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Register a new userReduced description method in the kinetic theory of Brownian motion with active fluctuations
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Added by
Oleksii Sliusarenko Yu.
Publication date
2016
fields
Physics
and research's language is
English
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We develop a microscopic approach to the kinetic theory of many-particle systems with dissipative and potential interactions in presence of active fluctuations. The approach is based on a generalization of Bogolyubov--Peletminsky reduced description method applied to the systems of many active particles. It is shown that the microscopic approach developed allows to construct the kinetic theory of two- and three-dimensional systems of active particles in presence of non-linear friction (dissipative interaction) and an external random field with active fluctuations. The kinetic equations for these systems in case of a weak interaction between the particles (both potential and dissipative) and low-intensity active fluctuations are obtained. We demonstrate particular cases in which the derived kinetic equations have solutions that match the results known in the literature. It is shown that the display of the head-tail asymmetry and self-propelling even in the case of a linear friction, is one of the consequences of the local nature of the active fluctuations.
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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 shows positive or negative deviations from a Gaussian behavior at intermediate times depending on the dominance of speed or orientational fluctuations.
Using an additivity property, we study particle-number fluctuations in a system of interacting self-propelled particles, called active Brownian particles (ABPs), which consists of repulsive disks with random self-propulsion velocities. From a fluctuation-response relation - a direct consequence of additivity, we formulate a thermodynamic theory which captures the previously observed features of nonequilibrium phase transition in the ABPs from a homogeneous fluid phase to an inhomogeneous phase of coexisting gas and liquid. We substantiate the predictions of additivity by analytically calculating the subsystem particle-number distributions in the homogeneous fluid phase away from criticality where analytically obtained distributions are compatible with simulations in the ABPs.
Combining experiments on active colloids, whose propulsion velocity can be controlled via a feedback loop, and theory of active Brownian motion, we explore the dynamics of an overdamped active particle with a motility that depends explicitly on the particle orientation. In this case, the active particle moves faster when oriented along one direction and slower when oriented along another, leading to an anisotropic translational dynamics which is coupled to the particles rotational diffusion. We propose a basic model of active Brownian motion for orientation-dependent motility. Based on this model, we obtain analytic results for the mean trajectories, averaged over the Brownian noise for various initial configurations, and for the mean-square displacements including their anisotropic non-Gaussian behavior. The theoretical results are found to be in good agreement with the experimental data. Our findings establish a methodology to engineer complex anisotropic motilities of active Brownian particles, with potential impact in the study of the swimming behavior of microorganisms subjected to anisotropic driving fields.
Microorganisms such as bacteria are active matters which consume chemical energy and generate their unique run-and-tumble motion. A swarm of such microorganisms provide a nonequilibrium active environment whose noise characteristics are different from those of thermal equilibrium reservoirs. One important difference is a finite persistence time, which is considerably large compared to that of the equilibrium noise, that is, the active noise is colored. Here, we study a mesoscopic energy-harvesting device (engine) with active reservoirs harnessing this noise nature. For a simple linear model, we analytically show that the engine efficiency can surpass the conventional Carnot bound, thus the power-efficiency tradeoff constraint is released, and the efficiency at the maximum power can overcome the Curzon-Ahlborn efficiency. We find that the supremacy of the active engine critically depends on the time-scale symmetry of two active reservoirs.
Brownian motion of a particle with an arbitrary shape is investigated theoretically. Analytical expressions for the time-dependent cross-correlations of the Brownian translational and rotational displacements are derived from the Smoluchowski equation. The role of the particle mobility center is determined and discussed.
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