Related papers: Fractional Brownian motion with a reflecting wall
Some probabilistic aspects of the number variance statistic are investigated. Infinite systems of independent Brownian motions and symmetric alpha-stable processes are used to construct new examples of processes which exhibit both divergent…
We consider a generic system operating under non-equilibrium conditions. Explicitly, we consider an inertial classical Brownian particle dwelling a periodic structure with a spatially broken reflection symmetry. The particle is coupled to a…
This paper studies the intermediate time behaviour of a small random perturbation of a periodic cellular flow. Our main result shows that on time scales shorter than the diffusive time scale, the limiting behaviour of trajectories that…
Security of oscillatory true random number generators remains not fully understood due to insufficient understanding of complex $1/f^\alpha$ phase noise. To bridge this gap, we introduce fractional Brownian motion as a comprehensive…
We demonstrate that continuous time random walks in which successive waiting times are correlated by Gaussian statistics lead to anomalous diffusion with mean squared displacement <r^2(t)>~t^{2/3}. Long-ranged correlations of the waiting…
Motivated by the anomalous diffusion observed in clusters of active Brownian particles (ABPs), where the center-of-mass diffusion coefficient scales as $D\sim N^{-1/2}$ with respect to the number $N$ of particles in the cluster, we derive a…
Electrokinetically-driven Janus colloids, e.g., with one metallic and one dielectric hemisphere, confined between parallel walls exhibit a boundary-accumulation mechanism enabled by an effective cross-channel diffusivity which is distinct…
Brownian particles in random potentials show an extended regime of subdiffusive dynamics at intermediate times. The asymptotic diffusive behavior is often established at very long times and thus cannot be accessed in experiments or…
A physical-mathematical approach to anomalous diffusion may be based on generalized diffusion equations (containing derivatives of fractional order in space or/and time) and related random walk models. The fundamental solution (for the…
Encounter-based models of diffusion provide a probabilistic framework for analyzing the effects of a partially absorbing reactive surface, in which the probability of absorption depends upon the amount of surface-particle contact time.…
In recent years, several experiments highlighted a new type of diffusion anomaly, which was called Brownian yet non-Gaussian diffusion. In systems displaying this behavior, the mean squared displacement of the diffusing particles grows…
Fractional Brownian motion is a non-Markovian Gaussian process $X_t$, indexed by the Hurst exponent $H$. It generalises standard Brownian motion (corresponding to $H=1/2$). We study the probability distribution of the maximum $m$ of the…
The horizontal dynamics of a bouncing ball interacting with an irregular surface is investigated and is found to demonstrate behavior analogous to a random walk. Its stochastic character is substantiated by the calculation of a permutation…
Consider a generic triangle in the upper half of the complex plane with one side on the real line. This paper presents a tailored construction of a discrete random walk whose continuum limit is a Brownian motion in the triangle, reflected…
Brownian diffusion of rod-like polymers in the presence of randomly distributed spherical obstacles is studied using molecular dynamics (MD) simulations. It is observed that dependence of the reduced diffusion coefficient of these…
We study the motion of a particle sliding under the action of an external field on a stochastically fluctuating one-dimensional Edwards-Wilkinson surface. Numerical simulations using the single-step model shows that the mean-square…
We show that the generalized diffusion coefficient of a subdiffusive intermittent map is a fractal function of control parameters. A modified continuous time random walk theory yields its coarse functional form and correctly describes a…
Einstein's theory of Brownian motion is revisited in order to formulate generalized kinetic theory of anomalous diffusion. It is shown that if the assumptions of analyticity and the existence of the second moment of the displacement…
We construct a Brownian motion on complex partial flag manifolds with blocks of equal size as a matrix-valued diffusion from a Brownian motion on the unitary group. This construction leads to an explicit expression for the characteristic…
Very recent experiments have discovered that localized light in strongly absorbing media displays intriguing diffusive phenomena. Here we develop a first-principles theory of light propagation in open media with arbitrary absorption…