Physics of microswimmers--single particle motion and collective behavior: a review

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.

Propelling ferrimagnetic domain walls by dynamical frustration

Many-particle systems driven out of thermal equilibrium can show properties qualitatively different from any thermal state. Here, we study a ferrimagnet in a weak oscillating magnetic field. In this model, domain walls are not static, but are shown to move actively in a direction chosen by spontaneous symmetry breaking. Thus they act like self-propelling units. Their collective behaviour is reminiscent of other systems with actively moving units studied in the field of 'active matter', where, e.g., flocks of birds are investigated. The active motion of the domain walls emerges from 'dynamical frustration'. The antiferromagnetic xy-order rotates clockwise or anticlockwise, determined by the sign of the ferromagnetic component. This necessarily leads to frustration at a domain wall, which gets resolved by propelling the domain wall with a velocity proportional to the square root of the driving power across large parameter regimes. This motion and strong hydrodynamic interactions lead to a linear growth of the magnetic correlation length over time, much faster than in equilibrium. The dynamical frustration furthermore makes the system highly resilient to noise. The correlation length of the weakly driven one-dimensional system can be orders of magnitude larger than in the corresponding equilibrium system with the same noise level.

Gating and tunable confinement of active colloids within patterned environments

Active colloidal particles typically exhibit a pronounced affinity for accumulating and being captured at boundaries. Here, we engineer long-range repulsive interactions between colloids that self-propel under an electric field and patterned obstacles. As a result of these interactions, particles turn away from obstacles and avoid accumulation. We show that by tuning the applied field frequency, we precisely and rapidly control the effective size of the obstacles and therefore modulate the particle approach distance. This feature allows us to achieve gating and tunable confinement of our active particles whereby they can access regions between obstacles depending on the applied field. Our work provides a versatile means to directly control confinement and organization, paving the way towards applications such as sorting particles based on motility or localizing active particles on demand.

Conformational properties of active polar semiflexible phantom polymers

The conformational properties of semiflexible active polar linear and ring phantom polymers are analyzed analytically to shed light on their dependence on activity. Special attention is paid to the influence of the implemented bond force for discrete and continuous polymer models. In detail, the Gaussian semiflexible polymer model and a model with a harmonic bond potential with finite bond length are considered. The studies reveal the immanent effects of the particular bond model on the polymer conformations as well as on the discrete or continuous representation. For continuum models, activity implies polymer end effects only, whereas for discrete models, all bonds can contribute to activity-dependent conformational changes. Ring polymers lack end effects; hence, continuous rings exhibit the same conformations as passive polymers. Similarly, the conformations of inextensible continuous polymers (Kratky-Porod worm-like chain) are activity-independent. These findings are in contrast to passive polymers, where a wide spectrum of bond potentials capture their generic features. Hence, this universality is broken by activity, and a model must be carefully selected to capture the characteristics observed in experiments.

Hydrodynamically Enhanced Brownian Motion in Flowing Polymer Solutions

Diffusion of a molecule in solution typically occurs via thermally driven Brownian motion, with solvent collisions leading to a random-walk trajectory for the solute. This physical principle guides our understanding of molecular transport in a wide variety of situations, ranging from protein diffusion in biological systems and mixing in solution processes to charge transport in polyelectrolyte solutions. Thermal diffusion represents a "speed limit" for molecular transport, which can typically only be surpassed by imposing a directional, external field. The other way particles expedite diffusion is via self-propulsion. This "active Brownian motion" is famously seen in some single-cell organisms and can also be shown in some colloidal systems, but because it requires self-propulsion, this is not seen at the molecular level. We show that it is possible to dramatically increase the diffusion of small molecules in a way that mimics active Brownian motion, instead driven by the disturbance flows of highly stretched polymers in strong flows to induce propulsion at a distance. We use molecular simulations that account for these hydrodynamic disturbances to demonstrate that it is possible to increase the effective diffusion constant by more than an order of magnitude, and we provide a mechanistic model for how the interplay of polymer concentration, flow-induced polymer stretching, and chain length gives rise to hydrodynamically enhanced Brownian motion. This effect has important implications for molecular transport, and we show that strong flows and a low concentration of stretched polymers can be used to promote rapid diffusion.

Emergent short-range repulsion for attractively coupled active particles

We show that heterogeneity in self-propulsion speed can lead to the emergence of a robust effective short-range repulsion among active particles interacting via long-range attractive potentials. Using the example of harmonically coupled active Brownian particles, we analytically derive the stationary distribution of the pairwise distances and reveal that the heterogeneity in propulsion speeds induces a characteristic scale of repulsion between particles. This length scale algebraically increases with the difference in their self-propulsion speeds. In contrast to the conventional view that activity in active matter systems typically leads to effective attraction, our results demonstrate that activity can give rise to an emergent repulsive interaction. This phenomenon is universal, independent of the specific dynamics of the particles or the presence of thermal fluctuations. We also discuss possible experimental realization of this counter-intuitive phenomenon.

Smart navigation through a rotating barrier: Deep reinforcement learning with application to size-based separation of active microagents

We employ deep reinforcement learning methods to investigate shortest-time navigation strategies for smart active Brownian particles (microagents), which self-propel through a rotating potential barrier in a static, viscous, fluid background. The microagent's motion begins at a specified origin and terminates at a designated destination. The potential barrier is modeled as a localized, repulsive Gaussian potential with finite support, whose peak location rotates at a given angular velocity about a fixed center within the plane of motion. We use the advantage actor-critic approach to train microagents for their origin-to-destination navigation through the barrier. By employing this approach, we demonstrate that the rotating potential (as opposed to a static one) enables size-based sorting and separation of the microagents. In other words, microagents of different radii arrive at the destination at sufficiently well-separated average times, facilitating their sorting. The efficiency of particle sorting is quantified by introducing specific separation measures. We also demonstrate how training the microagents in a noisy background, as opposed to a noise-free one, can improve the precision of their size-based sorting. Our findings suggest promising avenues for future research on smart active particles equipped with deep reinforcement learning to navigate complex environments, particularly in microscale applications.

