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A hallmark of bacteria is their so-called "run-and-tumble" motion, consisting of a sequence of linear directed "runs" and random rotations that constantly alternate due to biochemical feedback. It plays a crucial role in the ability of bacteria to move through chemical gradients and inspired a fundamental active particle model. Nevertheless, synthetic active particles generally do not exhibit run-and-tumble motion but rather active Brownian motion. We show in experiments that ellipsoidal thermophoretic Janus particles, propelling along their short axis, can yield run-and-tumble-like motion even without feedback. Their hydrodynamic wall interactions under strong confinement give rise to an effective double-well potential for the declination of the short axis. The geometry-induced timescale separation of the in-plane rotational dynamics and noise-induced transitions in the potential then yields run-and-tumble-like motion.

The processing of information is an indispensable property of living systems realized by networks of active processes with enormous complexity. They have inspired many variants of modern machine learning one of them being reservoir computing, in which stimulating a network of nodes with fading memory enables computations and complex predictions. Reservoirs are implemented on computer hardware, but also on unconventional physical substrates such as mechanical oscillators, spins, or bacteria often summarized as physical reservoir computing. Here we demonstrate physical reservoir computing with a synthetic active microparticle system that self-organizes from an active and passive component into inherently noisy nonlinear dynamical units. The self-organization and dynamical response of the unit is the result of a delayed propulsion of the microswimmer to a passive target. A reservoir of such units with a self-coupling via the delayed response can perform predictive tasks despite the strong noise resulting from Brownian motion of the microswimmers. To achieve efficient noise suppression, we introduce a special architecture that uses historical reservoir states for output. Our results pave the way for the study of information processing in synthetic self-organized active particle systems., Comment: 20 pages, 5 figures

Perception-reaction delays have experimentally been found to cause a spontaneous circling of microswimmers around a targeted center. Here we investigate the many-body version of this experiment with Brownian-dynamics simulations of active particles in a plane. For short delays, the soft spherical discs form a hexagonal colloidal crystallite around a fixed target particle. Upon increasing the delay time, we observe a bifurcation to a chiral dynamical state that we can map onto that found for a single active particle. The different angular velocities at different distances from the target induce shear stresses that grow with increasing delay. As a result, tangential and, later, also radial shear bands intermittently break the rotating crystallite. Eventually, for long delays, the discs detach from the target particle to circle around it near the preferred single-particle orbit, while spinning and trembling from tidal quakes, Comment: Videos available on https://youtube.com/playlist?list=PLDwaP_kIyigWI4637AQH1upD4seyYOynw

Through digital imaging, microscopy has evolved from primarily being a means for visual observation of life at the micro- and nano-scale, to a quantitative tool with ever-increasing resolution and throughput. Artificial intelligence, deep neural networks, and machine learning are all niche terms describing computational methods that have gained a pivotal role in microscopy-based research over the past decade. This Roadmap is written collectively by prominent researchers and encompasses selected aspects of how machine learning is applied to microscopy image data, with the aim of gaining scientific knowledge by improved image quality, automated detection, segmentation, classification and tracking of objects, and efficient merging of information from multiple imaging modalities. We aim to give the reader an overview of the key developments and an understanding of possibilities and limitations of machine learning for microscopy. It will be of interest to a wide cross-disciplinary audience in the physical sciences and life sciences.

Collective states of inanimate particles self-assemble through physical interactions and thermal motion. Despite some phenomenological resemblance, including signatures of criticality, the autonomous dynamics that binds motile agents into flocks, herds, or swarms allows for much richer behavior. Low-dimensional models have hinted at the crucial role played in this respect by perceived information, decision-making, and feedback implying that the corresponding interactions are inevitably retarded. Here we present experiments on spherical Brownian microswimmers with delayed self-propulsion toward a spatially fixed target. We observe a spontaneous symmetry breaking to a transiently chiral dynamical state and concomitant critical behavior that does not rely on many-particle cooperativity. By comparison with the stochastic delay differential equation of motion of a single swimmer, we pinpoint the delay-induced effective synchronization of the swimmers with their own past as its key mechanism. Increasing numbers of swimmers self-organize into layers with pro- and retrograde orbital motion, synchronized and stabilized by steric and hydrodynamic interactions. Our results demonstrate how even most simple retarded non-reciprocal interactions can foster emergent complex adaptive behavior in relatively small ensembles., Comment: 18 pages, 4 figures

