Polymer Systems with Correlated Activity: Stars Versus Linear Chains

We investigate conformations and dynamics of a polymer considering its monomers to be active Brownian particles. This active polymer shows very intriguing physical behavior which is absent in an active Rouse chain. The chain initially shrinks with active force, which starts swelling on further increase in force. The shrinkage followed by swelling is attributed purely to excluded-volume interactions among the monomers. In the swelling regime, the chain shows a crossover from the self-avoiding behavior to the Rouse behavior with scaling exponent ν_{a}≈1/2 for end-to-end distance. The nonmonotonicity in the structure is analyzed through various physical quantities; specifically, radial distribution function of monomers, scattering time, as well as various energy calculations. The chain relaxes faster than the Rouse chain in the intermediate force regime, with a crossover in variation of relaxation time at large active force as given by a power law τ_{r}∼Pe^{-4/3} (Pe is Péclet number).

We experimentally investigate the work fluctuations of an active Brownian particle (ABP) during its self-propelled motion in a viscoelastic medium. Under such conditions, ABPs display a persistent circular motion which allows the determination of the orientational work fluctuations along its trajectory. Due to the nonlinear coupling to the non-Markovian bath, we find strong deviations from the work fluctuation theorem (WFT) due to observed increased rotational ABP dynamics. Taking this enhanced rotational diffusion into account, the orientational work distributions can be recasted to be in accordance with the WFT by considering an effective temperature of about two orders of magnitude larger than k_{B}T. This approach is confirmed by the good agreement of the torque exerted by the viscoelastic bath on the ABP obtained from the WFT with the value obtained from the mean angular velocity and the friction coefficient of the ABP.

We apply the homotopy analysis method to the motion of noninteracting active Brownian particles (ABPs) under a general situation such as in the presence of external fields, external torques, or even moving on non-Euclidean geometries. Within this framework, a general expression as a series solution in time for the probability density function (PDF) satisfying the Fokker-Planck (FP) equation is elucidated. Using the latter PDF, their respective mean values (first and second moments) are also found in general. Applications of the present technique are offered by solving classic ABP situations, namely free noninteracting ABPs, ABPs under a Poiseuille flow, and even ABPs confined to move on any Riemannian manifold. To improve the convergence of the obtained series solution for each situation, Padé approximants are incorporated. It is worth mentioning that the offered methodology may exactly be applied to other fields such as chemistry, biology, or econophysics where a FP equation governs the system.

The collective properties of a binary mixture of A - and B -type self-steering particles endowed with visual perception are studied by computer simulations. Active Brownian particles (ABPs) are employed with an additional steering mechanism, which enables them to adjust their propulsion direction relative to the instantaneous positions of neighboring particles, depending on the species, either steering toward or away from them. Steering can be nonreciprocal, in particular between the A - and B -type particles. The underlying dynamical and structural properties of the system are governed by the strength and polarity of the maneuverabilities (i.e. maximum reorientation torques) associated with the vision-induced steering. The model predicts the emergence of a large variety of nonequilibrium behaviors, which we systematically characterize for all nine principal sign combinations of AA , BB , AB and BA maneuverabilites. In particular, we observe the formation of multimers, encapsulated aggregates, honeycomb lattices, and predator-prey pursuit. Notably, for a predator-prey system, the maneuverability and vision angle employed by a predator significantly impacts the spatial distribution of the surrounding prey particles. For systems with electric-charge-like interactions (i.e. like-particles repel, unlike attract) and nonstoichiometric composition (i.e. small number excess of one component), we obtain at intermediate activity levels an enhanced diffusion compared to non-steering ABPs.

Active particles self-propel themselves with a stochastically evolving velocity, generating a persistent motion leading to a non-diffusive behavior of the position distribution. Nevertheless, an effective diffusive behavior emerges at times much larger than the persistence time. Here we develop a general framework for studying the long-time behavior for a class of active particle dynamics and illustrate it using the examples of run-and-tumble particle, active Ornstein–Uhlenbeck particle, active Brownian particle, and direction reversing active Brownian particle. Treating the ratio of the persistence-time to the observation time as the small parameter, we show that the position distribution generically satisfies the diffusion equation at the leading order. We further show that the sub-leading contributions, at each order, satisfies an inhomogeneous diffusion equation, where the source term depends on the previous order solutions. We explicitly obtain a few sub-leading contributions to the Gaussian position distribution. As a part of our framework, we also prescribe a way to find the position moments recursively and compute the first few explicitly for each model.