Effects of curvature on growing films of microorganisms

To provide insight into the basic properties of emerging structures when bacteria or other microorganisms conquer surfaces, it is crucial to analyze their growth behavior during the formation of thin films. In this regard, many theoretical studies focus on the behavior of elongating straight objects. They repel each other through volume exclusion and divide into two halves when reaching a certain threshold length. However, in reality, hardly any object of a certain elongation is perfectly straight. Therefore, we here study the consequences of the curvature of individuals on the growth of colonies and thin active films. This individual curvature, so far hardly considered, turns out to qualitatively affect the overall growth behavior of the colony. Particularly, strings of stacked curved cells emerge that show branched structures, whereas the size of orientationally ordered domains in the colony is significantly decreased. Furthermore, we identify emergent spatio-orientational coupling that is not observed in colonies of straight cells. Our results are important for a fundamental understanding of the interaction and spreading of microorganisms on surfaces, with implications for medical applications and bioengineering.

Spontaneous generation of angular momentum in chiral active crystals

We study a two-dimensional chiral active crystal composed of underdamped chiral active particles. These particles, characterized by intrinsic handedness and persistence, interact via linear forces derived from harmonic potentials. Chirality plays a pivotal role in shaping the system's behavior: it reduces displacement and velocity fluctuations while inducing cross-spatial correlations among different Cartesian components of velocity. These features distinguish chiral crystals from their non-chiral counterparts, leading to the emergence of net angular momentum, as predicted analytically. This angular momentum, driven by the torque generated by the chiral active force, exhibits a non-monotonic dependence on the degree of chirality. Additionally, it contributes to the entropy production rate, as revealed through a path-integral analysis. We investigate the dynamic properties of the crystal in both Fourier and real space. Chirality induces a non-dispersive peak in the displacement spectrum, which underlies the generation of angular momentum and oscillations in time-dependent autocorrelation functions or mean-square displacement, all of which are analytically predicted.

Viscotaxis of beating flagella

Many biological microorganisms and artificial microswimmers react to external cues of environmental gradients by changing their swimming directions. We study here the behavior of eukaryotic flagellated microswimmers in linear viscosity gradients. Motivated by the near-surface motion of many microswimmers, we consider flagellar swimming in two spatial dimensions. We employ a model of flagellum consisting of a semi-flexible filament with a travelling wave of spontaneous curvature to study generic aspects of viscotaxis of actively beating flagella. The propulsion of the flagellum in a fluid due to a hydrodynamic friction anisotropy is described by resistive-force theory. Using numerical simulations and analytical theory, we show that beating flagella exhibit positive viscotaxis, reorienting themselves toward higher viscosity areas. We quantify this behavior by characterization of the dependence of the rotational velocity on gradient strength, beat amplitude, swimming speed, and wave length. We also examine the effects of asymmetric flagellar wave forms, which imply circular trajectories in the absence of viscosity gradients; here, large asymmetry leads to trochoid-like trajectories perpendicular to the gradient in the form of drifting circles. Flagellar deformability strongly reduce the beat amplitude and the viscotatic response. The viscotatic response is shown to be captured by a universal function of the sperm number.

Transport of partially active polymers in chemical gradients

The transport of molecules for chemical reactions is critically important in various cellular biological processes. Despite thermal diffusion being prevalent in many biochemical processes, it is unreliable for any sort of directed transport or preferential accumulation of molecules. In this paper, we propose a strategy for directed motion in which the molecules are transported by partially active polymeric structures. These polymers are assumed to be Rouse chains, in which the monomers are connected via harmonic springs and these chains are studied in environments that have activity varying spatially. The transport of such polymers is facilitated by these chemical/activity gradients which generate an effective drift. By marginalizing out the active degrees of freedom of the system, we obtain an effective Fokker-Planck equation for the Rouse modes of the polymer. In particular, we solve for the steady state distribution of the center of mass and its mean first passage time to reach an intended destination. We focus on how the arrangement of active units within the polymer affects its steady-state and dynamic behavior and how they can be optimized to achieve high accumulation or rapid motility.

Metareview: a survey of active matter reviews

In the past years, the amount of research on active matter has grown extremely rapidly, a fact that is reflected in particular by the existence of more than 1000 reviews on this topic. Moreover, the field has become very diverse, ranging from theoretical studies of the statistical mechanics of active particles to applied work on medical applications of microrobots and from biological systems to artificial swimmers. This makes it very difficult to get an overview over the field as a whole. Here, we provide such an overview in the form of a metareview article that surveys the existing review articles and books on active matter. Thereby, this article provides a useful starting point for finding literature about a specific topic.

Bacterial Swimming and Accumulation on Endothelial Cell Surfaces

Flagellar-driven locomotion plays a critical role in the bacterial attachment and colonization of surfaces, contributing to the risks of contamination and infection. Extensive efforts to uncover the underlying principles governing bacterial motility near surfaces have relied on idealized assumptions about surrounding artificial surfaces. However, in the context of living systems, the role of cells from tissues and organs becomes increasingly critical, particularly in bacterial swimming and adhesion, yet it remains poorly understood. Here, we propose using biological surfaces composed of vascular endothelial cells to experimentally investigate bacterial motion and interaction behaviors. Our results reveal that bacterial trapping observed on inorganic surfaces is counteractively manifested with reduced radii of circular motion on cellular surfaces. Additionally, two distinct modes of bacterial adhesion were identified: tight and loose adhesion. Interestingly, the presence of living cells enhances bacterial surface enrichment, and imposed flow intensifies this accumulation via a bias-swimming effect. These results surprisingly indicate that physical effects remain the dominant factor regulating bacterial motility and accumulation at the single-cell-layer level in vitro, bridging the gap between simplified hydrodynamic mechanisms and complex biological surfaces with relevance to biofilm formation and bacterial contamination.

