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Abstract Dynamical clustering is a key feature of active matter systems composed of self-propelled agents that convert environmental energy into mechanical motion. At the micron scale, where overdamped dynamics dominate, particles with opposite motility can obstruct each other’s movement, leading to transient dynamical arrest. This arrest can promote cluster formation and motility-induced phase separation. However, in macroscopic agents, where inertia plays a significant role, clustering is heavily influenced by bounce-back effects during collisions, which can impede cluster growth. Here we present an experiment based on active granular particles, in which inertia can be systematically tuned by changing the shaker frequency. As a result, a set of phenomena driven and controlled by inertia emerges. Before the suppression of clustering, inertia induces a transition in the cluster’s inner structure. For small inertia, clusters are characterized by the crystalline order typical of overdamped particles, while for large inertia clusters with liquid-like order are observed. In addition, in contrast to microswimmers, where active particles wet the boundary by primarily forming clusters attached to the container walls, in an underdamped inertial active system, walls do not favor cluster formation and effectively annihilate motility-induced wetting phenomena. As a consequence, inertia suppresses cluster nucleation at the system boundaries.

Abstract Group formation and coordination are fundamental characteristics of living matter, essential for performing tasks and ensuring survival. Interactions between individuals play a key role in group formation, and the impact of resource distributions is a vibrant area of research. As of now, an understanding of how patchy resource distributions determine group dynamics is not yet fully understood. Studying active particles in controlled optical landscapes as energy sources, we demonstrate a non-monotonic dependency of group size on landscape patchiness, with the smallest groups forming when the patches match the active particles’ size. A similar relationship is observed in terms of group stability, evidenced by a reduced rate of individual exchange in patchy environments compared to homogeneous conditions. Reduced group sizes can be beneficial to optimise resources in heterogeneous environments and to control information flow within populations. Our results provide insights into the role of patchy landscapes and uneven energy distributions in active matter and hold implications for refining swarm intelligence algorithms, enhancing crowd management techniques, and tailoring colloidal self-assembly.

We show that dry scalar-order active field theories (AFTs) are universally hyperuniform, i.e., density fluctuations are anomalously suppressed in the long-time limit regardless of the integrability or functional form of the active contributions up to third order in gradient terms. These AFTs include active model B, active model B+, and effective Cahn-Hilliard models. Moreover, density variances and spectral densities are virtually indistinguishable from that of passive phase-separated hyperuniform fields. Higher moments of the density fluctuations, however, reveal activity-dependent higher-order correlations that are not captured by conventional two-point measures that characterize hyperuniformity.

Abstract Zebrafish constitute a convenient laboratory–based biological system for studying collective behavior. It is possible to interpret a group of zebrafish as a system of interacting agents and to apply methods developed for the analysis of systems of active and even passive particles. Here, we consider the effect of group size. We focus on two– and many–body spatial correlations and dynamical order parameters to investigate the multistate behavior. For geometric reasons, the smallest group of fish which can exhibit this multistate behavior consisting of schooling, milling and swarming is three. We find that states exhibited by groups of three fish are similar to those of much larger groups, indicating that there is nothing more than a gradual change in weighting between the different states as the system size changes. Remarkably, when we consider small groups of fish sampled from a larger group, we find very little difference in the occupancy of the state with respect to isolated groups, nor is there much change in the spatial correlations between the fish. This indicates that fish interact predominantly with their nearest neighbors, perceiving the rest of the group as a fluctuating background. Therefore, the behavior of a crowd of fish is already apparent in groups of three fish.

Abstract In an equilibrium thermal environment, random elastic collisions between background particles and a tracer establish the picture of Brownian motion fulfilling the celebrated Einstein relation between diffusivity and mobility. However, extensions of the Einstein relation to link dissipation, fluctuations, and nonequilibrium dynamical mechanisms in active matter systems are still debated. Here, we investigate experimentally the impact of an active background on a passive tracer using vibrationally excited active particles, that result in multiple correlated tapping collisions with the tracer, for which a persistent memory emerges in the dynamics. The system is described by a generalized active Einstein relation that constrains fluctuations, dissipation, and effective activity, by taking the emerging tracer memory into account. Since the resulting persistence can largely be tuned by the environmental density and motility, our findings can be useful to engineer properties of various active systems in biomedical applications, microfluidics, chemical engineering, or swarm robotics.

