Smart active particles learn and transcend bacterial foraging strategies.

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

Motility-induced coexistence of a hot liquid and a cold gas.

If two phases exist at the same time, such as a gas and a liquid, they have the same temperature. This fundamental law of equilibrium physics is known to apply even to many non-equilibrium systems. However, recently, there has been much attention in the finding that inertial self-propelled particles like Janus colloids in a plasma or microflyers could self-organize into a hot gas-like phase that coexists with a colder liquid-like phase. Here, we show that a kinetic temperature difference across coexisting phases can occur even in equilibrium systems when adding generic (overdamped) self-propelled particles. In particular, we consider mixtures of overdamped active and inertial passive Brownian particles and show that when they phase separate into a dense and a dilute phase, both phases have different kinetic temperatures. Surprisingly, we find that the dense phase (liquid) cannot only be colder but also hotter than the dilute phase (gas). This effect hinges on correlated motions where active particles collectively push and heat up passive ones primarily within the dense phase. Our results answer the fundamental question if a non-equilibrium gas can be colder than a coexisting liquid and create a route to equip matter with self-organized domains of different kinetic temperatures.

Inverted Sedimentation of Active Particles in Unbiased ac Fields.

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

Self-Solidifying Active Droplets Showing Memory-Induced Chirality.

Most synthetic microswimmers do not reach the autonomy of their biological counterparts in terms of energy supply and diversity of motions. Here, this work reports the first all-aqueous droplet swimmer powered by self-generated polyelectrolyte gradients, which shows memory-induced chirality while self-solidifying. An aqueous solution of surface tension-lowering polyelectrolytes self-solidifies on the surface of acidic water, during which polyelectrolytes are gradually emitted into the surrounding water and induce linear self-propulsion via spontaneous symmetry breaking. The low diffusion coefficient of the polyelectrolytes leads to long-lived chemical trails which cause memory effects that drive a transition from linear to chiral motion without requiring any imposed symmetry breaking. The droplet swimmer is capable of highly efficient removal (up to 85%) of uranium from aqueous solutions within 90 min, benefiting from self-propulsion and flow-induced mixing. These results provide a route to fueling self-propelled agents which can autonomously perform chiral motion and collect toxins.

Writing Into Water.

Writing is an ancient communication technique dating back at least 30 000 years. While even sophisticated contemporary writing techniques hinge on solid surfaces for engraving or the deposition of ink, writing within a liquid medium requires a fundamentally different approach. The study here demonstrates the writing of lines, letters, and complex patterns in water by assembling lines of colloidal particles. Unlike established techniques for underwater writing on solid substrates, these lines are fully reconfigurable and do not require any fixation onto the substrate. Exploiting gravity, an ion-exchange bead (pen) is rolled across a layer of sedimented colloidal particles (ink). The pen evokes a hydrodynamic flow collecting ink-particles into a durable, high-contrast line along its trajectory. Deliberate substrate-tilting sequences facilitate pen-steering and thus drawing and writing. The experiments are complemented with a minimal model that quantitatively predicts the observed parameter dependence for writing in fluids and highlights the generic character of writing by line-assembly. Overall, the approach opens a versatile route for writing, drawing, and patterning fluids-even at the micro-scale.

Detecting Isotachophoresis Zones Hidden in Noise Using Signal Processing.

Lowering the limit of detection in chemical or biochemical analysis is key to extending the application scope of sensing schemes. Usually, this is related to an increased instrumentation effort, which in turn precludes many commercial applications. We demonstrate that the signal-to-noise ratio of isotachophoresis-based microfluidic sensing schemes can be substantially increased merely by postprocessing of recorded signals. This becomes possible by exploiting knowledge about the physics of the underlying measurement process. The implementation of our method is based on microfluidic isotachophoresis and fluorescence detection, for which we take advantage of the physics of electrophoretic sample transport and the structure of noise in the imaging process. We demonstrate that by processing only 200 images, the detectable concentration, compared to the detection from a single image, is already lowered by 2 orders of magnitude without any additional instrumentation effort. Furthermore, we show that the signal-to-noise ratio is proportional to the square root of the number of fluorescence images, which leaves room for further lowering of the detection limit. In the future, our results could be relevant for various applications where the detection of minute sample amounts plays a role.

