Based on the generalized Langevin equation for the momentum of a Brownian particle a generalized asymptotic Einstein relation is derived. It agrees with the well-known Einstein relation in the case of normal diffusion but continues to hold for sub- and super-diffusive spreading of the Brownian particle's mean square displacement. The generalized asymptotic Einstein relation is used to analyze d...

We follow the diffusive motion of colloidal particles of diameter d in soap films of varying thickness h with fluorescence microscopy. Diffusion constants are obtained both from one- and two-particle microrheological measurements of particle motion in these films. These diffusion constants are related to the surface viscosity of the interfaces comprising the soap films, by means of the Trapezni...

We report on video-microscopy measurements of the translational and rotational Brownian motions of isolated ellipsoidal particles in quasi-two-dimensional sample cells of increasing thickness. The long-time diffusion coefficients were measured along the long (Da) and short (Db) ellipsoid axes, respectively, and the ratio, Da/Db, was determined as a function of wall confinement and particle aspe...

We report new measurements of single particle dispersion in turbulent two-dimensional (2D) flows. Laboratory experiments in electromagnetically driven and Faraday wave driven turbulence reveal a transition from weakly dispersing superdiffusive regime to strongly dispersing Brownian diffusion as the flow energy is increased in a broad range. The transition to fully developed 2D turbulence is cha...

A relativistic bounce-averaged quasilinear diffusion equation is derived to describe stochastic particle transport associated with low-frequency electromagnetic fluctuations in a nonuniform magnetized plasma. Expressions for the relativistic quasilinear diffusion coefficients are calculated explicitly for magnetically-trapped particle distributions in axisymmetric magnetic geometry in terms of ...

Consider a Brownian particle in three dimensions in a random environment. The environment is determined by a potential random in space and time. It is shown that at small noise the large-time behavior of the particle is diffusive. The diffusion constant depends on the environment. This work generalizes previous results for random walk in a random environment. In these results the diffusion cons...

Single-file diffusion, prevalent in many processes, refers to the restricted motion of interacting particles in narrow micropores with the mutual passage excluded. A single-filing system was developed by confining colloidal spheres in one-dimensional circular channels of micrometer scale. Optical video microscopy study shows evidence that the particle self-diffusion is non-Fickian for long peri...

A new numerical algorithm that encompasses both the δf particle-in-cell (PIC) method and a continuum method has been developed, which is an extension to Denavit’s [J. Comput. Phys. 9 (1972) 75] original “hybrid” method. In this article we describe this new Particle-Continuum algorithm in general, and we note our methods of interpolation. The issue of phase space convergence of this algorithm is...

2 Diffusive limit for a particle in a random flow 7 2.1 Diffusion of a particle in a time-dependent random flow . . . . . . . . . . . . . . . . 7 2.1.1 The central limit theorem, purely time-dependent flows, and diffusion . . . . 8 2.1.2 Using formal asymptotic expansions . . . . . . . . . . . . . . . . . . . . . . . 9 2.1.3 Random flows with spatial-temporal dependence . . . . . . . . . . . . ...

Single particle tracking with a wide field microscope is used to study the solid liquid interface between the viscous liquid tetrakis(2-ethylhexoxy)-silane and a silicon dioxide surface. Silicon dioxide nanoparticles (5 nm diameter) marked with the fluorescent dye rhodamine 6G are used as probes. The distributions of diffusion coefficients, obtained by mean squared displacements, reveal heterog...