The 2025 motile active matter roadmap

Activity and autonomous motion are fundamental aspects of many living and engineering systems. Here, the scale of biological agents covers a wide range, from nanomotors, cytoskeleton, and cells, to insects, fish, birds, and people. Inspired by biological active systems, various types of autonomous synthetic nano- and micromachines have been designed, which provide the basis for multifunctional, highly responsive, intelligent active materials. A major challenge for understanding and designing active matter is their inherent non-equilibrium nature due to persistent energy consumption, which invalidates equilibrium concepts such as free energy, detailed balance, and time-reversal symmetry. Furthermore, interactions in ensembles of active agents are often non-additive and non-reciprocal. An important aspect of biological agents is their ability to sense the environment, process this information, and adjust their motion accordingly. It is an important goal for the engineering of micro-robotic systems to achieve similar functionality. Many fundamental properties of motile active matter are by now reasonably well understood and under control. Thus, the ground is now prepared for the study of physical aspects and mechanisms of motion in complex environments, the behavior of systems with new physical features like chirality, the development of novel micromachines and microbots, the emergent collective behavior and swarming of intelligent self-propelled particles, and particular features of microbial systems. The vast complexity of phenomena and mechanisms involved in the self-organization and dynamics of motile active matter poses major challenges, which can only be addressed by a truly interdisciplinary effort involving scientists from biology, chemistry, ecology, engineering, mathematics, and physics. The 2025 motile active matter roadmap of Journal of Physics: Condensed Matter reviews the current state of the art of the field and provides guidance for further progress in this fascinating research area.

Collective dynamics of intelligent active Brownian particles with visual perception and velocity alignment in 3D: spheres, rods, and worms

Many living systems, such as birds and fish, exhibit collective behaviors like flocking and swarming. Recently, an experimental system of active colloidal particles has been developed, where the motility of each particle is adjusted based on its visual detection of surrounding particles. These particles with visual-perception-dependent motility exhibit group formation and cohesion. Inspired by these behaviors, we investigate intelligent active Brownian particles (iABPs) equipped with visual perception and velocity alignment in three dimensions using computer simulations. The visual-perception-based self-steering describes the tendency of iABPs to move toward the center of mass of particles within their visual cones, while velocity alignment encourages alignment with neighboring particles. We examine how the behavior varies with the visual cone angle θ, self-propulsion speed (Péclet number Pe), and the interaction strengths of velocity alignment (Ωa) and visual-based self-steering (Ωv). Our findings show that spherical iABPs form dense clusters, worm-like clusters, milling behaviors, and dilute-gas phases, consistent with 2D studies. By reducing the simulation box size, we observe additional structures like band-like clusters and dense baitball formations. Additionally, rod-like iABPs form band-like, worm-like, radiating, and helical structures, while iABP worms exhibit band-like, streamlined, micellar-like and entangled structures. Many of these patterns resemble collective behaviors in nature, such as ant milling, fish baitballs, and worm clusters. Advances in synthetic techniques could enable nanorobots with similar capabilities, offering insights into multicellular systems through active matter.

Collective sperm movement in mammalian reproductive tracts

Mammalian sperm cells travel from their origin in the male reproductive tract to fertilization in the female tract through a complex process driven by coordinated mechanical and biochemical mechanisms. Recent experimental and theoretical advances have illuminated the collective behaviors of sperm both in vivo and in vitro. However, our understanding of the underlying mechano-chemical processes remains incomplete. This review integrates current insights into sperm group movement, examining both immotile and motile states, which are essential for passive transport and active swimming through the reproductive tracts. We provide an overview of the current understanding of collective sperm movement, focusing on the experimental and theoretical mechanisms behind these behaviors. We also explore how sperm motility is regulated through the coordination of mechanical and chemical processes. Emerging evidence highlights the mechanosensitive properties of a sperm flagellum, suggesting that mechanical stimuli regulate flagellar beating at both individual and collective levels. This self-regulatory, mechano-chemical system reflects a broader principle observed in multicellular systems, offering a system-level insight into the regulation of motility and collective dynamics in biological systems.

Dynamically induced spatial segregation in multispecies bacterial bioconvection

Active matter, from motile bacteria to animals, can exhibit striking collective and coherent behavior. Despite significant advances in understanding the behavior of homogeneous systems, little is known about the self-organization and dynamics of heterogeneous active matter, such as complex and diverse bacterial communities. Under oxygen gradients, many bacterial species swim towards air-liquid interfaces in auto-organized, directional bioconvective flows, whose spatial scales exceed the cell size by orders of magnitude. Here we show that multispecies bacterial suspensions undergoing oxytactic-driven bioconvection exhibit dynamically driven spatial segregation, despite the enhanced mixing of bioconvective flows, and the fact that these species coexist in their natural habitat. Segregation is observed as patterns of spatially interlocked domains, with local dominance of one of the constituent species in the suspension. Our findings suggest that segregation mechanisms are driven by species-specific motile behaviors under conditions of hydrodynamic flow, rather than biochemical repulsion. Thus, species with different motile characteristics in the same ecological context can enhance their access to limiting resources. This work provides novel insights on the role of heterogeneity in active matter, as well as on the dynamics of complex microbial communities, their spatial organization and their collective behavior.

Self-Generated Ions Modify the Pair Interaction and the Phase Separation of Chemically Active Colloids

Chemically active colloids that release/consume ions are an important class of active matter, and exhibit interesting collective behaviors such as phase separation, swarming, and waves. Key to these behaviors is the pair-wise interactions mediated by the concentration gradient of self-generated ions. This interaction is often simplified as a pair-wise force decaying at 1/r2, where r is the interparticle distance. Here, we show that this simplification fails for isotropic and immotile active colloids with net ion production, such as Ag colloids in H2O2. Specifically, the production of ions on the surface of the Ag colloids increases the local ion concentration, c, and attenuates the pair-wise interaction force that scales with ∇c/c. As a result, the attractive force between an Ag colloid and its neighbor (active or passive) decays at 1/r or 1/r2 for small or large r, respectively. In a population, the attraction of a colloid by a growing cluster also scales with ∇c/c, so that medium-sized clusters grow fastest, and that the cluster coarsening slows with time. These results, supported by finite element and Brownian dynamic simulations, highlight the important role of self-generated ions in shaping the collective behavior of chemically active colloids.