Acoustic Crystallization of 2D Colloidal Crystals.

2D colloidal crystallization provides a simple strategy to produce defined nanostructure arrays over macroscopic areas. Regularity and long-range order of such crystals is essential to ensure functionality, but difficult to achieve in self-assembling systems. Here, a simple loudspeaker setup for the acoustic crystallization of 2D colloidal crystals (ACDC) of polystyrene, microgels, and core-shell particles at liquid interfaces is introduced. This setup anneals an interfacial colloidal monolayer and affords an increase in average grain size by almost two orders of magnitude. The order is characterized via the structural color of the colloidal crystal, the acoustic annealing process is optimized via the frequency and the amplitude of the applied sound wave, and its efficiency is rationalized via the surface coverage-dependent interactions within the interfacial colloidal monolayer. Computer simulations show that multiple rearrangement mechanisms at different length scales, from the local motion around voids to grain boundary movements via consecutive particle rotations around common centers, collude to remove defects. The experimentally simple ACDC process, paired with the demonstrated applicability toward complex particle systems, provides access to highly defined nanostructure arrays for a wide range of research communities.

Active Refrigerators Powered by Inertia.

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

Charging of Dielectric Surfaces in Contact with Aqueous Electrolytes─the Influence of CO2.

The charge state of dielectric surfaces in aqueous environments is of fundamental and technological importance. Here, we study the influence of dissolved molecular CO2 on the charging of three chemically different surfaces (SiO2, Polystyrene, Perfluorooctadecyltrichlorosilane). We determine their charge state from electrokinetic experiments. We compare an ideal, CO2-free reference system to a system equilibrated against ambient CO2 conditions. In the reference system, the salt-dependent decrease of the magnitudes of ζ-potentials follows the expectations for a constant charge scenario. In the presence of CO2, the starting potential is lower by some 50%. The following salt-dependent decrease is weakened for SiO2 and inverted for the organic surfaces. We show that screening and pH-driven charge regulation alone cannot explain the observed effects. As an additional cause, we tentatively suggest dielectric regulation of surface charges due to a diffusively adsorbed thin layer of molecular CO2. The formation of such a dynamic layer, even at the hydrophilic and partially ionized silica surfaces, is supported by a minimal theoretical model and results from molecular simulations.

Mutation induced infection waves in diseases like COVID-19.

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.

Resonant Nanopumps: ac Gate Voltages in Conical Nanopores Induce Directed Electrolyte Flow.

Inducing transport in electrolyte-filled nanopores with dc fields has led to influential applications ranging from nanosensors to DNA sequencing. Here we use the Poisson-Nernst-Planck and Navier-Stokes equations to show that unbiased ac fields can induce comparable directional flows in gated conical nanopores. This flow exclusively occurs at intermediate driving frequencies and hinges on the resonance of two competing timescales, representing space charge development at the ends and in the interior of the pore. We summarize the physics of resonant nanopumping in an analytical model that reproduces the results of numerical simulations. Our findings provide a generic route toward real-time controllable flow patterns, which might find applications in controlling the translocation of small molecules or nanocolloids.

Collective self-optimization of communicating active particles.

