Dynamics of a homogeneous active dumbbell system

Collective dynamics of active dumbbells near a circular obstacle

In this article, we present the collective dynamics of active dumbbells in the presence of a static circular obstacle using Brownian dynamics simulation. The active dumbbells aggregate on the surface of a circular obstacle beyond a critical radius. The aggregation is non-uniform along the circumference, and the aggregate size increases with the activity (Pe) and the curvature radius (Ro). The dense aggregate of active dumbbells displays persistent rotational motion with a certain angular speed, which linearly increases with activity. Furthermore, we show a strong polar ordering of the active dumbbells within the aggregate. The polar ordering exhibits long-range correlation, with the correlation length corresponding to the aggregate size. Additionally, we show that the residence time of an active dumbbell on the obstacle surface increases rapidly with area fraction due to many-body interactions that lead to a slowdown of the rotational diffusion. This article further considers the dynamical behavior of a tracer particle in the solution of active dumbbells. Interestingly, the speed of the passive tracer particle displays a crossover from monotonically decreasing to increasing with the size of the tracer particle upon increasing the dumbbells' speed. Furthermore, the effective diffusion of the tracer particle displays non-monotonic behavior with the area fraction; the initial increase in diffusivity is followed by a decrease for a larger area fraction.

Phase separation kinetics and cluster dynamics in two-dimensional active dumbbell systems

Molecular dynamics simulations were employed to investigate the phase separation process of a two-dimensional active Brownian dumbbell model. We evaluated the time dependence of the typical size of the dense component using the scaling properties of the structure factor, along with the averaged number of clusters and their radii of gyration. The growth observed is faster than in active disk models, and this effect is further enhanced under stronger activity. Next, we focused on studying the hexatic order of the clusters. The length associated with the orientational order increases algebraically with time and faster than for spherical active Brownian particles. Under weak active forces, most clusters exhibit a uniform internal orientational order. However, under strong forces, large clusters consist of domains with different orientational orders. We demonstrated that the latter configurations are not stable, and given sufficient time to evolve, they eventually achieve homogeneous configurations as well. No gas bubbles are formed within the clusters, even when there are patches of different hexatic order. Finally, attention was directed towards the geometry and motion of the clusters themselves. By employing a tracking algorithm, we showed that clusters smaller than the typical size at the observation time exhibit regular shapes, while larger ones display fractal characteristics. In between collisions or break-ups, the clusters behave as solid bodies. Their centers of mass undergo circular motion, with radii increasing with the cluster size. The angular velocity of the center of mass equals that of the constituents with respect to their center of mass. These observations were rationalised with a simple mechanical model.

Fluctuation Theorems for Heat Exchanges between Passive and Active Baths

In addition to providing general constraints on probability distributions, fluctuation theorems allow us to infer essential information on the role played by temperature in heat exchange phenomena. In this numerical study, we measure the temperature of an out-of-equilibrium active bath using a fluctuation theorem that relates the fluctuations in the heat exchanged between two baths to their temperatures. Our setup consists of a single particle moving between two wells of a quartic potential accommodating two different baths. The heat exchanged between the two baths is monitored according to two definitions: as the kinetic energy carried by the particle whenever it jumps from one well to the other and as the work performed by the particle on one of the two baths when immersed in it. First, we consider two equilibrium baths at two different temperatures and verify that a fluctuation theorem featuring the baths temperatures holds for both heat definitions. Then, we introduce an additional Gaussian coloured noise in one of the baths, so as to make it effectively an active (out-of-equilibrium) bath. We find that a fluctuation theorem is still satisfied with both heat definitions. Interestingly, in this case the temperature obtained through the fluctuation theorem for the active bath corresponds to the kinetic temperature when considering the first heat definition, while it is larger with the second one. We interpret these results by looking at the particle jump phenomenology.

Microscopic origin of tunable assembly forces in chiral active environments

Across a variety of spatial scales, from nanoscale biological systems to micron-scale colloidal systems, equilibrium self-assembly is entirely dictated by-and therefore limited by-the thermodynamic properties of the constituent materials. In contrast, nonequilibrium materials, such as self-propelled active matter, expand the possibilities for driving the assemblies that are inaccessible in equilibrium conditions. Recently, a number of works have suggested that active matter drives or accelerates self-organization, but the emergent interactions that arise between solutes immersed in actively driven environments are complex and poorly understood. Here, we analyze and resolve two crucial questions concerning actively driven self-assembly: (i) how, mechanistically, do active environments drive self-assembly of passive solutes? (ii) Under which conditions is this assembly robust? We employ the framework of odd hydrodynamics to theoretically explain numerical and experimental observations that chiral active matter, i.e., particles driven with a directional torque, produces robust and long-ranged assembly forces. Together, these developments constitute an important step towards a comprehensive theoretical framework for controlling self-assembly in nonequilibrium environments.

