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...

We are interested in inhomogeneous diffusions in which the own law intervenes in the drift. This kind of diffusions corresponds to the hydrodynamical limit of some particle system. One also talks about propagation of chaos. It is well-known, for McKean-Vlasov diffusions, that such a propagation of chaos holds on finite interval. However, it has been proved that the lack of convexity of the exte...

We measure all nonzero elements of the three-dimensional diffusion tensor D for clusters of colloidal spheres to a precision of 1% or better using digital holographic microscopy. We study both dimers and triangular trimers of spheres, for which no analytical calculations of the diffusion tensor exist. We observe anisotropic rotational and translational diffusion arising from the asymmetries of ...

The stochastic dynamics of an active particle undergoing a constant speed and additionally driven by an overall fluctuating torque is investigated. The random torque forces are expressed by a stochastic differential equation for the angular dynamics of the particle determining the orientation of motion. In addition to a constant torque, the particle is supplemented by random torques, which are ...

Isotherms for the adsorption of KCl in PVOH-borate hydrogel was studied at 303 K by determining the amount of potassium and chloride ions adsorbed in PVOH-borate hydrogel using ion exchange chromatography and potentiometric titrations respectively. Experimental data was tested for Frendulich’s, Langmuir’s, Temkin’s and Dubinin–Radushkevich isotherms equations. The adsorption data follows isothe...

In this paper we present our detailed investigations on the nature of the phase transition in the scalar noise model (SNM) of collective motion. Our results confirm the original findings of Ref. [6] that the disorder-order transition in the SNM is a continuous, second order phase transition for small particle velocities (v ≤ 0.1). However, for large velocities (v ≥ 0.3) we find a strong anisotr...

A major aspect of describing transport in heterogeneous media has been that of relating effective diffusivities to the topological properties of the medium. While such effective transport coefficients may be useful for mass fractals or under steady state conditions, they are not adequate under transient conditions for self-similar pore fractal media. In porous formations without scale, diffusio...

While the theory of diffusion of a single Brownian particle in confined geometries is well-established by now, we discuss here the theoretical framework necessary to generalize the theory of diffusion to dense suspensions of strongly interacting Brownian particles. Dynamical density functional theory (DDFT) for classical Brownian particles represents an ideal tool for this purpose. After outlin...

We investigate experimentally and theoretically thin layers of colloid particles held adjacent to a solid substrate by gravity. Epifluorescence, confocal, and holographic microscopy, combined with Monte Carlo and hydrodynamic simulations, are applied to infer the height distribution function of particles above the surface, and their diffusion coefficient parallel to it. As the particle area fra...

We consider diffusion processes with a spatially varying diffusivity giving rise to anomalous diffusion. Such heterogeneous diffusion processes are analysed for the cases of exponential, power-law, and logarithmic dependencies of the diffusion coefficient on the particle position. Combining analytical approaches with stochastic simulations, we show that the functional form of the space-dependen...