Dynamical coexistence in moderately polydisperse hard-sphere glasses

We perform extensive numerical simulations of a paradigmatic model glass former, the hard-sphere fluid with 10% polydispersity. We sample from the ensemble of trajectories with fixed observation time, whereby single trajectories are generated by event-driven molecular dynamics. We show that these trajectories can be characterized in terms of the local structure, and we find a dynamical-structural (active-inactive) phase transition between two dynamical phases: one dominated by liquidlike trajectories with a low degree of local order and one dominated by glassylike trajectories with a high degree of local order. We show that both phases coexist and are separated by a spatiotemporal interface…

Three-body correlations and conditional forces in suspensions of active hard disks

Self-propelled Brownian particles show rich out-of-equilibrium physics, for instance, the motility-induced phase separation (MIPS). While decades of studying the structure of liquids have established a deep understanding of passive systems, not much is known about correlations in active suspensions. In this work we derive an approximate analytic theory for three-body correlations and forces in systems of active Brownian disks starting from the many-body Smoluchowski equation. We use our theory to predict the conditional forces that act on a tagged particle and their dependence on the propulsion speed of self-propelled disks. We identify preferred directions of these forces in relation to th…

Modeling non-linear dielectric susceptibilities of supercooled molecular liquids

Advances in high-precision dielectric spectroscopy have enabled access to non-linear susceptibilities of polar molecular liquids. The observed non-monotonic behavior has been claimed to provide strong support for theories of dynamic arrest based on the thermodynamic amorphous order. Here, we approach this question from the perspective of dynamic facilitation, an alternative view focusing on emergent kinetic constraints underlying the dynamic arrest of a liquid approaching its glass transition. We derive explicit expressions for the frequency-dependent higher-order dielectric susceptibilities exhibiting a non-monotonic shape, the height of which increases as temperature is lowered. We demons…

High-order simulation scheme for active particles driven by stress boundary conditions

Abstract We study the dynamics and interactions of elliptic active particles in a two dimensional solvent. The particles are self-propelled through prescribing a fluid stress at one half of the fluid-particle boundary. The fluid is treated explicitly solving the Stokes equation through a discontinuous Galerkin scheme, which allows to simulate strictly incompressible fluids. We present numerical results for a single particle and give an outlook on how to treat suspensions of interacting active particles.

Spontaneous Spatiotemporal Ordering of Shape Oscillations Enhances Cell Migration

The migration of cells is relevant for processes such as morphogenesis, wound healing, and invasion of cancer cells. In order to move, single cells deform cyclically. However, it is not understood how these shape oscillations influence collective properties. Here we demonstrate, using numerical simulations, that the interplay of directed motion, shape oscillations, and excluded volume enables cells to locally "synchronize" their motion and thus enhance collective migration. Our model captures elongation and contraction of crawling ameboid cells controlled by an internal clock with a fixed period, mimicking the internal cycle of biological cells. We show that shape oscillations are crucial f…

Thermodynamic formalism for transport coefficients with an application to the shear modulus and shear viscosity.

We discuss Onsager's thermodynamic formalism for transport coefficients and apply it to the calculation of the shear modulus and shear viscosity of a monodisperse system of repulsive particles. We focus on the concept of extensive "distance" and intensive "field" conjugated via a Fenchel-Legendre transform involving a thermodynamic(-like) potential, which allows to switch ensembles. Employing Brownian dynamics, we calculate both the shear modulus and the shear viscosity from strain fluctuations and show that they agree with direct calculations from strained and non-equilibrium simulations, respectively. We find a dependence of the fluctuations on the coupling strength to the strain reservoi…

Multiscale modelling of structure formation of C$_{60}$ on insulating CaF$_2$ substrates

Morphologies of adsorbed molecular films are of interest in a wide range of applications. To study the epitaxial growth of these systems in computer simulations requires access to long time and length scales, and one typically resorts to kinetic Monte Carlo (KMC) simulations. However, KMC simulations require as input transition rates and their dependence on external parameters (such as temperature). Experimental data allow only limited and indirect access to these rates, and models are often oversimplified. Here, we follow a bottom-up approach and aim at systematically constructing all relevant rates for an example system that has shown interesting properties in experiments, buckminsterfull…

Modeling Supramolecular Polymerization: The Role of Steric Effects and Hydrophobic Interactions

We present a combined experimental–simulation study of self-assembly into one-dimensional filaments. Experimentally, we study amphiphilic AuI-metallopeptides in neutral aqueous media. Our model foc...

