Related papers: Fractional Brownian motion with mean-density inter…
We consider scaled Brownian motion (sBm), a random process described by a diffusion equation with explicitly time-dependent diffusion coefficient $D(t) = D_0 t^{\alpha - 1}$ (Batchelor's equation) which, for $\alpha < 1$, is often used for…
The fractional Brownian motion with index $\alpha$ is introduced to construct the fractional excursion set model. A new mass function with single parameter $\alpha$ is derived within the formalism, of which the Press-Schechter mass function…
We show that the correlated stochastic fluctuation of the friction coefficient can give rise to long-range directional motion of a particle undergoing Brownian random walk in a constant periodic energy potential landscape. The occurrence of…
Approximations of fractional Brownian motion using Poisson processes whose parameter sets have the same dimensions as the approximated processes have been studied in the literature. In this paper, a special approximation to the…
We analyze \emph{fractional Brownian motion} and \emph{scaled Brownian motion} on the two-dimensional sphere $\mathbb{S}^{2}$. We find that the intrinsic long time correlations that characterize fractional Brownian motion collude with the…
The diffusion of chiral active Brownian particles in three-dimensional space is studied analytically, by consideration of the corresponding Fokker-Planck equation for the probability density of finding a particle at position…
Passive scalar motion in a family of random Gaussian velocity fields with long-range correlations is shown to converge to persistent fractional Brownian motions in long times.
Computing analytically the $n$-point density correlations in systems of interacting particles is a long-standing problem of statistical physics, with a broad range of applications, from the interpretation of scattering experiments in simple…
The effects of Brownian motion on particle interactions with heterogeneous collectors are evaluated by adding stochastic Brownian displacements to the particle trajectories and comparing those trajectories to those where Brownian motion is…
We investigate fractional Brownian motion with a microscopic random-matrix model and introduce a fractional Langevin equation. We use the latter to study both sub- and superdiffusion of a free particle coupled to a fractal heat bath. We…
In active Brownian motion, an internal propulsion mechanism interacts with translational and rotational thermal noise and other internal fluctuations to produce directed motion. We derive the distribution of its extreme fluctuations and…
The motion of a Brownian particle in the presence of Coulomb friction and an asymmetric spatial potential was evaluated in this study. The system exhibits a ratchet effect, i.e., an average directed motion even in the absence of an external…
Scaled Brownian motion (SBM) is widely used to model anomalous diffusion of passive tracers in complex and biological systems. It is a highly non-stationary process governed by the Langevin equation for Brownian motion, however, with a…
The aim of this Short Note is to highlight that the {\it generalized grey Brownian motion} (ggBm) is an anomalous diffusion process driven by a fractional integral equation in the sense of Erd\'elyi-Kober, and for this reason here it is…
Anomalous diffusion has been widely observed by single particle tracking microscopy in complex systems such as biological cells. The resulting time series are usually evaluated in terms of time averages. Often anomalous diffusion is…
Brownian motion is ballistic on short time scales and diffusive on long time scales. Our theoretical investigations indicate that one can observe the exact opposite - an "anomaleous diffusion process" where initially diffusive motion…
Brownian motion is essential for describing diffusion in systems ranging from simple to complex liquids. Unlike simple liquids, which consist of only a solvent, complex liquids, such as colloidal suspensions or the cytoplasm of a cell, are…
This paper deals with the identification of the multivariate fractional Brownian motion, a recently developed extension of the fractional Brownian motion to the multivariate case. This process is a $p$-multivariate self-similar Gaussian…
The motion of particles in random potentials occurs in several natural phenomena ranging from the mobility of organelles within a biological cell to the diffusion of stars within a galaxy. A Brownian particle moving in the random optical…
Observing finite regions of a bigger system is a common experience, from microscopy to molecular simulations. In the latter especially, there is ongoing interest in predicting thermodynamic properties from tracking fluctuations in finite…