We investigate fractional Brownian motion with a microscopic random-matrix model and introduce a fractional Langevin equation. We use the latter to study both subdiffusion and superdiffusion of a free particle coupled to a fractal heat bath. We further compare fractional Brownian motion with the fractal time process. The respective mean-square displacements of these two forms of anomalous diffu...

The stochastic dynamical behavior of a well-stirred mixture of N molecular species that chemically interact through M reaction channels is accurately described by the chemical master equation. It is shown here that, whenever two explicit dynamical conditions are satisfied, the microphysical premise from which the chemical master equation is derived leads directly to an approximate time-evolutio...

langevin equation for a nano-particle suspended in a laminar fluid flow was analytically studied. the brownian motion generated from molecular bombardment was taken as a wiener stochastic process and approximated by a gaussian white noise. euler-maruyama method was used to solve the langevin equation numerically. the accuracy of brownian simulation was checked by performing a series of simulati...

Abstract: The generalized elastic model encompasses several linear stochastic models describing the dynamics of polymers, membranes, rough surfaces, and fluctuating interfaces. While usually defined in the overdamped case, in this paper we formally include the inertial term to account for the initial diffusive stages of the stochastic dynamics. We derive the generalized Langevin equation for a ...

The paper presented a transient population dynamics of phase singularities in 2D Beeler-Reuter model. Two stochastic modelings are examined: (i) the Master equation approach with the transition rate (i.e., λ(n, t) = λ(t)n and μ(n, t) = μ(t)n) and (ii) the nonlinear Langevin equation approach with a multiplicative noise. The exact general solution of the Master equation with arbitrary time-depen...

The Langevin description of Brownian motion in inhomogeneous suspensions is here revisited. Inhomogeneous suspensions are characterized by a position-dependent friction coefficient, which can significantly influence the dynamics of the suspended particles. Outstanding examples are suspensions in confinement or in the presence of a temperature gradient. The Langevin approach in inhomogeneous sys...

Mode-coupling theory (MCT) of sheared dense granular liquids is formulated. Starting from the Liouville equation of granular particles, the generalized Langevin equation is derived with the aid of the projection operator technique. The MCT equation for the density correlation function obtained from the generalized Langevin equation is almost equivalent to MCT equation for elastic particles unde...

The individual motion of a colloidal particle is described by an overdamped Langevin equation. When rotational degrees of freedom are relevant, these are described by a corresponding Langevin process. Our purpose is to show that the microscopic local density of colloids, in terms of a space and rotation state, also evolves according to a Langevin equation. The latter can then be used as the sta...

We consider a multivariate Langevin equation in discrete time, driven by a force induced by certain Gibbs' states. The main goal of the paper is to study the asymptotic behavior of a random walk with stationary increments (which are interpreted as discrete-time speed terms) satisfying the Langevin equation. We observe that (stable) functional limit theorems and laws of iterated logarithm for re...

1 Prliminaries 2 1.1 Basic Probability concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Stochastic Differential Equations (SDE’s) . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2.1 Langevin equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2.2 Ito integral and basics of Ito calculus . . . . . . . . . . . . . . ....