Dynamics of Binary Active Clusters Driven by Ion-Exchange Particles

We present a framework to quantitatively predict the linear and rotational directed motion of synthetic modular microswimmers. To this end, we study binary dimers and characterize their approach motion as effective interactions within a minimal model. We apply this framework to the assembly of small aggregates composed of a cationic ion-exchange particle with up to five passive particles or anionic ion-exchange particles at dilute conditions. Particles sediment and move close to a substrate, above which the ion-exchange particles generate flow. This flow mediates long-range attractions leading to a slow collapse during which long-lived clusters of a few particles assemble. The effective int…

Gold Nanorods as Plasmonic Sensors for Particle Diffusion.

Plasmonic gold nanoparticles are normally used as sensor to detect analytes permanently bound to their surface. If the interaction between the analyte and the nanosensor surface is negligible, it only diffuses through the sensor’s sensing volume, causing a small temporal shift of the plasmon resonance position. By using a very sensitive and fast detection scheme, we are able to detect these small fluctuations in the plasmon resonance. With the help of a theoretical model consistent with our detection geometry, we determine the analyte’s diffusion coefficient. The method is verified by observing the trends upon changing diffusor size and medium viscosity, and the diffusion coefficients obtai…

Dynamical phase transitions and their relation to structural and thermodynamic aspects of glass physics.

We review recent developments in structural–dynamical phase transitions in trajectory space based on dynamic facilitation theory. An open question is how the dynamic facilitation perspective on the glass transition may be reconciled with thermodynamic theories that posit collective reorganization accompanied by a growing static length scale and, eventually, a vanishing configurational entropy. In contrast, dynamic facilitation theory invokes a dynamical phase transition between an active phase (close to the normal liquid) and an inactive phase, which is glassy and whose order parameter is either a time-averaged dynamic or structural quantity. In particular, the dynamical phase transition in…

Self-Assembly of Colloidal Molecules due to Self-Generated Flow.

The emergence of structure through aggregation is a fascinating topic and of both fundamental and practical interest. Here we demonstrate that self-generated solvent flow can be used to generate long-range attractions on the colloidal scale, with subpiconewton forces extending into the millimeter range. We observe a rich dynamic behavior with the formation and fusion of small clusters resembling molecules. The dynamics of this assembly is governed by an effective conservative energy that for large separations r decays as 1/r. Breaking the flow symmetry, these clusters can be made active.

New Insights into the Functional Morphology of the Lever Mechanism of Salvia pratensis (Lamiaceae)

† Background and Aims The functional morphology of Salvia pratensis flowers was re-investigated, after new insights revealed that pollen dispensing is one of the main functions of the staminal lever. In particular, no detailed information was available regarding the process of pollen transfer and the forces arising between the pollen-bearing thecae and the pollinating bee’s body. The assumption was made that these forces play a significant role in pollen dispensing. † Methods The functional morphology of S. pratensis flowers and the interaction between flowers and bees (Apis mellifera) were studied by reconstructing stress and strains by using qualitative and semi-quantitative theoretical a…

Preface: Special Issue on Structure in Glassy and Jammed Systems

This special issue presents new developments in our understanding of the role of structure in dynamical arrest and jamming. Articles highlight local geometric motifs and other forms of amorphous order, in experiment, computer simulation and theory.

Dynamical mean-field theory and weakly non-linear analysis for the phase separation of active Brownian particles

Recently, we have derived an effective Cahn-Hilliard equation for the phase separation dynamics of active Brownian particles by performing a weakly non-linear analysis of the effective hydrodynamic equations for density and polarization [Speck et al., Phys. Rev. Lett. 112, 218304 (2014)]. Here, we develop and explore this strategy in more detail and show explicitly how to get to such a large-scale, mean-field description starting from the microscopic dynamics. The effective free energy emerging from this approach has the form of a conventional Ginzburg-Landau function. On the coarsest scale, our results thus agree with the mapping of active phase separation onto that of passive fluids with …

Polydisperse hard spheres: crystallization kinetics in small systems and role of local structure

We study numerically the crystallization of a hard-sphere mixture with 8\% polydispersity. Although often used as a model glass former, for small system sizes we observe crystallization in molecular dynamics simulations. This opens the possibility to study the competition between crystallization and structural relaxation of the melt, which typically is out of reach due to the disparate timescales. We quantify the dependence of relaxation and crystallization times on density and system size. For one density and system size we perform a detailed committor analysis to investigate the suitability of local structures as order parameters to describe the crystallization process. We find that local…