Phase behaviour and dynamics of three-dimensional active dumbbell systems

We present a comprehensive numerical study of the phase behavior and dynamics of a three-dimensional active dumbbell system with attractive interactions. We demonstrate that attraction is essential for the system to exhibit nontrivial phases. We construct a detailed phase diagram by exploring the effects of the system's activity, density, and attraction strength. We identify several distinct phases, including a disordered, a gel, and a completely phase-separated phase. Additionally, we discover a novel dynamical phase, that we name percolating network, which is characterized by the presence of a spanning network of connected dumbbells. In the phase-separated phase we characterize numerically and describe analytically the helical motion of the dense cluster.

Phase behavior of active and passive dumbbells

We report phase separation in a mixture of "hot" and "cold" three-dimensional dumbbells which interact by Lennard-Jones potential. We also have studied the effect of asymmetry of dumbbells and the variation of ratio of "hot" and "cold" dumbbells on their phase separation. The ratio of the temperature difference between hot and cold dumbbells to the temperature of cold dumbbells is a measure of the activity χ of the system. From constant density simulations of symmetric dumbbells, we observe that the "hot" and "cold" dumbbells phase separate at higher activity ratio (χ>5.80) compared to that of a mixture of hot and cold Lennard-Jones monomers (χ>3.44). We find that, in the phase-separated system, the hot dumbbells have high effective volume and hence high entropy which is calculated by two-phase thermodynamic method. The high kinetic pressure of hot dumbbells forces the cold dumbbells to form dense clusters such that at the interface the high kinetic pressure of hot dumbbells is balanced by the virial pressure of cold dumbbells. We find that phase separation pushes the cluster of cold dumbbells to have solidlike ordering. Bond orientation order parameters reveal that the cold dumbbells form solidlike ordering consisting of predominantly face-centered cubic and hexagonal-close packing packing, but the individual dumbbells have random orientations. The simulation of the nonequilibrium system of symmetric dumbbells at different ratios of number of hot dumbbells to cold dumbbells reveals that the critical activity of phase separation decreases with increase in fraction of hot dumbbells. The simulation of equal mixture of hot and cold asymmetric dumbbells revealed that the critical activity of phase separation was independent of the asymmetry of dumbbells. We also observed that the clusters of cold asymmetric dumbbells showed both crystalline and noncrystalline order depending on the asymmetry of dumbbells.

Hydrodynamic effects on the liquid-hexatic transition of active colloids

We study numerically the role of hydrodynamics in the liquid-hexatic transition of active colloids at intermediate activity, where motility induced phase separation (MIPS) does not occur. We show that in the case of active Brownian particles (ABP), the critical density of the transition decreases upon increasing the particle's mass, enhancing ordering, while self-propulsion has the opposite effect in the activity regime considered. Active hydrodynamic particles (AHP), instead, undergo the liquid-hexatic transition at higher values of packing fraction [Formula: see text] than the corresponding ABP, suggesting that hydrodynamics have the net effect of disordering the system. At increasing densities, close to the hexatic-liquid transition, we found in the case of AHP the appearance of self-sustained organized motion with clusters of particles moving coherently.

Emergence of effective temperatures in an out-of-equilibrium model of biopolymer folding

We investigate the possibility of extending the notion of temperature in a stochastic model for the RNA or protein folding driven out of equilibrium. We simulate the dynamics of a small RNA hairpin subject to an external pulling force, which is time-dependent. First, we consider a fluctuation-dissipation relation (FDR) whereby we verify that various effective temperatures can be obtained for different observables, only when the slowest intrinsic relaxation timescale of the system regulates the dynamics of the system. Then, we introduce a different nonequilibrium temperature, which is defined from the rate of heat exchanged with a weakly interacting thermal bath. Notably, this "kinetic" temperature can be defined for any frequency of the external switching force. We also discuss and compare the behavior of these two emerging parameters, by discriminating the time-delayed nature of the FDR temperature from the instantaneous character of the kinetic temperature. The validity of our numerics are corroborated by a simple four-state Markov model which describes the long-time behavior of the RNA molecule.