A hitchhiker's guide to active motion

Intelligent decisions in response to external informative input can allow organisms to achieve their biological goals while spending very little of their own resources. In this paper, we develop and study a minimal model for a navigational task, performed by an otherwise completely motorless particle that possesses the ability of hitchhiking in a bath of active Brownian particles (ABPs). Hitchhiking refers to identifying and attaching to suitable surrounding bath particles. Using a reinforcement learning algorithm, such an agent, which we refer to as intelligent hitchhiking particle (IHP), is enabled to persistently navigate in the desired direction. This relatively simple IHP can also anticipate and react to characteristic motion patterns of their hosts, which we exemplify for a bath of chiral ABPs (cABPs). To demonstrate that the persistent motion of the IHP will outperform that of the bath particles in view of long-time ballistic motion, we calculate the mean-squared displacement and discuss its dependence on the density and persistence time of the bath ABPs by means of an analytic model.

Phase behavior and dynamics of active Brownian particles in an alignment field

Self-propelled particles that are subject to noise are a well-established generic model system for active matter. A homogeneous alignment field can be used to orient the direction of the self-propulsion velocity and to model systems like phoretic Janus particles with a magnetic dipole moment or magnetotactic bacteria in an external magnetic field. Computer simulations are used to predict the phase behavior and dynamics of self-propelled Brownian particles in a homogeneous alignment field in two dimensions. Phase boundaries of the gas-liquid coexistence region are calculated for various Péclet numbers, particle densities, and alignment field strengths. Critical points and exponents are calculated and, in agreement with previous simulations, do not seem to belong to the universality class of the 2D Ising model. Finally, the dynamics of spinodal decomposition for quenching the system from the one-phase to the two-phase coexistence region by increasing the Péclet number is characterized. Our results may help to identify parameters for optimal transport of active matter in complex environments.

Dynamics and Collective Behavior of Chemically Propelled Janus Sphere Dimers in Complex Solvents

The propulsion mechanisms and collective dynamics of chemically powered Janus sphere dimers at the micro- and nanoscales, confined in a quasi-two-dimensional geometry, are investigated using a coarse-grained microscopic dynamical model. These active Janus dimers consist of two identical Janus spheres, featuring a catalytic cap on one hemisphere. The chemical reaction taking place on the catalytic surface generates asymmetric concentration gradients of product molecules around the Janus sphere, leading to the self-propulsion of the dimers. Depending on the dimer configuration, they exhibit various motion behaviors such as forward propulsion, rotation, and restricted stochastic motion. Due to chemotactic effects and self-diffusiophoretic forces, ensembles of dimers spontaneously form diverse structures, such as transient clusters, stable rotational ensembles, and antiparallel aligned doublets. This study demonstrates that the configurations of Janus sphere dimers significantly influence their self-propulsion and collective behaviors, providing crucial insights for the design and control of active micro- and nanoscale systems.

Kinetic Theory of Self-Propelled Particles with Nematic Alignment

We present the results from kinetic theory for a system of self-propelled particles with alignment interactions of higher-order symmetry, particularly nematic ones. To this end, we use the Landau equation approach, a systematic approximation to the BBGKY hierarchy for small effective couplings. Our calculations are presented in a pedagogical way with the explicit goal of serving as a tutorial from a physicists' perspective into applying kinetic theory ideas beyond mean-field to active matter systems with essentially no prerequisites and yield predictions without free parameters that are in quantitative agreement with direct agent-based simulations.

Topological transition in filamentous cyanobacteria: from motion to structure

Many active systems are capable of forming intriguing patterns at scales significantly larger than the size of their individual constituents. Cyanobacteria are one of the most ancient and important phyla of organisms that has allowed the evolution of more complex life forms. Despite its importance, the role of motility on the pattern formation of their colonies is not understood. Here, we investigate the large-scale collective effects and rich dynamics of gliding filamentous cyanobacteria colonies, while still retaining information about the individual constituents' dynamics and their interactions. We investigate both the colony's transient and steady-state dynamics and find good agreement with experiments. We furthermore show that the Péclet number and aligning interaction strength govern the system's topological transition from an isotropic distribution to a state of large-scale reticulate patterns. Although the system is topologically non-trivial, the parallel and perpendicular pair correlation functions provide structural information about the colony, and thus can be used to extract information about the early stages of biofilm formation. Finally, we find that the effects of the filaments' length cannot be reduced to a system of interacting points. Our model proves to reproduce both cyanobacteria colonies and systems of biofilaments where curvature is transported by motility.

Modeling straight and circle swimmers: from single swimmer to collective motion

We propose a simple numerical model for the motion of microswimmers based on the immersed boundary method. The swimmer, either pusher or puller, is represented by a distribution of point forces corresponding to the body and the flagellum. We study in particular the minimal model consisting of only three beads (two for the body and one for the flagellum) connected by rigid, inextensible links. When the beads are collinear, standard straight swimming is realized and, in the absence of propulsion, we demonstrate that the model recovers Jeffery's equation for a thin rod. Conversely, by imposing an angle between body and flagellum the swimmer moves on circular orbits. We discuss how two swimmers, in collinear or non-collinear geometry, scatter upon encounter. Finally, we explore the dynamics of a large number of swimmers reacting to one another only via hydrodynamic interactions, and exemplify their complex collective dynamics in both straight and circular swimmers.

Dynamics of switching processes: general results and applications in intermittent active motion

Systems switching between different dynamical phases is a ubiquitous phenomenon. The general understanding of such a process is limited. To this end, we present a general expression that captures fluctuations of a system exhibiting a switching mechanism. Specifically, we obtain an exact expression of the Laplace-transformed characteristic function of the particle's position. Then, the characteristic function is used to compute the effective diffusion coefficient of a system performing intermittent dynamics. Furthermore, we employ two examples: (1) generalized run-and-tumble active particle, and (2) an active particle switching its dynamics between generalized active run-and-tumble motion and passive Brownian motion. In each case, explicit computations of the spatial cumulants are presented. Our findings reveal that the particle's position probability density function exhibit rich behaviours due to intermittent activity. Numerical simulations confirm our findings.

