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The properties of the thermal force driving micron particles in incompressible fluids are studied within the hydrodynamic theory of the Brownian motion. It is shown that the assumption used for the hydrodynamic Langevin equation in its…

We study the dynamics of Brownian particles in a heterogeneous one-dimensional medium with a spatially-dependent diffusion coefficient of the form $D(x)\sim |x|^c$, at constant temperature. The particle's probability distribution function…

The two-variable Langevin equations, modeling the Brownian motion of a particle moving in a potential and leading to the Maxwell-Boltzmann distribution of the corresponding Fokker-Planck equation, are shown to give rise to types of…

A diffusion process of a Brownian particle in a medium of temperature $T$ is re-considered. We assume that temperature of the medium fluctuates around its mean value. The velocity probability distribution is obtained. It is shown that the…

Diffusion of small particles is omnipresent in a plentiful number of processes occurring in Nature. As such, it is widely studied and exerted in almost all branches of sciences. It constitutes such a broad and often rather complex subject…

A Langevin equation is suggested to describe a system driven by correlated Gaussian white noise as well as with positive and negative damping demarcated by a critical velocity. The equation can be transformed into the Fokker-Planck equation…

For the Langevin model of the dynamics of a Brownian particle with perturbations orthogonal to its current velocity, in a regime when the particle velocity modulus becomes constant, an equation for the characteristic function $\psi…

We focus on the dynamics of a Brownian particle whose mass fluctuates. First we show that the behaviour is similar to that of a Brownian particle moving in a fluctuating medium, as studied by Beck [Phys. Rev. Lett. 87 (2001) 180601]. By…

We investigate anomalous diffusion processes governed by the fractional Langevin equation and confined to a finite or semi-infinite interval by reflecting potential barriers. As the random and damping forces in the fractional Langevin…

We present an insightful ``derivation'' of the Langevin equation and the fluctuation dissipation theorem in the specific context of a heavier particle moving through an ideal gas of much lighter particles. The Newton's Law of motion…

Distribution functions of relative velocities among particles in a vibrated bed of powder are studied both numerically and theoretically. In the solid phase where granular particles remain near their local stable states, the probability…

Brownian motion of single particles with various masses M and diameters D is studied by molecular dynamics simulations. Besides the momentum auto-correlation function of the Brownian particle the memory function and the fluctuating force…

We propose a Langevin equation to describe the quantum Brownian motion of bounded particles based on a distinctive formulation concerning both the fluctuation and dissipation forces. The fluctuation force is similar to that employed in the…

The diffusion of colloids inside an active system-e.g. within a living cell or the dynamics of active particles itself (e.g. self-propelled particles) can be modeled through overdamped Langevin equation which contains an additional noise…

We look at the equilibrium of a Brownian particle in an inhomogeneous space following the alternative approach proposed in ref.[1]. We consider a coordinate dependent damping that makes the stochastic dynamics the one with multiplicative…

The density distributions and Soret coefficient in a nonequilibrium colloidal system with nonuniform temperature are studied by the overdamped Langevin equation for Brownian motion in an inhomogeneous strong friction medium. Based on the…

Brownian motion occurs in a variety of fluids, from rare gases to liquids. The Langevin equation, describing friction and agitation forces in statistical balance, is one of the most successful ways to treat the phenomenon. In rare gases, it…

Using a time-averaging technique we obtain exactly the probability distribution for position and velocity of a Brownian particle under the influence of two heat baths at different temperatures. These baths are expressed by a white noise…

Nonlinear stochastic differential equations generating signals with 1/f spectrum have been used so far to describe socio-economical systems. In this paper we consider the motion of a Brownian particle in an inhomogeneous environment such…

We study the statistical properties of overdamped particles driven by two cross-correlated multiplicative Gaussian white noises in a time-dependent environment. Using the Langevin and Fokker-Planck approaches, we derive the exact…