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The trapping potential induced by the interaction of a highly focused laser light with a spherical dielectric particle can be accurately approximated by a parabolic potential. In this work, we revisit experimental and numerical methodologies used to characterize the Brownian motion of a colloidal particle under the influence of a simple harmonic potential produced by optical tweezers. A classic Brownian dynamics simulation is used to model the experimental results, focusing on statistical properties that can be measured by direct visualization of the system using videomicroscopy. This work represents a useful insight into the underlying physics behind the optical tweezers technique, also giving guidelines regarding programming protocols and experimental analysis methodologies, that may be of help for students working with such techniques, as well as for professors teaching undergraduate advanced optics courses. Editor's Note: Optical tweezers are fascinating tools to manipulate micrometer-size particles, such as cells or colloids, via the confining potential of a laser. This paper shows how this external potential hinders the Brownian motion of a colloid. It presents several usual theoretical approaches, including the Langevin equation, that one could use in class, as well as the Brownian dynamics simulations one can run to predict the trajectories of the confined colloid. It also details some experiments that would allow undergraduate students in a statistical physics course to measure such an effect. [ABSTRACT FROM AUTHOR]

Statistical physics courses typically employ abstract language that describes objects too small to be seen, making the topic challenging for students to understand. In this work, we introduce a simple experiment that allows conceptualizing some of the underlying ideas of stochastic processes through direct experimentation. Students analyze stochastic trajectories of beads in a bouncing bed of smaller beads subjected to an external periodic drive. The analysis of the trajectories involves the application of a vast toolkit of statistical estimators that are useful in many fields of physics. Editor's Note: This paper shows how colliding beads can be used to demonstrate stochastic trajectories. While the experiment is simple, students can analyze the trajectories using techniques with a range of sophistication, making the experiment appropriate for students at a wide range of levels. [ABSTRACT FROM AUTHOR]

This paper presents the stronger moment conditions which are sufficient to show the finiteness of the first collision time between N -dimensional Gaussian jump particle and another N -dimensional Brownian particle in a fractured medium. To obtain these conditions, we use the triangular arrays of the random sequence vector which gives all probable positions of the first collision at any time. This study is an extension of the analytical study which is detailed in Alzulaibani and El-Hadidy [Int. J. Mod. Phys. B 33(28) (2019) 1950334] using the uniform integrability conditions. [ABSTRACT FROM AUTHOR]

We point out that the mean-field theory of avalanches in the dynamics of elastic interfaces, the so-called Brownian force model (BFM) developed recently in non-equilibrium statistical physics, is equivalent to the so-called super-Brownian motion (SBM) developed in probability theory, a continuum limit of branching processes related to space-embedded Galtonâ€"Watson trees. In particular the exact solvability property recently (re-)discovered from the field theory in mean-field avalanches (the ‘instanton equation’) maps onto the so-called Dawsonâ€"Watanabe 1968 duality property. In the light of this correspondence we compare the results obtained independently in the two fields, and transport some of them from one field to the other. In particular, we discuss a scaling limit of the branching Brownian motion which maps onto the continuum field theory of mean-field avalanches. [ABSTRACT FROM AUTHOR]

We consider a countable system of interacting (possibly non-Markovian) stochastic differential equations driven by independent Brownian motions and indexed by the vertices of a locally finite graph G = (V , E). The drift of the process at each vertex is influenced by the states of that vertex and its neighbors, and the diffusion coefficient depends on the state of only that vertex. Such processes arise in a variety of applications including statistical physics, neuroscience, engineering and math finance. Under general conditions on the coefficients, we show that if the initial conditions form a second-order Markov random field on d -dimensional Euclidean space, then at any positive time, the collection of histories of the processes at different vertices forms a second-order Markov random field on path space. We also establish a bijection between (second-order) Gibbs measures on (R d) V (with finite second moments) and a set of (second-order) Gibbs measures on path space, corresponding respectively to the initial law and the law of the solution to the stochastic differential equation. As a corollary, we establish a Gibbs uniqueness property that shows that for infinite graphs the joint distribution of the paths is completely determined by the initial condition and the specifications, namely the family of conditional distributions on finite vertex sets given the configuration on the complement. Along the way, we establish approximation and projection results for Markov random fields on locally finite graphs that may be of independent interest. [ABSTRACT FROM AUTHOR]