Vorticity Determines the Force on Bodies Immersed in Active Fluids

When immersed into a fluid of active Brownian particles, passive bodies might start to undergo linear or angular directed motion depending on their shape. Here we exploit the divergence theorem to relate the forces responsible for this motion to the density and current induced by--but far away from--the body. In general, the force is composed of two contributions: due to the strength of the dipolar field component and due to particles leaving the boundary, generating a non-vanishing vorticity of the polarization. We derive and numerically corroborate results for periodic systems, which are fundamentally different from unbounded systems with forces that scale with the area of the system. We …

Non-equilibrium Markov state modeling of periodically driven biomolecules

Molecular dynamics simulations allow to study the structure and dynamics of single biomolecules in microscopic detail. However, many processes occur on time scales beyond the reach of fully atomistic simulations and require coarse-grained multiscale models. While systematic approaches to construct such models have become available, these typically rely on microscopic dynamics that obey detailed balance. In vivo, however, biomolecules are constantly driven away from equilibrium in order to perform specific functions and thus break detailed balance. Here we introduce a method to construct Markov state models for systems that are driven through periodically changing one (or several) external p…

Thermodynamic formalism and linear response theory for non-equilibrium steady states

We study the linear response in systems driven away from thermal equilibrium into a nonequilibrium steady state with nonvanishing entropy production rate. A simple derivation of a general response formula is presented under the condition that the generating function describes a transformation that (to lowest order) preserves normalization and thus describes a physical stochastic process. For Markov processes we explicitly construct the conjugate quantities and discuss their relation with known response formulas. Emphasis is put on the formal analogy with thermodynamic potentials and some consequences are discussed.

Ideal bulk pressure of active Brownian particles

The extent to which active matter might be described by effective equilibrium concepts like temperature and pressure is currently being discussed intensely. Here, we study the simplest model, an ideal gas of noninteracting active Brownian particles. While the mechanical pressure exerted onto confining walls has been linked to correlations between particles' positions and their orientations, we show that these correlations are entirely controlled by boundary effects. We also consider a definition of local pressure, which describes interparticle forces in terms of momentum exchange between different regions of the system. We present three pieces of analytical evidence which indicate that such…

From scalar to polar active matter: Connecting simulations with mean-field theory

We study numerically the phase behavior of self-propelled elliptical particles interacting through the ``hard'' repulsive Gay-Berne potential at infinite P\'eclet number. Changing a single parameter, the aspect ratio, allows us to continuously go from discoid active Brownian particles to elongated polar rods. Discoids show phase separation, which changes to a cluster state of polar domains, which then form polar bands as the aspect ratio is increased. From the simulations, we identify and extract the two effective parameters entering the mean-field description: the force imbalance coefficient and the effective coupling to the local polarization. These two coefficients are sufficient to obta…

Collective forces in scalar active matter.

Large-scale collective behavior in suspensions of many particles can be understood from the balance of statistical forces emerging beyond the direct microscopic particle interactions. Here we review some aspects of the collective forces that can arise in suspensions of self-propelled active Brownian particles: wall forces under confinement, interfacial forces, and forces on immersed bodies mediated by the suspension. Even for non-aligning active particles, these forces are intimately related to a non-uniform polarization of particle orientations induced by walls and bodies, or inhomogeneous density profiles. We conclude by pointing out future directions and promising areas for the applicati…

Hunting active Brownian particles: Learning optimal behavior

We numerically study active Brownian particles that can respond to environmental cues through a small set of actions (switching their motility and turning left or right with respect to some direction) which are motivated by recent experiments with colloidal self-propelled Janus particles. We employ reinforcement learning to find optimal mappings between the state of particles and these actions. Specifically, we first consider a predator-prey situation in which prey particles try to avoid a predator. Using as reward the squared distance from the predator, we discuss the merits of three state-action sets and show that turning away from the predator is the most successful strategy. We then rem…

Critical behavior of active Brownian particles

We study active Brownian particles as a paradigm for a genuine nonequilibrium phase transition requiring steady driving. Access to the critical point in computer simulations is obstructed by the fact that the density is conserved. We propose a method based on arguments from finite-size scaling to determine critical points and successfully test it for the two-dimensional (2D) Ising model. Using this method allows us to accurately determine the critical point of two-dimensional active Brownian particles at ${\mathrm{Pe}}_{\text{cr}}=40(2), {\ensuremath{\phi}}_{\text{cr}}=0.597(3)$. Based on this estimate, we study the corresponding critical exponents $\ensuremath{\beta}, \ensuremath{\gamma}/\…

Effective Cahn-Hilliard Equation for the Phase Separation of Active Brownian Particles

The kinetic separation of repulsive active Brownian particles into a dense and a dilute phase is analyzed using a systematic coarse-graining strategy. We derive an effective Cahn-Hilliard equation on large length and time scales, which implies that the separation process can be mapped onto that of passive particles. A lower density threshold for clustering is found, and using our approach we demonstrate that clustering first proceeds via a hysteretic nucleation scenario and above a higher threshold changes into a spinodal-like instability. Our results are in agreement with particle-resolved computer simulations and can be verified in experiments of artificial or biological microswimmers.

