Dynamics of a trapped Brownian particle in shear flows

Holzer, Lukas; Bammert, Jochen; Rzehak, Roland; Zimmermann, Walter

doi:10.1103/physreve.81.041124

Cited by 36 publications

(76 citation statements)

References 55 publications

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“…[34]. The correlation functions between the different particle displacements are calculated analytically and we show how a second Brownian particle influences the stochastic motion and the positional probability distribution of its neighbor compared to the single particle case [33,34]. In addition, we find that the anti cross-correlations between two fluctuating particles in a quiescent fluid, as described in Ref.…”

Section: Introductionmentioning

confidence: 78%

“…The correlation functions (20) depend via µ on the trap distance d , which leads to interesting corrections to the autocorrelations compared to the case of one isolated particle in Ref. [33]. The distinct relaxation rates given by eqs.…”

Section: One-particle Correlationsmentioning

confidence: 99%

“…This paper is an extension of the theoretical work on the single particle dynamics described in Ref. [33] to a pair of two hydrodynamically interacting point-particles with an effective hydrodynamic radius and trapped in a linear shear flow. It provides the theoretical background for the experimental results on the two-particle correlations presented in Ref.…”

Section: Introductionmentioning

confidence: 99%

“…[33] show that shear-induced cross-correlations between perpendicular random particle displacements, like xỹ = 0, survive if a particle experiences some constraints such as a harmonic potential. This is important from various points of view.…”

Section: Introductionmentioning

confidence: 99%

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Dynamics of two trapped Brownian particles: Shear-induced cross-correlations

2010

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The dynamics of two Brownian particles trapped by two neighboring harmonic potentials in a linear shear flow is investigated. The positional correlation functions in this system are calculated analytically and analyzed as a function of the shear rate and the trap distance. Shear-induced cross-correlations between particle fluctuations along orthogonal directions in the shear plane are found. They are linear in the shear rate, asymmetric in time, and occur for one particle as well as between both particles. Moreover, the shear rate enters as a quadratic correction to the well-known correlations of random displacements along parallel spatial directions. The correlation functions depend on the orientation of the connection vector between the potential minima with respect to the flow direction. As a consequence, the inter-particle cross-correlations between orthogonal fluctuations can have zero, one or two local extrema as a function of time. Possible experiments for detecting these predicted correlations are described.

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Section: Introductionmentioning

confidence: 78%

Section: One-particle Correlationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Dynamics of two trapped Brownian particles: Shear-induced cross-correlations

2010

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“…The nonequilibrium aspect of the medium is picked up in the effective force in the right-hand side of (1.3) and [Y ] will most likely not be constant in time; see also [19,20,21,11,6] for statistical forces from nonequilibrium. That can be imagined as caused by some rotational force F that acts on the medium particles (as illustrated in Section 4), or it can be the combined result of strong nonlinearities in the interaction Φ.…”

Section: Friction and Noise For A Probe In A Nonequilibrium Fluidmentioning

confidence: 99%

Friction and noise for a probe in a nonequilibrium fluid

Maes

Steffenoni

2015

Phys. Rev. E

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Abstract. We investigate the fluctuation dynamics of a probe around a deterministic motion induced by interactions with driven particles. The latter constitute the nonequilibrium medium in which the probe is immersed and is modelled as overdamped Langevin particle dynamics driven by nonconservative forces. The expansion that yields the friction and noise expressions for the reduced probe dynamics is based on linear response around a time-dependent nonequilibrium condition of the medium. The result contains an extension of the second fluctuation-dissipation relation between friction and noise for probe motion in a nonequilibrium fluid. The problemWhether the environment of a system is in equilibrium or is driven into a nonequilibrium condition is important for characterizing internal motions and reactions. In other words the reduced system dynamics will reflect whether the environment is driven or not.For example, the relation between noise and friction on the system need no longer be described via the standard second fluctuation-dissipation (or Einstein) relation, we cannot unambiguously speak about entropy fluxes into the environment in terms of heat as there would be no Clausius relation, and system fluctuations or noise level in general are not simply quantified by a reservoir temperature. The present paper takes up the challenge of characterizing such an effective dynamics for a probe in contact with a nonequilibrium medium. One should have in mind that the medium consists of active elements or driven particles themselves in contact with a big thermal equilibrium reservoir (like surrounding air or water). Combined, the medium and the heat bath make up the nonequilibrium fluid. The system is called a probe here, but it can in general also refer to a collective or with j = 1, . . . , N labeling the particles and subject to independent standard white noises ξ j t . The β denotes the inverse temperature of the background equilibrium reservoir but the particles are effectively driven by the nonconservative force F . For simplicity we have not introduced explicitly friction and mass parameters, keeping only λ (coupling) and β as parameters. The particle interaction is given through the potential Φ while the potential U depends on the position X t of the probe, thus representing the back-reaction of the probe on each particle. Other and different types of interaction between probe and medium are possible, e.g. in terms of their center of mass coordinate with a mean field type potential U ( j x j t − X t ), here not discussed and inessential for the present level of discussion. Keeping to (1.1) the probe dynamics itself iswhere we indicate by K X t ,Ẋ t other aspects of the probe motion in the fluid. Its mass M is obviously also an important parameter for separation of time-scales between probe and fluid particle motion.The equations (1.1) and (1.2) starting at t = 0 are the basic evolution equations representing the coupled dynamics of probe and fluid particles. Nonequilibrium works directly on the medium which is ...

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On the Second Fluctuation–Dissipation Theorem for Nonequilibrium Baths

Maes

2014

J Stat Phys

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Baths produce friction and random forcing on particles suspended in them. The relation between noise and friction in (generalized) Langevin equations is usually referred to as the second fluctuation-dissipation theorem. We show what is the proper nonequilibrium extension, to be applied when the environment is itself active and driven. In particular we determine the effective Langevin dynamics of a probe from integrating out a steady nonequilibrium environment. The friction kernel picks up a frenetic contribution, i.e., involving the environment's dynamical activity, responsible for the breaking of the standard Einstein relation. I. REDUCED DYNAMICSThe Langevin equation or its generalizations are effective diffusive dynamics to describe certain tagged degrees of freedom interacting with a heat bath. Best known is the case of a Brownian particle suspended in a fluid at rest. In a growing number of applications the tagged particle or probe moves in a driven or active medium of particles, the latter in turn being in contact with an equilibrium heat bath. In that way there are three levels of description: probe, driven particles and heat bath -see Fig. 1. For the driven particles we have in mind active media such as the cell environment of a living organism in which the motion of microprobes is studied [7,34], or spatially extended objects such as large polymers undergoing nonequilibrium forcing and for which the motion of a tagged monomer is investigated [18,33]. We can also imagine a sheared or non-uniformly rotating and thermostated fluid in which colloids or polymers are moving; see e.g. [8,11,22,40] among many possible references. In fact, baths can be out-of-equilibrium for a great variety of reasons. Here we do not concentrate on one special case but go for the general structure of the effective dynamics of a probe in weak contact with many constituents under steady driving. For better focus we do not consider the effect of time-dependent reservoirs like arXiv:1309.3160v1 [cond-mat.stat-mech]

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Dynamics of a trapped Brownian particle in shear flows

Cited by 36 publications

References 55 publications

Dynamics of two trapped Brownian particles: Shear-induced cross-correlations

Dynamics of two trapped Brownian particles: Shear-induced cross-correlations

Friction and noise for a probe in a nonequilibrium fluid

On the Second Fluctuation–Dissipation Theorem for Nonequilibrium Baths

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