The diffusion coefficient of nonlinear Brownian motion

Diffusion and Brownian motion in Lagrangian coordinates.

In this paper we consider the convection-diffusion problem of a passive scalar in Lagrangian coordinates, i.e., in a coordinate system fixed on fluid particles. Both the convection-diffusion partial differential equation and the Langevin equation are expressed in Lagrangian coordinates and are shown to be equivalent for uniform, isotropic diffusion. The Lagrangian diffusivity is proportional to...

Nonlinear Brownian Motion and Higgs Mechanism

An extension of the stochastic quantization scheme is proposed by adding nonlinear terms to the field equations. Our modification is motivated by the recently established theory of active Brownian motion. We discuss a way of promoting this theory to the case of infinite degrees of freedom. Equilibrium distributions can be calculated exactly and are interpreted as path integral densities of quan...

Brownian Motion: The Link Between Probability and Mathematical Analysis

This article has no abstract.

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion

Brownian motion in shear flow: direct observation of anomalous diffusion.

Brownian motion in a simple shear flow has been experimentally investigated by using a different method for observation and analysis. A number of polystyrene spheres dispersed in sheared water were tracked with a confocal scanning laser microscope, and the time dependences of their coordinates were obtained. Since in the usual mean-square displacement in the flow direction the contribution from...