Abstract The ultrafast control of materials has opened the possibility to investigate non-equilibrium states of matter with striking properties, such as transient superconductivity and ferroelectricity, ultrafast magnetization and demagnetization, as well as Floquet engineering. The characterization of the ultrafast thermodynamic properties within the material is key for their control and design. Here, we develop the ultrafast stochastic thermodynamics for laser-excited phonons. We calculate the entropy production and heat absorbed from experimental data for single phonon modes of driven materials from time-resolved X-ray scattering experiments where the crystal is excited by a laser pulse. The spectral entropy production is calculated for SrTiO3 and KTaO3 for different temperatures and reveals a striking relation with the power spectrum of the displacement-displacement correlation function by inducing a broad peak beside the eigenmode-resonance.

Abstract Mechanical stresses stemming from environmental factors are a key determinant of cellular behavior and physiology. Yet, the role of self-induced biomechanical stresses in growing bacterial colonies has remained largely unexplored. Here, we demonstrate how collective mechanical forcing plays an important role in the dynamics of the cell size of growing bacteria. We observe that the measured elongation rate of well-nourished Escherichia coli cells decreases over time, depending on the free area around each individual, and associate this behavior with the response of the growing cells to mechanical stresses. Via a cell-resolved model accounting for the feedback of collective forces on individual cell growth, we quantify the effect of this mechano-response on the structure and composition of growing bacterial colonies, including the local environment of each cell. Finally, we predict that a mechano-cross-response between competing bacterial strains with distinct growth rates affects their size distributions.

Abstract Self-propelled particles in anisotropic environments can exhibit a motility that depends on their orientation. This dependence is relevant for a plethora of living organisms but difficult to study in controlled environments. Here, we present a macroscopic system of self-propelled vibrated granular particles on a striated substrate that displays orientation-dependent motility. An extension of the active Brownian motion model involving orientation-dependent motility and inertial effects reproduces and explains our experimental observations. The model can be applied to general n-fold symmetric anisotropy and can be helpful for predictive optimization of the dynamics of active matter in complex environments.

Abstract Stimuli-responsive emulsions offer a dual advantage, combining long-term storage with controlled release triggered by external cues such as pH or temperature changes. This study establishes that thermo-responsive emulsion behaviour is primarily determined by interactions between, rather than within, interfaces. Consequently, the stability of these emulsions is intricately tied to the nature of the stabilizing microgel particles - whether they are more polymeric or colloidal, and the morphology they assume at the liquid interface. The colloidal properties of the microgels provide the foundation for the long-term stability of Pickering emulsions. However, limited deformability can lead to non-responsive emulsions. Conversely, the polymeric properties of the microgels enable them to spread and flatten at the liquid interface, enabling stimuli-responsive behaviour. Furthermore, microgels shared between two emulsion droplets in flocculated emulsions facilitate stimuli-responsiveness, regardless of their internal architecture. This underscores the pivotal role of microgel morphology and the forces they exert on liquid interfaces in the control and design of stimuli-responsive emulsions and interfaces.

It is intriguing but challenging to control the complex dynamics of topological defects that emerge in nonequilibrium spatiotemporal systems. Through an effective modelling this work explores a viable way to controllably vary the properties of persistent defect dynamics in self-propelled active smectics via the competition of activity and boundary confinements with different topology and geometry.

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

Abstract We propose a mesoscopic Brownian magneto heat pump made of a single charged Brownian particle that is steered by an external magnetic field. The particle is subjected to two thermal noises from two different heat sources. When confined, the particle performs gyrating motion around a potential energy minimum. We show that such a magneto-gyrator can be operated as both a heat engine and a refrigerator. The maximum power delivered by the engine and the performance of the refrigerator, namely the rate of heat transferred per unit external work, can be tuned and optimised by the applied magnetic field. Further tunability of the key properties of the engine, such as the direction of gyration and the torque exerted by the engine on the confining potential, is obtained by varying the strength and direction of the applied magnetic field. In principle, our predictions can be tested by experiments with colloidal particles and complex plasmas.

