We describe a two-dimensional model for active particles whose self-propulsion speed is not fixed, but varies in time, and whose motion is subject to both translational and rotational diffusion. In the conventional treatment of active Brownian motion, the self-propulsion speed is taken to be constant - an assumption convenient for analysis but poorly matched to many real systems. Here we relax that assumption, allowing the speed $v(t)$ to fluctuate stochastically between two values: $v=0$ (a passive state) and $v=s$ (an active state). Transitions between these states are taken to follow a random telegraph process. This ``active-passive Brownian particle'' inherits limiting behaviors from both the purely active and purely passive Brownian cases. Analytical expressions for the first two displacement moments, and for the resulting effective diffusion coefficient, make this dual character explicit. Moreover, by an appropriate identification of parameters, a run-and-tumble particle - such as a motile bacterium - can be mapped onto this model in such a way that their large-scale diffusivities coincide.
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 …
We investigate the phase behavior and kinetics of a monodisperse mixture of active (\textit{i.e.}, self-propelled) and passive isometric Brownian particles through Brownian dynamics simulations and theory. As in a purely active system, motility of the active component triggers phase separation into a dense and a dilute phase; in the dense phase we further find active-passive segregation, with "rafts" of passive particles in a "sea" of active particles. We find that phase separation from an initially disordered mixture can occur with as little as 15 percent of the particles being active. Finall…
We use a simple model of particle shape to investigate how particle asymmetry affects particle-surface interaction, orientation, and stochastic dynamics over a planar surface. With this geometric model, we construct potential energy curves as a function of particle orientation relative to the surface, and identify the potential energy minimum for particles of various shapes ranging from symmetric (sphere) to asymmetric (oval-shaped). The calculated difference between particle centroid position and potential energy minimum location is used to define an offset, which is useful for comparison wit…
Understanding the out-of-equilibrium properties of noisy microscale systems and the extent to which they can be modulated externally, is a crucial scientific and technological challenge. It holds the promise to unlock disruptive new technologies ranging from targeted delivery of chemicals within the body to directed assembly of new materials. Here we focus on how active matter can be harnessed to transport passive microscopic systems in a statistically predictable way. Using a minimal active-passive system of weakly Brownian particles and swimming microalgae, we show that spatial confinement l…
We consider the motion of an active Brownian particle with speed fluctuations in d-dimensions in the presence of both translational and orientational diffusion. We use an Ornstein-Uhlenbeck process for active speed generation. Using a Laplace transform approach, we describe and use a Fokker-Planck equation-based method to evaluate the exact time dependence of all relevant dynamical moments. We present explicit calculations of such moments and compare our analytical predictions against numerical simulations to demonstrate and analyze several dynamical crossovers. The kurtosis of displacement sh…
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 s…
Active particles may happen to be confined in channels so narrow that they cannot overtake each other (Single File conditions). This interesting situation reveals nontrivial physical features as a consequence of the strong inter-particle correlations developed in collective rearrangements. We consider a minimal model for active Brownian particles with the aim of studying the modifications introduced by activity with respect to the classical (passive) Single File picture. Depending on whether their motion is dominated by translational or rotational diffusion, we find that active Brownian partic…
We study the two-dimensional motion of an active Brownian particle of speed $v_0$, with intermittent directional reversals in the presence of a harmonic trap of strength $μ$. The presence of the trap ensures that the position of the particle eventually reaches a steady state where it is bounded within a circular region of radius $v_0/μ$, centered at the minimum of the trap. Due to the interplay between the rotational diffusion constant $D_R$, reversal rate $γ$, and the trap strength $μ$, the steady state distribution shows four different types of shapes, which we refer to as active-I & II, and…
Here, I review the large-scale properties of collections of active Brownian elongated objects, in particular rods, moving in a dissipative medium/substrate. I address the problem by presenting three different models of decreasing complexity, which I refer to as model I, II, and III, respectively.
We model a binary mixture of passive and active Brownian particles in two dimensions using the effective interaction between passive particles in the active bath. The activity of active particles and the size ratio of two types of particles are two control parameters in the system. The effective interaction is calculated from the average force on two particles generated by the active particles. The effective interaction can be attractive or repulsive, depending on the system parameters. The passive particles form four distinct structural orders for different system parameters viz; disorder (D)…
The equilibrium properties of a system of passive diffusing particles in an external magnetic field are unaffected by the Lorentz force. In contrast, active Brownian particles exhibit steady-state phenomena that depend on both the strength and the polarity of the applied magnetic field. The intriguing effects of the Lorentz force, however, can only be observed when out-of-equilibrium density gradients are maintained in the system. To this end, we use the method of stochastic resetting on active Brownian particles in two dimensions by resetting them to the line $x=0$ at a constant rate and peri…
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 non-equilibrium phase transition.