Animals follow specific movement patterns and search strategies to maximize encounters with essential resources (e.g. prey, favourable habitat) while minimizing exposures to suboptimal conditions (e.g. competitors, predators). While describing spatiotemporal patterns in animal movement from tracking data is common, understanding the associated search strategies employed continues to be a key challenge in ecology. Moreover, studies in marine ecology commonly focus on singular aspects of species' movements, however using multiple analytical approaches can further enable researchers to identify ecological phenomena and resolve fundamental ecological questions relating to movement. Here, we used a set of statistical physics‐based methods to analyze satellite tracking data from three co‐occurring apex predators (tiger, great hammerhead and bull sharks) that predominantly inhabit productive coastal regions of the northwest Atlantic Ocean and Gulf of Mexico. We analyzed data from 96 sharks and calculated a range of metrics, including each species' displacements, turning angles, dispersion, space‐use and community‐wide movement patterns to characterize each species' movements and identify potential search strategies. Our comprehensive approach revealed high interspecific variability in shark movement patterns and search strategies. Tiger sharks displayed near‐random movements consistent with a Brownian strategy commonly associated with movements through resource‐rich habitats. Great hammerheads showed a mixed‐movement strategy including Brownian and resident‐type movements, suggesting adaptation to widespread and localized high resource availability. Bull sharks followed a resident movement strategy with restricted movements indicating localized high resource availability. We hypothesize that the species‐specific search strategies identified here may help foster the co‐existence of these sympatric apex predators. Following this comprehensive approach provided novel insights into spatial ecology and assisted with identifying unique movement and search strategies. Similar future studies of animal movement will help characterize movement patterns and also enable the identification of search strategies to help elucidate the ecological drivers of movement and to understand species' responses to environmental change. [ABSTRACT FROM AUTHOR]

We consider a velocity field with linear viscous interactions defined on a one dimensional lattice. Brownian baths with different parameters can be coupled to the boundary sites and to the bulk sites, determining different kinds of non-equilibrium steady states or free-cooling dynamics. Analytical results for spatial and temporal correlations are provided by analytical diagonalisation of the system's equations in the infinite size limit. We demonstrate that spatial correlations are scale-free and time-scales become exceedingly long when the system is driven only at the boundaries. On the contrary, in the case a bath is coupled to the bulk sites too, an exponential correlation decay is found with a finite characteristic length. This is also true in the free cooling regime, but in this case the correlation length grows diffusively in time. We discuss the crucial role of boundary driving for long-range correlations and slow time-scales, proposing an analogy between this simplified dynamical model and dense vibro-fluidized granular materials. Several generalizations and connections with the statistical physics of active matter are also suggested. [ABSTRACT FROM AUTHOR]

The present article aims to study the effect of external parameters, such as the action of a constant force and the action of an external harmonic potential, on the trajectory of a charged particle in Brownian motion in a time-dependent magnetic field. The approach presented here builds on methods of statistical physics and produces an analytical and numerical general solution for the stochastic differential equations of motion. [ABSTRACT FROM AUTHOR]

We consider the problem of selecting a change of mean which minimizes the variance of Monte Carlo estimators for the expectation of a functional of a continuous Gaussian field, in particular continuous Gaussian processes. Functionals of Gaussian fields have taken up an important position in many fields including statistical physics of disordered systems and mathematical finance (see, for example, [A. Comtet, C. Monthus and M. Yor, Exponential functionals of Brownian motion and disordered systems, J. Appl. Probab. 35 1998, 2, 255–271], [D. Dufresne, The integral of geometric Brownian motion, Adv. in Appl. Probab. 33 2001, 1, 223–241], [N. Privault and W. I. Uy, Monte Carlo computation of the Laplace transform of exponential Brownian functionals, Methodol. Comput. Appl. Probab. 15 2013, 3, 511–524] and [V. R. Fatalov, On the Laplace method for Gaussian measures in a Banach space, Theory Probab. Appl. 58 2014, 2, 216–241]. Naturally, the problem of computing the expectation of such functionals, for example the Laplace transform, is an important issue in such fields. Some examples are considered, which, for particular Gaussian processes, can be related to option pricing. [ABSTRACT FROM AUTHOR]