Effective temperatures in inhomogeneous passive and active bidimensional Brownian particle systems

We study the stationary dynamics of an active interacting Brownian particle system. We measure the violations of the fluctuation dissipation theorem, and the corresponding effective temperature, in a locally resolved way. Quite naturally, in the homogeneous phases the diffusive properties and effective temperature are also homogeneous. Instead, in the inhomogeneous phases (close to equilibrium and within the MIPS sector) the particles can be separated in two groups with different diffusion properties and effective temperatures. Notably, at fixed activity strength the effective temperatures in the two phases remain distinct and approximately constant within the MIPS region, with values corresponding to the ones of the whole system at the boundaries of this sector of the phase diagram. We complement the study of the globally averaged properties with the theoretical and numerical characterization of the fluctuation distributions of the single-particle diffusion, linear response, and effective temperature in the homogeneous and inhomogeneous phases. We also distinguish the behavior of the (time-delayed) effective temperature from the (instantaneous) kinetic temperature, showing that the former is independent of the friction coefficient.

On the fluctuation-dissipation relation in non-equilibrium and non-Hamiltonian systems

We review generalized fluctuation-dissipation relations, which are valid under general conditions even in "nonstandard systems," e.g., out of equilibrium and/or without a Hamiltonian structure. The response functions can be expressed in terms of suitable correlation functions computed in the unperturbed dynamics. In these relations, typically, one has nontrivial contributions due to the form of the stationary probability distribution; such terms take into account the interaction among the relevant degrees of freedom in the system. We illustrate the general formalism with some examples in nonstandard cases, including driven granular media, systems with a multiscale structure, active matter, and systems showing anomalous diffusion.

Lattice Boltzmann methods and active fluids

We review the state of the art of active fluids with particular attention to hydrodynamic continuous models and to the use of Lattice Boltzmann Methods (LBM) in this field. We present the thermodynamics of active fluids, in terms of liquid crystals modelling adapted to describe large-scale organization of active systems, as well as other effective phenomenological models. We discuss how LBM can be implemented to solve the hydrodynamics of active matter, starting from the case of a simple fluid, for which we explicitly recover the continuous equations by means of Chapman-Enskog expansion. Going beyond this simple case, we summarize how LBM can be used to treat complex and active fluids. We then review recent developments concerning some relevant topics in active matter that have been studied by means of LBM: spontaneous flow, self-propelled droplets, active emulsions, rheology, active turbulence, and active colloids.

Clustering of microswimmers: interplay of shape and hydrodynamics

The spatiotemporal dynamics in systems of active self-propelled particles is controlled by the propulsion mechanism in combination with various direct interactions, such as steric repulsion and hydrodynamics. These direct interactions are typically anisotropic, and come in different "flavors", such as spherical and elongated particle shapes, pusher and puller flow fields, etc. The combination of the various aspects is expected to lead to new emergent behavior. However, it is a priori not evident whether shape and hydrodynamics act synergistically or antagonistically to generate motility-induced clustering (MIC) and phase separation (MIPS). We employ a model of prolate spheroidal microswimmers-called squirmers-in quasi-two-dimensional confinement to address this issue by mesoscale hydrodynamic simulations. For comparison, non-hydrodynamic active Brownian particles (ABPs) are considered to elucidate the contribution of hydrodynamic interactions. For spherical particles, the comparison between ABPs and hydrodynamic-squirmer ensembles reveals a suppression of MIPS due to hydrodynamic interactions. Yet, our analysis shows that dynamic clusters exist, with a broad size distribution. The fundamental difference between ABPs and squirmers is attributed to an increased reorientation of squirmers by hydrodynamic torques during their collisions. In contrast, for elongated squirmers, hydrodynamics interactions enhance MIPS. The transition to a phase-separated state strongly depends on the nature of the swimmer's flow field-with an increased tendency toward MIPS for pullers, and a reduced tendency for pushers. Thus, hydrodynamic interactions show opposing effects on MIPS for spherical and elongated microswimmers, and details of the propulsion mechanism of biological microswimmers may be very important to determine their collective behavior.

Active dumbbells: Dynamics and morphology in the coexisting region

With the help of molecular dynamics simulations we study an ensemble of active dumbbells in purely repulsive interaction. We derive the phase diagram in the density-activity plane and we characterise the various phases with liquid, hexatic and solid character. The analysis of the structural and dynamical properties, such as enstrophy, mean-square displacement, polarisation, and correlation functions, shows the continuous character of liquid and hexatic phases in the coexisting region when the activity is increased starting from the passive limit.