Abstract After more than 6 million deaths worldwide, the ongoing vaccination to conquer the COVID-19 disease is now competing with the emergence of increasingly contagious mutations, repeatedly supplanting earlier strains. Following the near-absence of historical examples of the long-time evolution of infectious diseases under similar circumstances, models are crucial to exemplify possible scenarios. Accordingly, in the present work we systematically generalize the popular susceptible-infected-recovered model to account for mutations leading to repeatedly occurring new strains, which we coarse grain based on tools from statistical mechanics to derive a model predicting the most likely outcomes. The model predicts that mutations can induce a super-exponential growth of infection numbers at early times, which self-amplify to giant infection waves which are caused by a positive feedback loop between infection numbers and mutations and lead to a simultaneous infection of the majority of the population. At later stages—if vaccination progresses too slowly—mutations can interrupt an ongoing decrease of infection numbers and can cause infection revivals which occur as single waves or even as whole wave trains featuring alternative periods of decreasing and increasing infection numbers. This panorama of possible mutation-induced scenarios should be tested in more detailed models to explore their concrete significance for specific infectious diseases. Further, our results might be useful for discussions regarding the importance of a release of vaccine-patents to reduce the risk of mutation-induced infection revivals but also to coordinate the release of measures following a downwards trend of infection numbers.

Bacteria and other self-propelling microorganisms produce and respond to signaling molecules to communicate with each other (quorum sensing) and to direct their collective behavior. Here, we explore agents (active particles) which communicate with each other to coordinate their collective dynamics for maximizing nutrient consumption. Using reinforcement learning and neural networks, we identify three different strategies: a ‘clustering strategy’, where the agents accumulate in regions of high nutrient concentration; a ‘spreading strategy’, where particles stay away from each other to avoid competing for sparse resources; and an ‘adaptive strategy’, where the agents adaptively decide to either follow or stay away from others. Our work exemplifies the idea that machine learning can be used to determine parameters that are evolutionarily optimized in biological systems but often occur as unknown parameters in mathematical models describing their dynamics.

Navigation through porous environments poses a major challenge for swimming microorganisms and future microrobots. This study predicts that their spreading becomes optimal when their run length is comparable to the longest available pore length.

Active matter can spontaneously form complex patterns and assemblies via a one-way energy flow from the environment into the system. Here, the authors demonstrate that a two-way coupling, where active particles act back on the environment can give rise to novel superstructures, named as active droploids.

Liquid crystals can self-organize into a layered smectic phase. While the smectic layers are typically straight, forming a lamellar pattern in bulk, external confinement may drastically distort the layers due to the boundary conditions imposed on the orientational director field. Resolving this distortion leads to complex structures with topological defects. Here, we explore the configurations adopted by two-dimensional colloidal smectics made from nearly hard rod-like particles in complex confinements, characterized by a button-like structure with two internal boundaries (inclusions): a two-holed disk and a double annulus. The topology of the confinement generates new structures which we classify in reference to previous work as generalized laminar and generalized Shubnikov states. To explore these configurations, we combine particle-resolved experiments on colloidal rods with three complementary theoretical approaches: Monte Carlo simulation, first-principles density functional theory, and phenomenological Q-tensor modeling. This yields a consistent and comprehensive description of the structural details. In particular, we characterize a nontrivial tilt angle between the direction of the layers and symmetry axes of the confinement.

Fick’s laws describe the essential physics of diffusion, but it is challenging to extend them to systems out of equilibrium. The authors derive the diffusivity of particles near active carpets - a surface covered with hydrodynamic actuators, which provides a framework for transport in living matter.

While control theory for optimal navigation is relevant across scales, from aeronautics to targeted drug delivery, the role of thermal fluctuations and hydrodynamic interactions with interfaces, walls and obstacles at the microscale remains an open question. Here, the authors explore optimal microswimming in the presence of walls or obstacles, and study how hydrodynamic microswimmer-wall interactions impact on optimal microswimming strategies.

Colloidal rod-like mesogens make the study of liquid crystal structures available to simple optical microscopy. Wittmann et al. study topological defects in smectic phases under annular confinement and reveal a remarkable, quantitative agreement with a theoretic density functional description.