We have performed a case study investigating a recently proposed scheme to obtain an effective pair potential for active Brownian particles [Farage et al., Phys. Rev. E 91, 042310 (2015)]. Applying this scheme to the Lennard-Jones potential, numerical simulations of active Brownian particles are compared to simulations of passive Brownian particles interacting by the effective pair potential. Analyzing the static pair correlations, our results indicate a limited range of activity parameters (speed and orientational correlation time) for which we obtain quantitative, or even qualitative, agreem…
We investigate the stochastic dynamics of one sedimenting active Brownian particle in three dimensions under the influence of gravity and passive fluctuations in the translational and rotational motion. We present an analytical solution of the Fokker--Planck equation for the stochastic process which allows us to describe the dynamics of the active Brownian particle in three dimensions. We address the time evolution of the monopole, the polarization, and the steady-state solution. We also perform Brownian dynamics simulations and study the effect of the activity of the particles on their collec…
We investigate the mean first passage time of an active Brownian particle in one dimension using numerical simulations. The activity in one dimension is modeled as a two state model; the particle moves with a constant propulsion strength but its orientation switches from one state to other as in a random telegraphic process. We study the influence of a finite resetting rate $r$ on the mean first passage time to a fixed target of a single free Active Brownian Particle and map this result using an effective diffusion process. As in the case of a passive Brownian particle, we can find an optimal …
We use a model based on the fractional Langevin equation with external noise to describe the anomalous dynamics observed in microrheology experiments in living cells. This model reproduces both the subdiffusive short-time and the superdiffusive long-time behavior. We show that the former reflects the equilibrium properties of the cell, while the latter is due to the nonequilibrium external noise. This allows to infer the transport properties of the system under active measurements from the transient behavior obtained from passive measurements, extending the connection between active and passiv…
We present a microscopic theory for the nonequilibrium interfacial tension $γ_{\rm gl}$ of the free interface between gas and liquid phases of active Brownian particles. The underlying square gradient treatment and the splitting of the force balance in flow and structural contributions is general and applies to inhomogeneous nonequilibrium steady states. We find $γ_{\rm gl}\geq 0$, which opposes claims by Bialké et al. [Phys. Rev. Lett. $\bf{115}$, 098301 (2015)] and delivers the theoretical justification for the widely observed interfacial stability in active Brownian dynamics many-body simul…
We use a first-passage time approach to study the statistics of the trapping times induced by persistent motion of active particles colliding with flat boundaries. The angular first-passage time distribution and mean first-passage time is calculated exactly for active Brownian and run-and-tumble particles and the results are compared. Theoretical predictions are in excellent agreement with Langevin simulations. Our results shed further light onto how active particles with different dynamics may be equivalent in the bulk, yet behave differently near boundaries or obstacles.
We study binary mixtures of small active and big passive athermal particles interacting via soft repulsive forces on a frictional substrate. Athermal self propelled particles are known to phase separate into a dense aggregate and a dilute gas-like phase at fairly low packing fractions. Known as {\emph {motility induced phase separation}}, this phenomenon governs the behaviour of binary mixtures for small to intermediate size ratios of the particle species. An effective attraction between passive particles, due to the surrounding active medium, leads to true phase separation for large size rati…
We derive a mode-coupling theory (MCT) to describe the dynamics of tracer particles in dense systems of active Brownian particles (ABPs) in two spatial dimensions. The ABP undergo translational and rotational Brownian dynamics, and are equipped with a fixed self-propulsion speed along their orientational vector that describes their active motility. The resulting equations of motion for the tagged-particle density correlation functions describe the various cases of tracer dynamics close to the glass transition: that of a passive colloidal particle in a suspension of ABP, that of a single active…
We study the dynamics of an active Brownian particle with a nonlinear friction function located in a spatial cubic potential. For strong but finite damping, the escape rate of the particle over the spatial potential barrier shows a nonmonotonic dependence on the noise intensity. We relate this behavior to the fact that the active particle escapes from a limit cycle rather than from a fixed point and that a certain amount of noise can stabilize the sojourn of the particle on this limit cycle.
We demonstrate that there is macroscopic co-existence between regions with hexatic order and regions in the liquid/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, similarly to what has been found in bidimensional systems of hard and soft disks. We did not find discontinuous behaviour upon increasing activity from the passive limit.
