Direct Observation of Nondiffusive Motion of a Brownian Particle

Lukić, Branimir; Jeney, Sylvia; Tischer, Christian; Kulik, Andrzej; Forró, Lászlø; Florin, Ernst‐Ludwig

doi:10.1103/physrevlett.95.160601

Cited by 176 publications

(172 citation statements)

References 28 publications

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“…Similarly, in accretion disks, the central gravitational force plays the role of driving force (cause) producing differential velocity (shear) in the flow. Hence, by the fluctuationdissipation theorem of statistical mechanics (see, e.g., Miyazaki & Bedeaux 1995;Lukić et al 2005), there must be some thermal fluctuations in such flows, with some temperature, however low it may be, and that cause the fluid particles to have Brownian motion. Therefore, the time variation (derivative) of this Brownian motion, which is defined as white noise, plays the role of the extra stochastic forcing term in the OrrSommerfeld equations (Equations (1) and (2)) which are present generically, in particular when perturbation is considered.…”

Section: Relevance Of White Noise In the Context Of Shear Flowsmentioning

confidence: 99%

A Pure Hydrodynamic Instability in Shear Flows and Its Application to Astrophysical Accretion Disks

Nath

Mukhopadhyay

2016

ApJ

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We provide a possible resolution for the century-old problem of hydrodynamic shear flows, which are apparently stable in linear analysis but shown to be turbulent in astrophysically observed data and experiments. This mismatch is noticed in a variety of systems, from laboratory to astrophysical flows. There are so many uncountable attempts made so far to resolve this mismatch, beginning with the early work of Kelvin, Rayleigh, and Reynolds toward the end of the nineteenth century. Here we show that the presence of stochastic noise, whose inevitable presence should not be neglected in the stability analysis of shear flows, leads to pure hydrodynamic linear instability therein. This explains the origin of turbulence, which has been observed/interpreted in astrophysical accretion disks, laboratory experiments, and direct numerical simulations. This is, to the best of our knowledge, the first solution to the long-standing problem of hydrodynamic instability of Rayleigh-stable flows.

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Section: Relevance Of White Noise In the Context Of Shear Flowsmentioning

confidence: 99%

A Pure Hydrodynamic Instability in Shear Flows and Its Application to Astrophysical Accretion Disks

Nath

Mukhopadhyay

2016

ApJ

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“…S1 and S2). The fluctuations may reflect nonequilibrium processes at even lower frequencies and inertial forces at still higher frequencies (13). We excluded the possibility that instrumental noise affected the high-frequency portion of the measured spectra by quantifying its power and by including it in our data analysis.…”

Section: Resultsmentioning

confidence: 99%

Anomalous Brownian motion discloses viscoelasticity in the ear’s mechanoelectrical-transduction apparatus

Kozlov

Andor-Ardó

Hudspeth

2012

Proc. Natl. Acad. Sci. U.S.A.

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The ear detects sounds so faint that they produce only atomic-scale displacements in the mechanoelectrical transducer, yet thermal noise causes fluctuations larger by an order of magnitude. Explaining how hearing can operate when the magnitude of the noise greatly exceeds that of the signal requires an understanding both of the transducer's micromechanics and of the associated noise. Using microrheology, we characterize the statistics of this noise; exploiting the fluctuation-dissipation theorem, we determine the associated micromechanics. The statistics reveal unusual Brownian motion in which the mean square displacement increases as a fractional power of time, indicating that the mechanisms governing energy dissipation are related to those of energy storage. This anomalous scaling contradicts the canonical model of mechanoelectrical transduction, but the results can be explained if the micromechanics incorporates viscoelasticity, a salient characteristic of biopolymers. We amend the canonical model and demonstrate several consequences of viscoelasticity for sensory coding.auditory system | hair cell | interferometry | vestibular system T he development of experimental and analytical tools has made possible high-resolution studies of the mechanical properties of biological macromolecules on time scales ranging from the picosecond fluctuations of single amide bonds in proteins, through the submillisecond dynamics of ion-channel gating and enzyme catalysis, to the much slower events involved in cell division and motility (1,2). These studies reveal that the energy landscapes in proteins are complex and that the associated hierarchy of time scales produces nonexponential temporal correlations (3,4). The absence of a single characteristic time scale implies stochastic processes with memory and therefore distinct from simple diffusion.Auditory physiology offers a unique perspective on biological micromechanics. The conversion of a sound's energy into an electrical signal in the ear is a molecular event that involves an ion channel linked mechanically to a gating spring, an elastic element whose tension is modulated by sound. The weakest sounds that we can hear extend the gating spring by less than a nanometer (5,6). Under these conditions, separating the signal from the intrinsic thermal noise is a formidable task, but one facilitated by the periodic structure of most sounds. Although random fluctuations are known to dominate hair-bundle kinematics and to influence signal detection through stochastic resonance (7), their origin and statistical properties have remained obscure. In this work we have experimentally characterized the random fluctuations of hair bundles by dual-beam differential interferometry, a technique that has allowed us to make large-bandwidth, high-resolution measurements of the nanometer-scale thermal motions of stereocilia in living hair bundles from the inner ear. We have interpreted the measurements by introducing a theoretical framework that incorporates viscoelasticity and the known principl...

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“…Instead of measuring a photon correlation function for laser light scattered off a suspension of micro-spheres, developments in instrumentation [22] and data analysis [21] for optical tweezers have made it possible now to measure directly, with accuracy and precision, on a single micro-sphere [24]. Thus it just might be possible to observe directly the "color" of the thermal noise, the frequency dependence of the non-white power spectrum, in a very challenging single-particle experiment with optical tweezers [30].…”

Section: Power-law Tailsmentioning

confidence: 99%