Phase Coexistence and Edge Currents in the Chiral Lennard-Jones Fluid.

We study a model chiral fluid in two dimensions composed of Brownian disks interacting via a Lennard-Jones potential and a nonconservative transverse force, mimicking colloids spinning at a given rate. The system exhibits a phase separation between a chiral liquid and a dilute gas phase that can be characterized using a thermodynamic framework. We compute the equations of state and show that the surface tension controls interface corrections to the coexisting pressure predicted from the equal-area construction. Transverse forces increase surface tension and generate edge currents at the liquid-gas interface. The analysis of these currents shows that the rotational viscosity introduced in chiral hydrodynamics is consistent with microscopic bulk mechanical measurements. Chirality can also break the solid phase, giving rise to a dense fluid made of rotating hexatic patches. Our Letter paves the way for the development of the statistical mechanics of chiral particles assemblies.

Work Fluctuations for a Harmonically Confined Active Ornstein-Uhlenbeck Particle.

We study the active work fluctuations of an active Ornstein-Uhlenbeck particle in the presence of a confining harmonic potential. We tackle the problem analytically both for stationary and generic uncorrelated initial states. Our results show that harmonic confinement can induce singularities in the active work rate function, with linear stretches at large positive and negative active work, at sufficiently large active and harmonic force constants. These singularities originate from big jumps in the displacement and in the active force, occurring at the initial or ending points of trajectories and marking the relevance of boundary terms in this problem.

Dynamics of Motility-Induced Clusters: Coarsening beyond Ostwald Ripening.

We study the dynamics of clusters of active Brownian disks generated by motility-induced phase separation, by applying an algorithm that we devised to track cluster trajectories. We identify an aggregation mechanism that goes beyond Ostwald ripening but also yields a dynamic exponent characterizing the cluster growth z=3, in the timescales explored numerically. Clusters of mass M self-propel with enhanced diffusivity D∼Pe^{2}/sqrt[M]. Their fast motion drives aggregation into large fractal structures, which are patchworks of diverse hexatic orders, and coexist with regular, orientationally uniform, smaller ones. To bring out the impact of activity, we perform a comparative study of a passive system that evidences major differences with the active case.

Unified analysis of topological defects in 2D systems of active and passive disks.

We provide a comprehensive quantitative analysis of localized and extended topological defects in the steady state of 2D passive and active repulsive Brownian disk systems. We show that, both in and out-of-equilibrium, the passage from the solid to the hexatic is driven by the unbinding of dislocations, in quantitative agreement with the KTHNY singularity. Instead, extended clusters of defects largely dominate below the solid-hexatic critical line. The latter percolate in the liquid phase very close to the hexatic-liquid transition, both for continuous and discontinuous transitions, in the homogeneous liquid regime. At critical percolation the clusters of defects are fractal with statistical and geometric properties that are independent of the activity and compatible with the universality class of uncorrelated critical percolation. We also characterize the spatial organization of point-like defects and we show that the disclinations are not free, but rather always very near more complex defect structures. At high activity, the bulk of the dense phase generated by Motility-Induced Phase Separation is characterized by a density of point-like defects, and statistics and morphology of defect clusters, set by the amount of activity and not the packing fraction. Hexatic domains within the dense phase are separated by grain-boundaries along which a finite network of topological defects resides, interrupted by gas bubbles in cavitation. This structure is dynamic in the sense that the defect network allows for an unzipping mechanism that leaves free space for gas bubbles to appear, close, and even be released into the dilute phase.

Rotation and propulsion in 3D active chiral droplets.

Chirality is a recurrent theme in the study of biological systems, in which active processes are driven by the internal conversion of chemical energy into work. Bacterial flagella, actomyosin filaments, and microtubule bundles are active systems that are also intrinsically chiral. Despite some exploratory attempt to capture the relations between chirality and motility, many features of intrinsically chiral systems still need to be explored and explained. To address this gap in knowledge, here we study the effects of internal active forces and torques on a 3-dimensional (3D) droplet of cholesteric liquid crystal (CLC) embedded in an isotropic liquid. We consider tangential anchoring of the liquid crystal director at the droplet surface. Contrary to what happens in nematics, where moderate extensile activity leads to droplet rotation, cholesteric active droplets exhibit more complex and variegated behaviors. We find that extensile force dipole activity stabilizes complex defect configurations, in which orbiting dynamics couples to thermodynamic chirality to propel screw-like droplet motion. Instead, dipolar torque activity may either tighten or unwind the cholesteric helix and if tuned, can power rotations with an oscillatory angular velocity of 0 mean.

Motility-Induced Microphase and Macrophase Separation in a Two-Dimensional Active Brownian Particle System.