Abstract Present hopes to conquer the Covid-19 epidemic are largely based on the expectation of a rapid availability of vaccines. However, once vaccine production starts, it will probably take time before there is enough vaccine for everyone, evoking the question how to distribute it best. While present vaccination guidelines largely focus on individual-based factors, i.e. on the question to whom vaccines should be provided first, e.g. to risk groups or to individuals with a strong social-mixing tendency, here we ask if a strategic spatiotemporal distribution of vaccines, e.g. to prioritize certain cities, can help to increase the overall survival rate of a population subject to an epidemic disease. To this end, we propose a strategy for the distribution of vaccines in time and space, which sequentially prioritizes regions with the most new cases of infection during a certain time frame and compare it with the standard practice of distributing vaccines demographically. Using a simple statistical model we find that, for a locally well-mixed population, the proposed strategy strongly reduces the number of deaths (by about a factor of two for basic reproduction numbers of $$R_0\sim 1.5-4$$ R 0 ∼ 1.5 - 4 and by about 35% for $$R_0\sim 1$$ R 0 ∼ 1 ). The proposed vaccine distribution strategy establishes the idea that prioritizing individuals not only regarding individual factors, such as their risk of spreading the disease, but also according to the region in which they live can help saving lives. The suggested vaccine distribution strategy can be tested in more detailed models in the future and might inspire discussions regarding the importance of spatiotemporal distribution rules for vaccination guidelines.

Active matter describes a group of interacting units showing collective motions by constantly consuming energy from the environment, but inertia has largely been overlooked in this context. Scholz et al. show how important it can be by characterizing the dynamics of self-propelled particles in a model system.

Abstract The coupling of active, self-motile particles to topological constraints can give rise to novel non-equilibrium dynamical patterns that lack any passive counterpart. Here we study the behavior of self-propelled rods confined to a compact spherical manifold by means of Brownian dynamics simulations. We establish the state diagram and find that short active rods at sufficiently high density exhibit a glass transition toward a disordered state characterized by persistent self-spinning motion. By periodically melting and revitrifying the spherical spinning glass, we observe clear signatures of time-dependent aging and rejuvenation physics. We quantify the crucial role of activity in these non-equilibrium processes, and rationalize the aging dynamics in terms of an absorbing-state transition toward a more stable active glassy state. Our results demonstrate both how concepts of passive glass phenomenology can carry over into the realm of active matter, and how topology can enrich the collective spatiotemporal dynamics in inherently non-equilibrium systems.

The collective motion of microswimmers is determined by not only their direct interaction, but also the hydrodynamics forces mediated by the surrounding flow field. Here, the authors detail in simulation the spontaneous assembly and disassembly of magnetic microswimmers into various structures.

The capability to move towards or away from light sources, namely phototaxis, is an essential feature of many microorganisms like bacteria or motile cells. Lozano et al. show an artificial phototaxis system that enables autonomous navigation of colloidal Janus spheres in a laser-generated light landscape.

The ability to navigate in complex, inhomogeneous environments is fundamental to survival at all length scales, giving rise to the rapid development of various subfields in biolocomotion such as the well established concept of chemotaxis. In this work, we extend this existing notion of taxis to rotating environments and introduce the idea of “rototaxis” to biolocomotion. In particular, we explore both overdamped and inertial dynamics of a model synthetic self-propelled particle in the presence of constant global rotation, focusing on the particle's ability to localize near a rotation center as a survival strategy. We find that, in the overdamped regime, a torque directing the swim orientation to the rotation origin enables the swimmer to remain on stable epicyclical-like trajectories. On the other hand, for underdamped motion with inertial effects, the intricate competition between self-propulsion and inertial forces, in conjunction with the rotation-induced torque, leads to complex dynamical behavior with nontrivial phase space of initial conditions which we reveal by numerical simulations. Our results are relevant for a wide range of setups, from vibrated granular matter on turntables to microorganisms or animals swimming near swirls or vortices.

