Brownian motion: a paradigm of soft matter and biological physics

Frey, Erwin; Kroy, Klaus

doi:10.1002/andp.200410132

Cited by 205 publications

(168 citation statements)

References 239 publications

(315 reference statements)

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“…These friction coefficients asymptotically vanish in the limit δ → 0 (with a logarithmic approach to 0, except for η (3) ), because then the prolate particle more and more resembles a one-dimensional rod-like object which experiences practically no friction when moving through the fluid. It is easy to verify though that even for δ → 0 inertia effects remain negligible compared to viscous friction forces, since the particle mass, being proportional to the particle volume, decreases much faster with δ → 0 than the friction coefficients (67).…”

Section: B Thin Prolate Spheroidmentioning

confidence: 99%

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Entropy production of a Brownian ellipsoid in the overdamped limit

2016

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We analyze the translational and rotational motion of an ellipsoidal Brownian particle from the viewpoint of stochastic thermodynamics. The particle's Brownian motion is driven by external forces and torques and takes place in an heterogeneous thermal environment where friction coefficients and (local) temperature depend on space and time. Our analysis of the particle's stochastic thermodynamics is based on the entropy production associated with single particle trajectories. It is motivated by the recent discovery that the overdamped limit of vanishing inertia effects (as compared to viscous fricion) produces a so-called "anomalous" contribution to the entropy production, which has no counterpart in the overdamped approximation, when inertia effects are simply discarded. Here, we show that rotational Brownian motion in the overdamped limit generates an additional contribution to the "anomalous" entropy. We calculate its specific form by performing a systematic singular perturbation analysis for the generating function of the entropy production. As a side result, we also obtain the (well-known) equations of motion in the overdamped limit. We furthermore investigate the effects of particle shape and give explicit expressions of the "anomalous entropy" for prolate and oblate spheroids and for near-spherical Brownian particles.

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Section: B Thin Prolate Spheroidmentioning

confidence: 99%

“…The theory of Brownian motion [1][2][3], developed in different formulations by Einstein [4], Smoluchowski [5] and Langevin [6] around 1905 and 1906, describes the dynamics of a particle suspended in a fluid. A prototypical example is a small colloidal object, e.g.…”

Section: Introductionmentioning

confidence: 99%

Entropy production of a Brownian ellipsoid in the overdamped limit

2016

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“…We refer the interested reader to the various reviews that have appeared in 2005 to celebrate the 100 years of Einstein's theory of Brownian motion, written either by mathematicians [80,87], by physicists [44,46,89], or by 'biology-oriented' physicists [32,58].…”

Section: Introductionmentioning

confidence: 99%

Random Walks and Polymers in the Presence of Quenched Disorder

Monthus

2006

Lett Math Phys

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After a general introduction to the field, we describe some recent results concerning disorder effects on both 'random walk models', where the random walk is a dynamical process generated by local transition rules, and on 'polymer models', where each random walk trajectory representing the configuration of a polymer chain is associated to a global Boltzmann weight. For random walk models, we explain, on the specific examples of the Sinai model and of the trap model, how disorder induces anomalous diffusion, aging behaviours and Golosov localization, and how these properties can be understood via a strong disorder renormalization approach. For polymer models, we discuss the critical properties of various delocalization transitions involving random polymers. We first summarize some recent progresses in the general theory of random critical points : thermodynamic observables are not self-averaging at criticality whenever disorder is relevant, and this lack of self-averaging is directly related to the probability distribution of pseudo-critical temperatures Tc(i, L) over the ensemble of samples (i) of size L. We describe the results of this analysis for the bidimensional wetting and for the Poland-Scheraga model of DNA denaturation.

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“…Our experimental observations show that the mean displacements are biased towards the center of hydrodynamic stress (CoH), and that the mean-square displacements exhibit a crossover from short time faster to long time slower diffusion with the short-time diffusion coefficients dependent on the points used for tracking. A model based on Langevin theory elucidates that these behaviors are ascribed to a superposition of two diffusive modes: the ellipsoidal motion of the CoH and the rotational motion of the tracking point with respect to the CoH.Brownian motion as a general phenomenon of the diffusion processes has inspired extensive research [1][2][3][4][5][6][7][8][9][10][11][12] due to both its interesting physics and practical applications such as in microrheology [13][14][15][16], selfpropelled microswimmers [17] and particle and molecular separation [18][19][20]. Inspired by the diverse geometric shapes of biological macromolecules, Brenner and others have extended the hydrodynamic theory of Brownian motion to particles with irregular shapes [21][22][23][24][25][26].…”

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confidence: 99%

Brownian Motion of Boomerang Colloidal Particles

et al. 2013

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Brownian Motion of Boomerang Colloidal ParticlesWe investigate the Brownian motion of boomerang colloidal particles confined between two glass plates. Our experimental observations show that the mean displacements are biased towards the center of hydrodynamic stress (CoH), and that the mean-square displacements exhibit a crossover from short time faster to long time slower diffusion with the short-time diffusion coefficients dependent on the points used for tracking. A model based on Langevin theory elucidates that these behaviors are ascribed to a superposition of two diffusive modes: the ellipsoidal motion of the CoH and the rotational motion of the tracking point with respect to the CoH.Brownian motion as a general phenomenon of the diffusion processes has inspired extensive research [1][2][3][4][5][6][7][8][9][10][11][12] due to both its interesting physics and practical applications such as in microrheology [13][14][15][16], selfpropelled microswimmers [17] and particle and molecular separation [18][19][20]. Inspired by the diverse geometric shapes of biological macromolecules, Brenner and others have extended the hydrodynamic theory of Brownian motion to particles with irregular shapes [21][22][23][24][25][26]. A set of hydrodynamic centers are introduced, which include the center of hydrodynamic stress (CoH) where the coupling diffusion matrix becomes zero, the center of reaction where the coupling resistance matrix becomes symmetric and the center of diffusion where the coupling diffusion matrix becomes symmetric [22,24,27]. For screw-like or skewed particles, the translational and rotational motions are intrinsically coupled, therefore, the CoH does not exist and the centers of diffusion and reaction differ from each other. By contrast, for non-skewed particles, there always exists a unique point at which these three hydrodynamic centers coincide.Thus far, experimental studies of Brownian motion have been focused primarily on spherical particles; it was only recently that the Brownian motion of lowsymmetry particles was explored in experiments [5,[28][29][30][31][32][33][34]. Particle shapes are critical to various applications such as self-propelled microswimmers and particle/molecular separations [17,35]. By engineering particle shapes, microswimmers may be tailored to perform circular, spinning-top or other types of motion [35][36][37]. Understanding the hydrodynamics of chiral particles may lead to new avenues towards separation of particle or molecular enantiomers [38].In this letter we study the Brownian motion of boomerang-shaped colloidal particles under quasi twodimensional confinements. The boomerang particles with C 2v mirror symmetry represent an attractive system for studying the Brownian motion of low symmetry particles because their CoM and CoH do not coincide and both lie outside the body. Especially, the location of the CoH is unknown before the motion of any tracking point (TP) is analyzed. Boomerang particles are also an interesting model system for active microswimmers [37], the elec...

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Brownian motion: a paradigm of soft matter and biological physics

Cited by 205 publications

References 239 publications

Entropy production of a Brownian ellipsoid in the overdamped limit

Entropy production of a Brownian ellipsoid in the overdamped limit

Random Walks and Polymers in the Presence of Quenched Disorder

Brownian Motion of Boomerang Colloidal Particles

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