Emergent clustering due to informatic interactions in active matter

Many organisms in nature use local interactions to generate global cooperative phenomena. To unravel how the behavior of individuals generates effective interactions within a group, we introduce a simple model, wherein each agent senses the presence of others nearby and changes its physical motion accordingly. This generates between agents interactions that are not physical but rather virtual. We study the radial distribution function to quantify the emergent interactions for both social and anti-social behavior; We identify social behavior as when an agent exhibits a tendency to remain in the vicinity of other agents, whereas anti-social behavior as when it displays a tendency to escape from the vicinity of others. Using Langevin dynamics simulations, we discover that under certain conditions, positive correlations, which indicate attraction can emerge even in the case of anti-social behavior. Our results are potentially useful for designing robotic swimmers that can swim collectively only based on sensing the distance to their neighbors, without measuring any orientational information

Fractional Brownian motion with random Hurst exponent: accelerating diffusion and persistence transitions

Fractional Brownian motion, a Gaussian non-Markovian self-similar process with stationary long-correlated increments, has been identified to give rise to the anomalous diffusion behavior in a great variety of physical systems. The correlation and diffusion properties of this random motion are fully characterized by its index of self-similarity, or the Hurst exponent. However, recent single particle tracking experiments in biological cells revealed highly complicated anomalous diffusion phenomena that can not be attributed to a class of self-similar random processes. Inspired by these observations, we here study the process which preserves the properties of fractional Brownian motion at a single trajectory level, however, the Hurst index randomly changes from trajectory to trajectory. We provide a general mathematical framework for analytical, numerical and statistical analysis of fractional Brownian motion with random Hurst exponent. The explicit formulas for probability density function, mean square displacement and autocovariance function of the increments are presented for three generic distributions of the Hurst exponent, namely two-point, uniform and beta distributions. The important features of the process studied here are accelerating diffusion and persistence transition which we demonstrate analytically and numerically.Comment: 16 pages, 10 figure

Nonequilibrium Probability Currents in Optically-Driven Colloidal Suspensions

In the absence of directional motion it is often hard to recognize athermal fluctuations. Probability currents provide such a measure in terms of the rate at which they enclose area in phase space. We measure this area enclosing rate for trapped colloidal particles, where only one particle is driven. By combining experiment, theory, and simulation, we single out the effect of the different time scales in the system on the measured probability currents. In this controlled experimental setup, particles interact hydrodynamically. These interactions lead to a strong spatial dependence of the probability currents and to a local influence of athermal agitation. In a multiple-particle system, we show that even when the driving acts only on one particle, probability currents occur between other, non-driven particles. This may have significant implications for the interpretation of fluctuations in biological systems containing elastic networks in addition to a suspending fluid.Comment: Submission to SciPost Physic

Fractional Brownian motion with random diffusivity: emerging residual nonergodicity below the correlation time

Abstract Numerous examples for a priori unexpected non-Gaussian behaviour for normal and anomalous diffusion have recently been reported in single-particle tracking experiments. Here, we address the case of non-Gaussian anomalous diffusion in terms of a random-diffusivity mechanism in the presence of power-law correlated fractional Gaussian noise. We study the ergodic properties of this model via examining the ensemble- and time-averaged mean-squared displacements as well as the ergodicity breaking parameter EB quantifying the trajectory-to-trajectory fluctuations of the latter. For long measurement times, interesting crossover behaviour is found as function of the correlation time τ characterising the diffusivity dynamics. We unveil that at short lag times the EB parameter reaches a universal plateau. The corresponding residual value of EB is shown to depend only on τ and the trajectory length. The EB parameter at long lag times, however, follows the same power-law scaling as for fractional Brownian motion. We also determine a corresponding plateau at short lag times for the discrete representation of fractional Brownian motion, absent in the continuous-time formulation. These analytical predictions are in excellent agreement with results of computer simulations of the underlying stochastic processes. Our findings can help distinguishing and categorising certain nonergodic and non-Gaussian features of particle displacements, as observed in recent single-particle tracking experiments

Bayesian inference with single-particle tracking data: model selection and parameter estimation of Levy walks

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Bayesian model comparison and parameter estimation with noisy discrete-time Levy walk

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Bayesian inference of Lévy walks via hidden Markov models: parameter estimation and model classification

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Bayesian model classification and mode-parameter estimation of discrete-time noisy Levy walk

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Bayesian inference of single particle tracking data: parameter estimation and model selection with Lévy walk

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