A computer simulation study of a chiral active ring polymer

We investigate a ring polymer under the influence of chiral active Brownian forces in two dimensions using coarse-grained computer simulations. We observe a non-monotonic behavior of the radius of gyration of an active Brownian ring as a function of active force. However, the shrinkage of the ring in the intermediate strength of active forces becomes more pronounced in the presence of chiral active forces, and the shrinkage is monotonic at a given activity level as a function of the angular frequency controlling the direction of the active force. The distribution of radius of gyration, inter-monomer distance, and radial distribution suggest that the monomers come close to each other, eventually leading to the shrinkage of the ring. Moreover, the bond-correlation suggests that the chirality introduces a local folding of the monomers. Furthermore, using the diameter correlation function, we show that the ring performs tank-treading motion with a frequency following power-law relation with active force with exponent 3/2. The mean squared displacement of the monomers further assists the tank-treading dynamics by exhibiting oscillatory behavior.

Making Mobile Nanotechnology Accessible: Is the Explicit Preparation of Janus Nanoparticle Necessary to Achieve Mobility?

This study compares the mobility behaviour, in a H2O2 environment, of three different geometries of hybrid particle made of silica core functionalized by gold (nanoparticles or layer). It is known that the decomposition of H2O2 on gold surfaces drives mobility; however, the link between mobility orientation and the organization of gold on silica surfaces is still questionable. While conventional wisdom posits that asymmetric designs are crucial for generating phoretic forces or localized bubble propulsion, recent research suggests that symmetrical particles may also exhibit motility. To address this debate, we developed a robust workflow for synthesizing gold grafted silica nanoparticles with precise control over size and shape, enabling the direct comparison of their motile behaviour by dynamic light scattering and particle tracking velocimetry. Our results indicate, first, that a combination of techniques is necessary to overcome their intrinsic limitation and, second, that the inherent asymmetry generated by isotropic gold nanoparticle deposition onto silica surfaces may enable particle motility.

Inertial Active Matter with Coulomb Friction

Friction is central to the motion of active (self-propelled) objects such as bacteria, animals, and robots. While in a viscous fluid friction is described by Stokes's law, objects in contact with other solid bodies are often governed by more complex empirical friction laws. Here, we study active particles subject to Coulomb friction using a combination of active granular experiments and simulations, supported by theoretical predictions. The interplay of friction and activity forces induces a rich behavior resulting in three distinct dynamical regimes. While for low activity Brownian motion is recovered, for large activity we observe a dynamical stop and go regime that continuously switches from diffusion and accelerated motion. For greater activity, we observe a supermobile dynamical regime characterized by a fully accelerated motion which is described by an anomalous scaling of the diffusion coefficient with the activity. These findings cannot be observed with Stokes viscous forces typical of active swimmers but are central in dry active objects.

Transition-path sampling for run-and-tumble particles

We elaborate and validate a generalization of the renowned transition-path-sampling algorithm for a paradigmatic model of active particles, namely, the run-and-tumble particles. Notwithstanding the nonequilibrium character of these particles, we show how the consequent lack of the microscopical reversibility property, which is usually required by transition-path sampling, can be circumvented by identifying reasonable backward dynamics with a well-defined path-probability density. Our method is then applied to characterize the structure and kinetics of rare transition pathways undergone by run-and-tumble particles having to cross a potential barrier in order to find a target.

Intermediate scattering function of a gravitactic circle swimmer

We analyze gravitaxis of a Brownian circle swimmer by deriving and analytically characterizing the experimentally measurable intermediate scattering function (ISF). To solve the associated Fokker-Planck equation, we use a spectral-theory approach, finding formal expressions in terms of eigenfunctions and eigenvalues of the overdamped-noisy-driven pendulum problem. We further perform a Taylor series of the ISF in the wavevector to extract the cumulants up to the fourth order. We focus on the skewness and kurtosis analyzed for four observation directions in the 2D plane. Validating our findings involves conducting Langevin-dynamics simulations and interpreting the results using a harmonic approximation. The skewness and kurtosis are amplified as the orienting torque approaches the intrinsic angular drift of the circle swimmer from above, highlighting deviations from Gaussian behavior. Transforming the ISF to the comoving frame, a measurable quantity, reveals gravitactic effects and diverse behaviors spanning from diffusive motion at low wavenumbers to circular motion at intermediate wavenumbers and directed motion at higher wavenumbers.

Learning protocols for the fast and efficient control of active matter

Exact analytic calculation shows that optimal control protocols for passive molecular systems often involve rapid variations and discontinuities. However, similar analytic baselines are not generally available for active-matter systems, because it is more difficult to treat active systems exactly. Here we use machine learning to derive efficient control protocols for active-matter systems, and find that they are characterized by sharp features similar to those seen in passive systems. We show that it is possible to learn protocols that effect fast and efficient state-to-state transformations in simulation models of active particles by encoding the protocol in the form of a neural network. We use evolutionary methods to identify protocols that take active particles from one steady state to another, as quickly as possible or with as little energy expended as possible. Our results show that protocols identified by a flexible neural-network ansatz, which allows the optimization of multiple control parameters and the emergence of sharp features, are more efficient than protocols derived recently by constrained analytical methods. Our learning scheme is straightforward to use in experiment, suggesting a way of designing protocols for the efficient manipulation of active matter in the laboratory.