As a result of nonequilibrium forces, purely repulsive self-propelled particles undergo macrophase separation between a dense and a dilute phase. We present a thorough study of the ordering kinetics of such motility-induced phase separation (MIPS) in active Brownian particles in two dimensions, and we show that it is generically accompanied by microphase separation. The growth of the dense phase follows a law akin to the one of liquid-gas phase separation. However, it is made of a mosaic of hexatic microdomains whose size does not coarsen indefinitely, leaving behind a network of extended topological defects from which microscopic dilute bubbles arise. The characteristic length of these finite-size structures increases with activity, independently of the choice of initial conditions.

Transcriptional Bursts in a Nonequilibrium Model for Gene Regulation by Supercoiling.

We analyze transcriptional bursting within a stochastic nonequilibrium model, which accounts for the coupling between the dynamics of DNA supercoiling and gene transcription. We find a clear signature of bursty transcription when there is a separation between the timescales of transcription initiation and supercoiling dissipation (the latter may either be diffusive or mediated by topological enzymes, such as type I or type II topoisomerases). In multigenic DNA domains, we observe either bursty transcription or transcription waves; the type of behavior can be selected for by controlling gene activity and orientation. In the bursty phase, the statistics of supercoiling fluctuations at the promoter are markedly non-Gaussian.

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.

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.

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.

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.

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.

Effect of gas turbulence in quartz-enhanced photoacoustic spectroscopy: A comprehensive flow field analysis.

Here we present a computational and experimental fluid dynamics study for the characterization of the flow field within the gas chamber of a Quartz-Enhanced Photoacoustic Spectroscopy (QEPAS) sensor, at different flow rates at the inlet of the chamber. The transition from laminar to turbulent regime is ruled both by the inlet flow conditions and dimension of the gas chamber. The study shows how the distribution of the flow field in the chamber can influence the QEPAS sensor sensitivity, at different operating pressures. When turbulences and eddies are generated within the gas chamber, the efficiency of photoacoustic generation is significantly altered.

Yield-stress transition in suspensions of deformable droplets.

Yield-stress materials, which require a sufficiently large forcing to flow, are currently ill-understood theoretically. To gain insight into their yielding transition, we study numerically the rheology of a suspension of deformable droplets in 2D. We show that the suspension displays yield-stress behavior, with droplets remaining motionless below a critical body-force. In this phase, droplets jam to form an amorphous structure, whereas they order in the flowing phase. Yielding is linked to a percolation transition in the contacts of droplet-droplet overlaps and requires strict conservation of the droplet area to exist. Close to the transition, we find strong oscillations in the droplet motion that resemble those found experimentally in confined colloidal glasses. We show that even when droplets are static, the underlying solvent moves by permeation so that the viscosity of the composite system is never truly infinite, and its value ceases to be a bulk material property of the system.

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.

Particle-based Ising model.

We characterize equilibrium properties and relaxation dynamics of a two-dimensional lattice containing, at each site, two particles connected by a double-well potential (dumbbell). Dumbbells are oriented in the orthogonal direction with respect to the lattice plane and interact with each other through a Lennard-Jones potential truncated at the nearest neighbor distance. We show that the system's equilibrium properties are accurately described by a two-dimensional Ising model with an appropriate coupling constant. Moreover, we characterize the coarsening kinetics by calculating the cluster size as a function of time and compare the results with Monte Carlo simulations based on Glauber or reactive dynamics rate constants.

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.

Kinetics of self-induced aggregation in Brownian particles.

We study a model of interacting random walkers that proposes a simple mechanism for the emergence of cooperation in a group of individuals. Each individual, represented by a Brownian particle, experiences an interaction produced by the local unbalance in the spatial distribution of the other individuals. This interaction results in a nonlinear velocity driving the particle trajectories in the direction of the nearest more crowded region; the competition among different aggregating centers generates nontrivial dynamical regimes. Our simulations show that for sufficiently low randomness the system evolves through a coalescence behavior characterized by clusters of particles growing with a power law in time. In addition, the typical scaling properties of the general theory of stochastic aggregation processes are verified.

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.

Condensation of fluctuations in and out of equilibrium.

Condensation of fluctuations is an interesting phenomenon conceptually distinct from condensation on average. One striking feature is that, contrary to what happens on average, condensation of fluctuations may occur even in the absence of interaction. The explanation emerges from the duality between large deviation events in the given system and typical events in a new and appropriately biased system. This phenomenon is investigated in the context of the Gaussian model, chosen as a paradigmatical noninteracting system, before and after an instantaneous temperature quench. It is shown that the bias induces a mean-field-like effective interaction responsible for the condensation on average. Phase diagrams, covering both the equilibrium and the off-equilibrium regimes, are derived for observables representative of generic behaviors.