Full Phase Diagram of Active Brownian Disks: From Melting to Motility-Induced Phase Separation

We establish the complete phase diagram of self-propelled hard disks in two spatial dimensions from the analysis of the equation of state and the statistics of local order parameters. The equilibrium melting scenario is maintained at small activities, with coexistence between active liquid and hexatic order, followed by a proper hexatic phase, and a further transition to an active solid. As activity increases, the emergence of hexatic and solid order is shifted towards higher densities. Above a critical activity and for a certain range of packing fractions, the system undergoes motility-induced phase separation and demixes into low and high density phases; the latter can be either disordered (liquid) or ordered (hexatic or solid) depending on the activity.

Activity-dependent self-regulation of viscous length scales in biological systems

The cellular cortex, which is a highly viscous thin cytoplasmic layer just below the cell membrane, controls the cell's mechanical properties, which can be characterized by a hydrodynamic length scale ℓ. Cells actively regulate ℓ via the activity of force-generating molecules, such as myosin II. Here we develop a general theory for such systems through a coarse-grained hydrodynamic approach including activity in the static description of the system providing an experimentally accessible parameter and elucidate the detailed mechanism of how a living system can actively self-regulate its hydrodynamic length scale, controlling the rigidity of the system. Remarkably, we find that ℓ, as a function of activity, behaves universally and roughly inversely proportional to the activity of the system. Our theory rationalizes a number of experimental findings on diverse systems, and comparison of our theory with existing experimental data shows good agreement.

Phase Coexistence in Two-Dimensional Passive and Active Dumbbell Systems

We demonstrate that there is a macroscopic coexistence between regions with hexatic order and regions in the liquid or gas phase over a finite interval of packing fractions in active dumbbell systems with repulsive power-law interactions in two dimensions. In the passive limit, this interval remains finite, similar to what has been found in two-dimensional systems of hard and soft disks. We did not find discontinuous behavior upon increasing activity from the passive limit.

Large Fluctuations and Dynamic Phase Transition in a System of Self-Propelled Particles

We study the statistics, in stationary conditions, of the work W_{τ} done by the active force in different systems of self-propelled particles in a time τ. We show the existence of a critical value W_{τ}^{†} such that fluctuations with W_{τ}>W_{τ}^{†} correspond to configurations where interaction between particles plays a minor role whereas those with W_{τ}<W_{τ}^{†} represent states with single particles dragged by clusters. This twofold behavior is fully mirrored by the probability distribution P(W_{τ}) of the work, which does not obey the large-deviation principle for W_{τ}<W_{τ}^{†}. This pattern of behavior can be interpreted as due to a phase transition occurring at the level of fluctuating quantities and an order parameter is correspondingly identified.

Recovery of mechanical pressure in a gas of underdamped active dumbbells with Brownian noise

In contrast with a gas at thermodynamic equilibrium, the mean force exerted on a wall by a gas of active particles usually depends on the confining potential, thereby preventing a proper definition of mechanical pressure. In this paper, we investigate numerically the properties of a gas of underdamped self-propelled dumbbells subject to Brownian noise of increasing intensity, in order to understand how the notion of pressure is recovered as noise progressively masks the effects of self-propulsion and the system approaches thermodynamic equilibrium. The simulations performed for a mobile asymmetric wall separating two chambers containing an equal number of active dumbbells highlight some subtle and unexpected properties of the system. First, Brownian noise of moderate intensity is sufficient to let mean forces equilibrate for small values of the damping coefficient, while much stronger noise is required for larger values of the damping coefficient. Moreover, the displacement of the mean position of the wall upon increase of the intensity of the noise is not necessarily monotonous and may instead display changes of direction. Both facts actually reflect the existence of several mechanisms leading to the rupture of force balance, which tend to displace the mean position of the wall towards different directions and display different robustness against an increase of the intensity of Brownian noise. This work therefore provides a clear illustration of the fact that driving an autonomous system towards (or away from) thermodynamic equilibrium may not be a straightforward process, but may instead proceed through the variations of the relative weights of several conflicting mechanisms.