The presence of active forces in various biological and artificial systems may change how those systems behaves under forcing. We present a minimal model of a suspension of passive or active swimmers driven on the boundaries by time-dependent forcing. In particular, we consider a time-periodic drive from which we determine the linear response functions of the suspension. The meaning of these response functions are interpreted in terms of the storage and dissipation of energy through the particles within the system. We find that while a slowly driven active system responds in a way similar to a…
Using Brownian dynamics simulations, the motion of active Brownian particles (ABPs) in the presence of fuel (or 'food') sources is studied. It is an established fact that within confined stationary systems, the activity of ABPs generates density profiles that are enhanced in regions of low activity, which is generally referred to as 'anti-chemotaxis'. We demonstrate that -- contrary to common believes -- in non-stationary setups, emerging here as a result of short fuel bursts, our model ABPs do instead exhibit signatures of chemotactic behavior. In direct competition with inactive, but otherwi…
We study the dynamics of a single active Brownian particle (ABP) in two spatial dimensions. The ABP has an intrinsic time scale $D_R^{-1}$ set by the rotational diffusion constant $D_R$. We show that, at short-times $t \ll D_R^{-1}$, the presence of `activness' results in a strongly anisotropic and non-diffusive dynamics in the $(xy)$ plane. We compute exactly the marginal distributions of the $x$ and $y$ position coordinates along with the radial distribution, which are all shown to be non-Brownian. In addition, we show that, at early times, the ABP has anomalous first-passage properties, cha…
We derive the hydrodynamic equations of motion for a fluid of active particles described by under- damped Langevin equations that reduce to the Active-Brownian-Particle model, in the overdamped limit. The contraction into the hydrodynamic description is performed by locally averaging the par- ticle dynamics with the non-equilibrium many-particle probability density, whose formal expression is found in the physically relevant limit of high-friction through a multiple-time-scale analysis. This approach permits to identify the conditions under which self-propulsion can be subsumed into the fluid …
We investigate the full pair-distribution function of a homogeneous suspension of spherical active Brownian particles interacting by a Weeks-Chandler-Andersen potential in two spatial dimensions. The full pair-distribution function depends on three coordinates describing the relative positions and orientations of two particles, the Péclet number specifying the activity of the particles, and their mean packing density. This five-dimensional function is obtained from Brownian dynamics simulations. We discuss its structure taking into account all of its degrees of freedom. In addition, we present…
We perform a coarse-graining analysis of the paradigmatic active matter model, Active Brownian Particles, yielding a continuum description in terms of balance laws for mass, linear and angular momentum, and energy. The derivation of the balance of linear momentum reveals that the active force manifests itself directly as a continuum-level body force proportional to an order parameter-like director field, which therefore requires its own evolution equation to complete the continuum description of the system. We derive this equation, demonstrating in the process that bulk currents may be sustain…
Localized contractile configurations or asters spontaneously appear and disappear as emergent structures in the collective stochastic dynamics of active polar actomyosin filaments. Passive parti- cles which (un)bind to the active filaments get advected into the asters, forming transient clusters. We study the phase segregation of such passive advective scalars in a medium of dynamic asters, as a function of the aster density and the ratio of the rates of aster remodeling to particle diffusion. The dynamics of coarsening shows strong violation of Porod behaviour, suggesting diffuse interfaces. …
We derive equations of motion for the mean-squared displacement (MSD) of an active Brownian particle (ABP) in a crowded environment modeled by a dense system of passive Brownian particles, and of a passive tracer particle in a dense active-Brownian particle system, using a projection-operator scheme. The interaction of the tracer particle with the dense host environment gives rise to strong memory effects. Evaluating these approximately in the framework of a recently developed mode-coupling theory for the glass transition in active Brownian particles (ABP-MCT), we discuss the various regimes o…
We investigate a model for a Stirling-like engine consisting of a passive Brownian particle confined by a harmonic potential and interacting with a suspension of active Brownian particles that self-propel in a viscous solvent, which cyclically operates under isothermal conditions by means of temporal variations of the trap stiffness and the self-propulsion speed of the active particles. We derive an effective stochastic equation of motion of the trapped Brownian particle, which includes a friction memory kernel as well as thermal and active fluctuating forces due to its coupling with the activ…
We study analytically the single-trajectory spectral density (STSD) of an active Brownian motion as exhibited, for example, by the dynamics of a chemically-active Janus colloid. We evaluate the standardly-defined spectral density, i.e. the STSD averaged over a statistical ensemble of trajectories in the limit of an infinitely long observation time $T$, and also go beyond the standard analysis by considering the coefficient of variation $γ$ of the distribution of the STSD. Moreover, we analyse the finite-$T$ behaviour of the STSD and $γ$, determine the cross-correlations between spatial compone…
We derive an analytic expression for the mechanical pressure of a generic one-dimensional model of confined active Brownian particles (ABPs) that is valid for all values of Peclet number Pe and all confining scenarios. Our model reproduces the known scaling of bulk pressure with Pe^2 while in strong confinement pressure scales with Pe. Our analytic results are very well reproduced by simulations of ABPs in 2D. We use the pressure formula to calculate both the work performed by an active engine and its efficiency. In particular, efficiency is maximized for work cycles with finite period and not…
