Les Atomes

Perrin,

doi:10.14375/np.9782369430230

Cited by 57 publications

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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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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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“…* villermaux@irphe.univ-mrs.fr hence bridging Brownian motion, random walks, and diffusion, a view soon quantified experimentally by Perrin [5].…”

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Superdiffusive trajectories in Brownian motion

Duplat

Kheifets

et al. 2013

Phys. Rev. E

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“…The robustness of the Brownian motion pointed to the deeper, unobservable agitations of molecules constituting the medium -just as the evident rocking of a far off ship betrays imperceptibly distant waves on the sea (Perrin [1913], p. 83). As Perrin summarized, after reviewing the history of experiments testing the robustness of Brownian motion, "All of these characteristics force us to conclude [...] that the agitation does not originate either in the particles themselves or in any cause external to the liquid, but must be attributed to internal movements, characteristic of the fluid state" (Perrin [1913], p. 86).…”

Section: Robustness Analysis In Sciencementioning

confidence: 99%

Robustness Analysis as Explanatory Reasoning

Schupbach

2018

The British Journal for the Philosophy of Science

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When scientists seek further confirmation of their results, they often attempt to duplicate the results using diverse means. To the extent that they are successful in doing so, their results are said to be robust. This paper investigates the logic of such "robustness analysis" [RA]. The most important and challenging question an account of RA can answer is what sense of evidential diversity is involved in RAs. I argue that prevailing formal explications of such diversity are unsatisfactory. I propose a unified, explanatory account of diversity in RAs. The resulting account is, I argue, truer to actual cases of RA in science; moreover, this account affords us a helpful, new foothold on the logic undergirding RAs.

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“…[10][11][12][13] Teško bi bilo izdvojiti događaj koji je to toga doveo; najbolje bi bilo reći da istraživanje strukture atoma i molekula započinje Arrheniusovom teorijom elektrolitičke disocijacije (1887. ), otkrićem elektrona (J. J.…”

Section: -9unclassified

Kemijska veza u hrvatskim udžbenicima

Raos¹

2016

Kem. Ind.

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Les Atomes

Cited by 57 publications

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Superdiffusive trajectories in Brownian motion

Superdiffusive trajectories in Brownian motion

Robustness Analysis as Explanatory Reasoning

Kemijska veza u hrvatskim udžbenicima

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