In our recent work, in lieu of using white noise, we examined Kolmogorov systems driven by wideband noise. Such systems naturally arise in statistical physics, biological and ecological systems, and many related fields. One of the motivations of our study is to treat more realistic models than the usually assumed stochastic differential equation models. The rationale is that a Brownian motion is an idealization used in a wide range of models, whereas wideband noise processes are much easier to be realized in the actual applications. This paper further investigates the case that in addition to the wideband noise process, there is a singularly perturbed Markov chain. The added Markov chain is used to model discrete events. Although it is a more realistic formulation, because of the non-Markovian formulation due to the wideband noise and the singularly perturbed Markov chain, the analysis is more difficult. Using weak convergence methods, we obtain a limit result. Then we provide several examples for the utility of our findings. [ABSTRACT FROM AUTHOR]

I survey and illustrate the main time series models that Mandelbrot introduced into time series analysis in the 1960s and 1970s. I focus particularly on the members of the additive fractional stable family including Lévy flights and fractional Brownian motion (fBm), noting some of the less well‐known aspects of this family, such as the cases when the self‐similarity exponent H and the Hurst exponent J differ. I briefly discuss the role of multiplicative models in modeling the physics of cascades. I then recount the still little‐known story of Mandelbrot's work on fractional renewal models in the late 1960s, explaining how these differ from their more familiar fBm counterpart and form a "missing link" between fBm and the problem of random change points. I conclude by highlighting the frontier problem of damped fractional models. Key Point: I summarize and illustrate the main fractal time series models that Mandelbrot introduced into time series analysis in the 1960s and 1970s and give pointers to the current state of the art [ABSTRACT FROM AUTHOR]

Brownian colloidal particles dispersed in a fluid with a temperature gradient experience a driving force which produces a large biased steady density profile. This phenomenon, named thermophoresis, is quantified by the Soret coefficient ST. This problem is studied here within the Fokker-Planck formalism. Using the experimental observation of ST it is possible to extract relevant analytical information about a temperature dependent nonequilibrium effective potential which can produce the thermophoresis force. It will be presented here a statistical physics derivation of this effective potential in terms of some physical parameters. Experimental data are analyzed within this theoretical scenario. [ABSTRACT FROM AUTHOR]

We study the noise induced thermally activated barrier crossing of Brownian particles that hop in a piecewise linear potential. Using the exact analytic solutions and via numerical simulations not only we explore the dependence for the first passage time of a single particle but also we calculate the first arrival time for one particle out of N particles. The first arrival time decreases as the number of particles increases as expected. We then explore the thermally activated barrier crossing rate of the system in the presence of time varying signal. The dependence of signal to noise ratio SNR as well as the power amplification (η) on model parameters is explored. η and SNR depict a pronounced peak at particular noise strength. In the presence of N particles, η is considerably amplified as N steps up showing the weak periodic signal plays a vital role in controlling the noise induced dynamics of the system. Moreover, for the sake of generality, the viscous friction γ is considered to decrease exponentially when the temperature T of the medium increases (γ=Be-AT) as proposed originally by Reynolds (Philos Trans R Soc Lond 177:157, 1886). [ABSTRACT FROM AUTHOR]

We establish in this paper the existence of weak solutions of infinite-dimensional shift invariant stochastic differential equations driven by a Brownian term. The drift function is very general, in the sense that it is supposed to be neither bounded or continuous, nor Markov. On the initial law we only assume that it admits a finite specific entropy and a finite second moment. The originality of our method leads in the use of the specific entropy as a tightness tool and in the description of such infinite-dimensional stochastic process as solution of a variational problem on the path space. Our result clearly improves previous ones obtained for free dynamics with bounded drift. [ABSTRACT FROM AUTHOR]

The article presents an experiment that may be used to introduce the diffusion of particles, resulting from Brownian motion, considered as a standard field in statistical physics education. It highlights the involvement of superparamagnetic colloids in the experiment, along with its potential to be used to show the relation between the current area of research and standard subjects of statistical physics. The opportunity offered by the experiment to introduce image analysis techniques is noted.

