and vortices: these exist close to the passive-active transition. Second, for larger activity, or deeper in the nematic phase, we find active turbulence, as in active gels of uniform composition, but with exceedingly large composition variation. In the third regime, which is uniquely associated with inhomogeneity and occurs for large nematic tendency and low activity, we observe spontaneous microphase separation into active and passive domains. The microphase separated regime is notable in view of the absence of an explicit demixing term in the underlying free energy which we use, and we provide a theoretical analysis based on the common tangent construction which explains its existence. We hope this regime can be probed experimentally in the future.

Quasi-two-dimensional bacterial swimming around pillars: Enhanced trapping efficiency and curvature dependence

Microswimmers exhibit more diverse behavior in quasi-two dimensions than in three dimensions. Such behavior remains elusive due to the analytical difficulty of dealing with two parallel solid boundaries. The existence of additional obstacles in quasi-two dimensional systems further complicates the analysis. Combining experiments and hydrodynamic simulations, we investigate how the spatial dimension affects the interactions between microswimmers and obstacles. We fabricated microscopic pillars in quasi-two dimensions by etching glass coverslips and observed bacterial swimming among the pillars. Bacteria got trapped around the circular pillars and the trapping efficiency increased as the quasi-two-dimensionality was increased or as the curvature of the pillars was decreased. Numerical simulations of the simplest situation of a confined squirmer showed anomalous increase of hydrodynamic attractions, establishing that the enhanced interaction is a universal property of quasi-two-dimensional microhydrodynamics. We also demonstrated that the local curvature of the obstacle controls the trapping efficiency by experiments with elliptic pillars.

Fluid circulation driven by collectively organized metachronal waves in swimming T. aceti nematodes

Recent experiments have shown that the nematode T. aceti can assemble into collectively undulating groups at the edge of fluid drops. This coordinated state consists of metachronal waves and drives fluid circulation inside the drop. We find that the circulation velocity is about 2 mm/s and nearly half the speed of the metachronal wave. We develop a quasi-two-dimensional hydrodynamics model using the Stokes flow approximation. The periodic motion of the nematodes constitute our moving boundary condition that drives the flow. Our model suggests that large-amplitude excursions of the nematode tails produce the fluid circulation. We discuss the constraints on containers that would enhance fluid motion, which could be used in the future design of on demand flow generating systems.

Phenotyping single-cell motility in microfluidic confinement

The movement trajectories of organisms serve as dynamic read-outs of their behaviour and physiology. For microorganisms this can be difficult to resolve due to their small size and fast movement. Here, we devise a novel droplet microfluidics assay to encapsulate single micron-sized algae inside closed arenas, enabling ultralong high-speed tracking of the same cell. Comparing two model species - Chlamydomonas reinhardtii (freshwater, 2 cilia), and Pyramimonas octopus (marine, 8 cilia), we detail their highly-stereotyped yet contrasting swimming behaviours and environmental interactions. By measuring the rates and probabilities with which cells transition between a trio of motility states (smooth-forward swimming, quiescence, tumbling or excitable backward swimming), we reconstruct the control network that underlies this gait switching dynamics. A simplified model of cell-roaming in circular confinement reproduces the observed long-term behaviours and spatial fluxes, including novel boundary circulation behaviour. Finally, we establish an assay in which pairs of droplets are fused on demand, one containing a trapped cell with another containing a chemical that perturbs cellular excitability, to reveal how aneural microorganisms adapt their locomotor patterns in real-time.

Incompressible Polar Active Fluids with Quenched Random Field Disorder in Dimensions d>2

We present a hydrodynamic theory of incompressible polar active fluids with quenched random field disorder. This theory shows that such fluids can overcome the disruption caused by the quenched disorder and move coherently, in the sense of having a nonzero mean velocity in the hydrodynamic limit. However, the scaling behavior of this class of active systems cannot be described by linearized hydrodynamics in spatial dimensions between 2 and 5. Nonetheless, we obtain the exact dimension-dependent scaling exponents in these dimensions.

Giant vortex dynamics in confined bacterial turbulence

We report the numerical evidence of a new state of bacterial turbulence in confined domains. By means of extensive numerical simulations of the Toner-Tu-Swift-Hohenberg model for dense bacterial suspensions in circular geometry, we discover the formation a stable, ordered state in which the angular momentum symmetry is broken. This is achieved by self-organization of a turbulent-like flow into a single, giant vortex of the size of the domain. The giant vortex is surrounded by an annular region close to the boundary, characterized by small-scale, radial vorticity streaks. The average radial velocity profile of the vortex is found to be in agreement with a simple analytical prediction. We also provide an estimate of the temporal and spatial scales of a suitable experimental setup comparable with our numerical findings.

Annealing and melting of active two-dimensional soliton lattices in chiral nematic films

In this work, thousands of electrically driven dissipative solitons, called directrons, are generated in a chiral nematic liquid crystal. The directrons start with random motions but soon synchronize their motions and self-organize into a two-dimensional hexagonal lattice. The directron lattice moves collectively and forms a hexatic phase. By increasing the applied voltage, the lattice exhibits a first-order hexatic-to-liquid phase transition.

Emergent collective dynamics of pusher and puller squirmer rods: swarming, clustering, and turbulence

We study the interplay of steric and hydrodynamic interactions in suspensions of elongated microswimmers by simulating the full hydrodynamics of squirmer rods in the quasi two-dimensional geometry of a Hele-Shaw cell. To create pusher or puller-type squirmer rods, we concentrate the surface slip-velocity field more to the back or to the front of the rod and thereby are able to tune the rod's force-dipole strength. We study a wide range of aspect ratios and area fractions and provide corresponding state diagrams. The flow field of pusher-type squirmer rods destabilizes ordered structures and favors the disordered state at small area fractions and aspect ratios. Only when steric interactions become relevant, we observe a turbulent and dynamic cluster state, while for large aspect ratios a single swarm and jammed cluster occurs. The power spectrum of the turbulent state shows two distinct energy cascades at small and large wave numbers with power-law scaling and non-universal exponents. Pullers show a strong tendency to form swarms instead of the disordered state found for neutral and pusher rods. At large area fractions a dynamic cluster is observed and at larger aspect ratio a single swarm or jammed cluster occurs.

Conservation of orbital angular momentum and polarization through biological waveguides

A major roadblock to the development of photonic sensors is the scattering associated with many biological systems. We show the conservation of photonic states through optically self-arranged biological waveguides, for the first time, which can be implemented to transmit light through scattering media. The conservation of optical properties of light through biological waveguides allows for the transmission of high bandwidth information with low loss through scattering media. Here, we experimentally demonstrate the conservation of polarization state and orbital angular momentum of light through a self-arranged biological waveguide, several centimeters long, in a sheep red blood cell suspension. We utilize nonlinear optical effects to self-trap cells, which form waveguides at 532 nm and 780 nm wavelengths. Moreover, we use the formed waveguide channels to couple and guide probe beams without altering the information. The formed biological waveguides are in a sub-diffusive scattering regime, so the photons’ information degrades insignificantly over several centimeters of propagation through the scattering media. Our results show the potential of biological waveguides as a methodology for the development of novel photonic biosensors, biomedical devices that require optical wireless communication, and the development of new approaches to noninvasive biomedical imaging.

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.