The manipulation of micro- and nano-objects is of great technological significance to construct new materials, manipulate tiny amounts of liquids in fluidic systems, or detect minute concentrations of analytes. It is commonly approached by the generation of potential energy landscapes, for example, with optical fields. Here we show that strong hydrodynamic boundary flows enable the trapping and manipulation of nano-objects near surfaces. These thermo-osmotic flows are induced by modulating the van der Waals interaction at a solid-liquid interface with optically induced temperature fields. We use a thin gold film on a glass substrate to provide localized but reconfigurable point-like optical heating. Convergent boundary flows with velocities of tens of micrometres per second are observed and substantiated by a quantitative physical model. The hydrodynamic forces acting on suspended nanoparticles and attractive van der Waals or depletion induced forces to enable precise positioning and guiding of the nanoparticles. Fast multiplexing of flow fields further provides the means for parallel manipulation of many nano-objects. Our findings have direct consequences for the field of plasmonic nano-tweezers and other thermo-plasmonic trapping schemes and pave the way for a general scheme of nanoscopic manipulation with boundary flows., Comment: 9 pages, 4 figures

Living many-body systems often exhibit scale-free collective behavior reminiscent of thermal critical phenomena. But their mutual interactions are inevitably retarded due to information processing and delayed actuation. We numerically investigate the consequences for the finite-size scaling in the Vicsek model of motile active matter. A growing delay time initially facilitates but ultimately impedes collective ordering and turns the dynamical scaling from diffusive to ballistic. It provides an alternative explanation of swarm traits previously attributed to inertia., Comment: 5 pages, 3 figures, supplementary information available on demand

The interactions of autonomous microswimmers play an important role for the formation of collective states of motile active matter. We study them in detail for the common microswimmer-design of two-faced Janus spheres with hemispheres made from different materials. Their chemical and physical surface properties may be tailored to fine-tune their mutual attractive, repulsive or aligning behavior. To investigate these effects systematically, we monitor the dynamics of a single gold-capped Janus particle in the external temperature field created by an optically heated metal nanoparticle. We quantify the orientation-dependent repulsion and alignment of the Janus particle and explain it in terms of a simple theoretical model for the induced thermoosmotic surface fluxes. The model reveals that the particle's angular velocity is solely determined by the temperature profile on the equator between the Janus particle's hemispehres and their phoretic mobility contrast. The distortion of the external temperature field by their heterogeneous heat conductivity is moreover shown to break the apparent symmetry of the problem., Comment: 16 pages, 11 figures

The co-localization of density modulations and particle polarization is a characteristic emergent feature of motile active matter in activity gradients. It can therefore play the role of a smoking gun for the mesoscale detection of intrinsic microscopic activity. We employ the active-Brownian-particle (ABP) model to derive precise analytical expressions for the density and polarization profiles of a single Janus-type swimmer in the vicinity of an abrupt activity step, including situations with an orientation-dependent propulsion speed. Our results agree well with measurement data for a hot microswimmer presented in the companion paper [1] and can serve as a template for more complex applications, e.g., to motility-induced phase separation or studies of physical boundaries. The essential physics behind our formal results is robustly captured and elucidated by a schematic two-species ``run-and-tumble'' model., Comment: 21 pages, 11 figures

Active-particle suspensions exhibit distinct polarization-density patterns in activity landscapes, even without anisotropic particle interactions. Such polarization without alignment forces is at work in motility-induced phase separation and betrays intrinsic microscopic activity to mesoscale observers. Using stable long-term confinement of a single hot microswimmer in a dedicated force-free particle trap, we examine the polarized interfacial layer at a motility step and confirm that it does not exert pressure onto the bulk. Our observations are quantitatively explained by an analytical theory that can also guide the analysis of more complex geometries and many-body effects., Comment: 5 pages, 3 figures

