Brownian motion at short time scales

Li, Tongcang; Raizen, Mark G.

doi:10.1002/andp.201200232

Cited by 129 publications

(133 citation statements)

References 91 publications

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“…The influence of fluid and particle inertia was also theoretically investigated [11], predicting the short time Brownian ballistic regime. Only recently, improvements in imaging techniques have allowed for experimental investigations of the Brownian ballistic regime [12,13,14] and the diffusion of shapes other than spheres [15,16,17,18]. Recent work in the biophysics of swimming microorganisms has raised interest into the diffusion of active particles which use internal processes to swim through the fluid.…”

Section: Introductionmentioning

confidence: 99%

The passive diffusion ofLeptospira interrogans

Koens

Lauga

2014

Phys. Biol.

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Abstract. Motivated by recent experimental measurements, the passive diffusion of the bacterium Leptospira interrogans is investigated theoretically. By approximating the cell shape as a straight helix and using the slender-body-theory approximation of Stokesian hydrodynamics, the resistance matrix of Leptospira is first determined numerically. The passive diffusion of the helical cell is then obtained computationally using a Langevin formulation which is sampled in time in a manner consistent with the experimental procedure. Our results are in excellent quantitative agreement with the experimental results with no adjustable parameters.

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Section: Introductionmentioning

confidence: 99%

The passive diffusion ofLeptospira interrogans

Koens

Lauga

2014

Phys. Biol.

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“…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]. The obtained results are well described by the hydrodynamic theory of the BM in harmonic potentials [9] and are interesting also because they can be considered as measurements of the "color" of the thermal noise driving the Brownian particles through collisions with the fluid molecules [3,10,11].…”

Section: Introductionmentioning

confidence: 84%

“…In several recent papers, see the review article [1], the positional fluctuations of Brownian microspheres were studied by confining the particles in an optical trap. These experiments clearly show the inadequacy of the standard Langevin theory [2] to describe the Brownian motion (BM) in fluids.…”

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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“…The role of Gaussian variables in probability led to a first theory of Brownian motion 10) . Paul Langevin introduced a stochastic force and derived Einstein's theory of Brownian motion from Newton's second law 11) . Thus, a recent study investigated the uncertainty of peak runoff height due to the uncertainty of rainfall pattern by using the Stochastic Differential Equation (SDE).…”

Section: Introductionmentioning

confidence: 99%

Uncertainty of Peak Runoff Height Associated With Uncertainty of Water Holding Capacity and Rainfall Pattern

Supraba

Yamada

2015

J. JSCE Ser. G

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Improving the accuracy of peak runoff height estimation for flood risk reduction purpose is one of the research targets in hydrology. Peak runoff height is generally simulated by hydrological models deterministically. A recent study suggested that the rainfall-runoff system can be expressed as a stochastic differential equation by adopting the Fokker-Planck equation in association with rainfall pattern. The objective of this study is to estimate the uncertainty of peak runoff height by considering uncertainty of effective rainfall through the water holding capacity in addition to the uncertainty of rainfall pattern. Results show that the uncertainty of peak runoff height increase with the increment of uncertainty associated with rainfall pattern, whereas uncertainty of water holding capacity needs to be considered in the quantification of the uncertainty of peak runoff height.

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Brownian motion at short time scales

Cited by 129 publications

References 91 publications

The passive diffusion ofLeptospira interrogans

The passive diffusion ofLeptospira interrogans

An Efficient Method to Study Nondiffusive Motion of Brownian Particles

Uncertainty of Peak Runoff Height Associated With Uncertainty of Water Holding Capacity and Rainfall Pattern

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