Related papers: An old efficient approach to anomalous Brownian mo…
We study the motion of an elastic object driven in a disordered environment in presence of both dissipation and inertia. We consider random forces with the statistics of random walks and reduce the problem to a single degree of freedom. It…
This paper is concerned with an inverse source problem for the stochastic wave equation driven by a fractional Brownian motion. Given the random source, the direct problem is to study the solution of the stochastic wave equation. The…
In this paper we study the convergence to fractional Brownian motion for long memory time series having independent innovations with infinite second moment. For the sake of applications we derive the self-normalized version of this theorem.…
We introduce numerical methods for simulating the diffusive motion of rigid bodies of arbitrary shape immersed in a viscous fluid. We parameterize the orientation of the bodies using normalized quaternions, which are numerically robust,…
A self-propelled artificial microswimmer is often modeled as a ballistic Brownian particle moving with constant speed aligned along one of its axis, but changing direction due to random collisions with the environment. Similarly to thermal…
We study the stochastic motion of particles driven by long-range correlated fractional Gaussian noise in a superharmonic external potential of the form $U(x)\propto x^{2n}$ ($n\in\mathbb{N}$). When the noise is considered to be external,…
The dynamical evolution of a Brownian particle in an inhomogeneous medium with spatially varying friction and temperature field is important to understand conceptually. It requires to address the basic problem of relative stability of…
We investigate the well-posedness of stochastic differential equations driven by fractional Brownian motion, focusing on the long-range dependent case $H \in (\frac{1}{2}, 1)$. While existing results on regularization by such noise…
We obtain Bargmann-Michel-Telegdi equations of motion of classical spinning particle using Lagrangian variational principle with Grassmann variables.
Standard algorithms for the numerical integration of the Langevin equation require that interactions are slowly varying during to the integration timestep. This in not the case for hard-body systems, where there is no clearcut between the…
The classical theory of Brownian dynamics follows from coarse-graining the underlying linearized fluctuating hydrodynamics of the solvent. We extend this procedure to globally non-isothermal conditions, requiring only a local thermal…
It is quite generally assumed that the overdamped Langevin equation provides a quantitative description of the dynamics of a classical Brownian particle in the long time limit. We establish and investigate a paradigm anomalous diffusion…
Recent experiments on Brownian colloidal particles have been studied theoretically in terms of overdamped Langevin equations with multiplicative white noise using an unconventional stochastic interpretation. Complementary numerical…
This paper derives a complete analytical solution for the probability distribution of the configuration of a non-holonomic vehicle that moves in two spatial dimensions by satisfying the unicycle kinematic constraints and in presence of…
Brownian dynamics algorithms integrate numerically Langevin equations and allow to probe long time scales in simulations. A common requirement for such algorithms is that interactions in the system should vary little during an integration…
In this paper, the three-dimensional stochastic nonhomogeneous incompressible Navier-Stokes equations driven by L\'evy process consisting of the Brownian motion, the compensated Poisson random measure and the Poisson random measure are…
Fractional Brownian motion is a Gaussian stochastic process with long-range correlations in time; it has been shown to be a useful model of anomalous diffusion. Here, we investigate the effects of mutual interactions in an ensemble of…
In this paper, we study a class of stochastic differential equations with additive noise that contains a fractional Brownian motion (fBM) and a Poisson point process of class (QL). The differential equation of this kind is motivated by the…
Brownian motion has played important roles in many different fields of science since its origin was first explained by Albert Einstein in 1905. Einstein's theory of Brownian motion, however, is only applicable at long time scales. At short…
A very simple and efficient local variational iteration method for solving problems of nonlinear science is proposed in this paper. The analytical iteration formula of this method is derived first using a general form of first order…