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Brownian Motion of an Ellipsoid
Science, 2006We studied the Brownian motion of isolated ellipsoidal particles in water confined to two dimensions and elucidated the effects of coupling between rotational and translational motion. By using digital video microscopy, we quantified the crossover from short-time anisotropic to long-time isotropic diffusion and directly measured probability ...
Han, Yilong +5 more
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On the Theory of the Brownian Motion
, 1930With a method first indicated by Ornstein the mean values of all the powers of the velocity $u$ and the displacement $s$ of a free particle in Brownian motion are calculated. It is shown that $u\ensuremath{-}{u}_{0}\mathrm{exp}(\ensuremath{-}\ensuremath{\
G. Uhlenbeck, L. Ornstein
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Catastrophes in Brownian motion
Physics Letters A, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Guz SA, MANNELLA, RICCARDO, Sviridov MV
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On the theory of brownian motion
, 1973The spectrum of the Fokker-Planck operator for weakly coupled gases is considered. The operator is decomposed into operators acting on functions whose angular dependence is given by spherical harmonics.
R. Mazo
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1969
Publisher Summary This chapter discusses the Brownian motion, and reviews the construction of the Brownian motion. The simplest properties of the Brownian motion are discussed. A Martingale inequality is discussed, and the law of the iterated logarithm is reviewed. Several-dimensional Brownian motion is also discussed in the chapter.
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Publisher Summary This chapter discusses the Brownian motion, and reviews the construction of the Brownian motion. The simplest properties of the Brownian motion are discussed. A Martingale inequality is discussed, and the law of the iterated logarithm is reviewed. Several-dimensional Brownian motion is also discussed in the chapter.
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Molecular Machines, 2018
This chapter provides an introduction to the main ideas of Brownian motion. Brownian motion connects equilibrium and nonequilibrium statistical mechanics. It connects diffusion—a nonequilibrium phenomenon—with thermal fluctuations—an equilibrium concept.
G. Zocchi
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This chapter provides an introduction to the main ideas of Brownian motion. Brownian motion connects equilibrium and nonequilibrium statistical mechanics. It connects diffusion—a nonequilibrium phenomenon—with thermal fluctuations—an equilibrium concept.
G. Zocchi
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Physical Review Letters, 1983
A new master equation describing the irreversible process of a quantum mechanical Brownian particle is proposed. The master equation is shown to obey the symmetry of detailed balance leading to a quantum analog of the reciprocity relations, and the fluctuation-dissipation theorem is obtained. The method is applied to the damped harmonic oscillator. The
Grabert, Hermann, Talkner, Peter
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A new master equation describing the irreversible process of a quantum mechanical Brownian particle is proposed. The master equation is shown to obey the symmetry of detailed balance leading to a quantum analog of the reciprocity relations, and the fluctuation-dissipation theorem is obtained. The method is applied to the damped harmonic oscillator. The
Grabert, Hermann, Talkner, Peter
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Role of Brownian motion in the enhanced thermal conductivity of nanofluids
, 2004We have found that the Brownian motion of nanoparticles at the molecular and nanoscale level is a key mechanism governing the thermal behavior of nanoparticle–fluid suspensions (“nanofluids”).
S. Jang, Stephen U. S. Choi
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Brownian Motion on a Hypersurface
Bulletin of the London Mathematical Society, 1985Let \(f:R^ d\to R\) be a \(C^ 2\) function and let \(V=f^{-1}(c)\) be a level surface on which grad f(x) is never zero and orient V with the field n(\(\cdot)\) of normal vectors. Let H(x) be the mean curvature at x. We prove the following: 1. A process X in \(R^ d\) with \(f(X_ 0)=c\) and \(dX=dB n(X)+2^{-1}(d- 1)H(X)n(X)dt\) is a Brownian motion on ...
John T. Lewis, M. van den Berg
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