Active matter exhibits many intriguing non-equilibrium characteristics, for instance, without any attractive and aligned interactions, the active Brownian particle (ABP) system undergoing motility-induced phase separation forms a high-density phase with both structural ordering and dynamical coherence. Recently, the velocity correlation among the particles in this high-density phase was found in non-thermal overdamped ABP systems. However, it seemed to disappear if thermal noises were included, bringing some confusion about the generality of the consistency between structures and dynamics in ABPs. Here, we demonstrate that the thermal noises imposing a large random term on the instantaneous velocity of ABPs hinder the observation of the inherent correlation in the motions of ABPs. By averaging the instantaneous velocity (or equivalently, calculating the displacement), we show that the inherent motions of thermal-fluctuated ABPs are highly coherent. Whether there is thermal noise or not, the inherent collective motions of ABPs do exist, and the collective motion domains are consistent spatially with the ordered clusters of ABPs in the high-density phase. At the boundary of these ordered clusters, the active forces of the particles tend to point inward and compress to sustain these clusters, thus the particles in the clusters move coherently to form some vortex-like or aligned velocity domains.

Phonons reveal coupled cholesterol-lipid dynamics in ternary membranes

This study aims to address the question of fluctuation-dissipation relationship in a non-equilibrium system comprising active Brownian particles. Specifically, the fluctuation power spectral densities (PSD) of an Induced-ChargeElectrophoresis-driven metallic Janus particle in an optical trap was measured and compared the PSDs to that of nondriven particles. Unlike the PSDs of Brownian particles where there exists only one characteristic frequency, the PSDs of active Brownian particles have two with the second frequency characterized by the particles’ rotation diffusion. Energy dissipation of such particles, defined as the integrated PSDs were examined. Finally, Effective temperatures defined by various means, including the probability distribution of the particle's positions in the trap, and the zero-frequency limit of the fluctuation power spectral densities, are examined for the active Brownian particles.

The Active Brownian Particle (ABP) model has become a prototype of self-propelled particles. ABPs move persistently at a constant speed V along a direction that changes slowly by rotational diffusion, characterized by a coefficient Dr. Persistent motion plus random reorientations generate a random walk at long times with a diffusion coefficient that, for isolated ABPs in two dimensions, is given by D0=V2/(2Dr). Here, we study the density effects on the self-diffusive dynamics using a recently proposed kinetic theory for ABPs, in which persistent collisions are described as producing a net displacement on the particles. On intermediate timescales, where many collisions have taken place but the director of the tracer particle has not yet changed, it is possible to solve the Lorentz kinetic equation for a tracer particle. It turns out that, as a result of collisions, the tracer follows an effective stochastic dynamics, characterized by an effective reduced streaming velocity Veff and anisotropic diffusion, with coefficients explicitly depending on the density. Based on this result, an effective theoretical and numerical approach is proposed in which the particles in a bath follow stochastic dynamics with mean-field interactions based on the local density. Finally, on time scales larger than Dr−1, studying the van Hove function at small wavevectors, it is shown that the tracer particle presents an effective diffusive motion with a coefficient D=Veff2/(2Dr). The dependence of Veff on the density indicates that the kinetic theory is limited to area fractions smaller than 0.42, and beyond this limit, unphysical results appear.

Active Brownian particles (ABPs) and Run-and-Tumble particles (RTPs) both self-propel at fixed speed $v$ along a body-axis ${\bf u}$ that reorients either through slow angular diffusion (ABPs) or sudden complete randomisation (RTPs). We compare the physics of these two model systems both at microscopic and macroscopic scales. Using exact results for their steady-state distribution in the presence of external potentials, we show that they both admit the same effective equilibrium regime perturbatively that breaks down for stronger external potentials, in a model-dependent way. In the presence of collisional repulsions such particles slow down at high density: their propulsive effort is unchanged, but their average speed along ${\bf u}$ becomes $v(\rho) < v$. A fruitful avenue is then to construct a mean-field description in which particles are ghost-like and have no collisions, but swim at a variable speed $v$ that is an explicit function or functional of the density $\rho$. We give numerical evidence that the recently shown equivalence of the fluctuating hydrodynamics of ABPs and RTPs in this case, which we detail here, extends to microscopic models of ABPs and RTPs interacting with repulsive forces.