The Jarzynski equality relates the free energy difference between two equilibrium states to the fluctuating irreversible work afforded to switch between them. The prescribed fixed temperature for the equilibrium states implicitly constrains the dissipative switching process that can take the system far from equilibrium. Here, we demonstrate theoretically and experimentally that such a relation also holds for the nonisothermal case, where the initial stationary state is not in equilibrium and the switching is effected by dynamically changing temperature gradients instead of a conservative force. Our demonstration employs a single colloidal particle trapped by optically induced thermophoretic drift currents. It relies on identifying suitable equivalents of classical work and heat and our ability to measure their distributions and express them in terms of a virtual potential.

The influence of microscopic force fields on the motion of Brownian particles plays a fundamental role in a broad range of fields, including soft matter, biophysics, and active matter. Often, the experimental calibration of these force fields relies on the analysis of the trajectories of these Brownian particles. However, such an analysis is not always straightforward, especially if the underlying force fields are non-conservative or time-varying, driving the system out of thermodynamic equilibrium. Here, we introduce a toolbox to calibrate microscopic force fields by analyzing the trajectories of a Brownian particle using machine learning, namely recurrent neural networks. We demonstrate that this machine-learning approach outperforms standard methods when characterizing the force fields generated by harmonic potentials if the available data are limited. More importantly, it provides a tool to calibrate force fields in situations for which there are no standard methods, such as non-conservative and time-varying force fields. In order to make this method readily available for other users, we provide a Python software package named DeepCalib, which can be easily personalized and optimized for specific applications., Comment: 11 Pages, 6 figures

We present an adapted single-shot convolutional neural network (YOLOv2) for the real-time localization and classification of particles in optical microscopy. As compared to previous works, we focus on the real-time detection capabilities of the system to allow for manipulation of microscopic objects in large heterogeneous ensembles with the help of feedback control. The network is capable of localizing and classifying several hundreds of microscopic objects even at very low signal-to-noise ratios for images as large as 416x416 pixels with an inference time of about 10 ms. We demonstrate the real-time detection performance by manipulating active particles propelled by laser-induced self-thermophoresis. In order to make our framework readily available for others, we provide all scripts and source code. The network is implemented in Python/Keras using the TensorFlow backend. A C library supporting GPUs is provided for the real-time inference.

Activity and autonomous motion are fundamental in living and engineering systems. This has stimulated the new field of active matter in recent years, which focuses on the physical aspects of propulsion mechanisms, and on motility-induced emergent collective behavior of a larger number of identical agents. The scale of agents ranges from nanomotors and microswimmers, to cells, fish, birds, and people. Inspired by biological microswimmers, various designs of autonomous synthetic nano- and micromachines have been proposed. Such machines provide the basis for multifunctional, highly responsive, intelligent (artificial) active materials, which exhibit emergent behavior and the ability to perform tasks in response to external stimuli. A major challenge for understanding and designing active matter is their inherent nonequilibrium nature due to persistent energy consumption, which invalidates equilibrium concepts such as free energy, detailed balance, and time-reversal symmetry. Unraveling, predicting, and controlling the behavior of active matter is a truly interdisciplinary endeavor at the interface of biology, chemistry, ecology, engineering, mathematics, and physics. The vast complexity of phenomena and mechanisms involved in the self-organization and dynamics of motile active matter comprises a major challenge. Hence, to advance, and eventually reach a comprehensive understanding, this important research area requires a concerted, synergetic approach of the various disciplines.

Hot microswimmers are self-propelled Brownian particles that exploit local heating for their directed self-thermophoretic motion. We provide a pedagogical overview of the key physical mechanisms underlying this promising new technology. It covers the hydrodynamics of swimming, thermophoresis and -osmosis, hot Brownian motion, force-free steering, and dedicated experimental and simulation tools to analyze hot Brownian swimmers.