We study the cut-off phenomenon for a family of stochastic small perturbations of a one dimensional dynamical system. We will focus in a semiflow of a deterministic differential equation which is perturbed by adding to the dynamics a white noise of small variance. Under suitable hypothesis on the potential we will prove that the family of perturbed stochastic differential equations present a profile cut-off phenomenon with respect to the total variation distance. We also prove a local cut-off phenomenon in a neighborhood of the local minima (metastable states) of multi-well potential. [ABSTRACT FROM AUTHOR]

We study the asymptotic behaviour of the time-changed stochastic process fX(t) = B(fS(t)), where B is a standard one-dimensional Brownian motion and fS is the (generalized) inverse of a subordinator, i.e. the first-passage time process corresponding to an increasing Lévy process with Laplace exponent f. This type of processes plays an important role in statistical physics in the modeling of anomalous subdiffusive dynamics. The main result of the paper is the proof of the mixing property for the sequence of stationary increments of a subdiffusion process. We also investigate various martingale properties, derive a generalized Feynman-Kac formula, the laws of large numbers and of the iterated logarithm for fX. [ABSTRACT FROM AUTHOR]

Statistical properties of Brownian motion that arise by analyzing, separately, trajectories over which the system energy increases (upside) or decreases (downside) with respect to a threshold energy level are derived. This selective analysis is applied to examine transport properties of a nonequilibrium Brownian process that is coupled to multiple thermal sources characterized by different temperatures. Distributions, moments, and correlation functions of a free particle that occur during upside and downside events are investigated for energy activation and energy relaxation processes and also for positive and negative energy fluctuations from the average energy. The presented results are sufficiently general and can be applied without modification to the standard Brownian motion. This article focuses on the mathematical basis of this selective analysis. In subsequent articles in this series, we apply this general formalism to processes in which heat transfer between thermal reservoirs is mediated by activated rate processes that take place in a system bridging them. [ABSTRACT FROM AUTHOR]

Fermi acceleration is the process of energy transfer from massive objects in slow motion to light objects that move fast. The model for such process is a time-dependent Hamiltonian system. As the parameters of the system change with time, the energy is no longer conserved, which makes the acceleration possible. One of the main problems is how to generate a sustained and robust energy growth. We show that the non-ergodicity of any chaotic Hamiltonian system must universally lead to the exponential growth of energy at a slow periodic variation of parameters. We build a model for this process in terms of a Geometric Brownian Motion with a positive drift and relate it to the entropy increase. [ABSTRACT FROM AUTHOR]

Interest in the concept of entropic forces has risen considerably since Verlinde proposed in 2011 to interpret the force in Newton's second law and gravity as entropic forces. Brownian motion--the motion of a small particle (pollen) driven by random impulses from the surrounding molecules--may be the first example of a stochastic process in which such forces are expected to emerge. In this article, it is shown that at least two types of entropic force can be identified in three-dimensional Brownian motion. This analysis yields simple derivations of known results of Brownian motion, Hooke's law, and--applying an external (non-radial) force--Curie's law and the Langevin-Debye equation. [ABSTRACT FROM AUTHOR]

In this paper, we study the dynamics of the activation of a Brownian particle using the path integral formalism in real time. Along with the construction of the saddle-point (instanton) solutions, we develop the formalism allowing to calculate the effect of the fluctuations near this solution in detail. In particular, it is shown that there is a soft mode for which the integration is not Gaussian and just this mode is responsible for the finite probability flux. [ABSTRACT FROM AUTHOR]

