Direct observation of the full transition from ballistic to diffusive Brownian motion in a liquid

Huang, Ronald; Chavez, Isaac; Taute, Katja M.; Lukić, Branimir; Jeney, Sylvia; Raizen, Mark G.; Florin, Ernst‐Ludwig

doi:10.1038/nphys1953

Cited by 375 publications

(363 citation statements)

References 31 publications

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“…Our work indicates the interest of measuring the different phases of the transport. In particular, an experiment should be attempted to measure r 2 from the ballistic to the interaction phase, as was done for fluids recently by Huang et al 35 For this measurement, resolution in the toroidal direction is required, which will soon be possible in TORPEX with a toroidally moving source. Based on our earlier discussion of the ballistic phase, the toroidal separation of the source from the detector, L b , at the end of this phase is L b ¼ s ba hv 0;jj i:…”

Section: Discussionmentioning

confidence: 99%

“…Suprathermal ions in the SMT have an initial ballistic spreading, analogous to the short ballistic transport phase in a typical collisional random walk observed recently by Huang et al 35 in a neutral fluid. During this ballistic phase, particles move relatively unperturbed with respect to the initial velocity, unaffected by the turbulence, and therefore have a uniform motion.…”

Section: A Ballistic Phasementioning

confidence: 99%

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Suprathermal ion transport in simple magnetized torus configurations

et al. 2012

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Inspired by suprathermal ion experiments in the basic plasma experiment TORPEX, the transport of suprathermal ions in ideal interchange mode turbulence is theoretically examined in the simple magnetized torus configuration. We follow ion tracer trajectories as specified by ideal interchange mode turbulence imported from a numerical simulation of drift-reduced Braginskii equations. Using the variance of displacements, σ2(t)∼tγ, we find that γ depends strongly on suprathermal ion injection energy and the relative magnitude of turbulent fluctuations. The value of γ also changes significantly as a function of time after injection, through three distinguishable phases: ballistic, interaction, and asymmetric. During the interaction phase, we find the remarkable presence of three regimes of dispersion: superdiffusive, diffusive, and subdiffusive, depending on the energy of the suprathermal ions and the amplitude of the turbulent fluctuations. We contrast these results with those from a “slab” magnetic geometry in which subdiffusion does not occur during the interaction phase. Initial results from TORPEX are consistent with data from a new synthetic diagnostic used to interpret our simulation results. The simplicity of the simple magnetized torus makes the present work of interest to analyses of more complicated contexts ranging from fusion devices to astrophysics and space plasma physics.

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Section: Discussionmentioning

confidence: 99%

Section: A Ballistic Phasementioning

confidence: 99%

Suprathermal ion transport in simple magnetized torus configurations

et al. 2012

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“…(1) correctly predicts the diffusive motion of Brownian particles immersed in a thermal bath at all time scales. In the case of a thermal distribution of initial conditions, the long-and short-time predictions have been confirmed experimentally [5,[13][14][15]. In order to observe super-diffusion in standard Brownian motion, it is necessary to perform conditional statistics on Brownian trajectories with fixed (or narrowly distributed) initial velocity, so that dispersion statistics can be calculated for sets of trajectories with zero (or very small) relative initial velocity.…”

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confidence: 99%

Superdiffusive trajectories in Brownian motion

Duplat

Kheifets

et al. 2013

Phys. Rev. E

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The Brownian motion of a microscopic particle in a fluid is one of the cornerstones of statistical physics and the paradigm of a random process. One of the most powerful tools to quantify it was provided by Langevin, who explicitly accounted for a short-time correlated "thermal" force. The Langevin picture predicts ballistic motion, x 2 ∼ t 2 at short-time scales, and diffusive motion x 2 ∼ t at long-time scales, where x is the displacement of the particle during time t, and the average is taken over the thermal distribution of initial conditions. The Langevin equation also predicts a superdiffusive regime, where x 2 ∼ t 3 , under the condition that the initial velocity is fixed rather than distributed thermally. We analyze the motion of an optically trapped particle in air and indeed find t 3 dispersion. This observation is a direct proof of the existence of the random, rapidly varying force imagined by Langevin. Langevin [4], who introduced a stochastic differential equation for the motion of a particle in a thermal bath, with an explicit rapidly varying force f (t) constantly exerted on the particle by the fluid molecules of the bath.The Langevin equation governs the velocity v =ẋ of a free particle in a viscous fluid, in the absence of hydrodynamic memory effects:vwhere m is the particle mass, and τ = m/6πηa is the viscous relaxation time of the spherical particle of radius a in a fluid with viscosity η. The force f is "delta-correlated," meaning that its fluctuations are present down to arbitrarily short-time scales. This is equivalent to having a flat spectrum up to arbitrarily high frequencies; hence, it is referred to as white noise. The variance of the particle velocity is v 2 eq = τ at equilibrium, and thanks to the equipartition theorem is such that v 2 eq = k B T /m, thus, relating temperature T and damping rate 1/τ with the magnitude of the random force, a manifestation of the fluctuation-dissipation theorem.Langevin did not exhaust all the riches of his model but used it to compute the ensemble average squared position of the particle in the long-time limit (t τ ) and found, for particles all starting at x 0 = 0, that (and Fürth [7]) devised a similar model and reached the same conclusion regarding the existence of a diffusive régime [Eq. (2)] but also noted the existence of ballistic behavior, x 2 = τ t 2 , in the shorttime limit t τ . This result, however, still depends on an average being performed on an initial condition of particles with distributed velocities. We come back below to that crucial point, not singled-out as such by either Taylor or Langevin.Consider a particle released at t = 0 in a thermalized medium (i.e., a bath of uniform temperature T ), with constrained initial velocity v 0 (whether it is equal to zero or not) and position x 0 = 0. Solving the Langevin model [Eq. (1)] for the displacement x(t) gives a meanwhere ·|x 0 ,v 0 denotes an average over many realizations of the thermal force, with fixed initial conditions (as opposed to an average over the thermal distribution of...

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“…These experiments clearly show the inadequacy of the standard Langevin theory [2] to describe the Brownian motion (BM) in fluids. So, in contrast to the commonly assumed overdamped motion, experimental access to short timescales has revealed a resonance peak in the spectrum of the particle fluctuations in a liquid [3], the transition from ballistic to diffusive BM has been observed [4] and even, as reported in [5], the instantaneous velocity of a Brownian particle has been measured for the first time in air. For the history and more references on the experiments and theory of the BM we refer to [1,[6][7][8].…”

Section: Introductionmentioning

confidence: 99%

An Efficient Method to Study Nondiffusive Motion of Brownian Particles

Lisý

Tóthová

2016

EPJ Web of Conferences

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Abstract. The experimental access to short timescales has pointed to the inadequacy of the standard Langevin theory of the Brownian motion (BM) in fluids. The hydrodynamic theory of the BM describes well the observed motion of the particles; however, the published approach should be improved in several points. In particular, it leads to incorrect correlation properties of the thermal noise driving the particles. In our contribution we present an efficient method, which is applicable to linear generalized Langevin equations describing the BM of particles with any kind of memory and apply it to interpret the experiments where nondiffusive BM of particles was observed. It is shown that the applicability of the method is much broader, allowing, among all, to obtain efficient solutions of various problems of anomalous BM.

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Direct observation of the full transition from ballistic to diffusive Brownian motion in a liquid

Cited by 375 publications

References 31 publications

Suprathermal ion transport in simple magnetized torus configurations

Suprathermal ion transport in simple magnetized torus configurations

Superdiffusive trajectories in Brownian motion

An Efficient Method to Study Nondiffusive Motion of Brownian Particles

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