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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 ∼ 1.5 - 4 and by about 35% for 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.

Efficient navigation through disordered, porous environments poses a major challenge for swimming microorganisms and future synthetic cargo-carriers. We perform Brownian dynamics simulations of active stiff polymers undergoing run-reverse dynamics, and so mimic bacterial swimming, in porous media. In accord with experiments of Escherichia coli , the polymer dynamics are characterized by trapping phases interrupted by directed hopping motion through the pores. Our findings show that the spreading of active agents in porous media can be optimized by tuning their run lengths, which we rationalize using a coarse-grained model. More significantly, we discover a geometric criterion for the optimal spreading, which emerges when their run lengths are comparable to the longest straight path available in the porous medium. Our criterion unifies results for porous media with disparate pore sizes and shapes and for run-and-tumble polymers. It thus provides a fundamental principle for optimal transport of active agents in densely-packed biological and environmental settings. 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.

The motion of self-propelled massive particles through a gaseous medium is dominated by inertial effects. Examples include vibrated granulates, activated complex plasmas and flying insects. However, inertia is usually neglected in standard models. Here, we experimentally demonstrate the significance of inertia on macroscopic self-propelled particles. We observe a distinct inertial delay between orientation and velocity of particles, originating from the finite relaxation times in the system. This effect is fully explained by an underdamped generalisation of the Langevin model of active Brownian motion. In stark contrast to passive systems, the inertial delay profoundly influences the long-time dynamics and enables new fundamental strategies for controlling self-propulsion in active matter. 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.

Many microorganisms, with phytoplankton and zooplankton as prominent examples, display phototactic behaviour, that is, the ability to perform directed motion within a light gradient. Here we experimentally demonstrate that sensing of light gradients can also be achieved in a system of synthetic photo-activated microparticles being exposed to an inhomogeneous laser field. We observe a strong orientational response of the particles because of diffusiophoretic torques, which in combination with an intensity-dependent particle motility eventually leads to phototaxis. Since the aligning torques saturate at high gradients, a strongly rectified particle motion is found even in periodic asymmetric intensity landscapes. Our results are in excellent agreement with numerical simulations of a minimal model and should similarly apply to other particle propulsion mechanisms. Because light fields can be easily adjusted in space and time, this also allows to extend our approach to dynamical environments. 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.

Biological activity is often highly concentrated on surfaces, across the scales from molecular motors and ciliary arrays to sessile and motile organisms. These ‘active carpets’ locally inject energy into their surrounding fluid. Whereas Fick’s laws of diffusion are established near equilibrium, it is unclear how to solve non-equilibrium transport driven by such boundary-actuated fluctuations. Here, we derive the enhanced diffusivity of molecules or passive particles as a function of distance from an active carpet. Following Schnitzer’s telegraph model, we then cast these results into generalised Fick’s laws. Two archetypal problems are solved using these laws: First, considering sedimentation towards an active carpet, we find a self-cleaning effect where surface-driven fluctuations can repel particles. Second, considering diffusion from a source to an active sink, say nutrient capture by suspension feeders, we find a large molecular flux compared to thermal diffusion. Hence, our results could elucidate certain non-equilibrium properties of active coating materials and life at interfaces. 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.

Confined samples of liquid crystals are characterized by a variety of topological defects and can be exposed to external constraints such as extreme confinements with nontrivial topology. Here we explore the intrinsic structure of smectic colloidal layers dictated by the interplay between entropy and an imposed external topology. Considering an annular confinement as a basic example, a plethora of competing states is found with nontrivial defect structures ranging from laminar states to multiple smectic domains and arrays of edge dislocations, which we refer to as Shubnikov states in formal analogy to the characteristic of type-II superconductors. Our particle-resolved results, gained by a combination of real-space microscopy of thermal colloidal rods and fundamental-measure-based density functional theory of hard anisotropic bodies, agree on a quantitative level. 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.

Many motile microorganisms adjust their swimming motion relative to the gravitational field and thus counteract sedimentation to the ground. This gravitactic behaviour is often the result of an inhomogeneous mass distribution, which aligns the microorganism similar to a buoy. However, it has been suggested that gravitaxis can also result from a geometric fore–rear asymmetry, typical for many self-propelling organisms. Despite several attempts, no conclusive evidence for such an asymmetry-induced gravitactic motion exists. Here, we study the motion of asymmetric self-propelled colloidal particles which have a homogeneous mass density and a well-defined shape. In experiments and by theoretical modelling, we demonstrate that a shape anisotropy alone is sufficient to induce gravitactic motion with either preferential upward or downward swimming. In addition, also trochoid-like trajectories transversal to the direction of gravity are observed. Gravitaxis describes the ability of microorganisms to adjust their swimming motion on the gravitational field, yet its mechanism remains unclear. Here, the authors show that an asymmetric shape of colloidal particles is alone sufficient to induce gravitactic motion in the absence of density inhomogeneity.

Fission and fusion processes of particle clusters occur in many areas of physics and chemistry from subnuclear to astronomic length scales. Here we study fission and fusion of magnetic microswimmer clusters as governed by their hydrodynamic and dipolar interactions. Rich scenarios are found that depend crucially on whether the swimmer is a pusher or a puller. In particular a linear magnetic chain of pullers is stable while a pusher chain shows a cascade of fission (or disassembly) processes as the self-propulsion velocity is increased. Contrarily, magnetic ring clusters show fission for any type of swimmer. Moreover, we find a plethora of possible fusion (or assembly) scenarios if a single swimmer collides with a ringlike cluster and two rings spontaneously collide. Our predictions are obtained by computer simulations and verifiable in experiments on active colloidal Janus particles and magnetotactic bacteria. 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.

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. 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.

Turbulence is ubiquitous, from oceanic currents to small-scale biological and quantum systems. Self-sustained turbulent motion in microbial suspensions presents an intriguing example of collective dynamical behavior among the simplest forms of life and is important for fluid mixing and molecular transport on the microscale. The mathematical characterization of turbulence phenomena in active nonequilibrium fluids proves even more difficult than for conventional liquids or gases. It is not known which features of turbulent phases in living matter are universal or system-specific or which generalizations of the Navier–Stokes equations are able to describe them adequately. Here, we combine experiments, particle simulations, and continuum theory to identify the statistical properties of self-sustained meso-scale turbulence in active systems. To study how dimensionality and boundary conditions affect collective bacterial dynamics, we measured energy spectra and structure functions in dense Bacillus subtilis suspensions in quasi-2D and 3D geometries. Our experimental results for the bacterial flow statistics agree well with predictions from a minimal model for self-propelled rods, suggesting that at high concentrations the collective motion of the bacteria is dominated by short-range interactions. To provide a basis for future theoretical studies, we propose a minimal continuum model for incompressible bacterial flow. A detailed numerical analysis of the 2D case shows that this theory can reproduce many of the experimentally observed features of self-sustained active turbulence.