We consider scaled Brownian motion (sBm), a random process described by a diffusion equation with explicitly time-dependent diffusion coefficient D{t) = αD0tα-1 (Batchelor's equation) which, for α < 1, is often used for fitting experimental data for subdiffusion of unclear genesis. We show that this process is a close relative of subdiffusive continuous-time random walks and describes the motion of the rescaled mean position of a cloud of independent walkers. It shares with subdiffusive continuous-time random walks its nonstationary and nonergodic properties. The nonergodicity of sBm does not however go hand in hand with strong difference between its different realizations: its heterogeneity ("ergodicity breaking") parameter tends to zero for long trajectories. [ABSTRACT FROM AUTHOR]

We show that directed ratchet transport of a driven overdamped Brownian particle subjected to a spatially periodic and symmetric potential can be reliably controlled by tailoring a biharmonic temporal force, in coherence with the degree-of-symmetry-breaking mechanism. We demonstrate that the effect of finite temperature on the purely deterministic ratchet scenario can be understood as an effective noise-induced change of the potential barrier which is in turn controlled by the degree-of-symmetry-breaking mechanism. Remarkably, we find that the same universal scenario holds for any symmetric periodic potential, while optimal directed ratchet transport occurs when the impulse transmitted (spatial integral over a half period) by the symmetric spatial force is maximum. [ABSTRACT FROM AUTHOR]

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, (χ²) ~ t² at short-time scales, and diffusive motion (χ²) ~ 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 (χ² ~ t³ 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 t³ dispersion. This observation is a direct proof of the existence of the random, rapidly varying force imagined by Langevin. [ABSTRACT FROM AUTHOR]

We consider an N-particle system of noncolliding Brownian motion starting from x≤ x≤...≤ x with drift coefficients ν, 1≤ j≤ N satisfying ν≤ ν≤...≤ ν. When all of the initial points are degenerated to be zero, x=0, 1≤ j≤ N, the equivalence is proved between a dilatation with factor 1/ t of this drifted process and the noncolliding Brownian motion starting from ν≤ ν≤...≤ ν without drift observed at reciprocal time 1/ t, for arbitrary t>0. Using this reciprocal time relation, we study the determinantal property of the noncolliding Brownian motion with drift having finite and infinite numbers of particles. [ABSTRACT FROM AUTHOR]

We study the distribution of the maximal height of the outermost path in the model of N nonintersecting Brownian motions on the half-line as N→∞, showing that it converges in the proper scaling to the Tracy-Widom distribution for the largest eigenvalue of the Gaussian orthogonal ensemble. This is as expected from the viewpoint that the maximal height of the outermost path converges to the maximum of the Airy process minus a parabola. Our proof is based on Riemann-Hilbert analysis of a system of discrete orthogonal polynomials with a Gaussian weight in the double scaling limit as this system approaches saturation. We consequently compute the asymptotics of the free energy and the reproducing kernel of the corresponding discrete orthogonal polynomial ensemble in the critical scaling in which the density of particles approaches saturation. Both of these results can be viewed as dual to the case in which the mean density of eigenvalues in a random matrix model is vanishing at one point. [ABSTRACT FROM AUTHOR]

In this work, higher-order moving average polynomials are defined by straightforward generalization of the standard moving average. The self-similarity of the polynomials is analyzed for fractional Brownian series and quantified in terms of the Hurst exponent H by using the detrending moving average method. We prove that the exponent H of the fractional Brownian series and of the detrending moving average variance asymptotically agree for the first-order polynomial. Such asymptotic values are compared with the results obtained by the simulations. The higher-order polynomials correspond to trend estimates at shorter time scales as the degree of the polynomial increases. Importantly, the increase of polynomial degree does not require to change the moving average window. Thus trends at different time scales can be obtained on data sets with the same size. These polynomials could be interesting for those applications relying on trend estimates over different time horizons (financial markets) or on filtering at different frequencies (image analysis). [ABSTRACT FROM AUTHOR]

Functionals of Brownian motion have diverse applications in physics, mathematics, and other fields. The probability density function (PDF) of Brownian functionals satisfies the Feynman-Kac formula, which is a Schrödinger equation in imaginary time. In recent years there is a growing interest in particular functionals of non-Brownian motion, or anomalous diffusion, but no equation existed for their PDF. Here, we derive a fractional generalization of the Feynman-Kac equation for functionals of anomalous paths based on sub-diffusive continuous-time random walk. We also derive a backward equation and a generalization to Lévy flights. Solutions are presented for a wide number of applications including the occupation time in half space and in an interval, the first passage time, the maximal displacement, and the hitting probability. We briefly discuss other fractional Schrödinger equations that recently appeared in the literature. [ABSTRACT FROM AUTHOR]