Synergistic phenotypic adaptations of motile purple sulphur bacteria Chromatium okenii during lake-to-laboratory domestication

Isolating microorganisms from natural environments for cultivation under optimized laboratory settings has markedly improved our understanding of microbial ecology. Artificial growth conditions often diverge from those in natural ecosystems, forcing wild isolates into distinct selective pressures, resulting in diverse eco-physiological adaptations mediated by modification of key phenotypic traits. For motile microorganisms we still lack a biophysical understanding of the relevant traits emerging during domestication and their mechanistic interplay driving short-to-long-term microbial adaptation under laboratory conditions. Using microfluidics, atomic force microscopy, quantitative imaging, and mathematical modeling, we study phenotypic adaptation of Chromatium okenii, a motile phototrophic purple sulfur bacterium from meromictic Lake Cadagno, grown under laboratory conditions over multiple generations. Our results indicate that naturally planktonic C. okenii leverage shifts in cell-surface adhesive interactions, synergistically with changes in cell morphology, mass density, and distribution of intracellular sulfur globules, to suppress their swimming traits, ultimately switching to a sessile lifeform. A computational model of cell mechanics confirms the role of such phenotypic shifts in suppressing the planktonic lifeform. By investigating key phenotypic traits across different physiological stages of lab-grown C. okenii, we uncover a progressive loss of motility during the early stages of domestication, followed by concomitant deflagellation and enhanced surface attachment, ultimately driving the transition of motile sulfur bacteria to a sessile state. Our results establish a mechanistic link between suppression of motility and surface attachment via phenotypic changes, underscoring the emergence of adaptive fitness under laboratory conditions at the expense of traits tailored for natural environments.

Efficient Transport Controlled by Biharmonic Frictional Driving

Dry friction has been proposed as a rectifying mechanism allowing mass transport over a vibrating surface, even when vibrations are horizontal and unbiased. It has been suggested that the drift velocity will always saturate when the energy of the input oscillation increases, leading to a vanishing efficiency that would hinder the applicability of this phenomenon. Contrary to this conjecture, in this Letter we experimentally demonstrate that, by carefully controlling the forcing oscillations, this system can maintain a finite transport efficiency for any input energy. A minimal friction model explains the observed dependencies of the drift velocity on the signal parameters in the case of biharmonic base oscillations, which can be extended to obtain efficiency estimates for any periodic excitation.

Microfluidic sperm trap array for single-cell flagellar analysis with unrestricted 2D flagellar movement

Sperm capture techniques that immobilize sperm to halt their motility are essential for the long-term analysis of individual sperm. These techniques are beneficial in assisted reproductive technologies such as intracytoplasmic sperm injection (ICSI) by allowing selective screening of sperm. However, there is a notable lack of high-throughput and non-destructive sperm capture methods that allow the flagellum to beat freely, which is crucial for accurately reflecting the behavior of unfettered, freely swimming sperm. To bridge this gap, we introduce a novel microfluidic device specifically engineered to capture sperm without restricting flagellar motion. The design utilizes sperm's innate boundary-following behavior in both 3D and 2D environments to direct them into a capture zone. Once captured, the sperm head is restrained while the flagellum remains free to exhibit natural beating patterns. Utilizing this device, we explore the effects of hyperactivating agents, temperature, and their combined influence on the dynamics of bovine sperm flagella. The unrestricted flagellar motion offered by our device yields two prominent advantages: it mirrors the flagellar behavior of free-swimming sperm, ensuring research findings are consistent with natural sperm activity, and it prevents imaging overlap between the flagellum and the capture structures, simplifying the automation of flagellar tracking and analysis. This technological advancement facilitates the collection of waveform parameters along the entire flagellum, addressing inconsistencies that have arisen in previous research due to differing measurement sites, and enabling precise extraction of sperm behavioral properties.

Structural dynamics and optimal transport of an active polymer

We study the spontaneous configuration transitions of an active semi-flexible polymer between spiral and non-spiral states, and show that the configuration dynamics is fully described by a subcritical pitchfork bifurcation. Exploiting the fact that an active polymer barely moves in spiral states and exhibits net displacements in non-spiral states, we theoretically prove that the motion of the active polymer is consistent with a run-and-tumble-like dynamics. Moreover, we find that there exists an optimal self-propelling force that maximizes the diffusion coefficient.

Anomalous diffusion of active Brownian particles in responsive elastic gels: Nonergodicity, non-Gaussianity, and distributions of trapping times

Understanding actual transport mechanisms of self-propelled particles (SPPs) in complex elastic gels-such as in the cell cytoplasm, in in vitro networks of chromatin or of F-actin fibers, or in mucus gels-has far-reaching consequences. Implications beyond biology/biophysics are in engineering and medicine, with a particular focus on microrheology and on targeted drug delivery. Here, we examine via extensive computer simulations the dynamics of SPPs in deformable gellike structures responsive to thermal fluctuations. We treat tracer particles comparable to and larger than the mesh size of the gel. We observe distinct trapping events of active tracers at relatively short times, leading to subdiffusion; it is followed by an escape from meshwork-induced traps due to the flexibility of the network, resulting in superdiffusion. We thus find crossovers between different transport regimes. We also find pronounced nonergodicity in the dynamics of SPPs and non-Gaussianity at intermediate times. The distributions of trapping times of the tracers escaping from "cages" in our quasiperiodic gel often reveal the existence of two distinct timescales in the dynamics. At high activity of the tracers these timescales become comparable. Furthermore, we find that the mean waiting time exhibits a power-law dependence on the activity of SPPs (in terms of their Péclet number). Our results additionally showcase both exponential and nonexponential trapping events at high activities. Extensions of this setup are possible, with the factors such as anisotropy of the particles, different topologies of the gel network, and various interactions between the particles (also of a nonlocal nature) to be considered.