It is well known that the path probabilities of Brownian motion correspond to the equilibrium configurational probabilities of flexible Gaussian polymers, while those of active Brownian motion correspond to in-extensible semiflexible polymers. Here we investigate the properties of the equilibrium polymer that corresponds to the trajectories of particles acted on simultaneously by both Brownian and active noise. Through this mapping we can see interesting crossovers in the mechanical properties of the polymer with changing contour length. The polymer end-to-end distribution exhibits Gaussian behaviour for short lengths, which changes to the form of semiflexible filaments at intermediate lengths, to finally go back to a Gaussian form for long contour lengths. By performing a Laplace transform of the governing Fokker-Planck equation of the active Brownian particle, we discuss a direct method to derive exact expressions for all the moments of the relevant dynamical variables, in arbitrary dimensions. These are verified via numerical simulations and used to describe interesting qualitative features such as, for example, dynamical crossovers. Finally we discuss the kurtosis of the ABP's position, which we compute exactly, and show that it can be used to differentiate between active Brownian particles and the active Ornstein-Uhlenbeck process.

Active Brownian particles (ABPs, such as self-phoretic colloids) swim at fixed speed v along a body-axis u that rotates by slow angular diffusion. Run-and-tumble particles (RTPs, such as motile bacteria) swim with constant u until a random tumble event suddenly decorrelates the orientation. We show that when the motility parameters depend on density ρ but not on u, the coarse-grained fluctuating hydrodynamics of interacting ABPs and RTPs can be mapped onto each other and are thus strictly equivalent. In both cases, a steeply enough decreasing v(ρ) causes phase separation in dimensions d = 2,3, even when no attractive forces act between the particles. This points to a generic role for motility-induced phase separation in active matter. However, we show that the ABP/RTP equivalence does not automatically extend to the more general case of u-dependent motilities.

A quantitatively accurate prediction of properties for entangled polymers is a long-standing challenge that must be addressed to enable efficient development of these materials. The complex nature of polymers is the fundamental origin of this challenge. Specifically, the chemistry, structure, and dynamics at the atomistic scale affect properties at the meso and macro scales. Therefore, quantitative predictions must start from atomistic molecular dynamics (AMD) simulations. Combined use of atomistic and coarse-grained (CG) models is a promising approach to estimate long-timescale behavior of entangled polymers. However, a systematic coarse-graining is still to be done for bridging the gap of length and time scales while retaining atomistic characteristics. Here we examine the gaps among models, using a generic mapping scheme based on power laws that are closely related to universality in polymer structure and dynamics. The scheme reveals the characteristic length and time for the onset of universality between the vastly different scales of an atomistic model of polyethylene and the bead-spring Kremer–Grest (KG) model. The mapping between CG model of polystyrene and the KG model demonstrates the fast onset of universality, and polymer dynamics up to the subsecond time scale are observed. Thus, quantitatively traceable timescales of polymer MD simulations can be significantly increased.

Active Brownian particles (ABPs) serve as a minimal model of active matter systems. When ABPs are sufficiently persistent, they undergo a liquid-gas phase separation and, in the presence of obstacles, accumulate around them, forming a wetting layer. Here, we perform simulations of ABPs in a quasi-one-dimensional domain in the presence of a wall, studying the dynamics of the polarization field. Over the course of time, we observe a transition from a homogeneous (where all particles are aligned) to a heterogeneous (where particles align only at the interface) polarization regime. We propose coarse-grained equationsfor the density and polarization fields based on microscopic and phenomenological arguments that correctly account for the observed phenomena.

Many microorganisms use chemical 'signaling' - a quintessential self-organizing strategy in non-equilibrium - that can induce spontaneous aggregation and coordinated motion. Using synthetic signaling as a design principle, we construct a minimal model of active Brownian particles (ABPs) having soft repulsive interactions on a chemically quenched patterned substrate. The interplay between chemo-phoretic interactions and activity is numerically investigated for a proposed variant of the Keller-Segel model for chemotaxis. Such competition not only results in a chemo-motility-induced phase-separated state, but also results in a new cohesive clustering phase with synchronized rotations. Our results suggest that rotational order can emerge in systems by virtue of activity and repulsive interactions alone without an explicit alignment interaction. These rotations can also be exploited by designing mechanical devices that can generate reorienting torques using active particles.