Szász and Telcs (J. Stat. Phys. 26(3), ) have shown that for the diffusively scaled, simple symmetric random walk, weak convergence to the Brownian motion holds even in the case of local impurities if d≥2. The extension of their result to finite range random walks is straightforward. Here, however, we are interested in the situation when the random walk has unbounded range. Concretely we generalize the statement of Szász and Telcs (J. Stat. Phys. 26(3), ) to unbounded random walks whose jump distribution belongs to the domain of attraction of the normal law. We do this first: for diffusively scaled random walks on Z ( d≥2) having finite variance; and second: for random walks with distribution belonging to the non-normal domain of attraction of the normal law. This result can be applied to random walks with tail behavior analogous to that of the infinite horizon Lorentz-process; these, in particular, have infinite variance, and convergence to Brownian motion holds with the superdiffusive $\sqrt{n\log n}$ scaling. [ABSTRACT FROM AUTHOR]

Motivated by Kesten’s bridge decomposition for two-dimensional self-avoiding walks in the upper half plane, we show that the conjectured scaling limit of the half-plane SAW, the SLE(8/3) process, also has an appropriately defined bridge decomposition. This continuum decomposition turns out to entirely be a consequence of the restriction property of SLE(8/3), and as a result can be generalized to the wider class of restriction measures. Specifically we show that the restriction hulls with index less than one can be decomposed into a Poisson Point Process of irreducible bridges in a way that is similar to Itô’s excursion decomposition of a Brownian motion according to its zeros. [ABSTRACT FROM AUTHOR]

We first recall the laws of classical thermodynamics and the fundamental principles of statistical mechanics and emphasize the fact that the fluctuations of a system in macroscopic equilibrium, such as Brownian motion, can be explained by statistical mechanics and not by thermodynamics. In the vicinity of equilibrium, the susceptibility of a system to an infinitesimal external perturbation is related to the amplitude of the fluctuations at equilibrium (Einstein's relation) and exhibits a symmetry discovered by Onsager. We shall then focus on the mathematical description of systems out of equilibrium using Markovian dynamics. This will allow us to present some remarkable relations derived during the last decade and valid arbitrarily far from equilibrium: the Gallavotti-Cohen fluctuation theorem and Jarzynski's non-equilibrium work identities. These recent results will be illustrated by applying them to simple systems such as the Brownian ratchet model for molecular motors and the asymmetric exclusion process which is a basic example of a driven lattice gas. [ABSTRACT FROM AUTHOR]

Many situations of physical and biological interest involve diffusions on manifolds. It is usually assumed that irregularities in the geometry of these manifolds do not influence diffusions. The validity of this assumption is put to test by studying Brownian motions on nearly flat 2D surfaces. It is found by perturbative calculations that irregularities in the geometry have a cumulative and drastic influence on diffusions, and that this influence typically grows exponentially with time. The corresponding characteristic times are computed and discussed. [ABSTRACT FROM AUTHOR]

A small object (Solid or droplet) is placed on a horizontally vibrating plate, imposing an acceleration γ( t) in the form of a white noise. The object experiences dry friction (due to soild/solid interaction, or to contact angle hysteresis in the case of a droplet). The object is driven by a force γ( t) – Δσ( t) where σ( t), =±1, depending on the sign of the velocity. We discuss the motion at two levels: (i) in terms of simple scaling laws, (ii) by a propagator technique. (a) When Δ is below a certain crossover value Δ*, we expect an unperturbed (Langevin) Brownian motion. (b) When Δ > Δ*, we expect a reduced diffusion coefficient proportional to Δ−4 for small Δ. [ABSTRACT FROM AUTHOR]

