RESUMO

A model for anomalous transport of tracer particles diffusing in complex media in two dimensions is proposed. The model takes into account the characteristics of persistent motion that an active bath transfers to the tracer; thus, the model proposed here extends active Brownian motion, for which the stochastic dynamics of the orientation of the propelling force is described by scaled Brownian motion (sBm), identified by time-dependent diffusivity of the form D_{ß}∝t^{ß-1}, ß>0. If ß≠1, sBm is highly nonstationary and suitable to describe such nonequilibrium dynamics induced by complex media. In this paper, we provide analytical calculations and computer simulations to show that genuine anomalous diffusion emerges in the long-time regime, with a time scaling of the mean-squared displacement t^{2-ß}, while ballistic transport t^{2}, characteristic of persistent motion, is found in the short-time regime. We also analyze the time dependence of the kurtosis, and the intermediate scattering function of the position distribution, as well as the propulsion autocorrelation function, which defines the effective persistence time.

RESUMO

Correction for 'Collective motion of chiral Brownian particles controlled by a circularly-polarized laser beam' by Raúl Josué Hernández et al., Soft Matter, 2020, 16, 7704-7714, DOI: .

RESUMO

We demonstrate the emergence of circular collective motion in a system of spherical light-propelled Brownian particles. Light-propulsion occurs as consequence of the coupling between the chirality of polymeric particles - left (L)- or right (R)-type - and the circularly-polarized light that irradiates them. Irradiation with light that has the same helicity as the particle material leads to a circular cooperative vortical motion between the chiral Brownian particles. In contrast, opposite circular-polarization does not induce such coupling among the particles but only affects their Brownian motion. The mean angular momentum of each particle has a value and sign that distinguishes between chiral activity dynamics and typical Brownian motion. These outcomes have relevant implications for chiral separation technologies and provide new strategies for optical torque tunability in mesoscopic optical array systems, micro- and nanofabrication of light-activated engines with selective control and collective motion.

RESUMO

We present an analysis of the stationary distributions of run-and-tumble particles trapped in external potentials in terms of a thermophoretic potential that emerges when trapped active motion is mapped to trapped passive Brownian motion in a fictitious inhomogeneous thermal bath. We elaborate on the meaning of the non-Boltzmann-Gibbs stationary distributions that emerge as a consequence of the persistent motion of active particles. These stationary distributions are interpreted as a class of distributions in nonequilibrium statistical mechanics known as superstatistics. Our analysis provides an original insight on the link between the intrinsic nonequilibrium nature of active motion and the well-known concept of local equilibrium used in nonequilibrium statistical mechanics and contributes to the understanding of the validity of the concept of effective temperature. Particular cases of interest, regarding specific trapping potentials used in other theoretical or experimental studies, are discussed. We point out as an unprecedented effect, the emergence of new modes of the stationary distribution as a consequence of the coupling of persistent motion in a trapping potential that varies highly enough with position.

RESUMO

The diffusion of chiral active Brownian particles in three-dimensional space is studied analytically, by consideration of the corresponding Fokker-Planck equation for the probability density of finding a particle at position x and moving along the direction v[over ̂] at time t, and numerically, by the use of Langevin dynamics simulations. The analysis is focused on the marginal probability density of finding a particle at a given location and at a given time (independently of its direction of motion), which is found from an infinite hierarchy of differential-recurrence relations for the coefficients that appear in the multipole expansion of the probability distribution, which contains the whole kinematic information. This approach allows the explicit calculation of the time dependence of the mean-squared displacement and the time dependence of the kurtosis of the marginal probability distribution, quantities from which the effective diffusion coefficient and the "shape" of the positions distribution are examined. Oscillations between two characteristic values were found in the time evolution of the kurtosis, namely, between the value that corresponds to a Gaussian and the one that corresponds to a distribution of spherical shell shape. In the case of an ensemble of particles, each one rotating around a uniformly distributed random axis, evidence is found of the so-called effect "anomalous, yet Brownian, diffusion," for which particles follow a non-Gaussian distribution for the positions yet the mean-squared displacement is a linear function of time.

RESUMO

By studying a system of Brownian particles that interact among themselves only through a local velocity-alignment force that does not affect their speed, we show that self-propulsion is not a necessary feature for the flocking transition to take place as long as underdamped particle dynamics can be guaranteed. Moreover, the system transits from stationary phases close to thermal equilibrium, with no net flux of particles, to far-from-equilibrium ones exhibiting collective motion, phase coexistence, long-range order, and giant number fluctuations, features typically associated with ordered phases of models where self-propelled particles with overdamped dynamics are considered.

Assuntos

RESUMO

We study the free diffusion in two dimensions of active Brownian swimmers subject to passive fluctuations on the translational motion and to active fluctuations on the rotational one. The Smoluchowski equation is derived from a Langevin-like model of active swimmers and analytically solved in the long-time regime for arbitrary values of the Péclet number; this allows us to analyze the out-of-equilibrium evolution of the positions distribution of active particles at all time regimes. Explicit expressions for the mean-square displacement and for the kurtosis of the probability distribution function are presented and the effects of persistence discussed. We show through Brownian dynamics simulations that our prescription for the mean-square displacement gives the exact time dependence at all times. The departure of the probability distribution from a Gaussian, measured by the kurtosis, is also analyzed both analytically and computationally. We find that for the inverse of Péclet numbers ≲0.1, the distance from Gaussian increases as ∼t(-2) at short times, while it diminishes as ∼t(-1) in the asymptotic limit.

RESUMO

Starting from a Langevin description of active particles that move with constant speed in infinite two-dimensional space and its corresponding Fokker-Planck equation, we develop a systematic method that allows us to obtain the coarse-grained probability density of finding a particle at a given location and at a given time in arbitrary short-time regimes. By going beyond the diffusive limit, we derive a generalization of the telegrapher equation. Such generalization preserves the hyperbolic structure of the equation and incorporates memory effects in the diffusive term. While no difference is observed for the mean-square displacement computed from the two-dimensional telegrapher equation and from our generalization, the kurtosis results in a sensible parameter that discriminates between both approximations. We carry out a comparative analysis in Fourier space that sheds light on why the standard telegrapher equation is not an appropriate model to describe the propagation of particles with constant speed in dispersive media.

Assuntos