Estimation of the critical behavior in an active colloidal system with Vicsek-like interactions

We study numerically the critical behavior of a modified, active Asakura-Oosawa model for colloid-polymer mixtures. The colloids are modeled as self-propelled particles with Vicsek-like interactions. This system undergoes phase separation between a colloid-rich and a polymer-rich phase, whereby the phase diagram depends on the strength of the Vicsek-like interactions. Employing a subsystem-block-density distribution analysis, we determine the critical point and make an attempt to estimate the critical exponents. In contrast to the passive model, we find that the critical point is not located on the rectilinear diameter. A first estimate of the critical exponents $\beta$ and $\nu$ is consist…

Unfolding dynamics of small peptides biased by constant mechanical forces

We show how multi-ensemble Markov state models can be combined with constant-force equilibrium simulations. Besides obtaining the unfolding/folding rates, Markov state models allow gaining detailed insights into the folding dynamics and pathways through identifying folding intermediates and misfolded structures. For two specific peptides, we demonstrate that the end-to-end distance is an insufficient reaction coordinate. This problem is alleviated through constructing models with multiple collective variables, for which we employ the time-lagged independent component analysis requiring only minimal prior knowledge. Our results show that combining Markov state models with constant-force simu…

Finite-size scaling of charge carrier mobility in disordered organic semiconductors

Simulations of charge transport in amorphous semiconductors are often performed in microscopically sized systems. As a result, charge carrier mobilities become system-size dependent. We propose a simple method for extrapolating a macroscopic, nondispersive mobility from the system-size dependence of a microscopic one. The method is validated against a temperature-based extrapolation [A. Lukyanov and D. Andrienko, Phys. Rev. B 82, 193202 (2010)]. In addition, we provide an analytic estimate of system sizes required to perform nondispersive charge transport simulations in systems with finite charge carrier density, derived from a truncated Gaussian distribution. This estimate is not limited t…

Stochastic thermodynamics for active matter

The theoretical understanding of active matter, which is driven out of equilibrium by directed motion, is still fragmental and model oriented. Stochastic thermodynamics, on the other hand, is a comprehensive theoretical framework for driven systems that allows to define fluctuating work and heat. We apply these definitions to active matter, assuming that dissipation can be modelled by effective non-conservative forces. We show that, through the work, conjugate extensive and intensive observables can be defined even in non-equilibrium steady states lacking a free energy. As an illustration, we derive the expressions for the pressure and interfacial tension of active Brownian particles. The l…

Coexistence of active Brownian disks: van der Waals theory and analytical results

At thermal equilibrium, intensive quantities like temperature and pressure have to be uniform throughout the system, restricting inhomogeneous systems composed of different phases. The paradigmatic example is the coexistence of vapor and liquid, a state that can also be observed for active Brownian particles steadily driven away from equilibrium. Recently, a strategy has been proposed that allows to predict phase equilibria of active particles [Solon et al., Phys. Rev. E 97, 020602(R) (2018)2470-004510.1103/PhysRevE.97.020602]. Here we elaborate on this strategy and formulate it in the framework of a van der Waals theory for active disks. For a given equation of state, we derive the effecti…

Back Cover: Mobilization upon Cooling (Angew. Chem. Int. Ed. 35/2021)

Mobilization upon Cooling

Abstract Phase transitions between different aggregate states are omnipresent in nature and technology. Conventionally, a crystalline phase melts upon heating as we use ice to cool a drink. Already in 1903, Gustav Tammann speculated about the opposite process, namely melting upon cooling. So far, evidence for such “inverse” transitions in real materials is rare and limited to few systems or extreme conditions. Here, we demonstrate an inverse phase transition for molecules adsorbed on a surface. Molybdenum tetraacetate on copper(111) forms an ordered structure at room temperature, which dissolves upon cooling. This transition is mediated by molecules becoming mobile, i.e., by mobilization up…

Non-Equilibrium Markov State Modeling of the Globule-Stretch Transition

We describe a systematic approach to construct coarse-grained Markov state models from molecular dynamics data of systems driven into a nonequilibrium steady state. We apply this method to study the globule-stretch transition of a single tethered model polymer in shear flow. The folding and unfolding rates of the coarse-grained model agree with the original detailed model. We demonstrate that the folding and unfolding proceeds through the same narrow region of configuration space but along different cycles.