The quest for how to collectively self-organize in order to maximize the survival chances of the members of a social group requires finding an optimal compromise between maximizing the well-being of an individual and that of the group. Here we develop a minimal model describing active individuals which consume or produce, and respond to a shared resource-such as the oxygen concentration for aerotactic bacteria or the temperature field for penguins-while urging for an optimal resource value. Notably, this model can be approximated by an attraction-repulsion model, but, in general, it features many-body interactions. While the former prevents some individuals from closely approaching the optimal value of the shared "resource field," the collective many-body interactions induce aperiodic patterns, allowing the group to collectively self-optimize. Arguably, the proposed optimal field-based collective interactions represent a generic concept at the interface of active matter physics, collective behavior, and microbiological chemotaxis. This concept might serve as a useful ingredient to optimize ensembles of synthetic active agents or to help unveil aspects of the communication rules which certain social groups use to maximize their survival chances.

Interactions in active colloids.

The past two decades have seen a remarkable progress in the development of synthetic colloidal agents which are capable of creating directed motion in an unbiased environment at the microscale. These self-propelling particles are often praised for their enormous potential to self-organize into dynamic nonequilibrium structures such as living clusters, synchronized super-rotor structures or self-propelling molecules featuring a complexity which is rarely found outside of the living world. However, the precise mechanisms underlying the formation and dynamics of many of these structures are still barely understood, which is likely to hinge on the gaps in our understanding of how active colloids interact. In particular, besides showing comparatively short-ranged interactions which are well known from passive colloids (Van der Waals, electrostatic etc), active colloids show novel hydrodynamic interactions as well as phoretic and substrate-mediated 'osmotic' cross-interactions which hinge on the action of the phoretic field gradients which are induced by the colloids on other colloids in the system. The present article discusses the complexity and the intriguing properties of these interactions which in general are long-ranged, non-instantaneous, non-pairwise and non-reciprocal and which may serve as key ingredients for the design of future nonequilibrium colloidal materials. Besides providing a brief overview on the state of the art of our understanding of these interactions a key aim of this review is to emphasize open key questions and corresponding open challenges.

Non-monotonic speed-dependence of microswimmers on wall distance.

While substrates naturally occur in most microswimmer experiments, their impact on the swimming performance is not well understood. In the present study, we functionalize substrates with polymer brushes of varying swelling properties, grafting densities and brush lengths to systematically modify and explore the substrate-swimmer interactions. Notably, the swimming speed does not monotonically change with brush thickness, but shows a distinct maximum at a certain intermediate thickness, which results from two counteracting factors: surface charge and surface roughness. The results show that the speed of thermophoretic microswimmers does not only depend on the particle properties but is also strongly influenced by the properties of the underlying substrate. This provides a route to control the speed of microswimmers via the underlying substrate, which could be applied in the future e.g. to design complex motility landscapes by patterning substrates with polymer brushes. It is expected that similar effects would occur for diffusio- and electrophoretic particles.

Active droploids.

Active matter comprises self-driven units, such as bacteria and synthetic microswimmers, that can spontaneously form complex patterns and assemble into functional microdevices. These processes are possible thanks to the out-of-equilibrium nature of active-matter systems, fueled by a one-way free-energy flow from the environment into the system. Here, we take the next step in the evolution of active matter by realizing a two-way coupling between active particles and their environment, where active particles act back on the environment giving rise to the formation of superstructures. In experiments and simulations we observe that, under light-illumination, colloidal particles and their near-critical environment create mutually-coupled co-evolving structures. These structures unify in the form of active superstructures featuring a droplet shape and a colloidal engine inducing self-propulsion. We call them active droploids-a portmanteau of droplet and colloids. Our results provide a pathway to create active superstructures through environmental feedback.

Shaping the gradients driving phoretic micro-swimmers: influence of swimming speed, budget of carbonic acid and environment.

pH gradient-driven modular micro-swimmers are investigated as a model for a large variety of quasi-two-dimensional chemi-phoretic self-propelled entities. Using three-channel micro-photometry, we obtain a precise large field mapping of pH at a spatial resolution of a few microns and a pH resolution of [Formula: see text] units for swimmers of different velocities propelling on two differently charged substrates. We model our results in terms of solutions of the three-dimensional advection-diffusion equation for a 1:1 electrolyte, i.e. carbonic acid, which is produced by ion exchange and consumed by equilibration with dissolved [Formula: see text]. We demonstrate the dependence of gradient shape and steepness on swimmer speed, diffusivity of chemicals, as well as the fuel budget. Moreover, we experimentally observe a subtle, but significant feedback of the swimmer's immediate environment in terms of a substrate charge-mediated solvent convection. We discuss our findings in view of different recent results from other micro-fluidic or active matter investigations. We anticipate that they are relevant for quantitative modelling and targeted applications of diffusio-phoretic flows in general and artificial micro-swimmers in particular.