The behavior of living systems is based on the experience they gained through their interactions with the environment [1]. This experience is stored in the complex biochemical networks of cells and organisms to provide a relationship between a sensed situation and what to do in this situation [2-4]. An implementation of such processes in artificial systems has been achieved through different machine learning algorithms [5, 6]. However, for microscopic systems such as artificial microswimmers which mimic propulsion as one of the basic functionalities of living systems [7, 8] such adaptive behavior and learning processes have not been implemented so far. Here we introduce machine learning algorithms to the motion of artificial microswimmers with a hybrid approach. We employ self-thermophoretic artificial microswimmers in a real world environment [9, 10] which are controlled by a real-time microscopy system to introduce reinforcement learning [11-13]. We demonstrate the solution of a standard problem of reinforcement learning - the navigation in a grid world. Due to the size of the microswimmer, noise introduced by Brownian motion if found to contribute considerably to both the learning process and the actions within a learned behavior. We extend the learning process to multiple swimmers and sharing of information. Our work represents a first step towards the integration of learning strategies into microsystems and provides a platform for the study of the emergence of adaptive and collective behavior.

Self-organization is the generation of order out of local interactions in non-equilibrium [1]. It is deeply connected to all fields of science from physics, chemistry to biology where functional living structures self-assemble[2] and constantly evolve[3] all based on physical interactions. The emergence of collective animal behavior[4], of society or language are the results of self-organization processes as well though they involve abstract interactions arising from sensory inputs, information processing, storage and feedback[5-7]. Resulting collective behaviors are found for example in crowds of people, flocks of birds, schools of fish or swarms of bacteria[8,9]. Here we introduce such information based interactions to the behavior of active microparticles. A real time feedback of active particle positions controls the propulsion direction these active particles. The emerging structures are bound by dissipation and reveal frustrated geometries due to confinement to two dimensions. They diffuse like passive clusters of colloids, but possess internal dynamical degrees of freedom that are determined by the feed- back and the noise in the system. As the information processing in the feedback loops can be designed almost arbitrarily, new perspectives for self-organization studies involving coupled feedback systems with separate timescales, machine learning and swarm intelligence arise., Comment: 13 pages, 4 figures

By converting energy into mechanical work, engines play a central role in most biological and technological processes. In particular, within the current trend towards the development of nanoscience and nanotechnology, microscopic engines have been attracting an ever-increasing interest. On the one hand, there has been a quest to understand how biological molecular motors work. On the other hand, several approaches have been proposed to realize artificial microscopic engines, which have been powered by the transfer of light momentum, by external magnetic fields, by in situ chemical reactions, or by the energy flow between hot and cold heat reservoirs, in scaled-down versions of macroscopic heat engines. Here, we experimentally demonstrate a microscopic engine powered by the local reversible demixing of a critical mixture. We show that, when an absorbing microsphere is optically trapped by a focused laser beam in a sub-critical mixture, it is set into rotation around the optical axis of the beam because of the emergence of diffusiophoretic propulsion; this behavior can be controlled by adjusting the optical power, the temperature, and the criticality of the mixture. Given its simplicity, this microscopic engine provides a powerful tool to power micro- and nanodevices. Furthermore, since many biological systems are tuned near criticality, this mechanism might already be at work within living organisms, for example in proteins and in cellular membranes., Comment: 9 pages, 6 figures

Symmetries constrain dynamics. We test this fundamental physical principle, experimentally and by molecular dynamics simulations, for a hot Janus swimmer operating far from thermal equilibrium. Our results establish scalar and vectorial steady-state fluctuation theorems and a thermodynamic uncertainty relation that link the fluctuating particle current to its entropy production at an effective temperature. A Markovian minimal model elucidates the underlying non-equilbrium physics., Comment: 5 pages, 3 figures

In this article we explore the dynamics of a Brownian particle in a feedback-free dynamic thermophoretic trap. The trap contains a focused laser beam heating a circular gold structure locally and creating a repulsive thermal potential for a Brownian particle. In order to confine a particle the heating beam is steered along the circumference of the gold structure leading to a non-trivial motion of the particle. We theoretically find a stability condition by switching to a rotating frame, where the laser beam is at rest. Particle trajectories and stable points are calculated as a function of the laser rotations frequency and are experimentally confirmed. Additionally, the effect of Brownian motion is considered. The present study complements the dynamic thermophoretic trapping with a theoretical basis and will enhance the applicability in micro- and nanofluidic devices., Comment: 7 pages, 6 figures