Devitrification of the Kob-Andersen glass former: Competition with the locally favored structure

Abstract Supercooled liquids are kinetically trapped materials in which the transition to a thermodynamically more stable state with long-range order is strongly suppressed. To assess the glass-forming abilities of a liquid empirical rules exist, but a comprehensive microscopic picture of devitrification is still missing. Here we study the crystallization of a popular model glass former, the binary Kob-Andersen mixture, in small systems. We perform trajectory sampling employing the population of the locally favored structure as order parameter. While for large population a dynamical phase transition has been reported, here we show that biasing towards a small population of locally favored s…

Collective behavior of quorum-sensing run-and-tumble particles in confinement

We study a generic model for quorum-sensing bacteria in circular confinement. Every bacterium produces signaling molecules, the local concentration of which triggers a response when a certain threshold is reached. If this response lowers the motility then an aggregation of bacteria occurs, which differs fundamentally from standard motility-induced phase separation due to the long-ranged nature of the concentration of signal molecules. We analyze this phenomenon analytically and by numerical simulations employing two different protocols leading to stationary cluster and ring morphologies, respectively.

Publisher's Note: "Thermodynamic formalism for transport coefficients with an application to the shear modulus and shear viscosity" [J. Chem. Phys. 146, 124130 (2017)].

Self-organization of active particles by quorum sensing rules

Many microorganisms regulate their behaviour according to the density of neighbours. Such quorum sensing is important for the communication and organisation within bacterial populations. In contrast to living systems, where quorum sensing is determined by biochemical processes, the behaviour of synthetic active particles can be controlled by external fields. Accordingly they allow to investigate how variations of a density-dependent particle response affect their self-organisation. Here we experimentally and numerically demonstrate this concept using a suspension of light-activated active particles whose motility is individually controlled by an external feedback-loop, realised by a particl…

The role of shear in crystallization kinetics: From suppression to enhancement

In many technical applications, but also in natural processes like ice nucleation in clouds, crystallization proceeds in the presence of stresses and flows, hence the importance to understand the crystallization mechanism in simple situations. We employ molecular dynamics simulations to study the crystallization kinetics of a nearly hard sphere liquid that is weakly sheared. We demonstrate that shear flow both enhances and suppresses the crystallization kinetics of hard spheres. The effect of shear depends on the quiescent mechanism: suppression in the activated regime and enhancement in the diffusion-limited regime for small strain rates. At higher strain rates crystallization again become…

Aggregation and sedimentation of active Brownian particles at constant affinity.

We study the motility-induced phase separation of active particles driven through the interconversion of two chemical species controlled by ideal reservoirs (chemiostats). As a consequence, the propulsion speed is non-constant and depends on the actual inter-particle forces, enhancing the positive feedback between increased density and reduced motility that is responsible for the observed inhomogeneous density. For hard discs, we find that this effect is negligible and that the phase separation is controlled by the average propulsion speed. For soft particles and large propulsion speeds, however, we predict an observable impact on the collective behavior. We briefly comment on the reentrant…

Nucleation pathway and kinetics of phase-separating active Brownian particles

Suspensions of purely repulsive but self-propelled Brownian particles might undergo phase separation, a phenomenon that strongly resembles the phase separation of passive particles with attractions. Here we employ computer simulations to study the nucleation kinetics and the microscopic pathway active Brownian disks take in two dimensions when quenched from the homogeneous suspension to propulsion speeds beyond the binodal. We find the same qualitative behavior for the nucleation rate as a function of density as for a passive suspension undergoing liquid-vapor separation, suggesting that the scenario of an effective free energy also extends to the kinetics of phase separation. We study the …

Coupling between criticality and gelation in "sticky" spheres: a structural analysis.