Strategic spatiotemporal vaccine distribution increases the survival rate in an infectious disease like Covid-19.

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 [Formula: see text] and by about 35% for [Formula: see text]). 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.

Actomyosin Contraction Induces In-Bulk Motility of Cells and Droplets.

Cell crawling on two-dimensional surfaces is a relatively well-understood phenomenon that is based on actin polymerization at a cell's front edge and anchoring on a substrate, allowing the cell to pull itself forward. However, some cells, such as cancer cells invading a three-dimensional matrigel, can also swim in the bulk, where surface adhesion is impossible. Although there is strong evidence that the self-organized engine that drives cells forward in the bulk involves myosin, the specific propulsion mechanism remains largely unclear. Here, we propose a minimal model for in-bulk self-motility of a droplet containing an isotropic and compressible contractile gel, representing a cell extract containing a disordered actomyosin network. In our model, contraction mediates a feedback loop between myosin-induced flow and advection-induced myosin accumulation, which leads to clustering and locally enhanced flow. The symmetry of such flow is then spontaneously broken through actomyosin-membrane interactions, leading to self-organized droplet motility relative to the underlying solvent. Depending on the balance between contraction, diffusion, detachment rate of myosin, and effective surface tension, this motion can be either straight or circular. Our simulations and analytical results shed new light on in-bulk myosin-driven cell motility in living cells and provide a framework to design a novel type of synthetic active matter droplet potentially resembling the motility mechanism of biological cells.

Active Assembly of Spheroidal Photocatalytic BiVO4 Microswimmers.

We create single-component photocatalytic bismuth vanadate (BiVO4) microswimmers with a spheroidal shape that move individually upon irradiation without any asymmetrization step. These particles form active assemblies which we investigate combining an experimental approach with numerical simulations and analytical calculations. We systematically explore the speed and assembly of the swimmers into clusters of up to four particles and find excellent agreement between experiment and theory, which helps us to understand motion patterns and speed trends. Moreover, different batches of particles can be functionalized separately, making them ideal candidates to fulfill a multitude of tasks, such as sensing or environmental remediation. To exemplify this, we coat our swimmers with silica (SiO2) and selectively couple some of their modules to fluorophores in a way which does not inhibit self-propulsion. The present work establishes spheroidal BiVO4 microswimmers as a versatile platform to design multifunctional microswimmers.

Swarm Hunting and Cluster Ejections in Chemically Communicating Active Mixtures.

A large variety of microorganisms produce molecules to communicate via complex signaling mechanisms such as quorum sensing and chemotaxis. The biological diversity is enormous, but synthetic inanimate colloidal microswimmers mimic microbiological communication (synthetic chemotaxis) and may be used to explore collective behaviour beyond the one-species limit in simpler setups. In this work we combine particle based and continuum simulations as well as linear stability analyses, and study a physical minimal model of two chemotactic species. We observed a rich phase diagram comprising a "hunting swarm phase", where both species self-segregate and form swarms, pursuing, or hunting each other, and a "core-shell-cluster phase", where one species forms a dense cluster, which is surrounded by a (fluctuating) corona of particles from the other species. Once formed, these clusters can dynamically eject their core such that the clusters almost turn inside out. These results exemplify a physical route to collective behaviours in microorganisms and active colloids, which are so-far known to occur only for comparatively large and complex animals like insects or crustaceans.