Small Activity Differences Drive Phase Separation in Active-Passive Polymer Mixtures

Recent theoretical studies found that mixtures of active and passive colloidal particles phase separate but only at very high activity ratio. The high value poses serious obstacles for experimental exploration of this phenomenon. Here we show using simulations that when the active and passive particles are polymers, the critical activity ratio decreases with the polymer length. This not only facilitates the experiments but also has implications on the DNA organization in living cell nuclei. Entropy production can be used as an accurate indicator of this nonequilibrium phase transition.

Dynamics of flexible active Brownian dumbbells in the absence and the presence of shear flow

The dynamical properties of a flexible dumbbell composed of active Brownian particles are analytically analyzed. The dumbbell is considered as a simplified description of a linear active polymer. The two beads are independently propelled in directions which change in a diffusive manner. The relaxation behavior of the internal degree of freedom is tightly coupled to the dumbbell activity. The latter dominates the dynamics for strong propulsion. As is shown, limitations in bond stretching strongly influence the relaxation behavior. Similarly, under shear flow, activity determines the relaxation and tumbling behavior at strong propulsion. Moreover, shear leads to a preferred alignment and consequently to shear thinning. Thereby, a different power-law dependence on the shear rate compared to passive dumbbells under flow is found.

Pressure of a gas of underdamped active dumbbells

The pressure exerted on a wall by a gas at equilibrium does not depend on the shape of the confining potential defining the walls. In contrast, it has been shown recently [A. P. Solon et al., Nat. Phys. 11, 673 (2015)] that a gas of overdamped active particles exerts on a wall a force that depends on the confining potential, resulting in a net force on an asymmetric wall between two chambers at equal densities. Here, considering a model of underdamped self-propelled dumbbells in two dimensions, we study how the behavior of the pressure depends on the damping coefficient of the dumbbells, thus exploring inertial effects. We find in particular that the force exerted on a moving wall between two chambers at equal density continuously vanishes at low damping coefficient, and exhibits a complex dependence on the damping coefficient at low density, when collisions are scarce. We further show that this behavior of the pressure can to a significant extent be understood in terms of the trajectories of individual particles close to and in contact with the wall.

Spontaneous flow in polar active fluids: the effect of a phenomenological self propulsion-like term

We present hybrid lattice Boltzmann simulations of extensile and contractile active fluids where we incorporate phenomenologically the tendency of active particles such as cell and bacteria, to move, or swim, along the local orientation. Quite surprisingly, we show that the interplay between alignment and activity can lead to completely different results, according to geometry (periodic boundary conditions or confinement between flat walls) and nature of the activity (extensile or contractile). An interesting generic outcome is that the alignment interaction can transform stationary active patterns into continuously moving ones: the dynamics of these evolving patterns can be oscillatory or chaotic according to the strength of the alignment term. Our results suggest that flow-polarisation alignment can have important consequences on the collective dynamics of active fluids and active gel.

Rotational and translational diffusion in an interacting active dumbbell system

We study the dynamical properties of a two-dimensional ensemble of self-propelled dumbbells with only repulsive interactions. This model undergoes a phase transition between a homogeneous and a segregated phase and we focus on the former. We analyze the translational and rotational mean-square displacements in terms of the Péclet number, describing the relative role of active forces and thermal fluctuations, and of particle density. We find that the four distinct regimes of the translational mean-square displacement of the single active dumbbell survive at finite density for parameters that lead to a separation of time scales. We establish the Péclet number and density dependence of the diffusion constant in the last diffusive regime. We prove that the ratio between the diffusion constant and its value for the single dumbbell depends on temperature and active force only through the Péclet number at all densities explored. We also study the rotational mean-square displacement proving the existence of a rich behavior with intermediate regimes only appearing at finite density. The ratio of the rotational late-time diffusion constant and its vanishing density limit depends on the Péclet number and density only. At low Péclet number it is a monotonically decreasing function of density. At high Péclet number it first increases to reach a maximum and then decreases as a function of density. We interpret the latter result advocating the presence of large-scale fluctuations close to the transition, at large-enough density, that favor coherent rotation inhibiting, however, rotational motion for even larger packing fractions.

Stochastic dynamics of collective modes for Brownian dipoles

The individual motion of a colloidal particle is described by an overdamped Langevin equation. When rotational degrees of freedom are relevant, these are described by a corresponding Langevin process. Our purpose is to show that the microscopic local density of colloids, in terms of a space and rotation state, also evolves according to a Langevin equation. The latter can then be used as the starting point of a variety of approaches, ranging from dynamical density functional theory to mode-coupling approximations.