We combine experiments and simulations to study the link between criticality and gelation in sticky spheres. We employ confocal microscopy to image colloid-polymer mixtures and Monte Carlo simulations of the square-well (SW) potential as a reference model. To this end, we map our experimental samples onto the SW model. We find an excellent structural agreement between experiments and simulations, both for locally favored structures at the single particle level and large-scale fluctuations at criticality. We follow in detail the rapid structural change in the critical fluid when approaching the gas-liquid binodal and highlight the role of critical density fluctuations for this structural cro…

Modeling of biomolecular machines in non-equilibrium steady states

Numerical computations have become a pillar of all modern quantitative sciences. Any computation involves modeling--even if often this step is not made explicit--and any model has to neglect details while still being physically accurate. Equilibrium statistical mechanics guides both the development of models and numerical methods for dynamics obeying detailed balance. For systems driven away from thermal equilibrium such a universal theoretical framework is missing. For a restricted class of driven systems governed by Markov dynamics and local detailed balance, stochastic thermodynamics has evolved to fill this gap and to provide fundamental constraints and guiding principles. The next step…

Von geordneten zu mobilen Molekülen durch Kühlen

Phasenübergänge zwischen unterschiedlichen Aggregatzuständen sind in Natur und Technik allgegenwärtig. Üblicherweise schmilzt ein Kristall, wenn er erwärmt wird. Daher nutzen wir Eis, um einen Drink zu kühlen. Bereits im Jahre 1903 spekulierte Gustav Tammann über den umgekehrten Prozess des Schmelzens durch Kühlen. Bisher gibt es allerdings nur sehr wenige Beispiele für solche “inversen” Phasenübergänge, die meist auch auf extreme Bedingungen beschränkt sind. Hier zeigen wir einen inversen Phasenübergang von adsorbierten Molekülen auf einer Oberfläche. Molybdänacetat bildet bei Zimmertemperatur eine geordnete Struktur auf der (111)-Oberfläche von Kupfer, die sich beim Kühlen auflöst. Dieser…

Tip-induced mobilization upon cooling of Ni monolayers on Re(0001)

Usually, cooling a metal sample down to cryogenic temperatures leads to immobilization of the surface atoms. In this study, we demonstrate a movement of Ni adatoms at $4.6\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ on Ni films grown on a Re(0001) single crystal, while the surface is rigid at room temperature. The mobility is observed from 2 to 20 atomic-layer-thick films. Measurements at intermediate temperatures reveal an increasing mobility with decreasing temperature. The observed velocity of advancing steps is consistent with a model considering a sudden release of material, eventually triggered by the tip, followed by free diffusion. According to the model, an increasing length scale for t…

Crystallization of hard spheres revisited. I. Extracting kinetics and free energy landscape from forward flux sampling

We investigate the kinetics and the free energy landscape of the crystallization of hard spheres from a supersaturated metastable liquid though direct simulations and forward flux sampling. In this first paper, we describe and test two different ways to reconstruct the free energy barriers from the sampled steady state probability distribution of cluster sizes without sampling the equilibrium distribution. The first method is based on mean first passage times, and the second method is based on splitting probabilities. We verify both methods for a single particle moving in a double-well potential. For the nucleation of hard spheres, these methods allow us to probe a wide range of supersatura…

Active colloidal suspensions: Clustering and phase behavior

We review recent experimental, numerical, and analytical results on active suspensions of self-propelled colloidal beads moving in (quasi) two dimensions. Active colloids form part of the larger theme of active matter, which is noted for the emergence of collective dynamic phenomena away from thermal equilibrium. Both in experiments and computer simulations, a separation into dense aggregates, i.e., clusters, and a dilute gas phase has been reported even when attractive interactions and an alignment mechanism are absent. Here, we describe three experimental setups, discuss the different propelling mechanisms, and summarize the evidence for phase separation. We then compare experimental obse…

The staminal lever mechanism in Salvia L. (Lamiaceae): a key innovation for adaptive radiation?

Abstract Floral key innovations play a significant role in the discussion of adaptive radiation in plants. The paper brings together a brief review of morphological key innovations in plants, elucidating their evolutionary significance in flower–pollinator interactions, and new data on Salvia, a genus being examined as an example for presumed adaptive radiation. We hypothesize that the characteristic staminal lever mechanism functions as a key innovation. It is defined as a functional unit including the modification of stamens to lever-like structures, their reversible movement, and the organization of the remaining floral structures involved in the process of pollen transfer. We follow the…

Focus on Active Colloids and Nanoparticles

Highly controlled optical transport of cold atoms into a hollow-core fiber

We report on an efficient and highly controlled cold atom hollow-core fiber interface, suitable for quantum simulation, information, and sensing. The main focus of this manuscript is a detailed study on transporting cold atoms into the fiber using an optical conveyor belt. We discuss how we can precisely control the spatial, thermal, and temporal distribution of the atoms by, e.g., varying the speed at which the atoms are transported or adjusting the depth of the transport potential according to the atomic position. We characterize the transport of atoms to the fiber tip for these different parameters. In particular, we show that by adapting the transport potential we can lower the temperat…

Rücktitelbild: Von geordneten zu mobilen Molekülen durch Kühlen (Angew. Chem. 35/2021)