We study the pair correlation of Active Brownian Particles at low density using numerical simulations and analytical calculations. We observe a winged pair correlation: while particles accumulate in front of an active particle as expected, the depletion wake consists of two depletion wings. In the limit of soft particles, we obtain a closed equation for the pair correlation, allowing us to characterize the depletion wings. In particular, we unveil two regimes at high activity where the wings adopt a self-similar profile and decay algebraically. We also perform experiments of self-propelled Jan…
Directed transport of interacting active (self-propelled)Brownian particles is numerically investigated in confined geometries (entropic barriers). The self-propelled velocity can break thermodynamical equilibrium and induce the directed transport. It is found that the interaction between active particles can greatly affect the ratchet transport. For attractive particles, on increasing the interaction strength, the average velocity firstly decreases to its minima, then increases, and finally decreases to zero. For repulsive particles, when the interaction is very weak, there exists a critical …
By now active Brownian motion is a well-established model to describe the motion of mesoscopic self-propelled particles in a Newtonian fluid. On the basis of the generalized Langevin equation, we present an analytic framework for active Brownian motion with memory delay assuming time-dependent friction kernels for both translational and orientational degrees of freedom to account for the time-delayed response of a viscoelastic medium. Analytical results are obtained for the orientational correlation function, mean displacement and mean-square displacement which we evaluate in particular for a …
Helicase opening of double-stranded nucleic acids may be "active" (the helicase directly destabilizes the dsNA to promote opening) or "passive" (the helicase binds ssNA available due to a thermal fluctuation which opens part of the dsNA). We describe helicase opening of dsNA, based on helicases which bind single NA strands and move towards the double-stranded region, using a discrete ``hopping'' model. The interaction between the helicase and the junction where the double strand opens is characterized by an interaction potential. The form of the potential determines whether the opening is acti…
Miniaturized, self-propelled locomotors use chemo-mechanical transduction mechanisms to convert fuel in the environment to autonomous motion. Recent experimental and theoretical studies demonstrate that these autonomous engines can passively follow the contours of solid boundaries they encounter. Boundary guidance, however, is not necessarily stable: Mechanical disturbances can cause the motor to hydrodynamically depart from the passively guided pathway. Furthermore, given the scaled-down size of micromotors (typically 100 nm -10 $μ$m), Brownian thermal fluctuation forces are necessarily impor…
We consider a phase field crystal modeling approach for binary mixtures of interacting active and passive particles. The approach allows to describe generic properties for such systems within a continuum model. We validate the approach by reproducing experimental results, as well as results obtained with agent-based simulations, for the whole spectrum from highly dilute suspensions of passive particles to interacting active particles in a dense background of passive particles.
We develop an exact Green-Kubo formula relating nonequilibrium averages in systems of interacting active Brownian particles to equilibrium time-correlation functions. The method is applied to calculate the density-dependent average swim speed, which is a key quantity entering coarse grained theories of active matter. The average swim speed is determined by integrating the equilibrium autocorrelation function of the interaction force acting on a tagged particle. Analytical results are validated using Brownian dynamics simulations.
We investigate the influence of external forces on the collective dynamics of interacting active Brownian particles in two as well as three spatial dimensions. Via explicit coarse graining, we derive predictive models that are applicable for space- and time-dependent external force fields. We study these models for the cases of gravity and harmonic traps. In particular, we derive a generalized barometric formula for interacting active Brownian particles under gravity that is valid for low to high concentrations and activities of the particles. Furthermore, we show that one can use an external …
Using Langevin dynamics simulations, we study a system of transversely propelling filament and passive Brownian particles. We consider a polymer whose monomers experience a constant propulsion force perpendicular to the local tangent in the presence of passive particles undergoing thermal fluctuations in two dimensions. We demonstrate that the sideways propelling polymer can act as a sweeper to collect the passive Brownian particles, mimicking a shuttle-cargo system. The number of particles the polymer collects during its motion increases with time and finally saturates to a maximum number. Mo…
A particle that is immersed in a uniform temperature bath performs Brownian diffusion, as discussed by Einstein. But Sinai has realized that in a "random environment" the diffusion is suppressed. Follow-up works have pointed out that in the presence of bias $f$ there are delocalization and sliding transitions, with threshold value $f_c$ that depends on the disorder strength. We discuss in a critical way the emergence of Sinai physics for both passive and active Brownian particles. Tight-binding and Fokker-Planck versions of the model are addressed on equal footing. We assume that the transitio…
Efficient nutrient mixing is crucial for the survival of bacterial colonies and other living systems. This raises the question of whether the optimization of mixing through the emergence of active turbulent motion in bacterial swarms played a role in the evolution of bacterial shapes. Here, to address this question, we solve the hydrodynamic equation for active nematics coupled with an advection-diffusion equation for the nutrients. The latter models a conserved activity field and mimics the conservation of nutrients in bacterial swarms. At the interface between active and passive nematic phas…