Hybrid motility mechanism of sperm at viscoelastic fluid-solid interface

To fertilize eggs, sperm must pass through narrow, complex channels filled with viscoelastic fluids in the female reproductive tract. While it is known that the topography of the surfaces plays a role in guiding sperm movement, sperm have been thought of as swimmers, i.e., their motility comes solely from sperm interaction with the surrounding fluid, and therefore, the surfaces have no direct role in the motility mechanism itself. Here, we examined the role of solid surfaces in the movement of sperm in a highly viscoelastic medium. By visualizing the flagellum interaction with surfaces in a microfluidic device, we found that the flagellum stays close to the surface while the kinetic friction between the flagellum and the surface is in the direction of sperm movement, providing thrust. Additionally, the flow field generated by sperm suggests slippage between the viscoelastic fluid and the solid surface, deviating from the no-slip boundary typically used in standard fluid dynamics models. These observations point to hybrid motility mechanisms in sperm involving direct flagellum-surface interaction in addition to flagellum pushing the fluid. This finding signifies an evolutionary strategy of mammalian sperm crucial for their efficient migration through narrow, mucus-filled passages of the female reproductive tract.

Active string fluids and gels formed by dipolar active Brownian particles in 3D

Self-propelled particles possessing permanent magnetic dipole moments occur naturally in magnetotactic bacteria and can be built into man-made systems such as active colloids or micro-robots. Yet, the interplay between self-propulsion and anisotropic dipole-dipole interactions on dynamic self-assembly in three dimensions (3D) remains poorly understood. We conduct Brownian dynamics simulations of active dipolar particles in 3D, focusing on the low-density regime, where dipolar hard spheres tend to form chain-like aggregates and percolated networks with increasing dipolar coupling strength. We find that strong active forces override dipolar attractions, effectively inhibiting chain-like aggregation and network formation. Conversely, activating particles with low to moderate forces results in a fluid composed of active chains and rings. At strong dipolar coupling strengths, this active fluid transitions into an active gel, consisting of a percolated network of active chains. Although the overall structure of the active gel remains interconnected, the network experiences more frequent configurational rearrangements due to the reduced bond lifetime of active dipolar particles. Consequently, particles exhibit enhanced translational and rotational diffusion within the active fluid of strings and active gels compared to their passive counterparts. We quantify the influence of activity on aggregate topology as they transition from branched structures to unconnected chains and rings. Our findings are summarized in a state diagram, delineating the impact of dipolar coupling strength and active force magnitude on the system.

Multicellularity and increasing Reynolds number impact on the evolutionary shift in flash-induced ciliary response in Volvocales

BACKGROUND

Volvocales in green algae have evolved by multicellularity of Chlamydomonas-like unicellular ancestor. Those with various cell numbers exist, such as unicellular Chlamydomonas, four-celled Tetrabaena, and Volvox species with different cell numbers (~1,000, ~5,000, and ~10,000). Each cell of these organisms shares two cilia and an eyespot, which are used for swimming and photosensing. They are all freshwater microalgae but inhabit different fluid environments: unicellular species live in low Reynolds-number (Re) environments where viscous forces dominate, whereas multicellular species live in relatively higher Re where inertial forces become non-negligible. Despite significant changes in the physical environment, during the evolution of multicellularity, they maintained photobehaviors (i.e., photoshock and phototactic responses), which allows them to survive under changing light conditions.

RESULTS

In this study, we utilized high-speed imaging to observe flash-induced changes in the ciliary beating manner of 27 Volvocales strains. We classified flash-induced ciliary responses in Volvocales into four patterns: "1: temporal waveform conversion", "2: no obvious response", "3: pause in ciliary beating", and "4: temporal changes in ciliary beating directions". We found that which species exhibit which pattern depends on Re, which is associated with the individual size of each species rather than phylogenetic relationships.

CONCLUSIONS

These results suggest that only organisms that acquired different patterns of ciliary responses survived the evolutionary transition to multicellularity with a greater number of cells while maintaining photobehaviors. This study highlights the significance of the Re as a selection pressure in evolution and offers insights for designing propulsion systems in biomimetic micromachines.

Migration and Separation of Polymers in Nonuniform Active Baths

Polymerlike structures are ubiquitous in nature and synthetic materials. Their configurational and migration properties are often affected by crowded environments leading to nonthermal fluctuations. Here, we study an ideal Rouse chain in contact with a nonhomogeneous active bath, characterized by the presence of active self-propelled agents which exert time-correlated forces on the chain. By means of a coarse-graining procedure, we derive an effective evolution for the center of mass of the chain and show its tendency to migrate toward and preferentially localize in regions of high and low bath activity depending on the model parameters. In particular, we demonstrate that an active bath with nonuniform activity can be used to separate efficiently polymeric species with different lengths and/or connectivity.

Active particle motion in Poiseuille flow through rectangular channels

We investigate the dynamics of a pointlike active particle suspended in fluid flow through a straight channel. For this particle-fluid system, we derive a constant of motion for a general unidirectional fluid flow and apply it to an approximation of Poiseuille flow through channels with rectangular cross- sections. We obtain a 4D nonlinear conservative dynamical system with one constant of motion and a dimensionless parameter describing the ratio of maximum flow speed to intrinsic active particle speed. Applied to square channels, we observe a diverse set of active particle trajectories with variations in system parameters and initial conditions which we classify into different types of swinging, trapping, tumbling, and wandering motion. Regular (periodic and quasiperiodic) motion as well as chaotic active particle motion are observed for these trajectories and quantified using largest Lyapunov exponents. We explore the transition to chaotic motion using Poincaré maps and show "sticky" chaotic tumbling trajectories that have long transients near a periodic state. We briefly illustrate how these results extend to rectangular cross-sections with a width-to-height ratio larger than one. Outcomes of this paper may have implications for dynamics of natural and artificial microswimmers in experimental microfluidic channels that typically have rectangular cross sections.

Statistical Mobility of Multicellular Colonies of Flagellated Swimming Cells

We study the stochastic hydrodynamics of colonies of flagellated swimming cells, typified by multicellular choanoflagellates, which can form both rosette and chainlike shapes. The objective is to link cell-scale dynamics to colony-scale dynamics for various colonial morphologies. Via autoregressive stochastic models for the cycle-averaged flagellar force dynamics and statistical models for demographic cell-to-cell variability in flagellar properties and placement, we derive effective transport properties of the colonies, including cell-to-cell variability. We provide the most quantitative detail on disclike geometries to model rosettes, but also present formulas for the dynamics of general planar colony morphologies, which includes planar chain-like configurations.