Dynamic coarse-graining fills the gap between atomistic simulations and experimental investigations of mechanical unfolding

We present a dynamic coarse-graining technique that allows to simulate the mechanical unfolding of biomolecules or molecular complexes on experimentally relevant time scales. It is based on Markov state models (MSM), which we construct from molecular dynamics simulations using the pulling coordinate as an order parameter. We obtain a sequence of MSMs as a function of the discretized pulling coordinate, and the pulling process is modeled by switching among the MSMs according to the protocol applied to unfold the complex. This way we cover seven orders of magnitude in pulling speed. In the region of rapid pulling we additionally perform steered molecular dynamics simulations and find excellen…

Experimental Evidence for a Structural-Dynamical Transition in Trajectory Space.

Among the key insights into the glass transition has been the identification of a non-equilibrium phase transition in trajectory space which reveals phase coexistence between the normal supercooled liquid (active phase) and a glassy state (inactive phase). Here we present evidence that such a transition occurs in experiment. In colloidal hard spheres we find a non-Gaussian distribution of trajectories leaning towards those rich in locally favoured structures (LFS), associated with the emergence of slow dynamics. This we interpret as evidence for an non-equilibrium transition to an inactive LFS-rich phase. Reweighting trajectories reveals a first-order phase transition in trajectory space be…

Negative Interfacial Tension in Phase-Separated Active Brownian Particles.

We study numerically a model for active suspensions of self-propelled repulsive particles, for which a stable phase separation into a dilute and a dense phase is observed. We exploit the fact that for nonsquare boxes a stable "slab" configuration is reached, in which interfaces align with the shorter box edge. Evaluating a recent proposal for an intensive active swimming pressure, we demonstrate that the excess stress within the interface separating both phases is negative. The occurrence of a negative tension together with stable phase separation is a genuine nonequilibrium effect that is rationalized in terms of a positive stiffness, the estimate of which agrees excellently with the numer…

Vascular bundle modifications in nodes and internodes of climbing Marantaceae

AbstractNodes are interfaces between stems and leaves. Vascular bundles originate here and elongate into leaves and internodes. In Marantaceae, internodal bundles are highly diverse, including inverted bundles in the climbing genus Haumania. The objective of this paper is to characterize bundle forms, their position across the stem and their connection to leaves and short shoots in Haumania spp. and other unrelated African branch-angle climbers in the family (Hypselodelphys, Trachyphrynium). We question whether bundle inversion is a genus-specific trait in Haumania or related to the climbing growth form. Vascular bundles in internodes are scattered across the stem diameter in a characterist…

Thermodynamic Approach to the Self-Diffusiophoresis of Colloidal Janus Particles

Most available theoretical predictions for the self-diffusiophoretic motion of colloidal particles are based on the hydrodynamic thin boundary layer approximation in combination with a solvent body force due to a self-generated local solute gradient. This gradient is enforced through specifying boundary conditions, typically without accounting for the thermodynamic cost to maintain the gradient. Here, we present an alternative thermodynamic approach that exploits a direct link between dynamics and entropy production: the local detailed balance condition. We study two cases: First, we revisit self-propulsion in a demixing binary solvent. At variance with a slip velocity, we find that propuls…

Discontinuous thinning in active microrheology of soft complex matter

Employing theory and numerical simulations, we demonstrate discontinuous force thinning due to the driven motion of an external probe in a host medium. We consider two cases: an ideal structureless medium (modeling ultrasoft materials such as polymer melts) and a dilute bath of interacting repulsive particles. When the driving of the probe exceeds a critical force, the microviscosity of the medium drops abruptly by about an order of magnitude. This phenomenon occurs for strong attractive interactions between a large probe and a sufficiently dense host medium.

Driven Brownian particle as a paradigm for a nonequilibrium heat bath: Effective temperature and cyclic work extraction

We apply the concept of a frequency-dependent effective temperature based on the fluctuation-dissipation ratio to a driven Brownian particle in a nonequilibrium steady state. Using this system as a thermostat for a weakly coupled harmonic oscillator, the oscillator thermalizes according to a canonical distribution at the respective effective temperature across the entire frequency spectrum. By turning the oscillator from a passive "thermometer" into a heat engine, we realize the cyclic extraction of work from a single thermal reservoir, which is feasible only due to its nonequilibrium nature.