We report on the first micro-scale observation of the velocity field imposed by a non-uniform heat content along the solid/liquid boundary. We determine both radial and vertical velocity components of this thermo-osmotic flow field by tracking single tracer nanoparticles. The measured flow profiles are compared to an approximate analytical theory and to numerical calculations. From the measured slip velocity we deduce the thermo-osmotic coefficient for both bare glass and Pluronic F-127 covered surfaces. The value for Pluronic F-127 agrees well with Soret data for polyethylene glycol, whereas that for glass differs from literature values and indicates the complex boundary layer thermodynamics of glass-water interfaces., Comment: 12 pages, 4 figures

The literature on the theory of the photothermal imaging of single nano objects is reviewed. Several models have been devised to describe the signals magnitude, phase and shape in dependence on the experimental and sample parameters (particle position and optical properties, laser beams and their offset, modulation frequency, (thermo-)refractive coefficients, thermal constants). The benefits and limitations of these models are summarized allowing the proper choice of a framework for future investigations using photothermal microscopy of single absorbers.

The transmission characteristics of a spherical (possibly multilayered) particle of arbitrary size under focused illumination are discussed within the generalized Lorenz-Mie theory. Expressions generalizing the total extinction and scattering cross-sections to their fractional counterparts are presented which allow for a convenient modeling of transmission signals, both on-axis and off-axis. The strong dependence of the signal on the collection angle and the complex polarizability are readily included in this minimal, yet accurate model. The precise signature of the energy redistribution and absorption are found for particles of arbitrary complex-valued polarizability. For perfect dielectrics, a transition from sensitive extinction to insensitive scattering signals is observed and quantified for apertures including angles larger than twice the beam's angle of divergence. Implications for positioning, temperature control, spectroscopy and optimized extinction measurements are discussed., Comment: 15 pages, 9 figures

Using Fermat's least optical path principle the family of ray-trajectories through a special but common type of a gradient refractive index lens, n(r)=n_0+\Delta n R/r, is solved analytically. The solution, i.e. the ray-equation r(phi), is shown to be closely related to the famous Rutherford scattering and therefore termed photonic Rutherford scattering. It is shown that not only do these classical limits correspond, but also the wave-mechanical pictures coincide: The time-independent Schr\"odingier equation and the inhomogeneous Helmholz equation permit the same mapping between massive particle scattering and diffracted optical scalar waves. Scattering of narrow wave-packets finally recovers the classical trajectories. The analysis suggests that photothermal single particle microscopy infact measures photonic Rutherford scattering in specific limits., Comment: 14 pages, 12 figures

Photothermal microscopy has recently complemented single molecule fluorescence microscopy by the detection of individual nano-objects in absorption. Photothermal techniques gain their superior sensitivity by exploiting a heat induced refractive index change around the absorbing nano-object. Numerous new applications to nanoparticles, nanorods and even single molecules have been reported all refering to the fact that photothermal microscopy is an extinction measurement on a heat induced refractive index profile. Here, we show that the actual physical mechanism generating a photothermal signal from a single molecule/particle is fundamentally different from the assumed extinction measurement. Combining photothermal microscopy, light scattering microscopy as well as accurate Mie scattering calculations to single gold nanoparticles, we reveal that the detection mechanism is quantitatively explained by a nanolensing effect of the long range refractive index profile. Our results lay the foundation for future developments and quantitative applications of single molecule absorption microscopy., Comment: main manuscript (5 figures), 1 supplement (3 figures)

We derive the generalized Markovian description for the non-equilibrium Brownian motion of a heated particle in a simple solvent with a temperature-dependent viscosity. Our analytical results for the generalized fluctuation-dissipation and Stokes-Einstein relations compare favorably with measurements of laser-heated gold nano-particles and provide a practical rational basis for emerging photothermal technologies., Comment: 10 pages, 5 figures