Following the goal of using active particles as targeted cargo carriers aimed, for example, to deliver drugs towards cancer cells, the quest for the control of individual active particles with external fields is among the most explored topics in active matter. Here, we provide a scheme allowing to control collective behaviour in active matter, focusing on the fluctuating band patterns naturally occurring e.g. in the Vicsek model. We show that exposing these patterns to a travelling wave potential tames them, yet in a remarkably nontrivial way: the bands, which initially pin to the potential and comove with it, upon subsequent collisions, self-organize into a macroband, featuring a predictable transport against the direction of motion of the travelling potential. Our results provide a route to simultaneously control transport and structure, i.e. micro- versus macrophase separation, in polar active matter.

With the rapid advent of biomedical and biotechnological innovations, a deep understanding of the nature of interaction between nanomaterials and cell membranes, tissues, and organs, has become increasingly important. Active penetration of nanoparticles through cell membranes is a fascinating phenomenon that may have important implications in various biomedical and clinical applications. Using a fully analytical theory supplemented by particle-based computer simulations, the penetration process of an active particle through a planar two-dimensional elastic membrane is studied. The membrane is modeled as a self-assembled sheet of particles, uniformly arranged on a square lattice. A coarse-grained model is introduced to describe the mutual interactions between the membrane particles. The active penetrating particle is assumed to interact sterically with the membrane particles. State diagrams are presented to fully characterize the system behavior as functions of the relevant control parameters governing the transition between different dynamical states. Three distinct scenarios are identified. These compromise trapping of the active particle, penetration through the membrane with subsequent self-healing, in addition to penetration with permanent disruption of the membrane. The latter scenario may be accompanied by a partial fragmentation of the membrane into bunches of isolated or clustered particles and creation of a hole of a size exceeding the interaction range of the membrane components. It is further demonstrated that the capability of penetration is strongly influenced by the size of the approaching particle relative to that of the membrane particles. Accordingly, active particles with larger size are more likely to remain trapped at the membrane for the same propulsion speed. Such behavior is in line with experimental observations. Our analytical theory is based on a combination of a perturbative expansion technique and a discrete-to-continuum formulation. It well describes the system behavior in the small-deformation regime. Particularly, the theory allows to determine the membrane displacement of the particles in the trapping state. Our approach might be helpful for the prediction of the transition threshold between the trapping and penetration in real-space experiments involving motile swimming bacteria or artificial active particles.

Nature Communications 7: Article number: 13519 (2016); Published 22 November 2016; Updated 17 January 2017 This Article contains an error in Reference 18 that was introduced during the production process. The correct reference should be: Steinbach, G. et al. Stirrers and movers actuated by oscillating fields.

In this article we examine the dynamics of a colloidal particle driven by a modulated force over a sinusoidal optical potential energy landscape. Coupling between the competing frequencies of the modulated drive and that of particle motion over the periodic landscape leads to synchronisation of particle motion into discrete modes. This synchronisation manifests as steps in the average particle velocity, with mode locked steps covering a range of average driving velocities. The amplitude and frequency dependence of the steps are considered, and compared to results from analytic theory, Langevin dynamics simulations, and dynamic density functional theory. Furthermore, the critical driving velocity is studied, and simulation used to extend the range of conditions accessible in experiments alone. Finally, state diagrams from experiment, simulation, and theory are used to show the extent of the dynamically locked modes in two dimensions, as a function of both the amplitude and frequency of the modulated drive.

The majority of studies on self-propelled particles and microswimmers concentrates on objects that do not feature a deterministic bending of their trajectory. However, perfect axial symmetry is hardly found in reality, and shape-asymmetric active microswimmers tend to show a persistent curvature of their trajectories. Consequently, we here present a particle-scale statistical approach to circle-swimmer suspensions in terms of a dynamical density functional theory. It is based on a minimal microswimmer model and, particularly, includes hydrodynamic interactions between the swimmers. After deriving the theory, we numerically investigate a planar example situation of confining the swimmers in a circularly symmetric potential trap. There, we find that increasing curvature of the swimming trajectories can reverse the qualitative effect of active drive. More precisely, with increasing curvature, the swimmers less effectively push outwards against the confinement, but instead form high-density patches in the center of the trap. We conclude that the circular motion of the individual swimmers has a localizing effect, also in the presence of hydrodynamic interactions. Parts of our results could be confirmed experimentally, for instance, using suspensions of L-shaped circle swimmers of different aspect ratio.