Quorum-sensing active particles with discontinuous motility

We develop a dynamic mean-field theory for polar active particles that interact through a self-generated field, in particular one generated through emitting a chemical signal. While being a form of chemotactic response, it is different from conventional chemotaxis in that particles discontinuously change their motility when the local concentration surpasses a threshold. The resulting coupled equations for density and polarization are linear and can be solved analytically for simple geometries, yielding inhomogeneous density profiles. Specifically, here we consider a planar and circular interface. Our theory thus explains the observed coexistence of dense aggregates with an active gas. There…

Employing artificial neural networks to find reaction coordinates and pathways for self-assembly

Capturing the autonomous self-assembly of molecular building blocks in computer simulations is a persistent challenge, requiring to model complex interactions and to access long time scales. Advanced sampling methods allow to bridge these time scales but typically require to construct accurate low-dimensional representations of the transition pathways. In this work, we demonstrate for the self-assembly of two single-stranded DNA fragments into a ring-like structure how autoencoder architectures based on unsupervised neural networks can be employed to reliably expose transition pathways and to provide a suitable low-dimensional representation. The assembly occurs as a two-step process throug…

Crystallization of hard spheres revisited. II. Thermodynamic modeling, nucleation work, and the surface of tension

Combining three numerical methods (forward flux sampling, seeding of droplets, and finite-size droplets), we probe the crystallization of hard spheres over the full range from close to coexistence to the spinodal regime. We show that all three methods allow us to sample different regimes and agree perfectly in the ranges where they overlap. By combining the nucleation work calculated from forward flux sampling of small droplets and the nucleation theorem, we show how to compute the nucleation work spanning three orders of magnitude. Using a variation of the nucleation theorem, we show how to extract the pressure difference between the solid droplet and ambient liquid. Moreover, combining th…

Modeling epitaxial film growth of C$_{60}$ revisited

Epitaxial films evolve on time and length scales that are inaccessible to atomistic computer simulation methods like molecular dynamics (MD). To numerically predict properties for such systems, a common strategy is to employ kinetic Monte Carlo simulations, for which one needs to know the transition rates of the involved elementary steps. The main challenge is thus to formulate a consistent model for the set of transition rates and to determine its parameters. Here, we revisit a well-studied model system, the epitaxial film growth of the fullerene ${\mathrm{C}}_{60}$ on an ordered ${\mathrm{C}}_{60}$ substrate (111). We implement a systematic multiscale approach in which we determine transi…

Classical nucleation theory for the crystallization kinetics in sheared liquids

While statistical mechanics provides a comprehensive framework for the understanding of equilibrium phase behavior, predicting the kinetics of phase transformations remains a challenge. Classical nucleation theory (CNT) provides a thermodynamic framework to relate the nucleation rate to thermodynamic quantities such as pressure difference and interfacial tension through the nucleation work necessary to spawn critical nuclei. However, it remains unclear whether such an approach can be extended to the crystallization of driven melts that are subjected to mechanical stresses and flows. Here, we demonstrate numerically for hard spheres that the impact of simple shear on the crystallization rate…

Meta-work and the analogous Jarzynski relation in ensembles of dynamical trajectories

Recently there has been growing interest in extending the thermodynamic method from static configurations to dynamical trajectories. In this approach, ensembles of trajectories are treated in an analogous manner to ensembles of configurations in equilibrium statistical mechanics: generating functions of dynamical observables are interpreted as partition sums, and the statistical properties of trajectory ensembles are encoded in free-energy functions that can be obtained through large-deviation methods in a suitable large time limit. This establishes what one can call a 'thermodynamics of trajectories'. In this paper we go a step further, and make a first connection to fluctuation theorems b…

Transmission of torque at the nanoscale

In macroscopic mechanical devices torque is transmitted through gearwheels and clutches. In the construction of devices at the nanoscale, torque and its transmission through soft materials will be a key component. However, this regime is dominated by thermal fluctuations leading to dissipation. Here we demonstrate the principle of torque transmission for a disc-like colloidal assembly exhibiting clutch-like behaviour, driven by $27$ particles in optical traps. These are translated on a circular path to form a rotating boundary that transmits torque to additional particles confined to the interior. We investigate this transmission and find that it is determined by solid-like or fluid-like be…

Nonequilibrium depletion interactions in active microrheology.

Entropic depletion forces arise between mesoscopic bodies that are immersed in a suspension of macromolecules, such as colloid-polymer mixtures. Here we consider the case of a driven colloidal probe in the presence of another, passive colloidal particle, both solvated in an ideal bath of small spherical particles. We calculate the nonequilibrium forces mediated by the depletants on the two colloidal particles within a dynamical superposition approximation (DSA) scheme. In order to assess the quality of this approximation, and to obtain the colloidal microstructure around the driven probe, we corroborate our theoretical results with Brownian dynamics simulations.