Power-law intermittency in the gradient-induced self-propulsion of colloidal swimmers

Active colloidal microswimmers serve as archetypical active fluid systems, and as models for biological swimmers. Here, by studying in detail their velocity traces, we find robust power-law intermittency with system-dependent exponential cut off. We model the intermittent motion by an interplay of the field gradient-dependent active force, which depends on a fluid gradient and is reduced when the swimmer moves, and the locally fluctuating hydrodynamic drag, that is set by the wetting properties of the substrate. The model closely describes the velocity distributions of two disparate swimmer systems: AC field activated and catalytic swimmers. The generality is highlighted by the collapse of all data in a single master curve, suggesting the applicability to further systems, both synthetic and biological.

Spontaneous separation of attractive chiral mixtures

The separation of chiral matter has garnered significant attention due to its wide-ranging applications in biological and chemical processes. In prior researches, particle interactions were predominantly repulsive, but the indiscriminate attraction among particles under attractive interactions makes the separation of mixtures more difficult. The question of whether chiral mixed particles, characterized by attractive effects, can undergo spontaneous separation, remains unresolved. We study a binary mixture of chiral (counterclockwise or clockwise) active particles with attractive interactions. It is demonstrated that attractive chiral particles can undergo spontaneous separation without the aid of any specific strategies. The key factor driving the separation is the attractive interactions, enabling the formation of stable clusters of particles with same chirality. There exist optimal parameters (self-propelled velocity, angular velocity, and packing fraction) at which the separation is optimal. Our results may contribute to a deeper understanding of the mechanisms behind chiral matter separation and potentially catalyze further experimental investigations in this field.

Biomimetic Synchronization in Biciliated Robots

Direct mechanical coupling is known to be critical for establishing synchronization among cilia. However, the actual role of the connections is still elusive-partly because controlled experiments in living samples are challenging. Here, we employ an artificial ciliary system to address this issue. Two cilia are formed by chains of self-propelling robots and anchored to a shared base so that they are purely mechanically coupled. The system mimics biological ciliary beating but allows fine control over the beating dynamics. With different schemes of mechanical coupling, artificial cilia exhibit rich motility patterns. Particularly, their synchronous beating display two distinct modes-analogous to those observed in C. reinhardtii, the biciliated model organism for studying synchronization. Close examination suggests that the system evolves towards the most dissipative mode. Using this guideline in both simulations and experiments, we are able to direct the system into a desired state by altering the modes' respective dissipation. Our results have significant implications in understanding the synchronization of cilia.

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.

Scalable high-throughput microfluidic separation of magnetic microparticles

Surface-engineered magnetic microparticles are used in chemical and biomedical engineering due to their ease of synthesis, high surface-to-volume ratio, selective binding, and magnetic separation. To separate them from fluid suspensions, existing methods rely on the magnetic force introduced by the local magnetic field gradient. However, this strategy has poor scalability because the magnetic field gradient decreases rapidly as one moves away from the magnets. Here, we present a scalable high-throughput magnetic separation strategy using a rotating permanent magnet and two-dimensional arrays of micromagnets. Under a dynamic magnetic field, nickel micromagnets allow the surrounding magnetic microparticles to self-assemble into large clusters and effectively propel themselves through the flow. The collective speed of the microparticle swarm reaches about two orders of magnitude higher than the gradient-based separation method over a wide range of operating frequencies and distances from a rotating magnet.

Clustering induces switching between phoretic and osmotic propulsion in active colloidal rafts

Active particles driven by chemical reactions are the subject of intense research to date due to their rich physics, being intrinsically far from equilibrium, and their multiple technological applications. Recent attention in this field is now shifting towards exploring the fascinating dynamics of active and passive mixtures. Here we realize active colloidal rafts, composed of a single catalytic particle encircled by several shells of passive microspheres, and assembled via light-activated chemophoresis. We show that the cluster propulsion mechanism transits from diffusiophoretic to diffusioosmotic as the number of colloidal shells increases. Using the Lorentz reciprocal theorem, we demonstrate that in large clusters self-propulsion emerges by considering the hydrodynamic flow via the diffusioosmotic response of the substrate. The dynamics in our active colloidal rafts are governed by the interplay between phoretic and osmotic effects. Thus, our work highlights their importance in understanding the rich physics of active catalytic systems.

Extremely persistent dense active fluids

We study the dynamics of dense three-dimensional systems of active particles for large persistence times τp at constant average self-propulsion force f. These systems are fluid counterparts of previously investigated extremely persistent systems, which in the large persistence time limit relax only on the time scale of τp. We find that many dynamic properties of the systems we study, such as the mean-squared velocity, the self-intermediate scattering function, and the shear-stress correlation function, become τp-independent in the large persistence time limit. In addition, the large τp limits of many dynamic properties, such as the mean-square velocity and the relaxation times of the scattering function, and the shear-stress correlation function, depend on f as power laws with non-trivial exponents. We conjecture that these systems constitute a new class of extremely persistent active systems.

Viscous Loading Regulates the Flagellar Energetics of Human and Bull Sperm

The viscoelastic properties of the female reproductive tract influence sperm swimming behavior, but the exact role of these rheological changes in regulating sperm energetics remains unknown. Using high-speed dark-field microscopy, the flagellar dynamics of free-swimming sperm across a physiologically relevant range of viscosities is resolved. A transition from 3D to 2D slither swimming under an increased viscous loading is revealed, in the absence of any geometrical or chemical stimuli. This transition is species-specific, aligning with viscosity variations within each species' reproductive tract. Despite substantial drag increase, 2D slithering sperm maintain a steady swimming speed across a wide viscosity range (20-250 and 75-1000 mPa s for bull and human sperm) by dissipating over sixfold more energy into the fluid without elevating metabolic activity, potentially by altering the mechanisms of dynein motor activity. This energy-efficient motility mode is ideally suited for the viscous environment of the female reproductive tract.