In the last decade there has been an increasing interest in generating useful work on the nano-scale to promote transport of particles. The essential theoretical formalism, rooted in non-equilibrium statistical physics, has been successfully applied to the description of physical principles underlying biological motors. In most cases, the principle behind the rectifying motion is the famous Feynman''s ratchet and pawl model. We give an overview of the core statistical physics fundamentals in this rapidly developing field. [Copyright &y& Elsevier]

The distribution of interval lengths between Brownian walkers on the line is investigated. The walkers are independent until collision; at collision, the left walker disappears, and the right walker survives with probability p. This problem arises in the context of diffusion-limited reactions and also in the scaling limit of the voter model. A systematic expansion in correlation between neighbor intervals gives a series of approximations of increasing accuracy for the probability density functions of interval lengths. The first approximation beyond mere statistical independence between successive intervals already gives excellent results, as established by comparison with direct numerical simulations. [ABSTRACT FROM AUTHOR]

In this article, we review both theoretical models and experimental results on the motion of micro- and nano- particles that are close to a fluid interface or move in between two fluids. Viscous drags together with dissipations due to fluctuations of the fluid interface and its physicochemical properties affect strongly the translational and rotational drags of colloidal particles, which are subjected to Brownian motion in thermal equilibrium. Even if many theoretical and experimental investigations have been carried out, additional scientific efforts in hydrodynamics, statistical physics, wetting and colloid science are still needed to explain unexpected experimental results and to measure particle motion in time and space scales, which are not accessible so far. • Particle translational and rotational drag coefficients close to a fluid interface are reviewed. • Experimental results show significant deviations with respect to hydrodynamic predictions. • Beyond hydrodynamics, additional drags should be taken into account. • New experimental investigations must be designed for future research. [ABSTRACT FROM AUTHOR]

The clogging behavior of a symmetric binary mixture of colloidal particles that are driven in opposite directions through constrictions is explored by Brownian dynamics simulations and theory. A dynamical state with a spontaneously broken symmetry occurs where one species is flowing and the other is blocked for a long time, which can be tailored by the size of the constrictions. Moreover, we find self-organized oscillations in clogging and unclogging of the two species. Apart from statistical physics, our results are of relevance for fields like biology, chemistry, and crowd management, where ions, microparticles, pedestrians, or other particles are driven in opposite directions through constrictions. [ABSTRACT FROM AUTHOR]

Colloid sedimentation has played a seminal role in the development of statistical physics thanks to the celebrated experiments by Perrin, which provided a concrete demonstration of molecular reality and gave strong support to Einstein's theory of Brownian motion. This review, which mostly focuses on settling at low Peclét number, where Brownian fluctuations are dominant, aims to show that a lot more can be learnt both from the sedimentation equilibrium and from the particle settling dynamics of a wide class of systems, ranging from simple colloids to mesogenic suspensions, from soft solids to active particles and living organisms. At the same time, the occurrence of unexpected and surprising effects brings about challenging questions in statistical and fluid mechanics that make sedimentation an exciting field of research. [ABSTRACT FROM AUTHOR]

We derive the virial theorem for an overdamped system of rotating self-gravitating Brownian particles. We show that, in the two-dimensional case, it takes a closed form that can be used to obtain general results about the dynamics without being required to solve the Smoluchowski-Poisson system explicitly. In particular, we obtain the exact analytical expression of the mean square displacement 〈r2〉(t) of the interacting Brownian particles. We exhibit a critical temperature below which the system collapses, and above which it evaporates, and we determine how this temperature is affected by a solid rotation. We also develop an analogy between self-gravitating systems and two-dimensional point vortices. We derive a virial-like relation for point vortices at statistical equilibrium relating the angular velocity to the angular momentum and the temperature. [ABSTRACT FROM AUTHOR]

We address the problem of the chaotic transport of particles in an asymmetric periodic ratchet potential. We consider the case of deterministic rocking ratchets and analyze different regimes for the amplitude of rocking. When the inertial term is taken into account, the dynamics can be chaotic and modify the transport properties. We compare the dynamics of point particles and extended objects under the action of the ratchet potential and show that we can segregate particles according to its size. [ABSTRACT FROM AUTHOR]