Analyses of random walks traditionally use the mean square displacement (MSD) as an order parameter characterizing dynamics. We show that the distribution of relative angles of motion between successive time intervals of random walks in two or more dimensions provides information about stochastic processes beyond the MSD. We illustrate the behavior of this measure for common models and apply it to experimental particle tracking data. For a colloidal system, the distribution of relative angles reports sensitively on caging as the density varies. For transport mediated by molecular motors on filament networks in vitro and in vivo, we discover self-similar properties that cannot be described by existing models and discuss possible scenarios that can lead to the elucidated statistical features.

Colloidal suspensions exhibit shear thinning and shear thickening. The most common interpretation of these phenomena identifies layering of the fluid perpendicular to the shear gradient as the driver for the observed behavior. However, studies of the particle configurations associated with shear thinning and thickening cast doubt on that conclusion and leave unsettled whether these nonequilibrium phenomena are caused primarily by correlated particle motions or by changes in particle packing structure. We report the results of Stokesian dynamics simulations of suspensions of hard spheres that illuminate the relation among the suspension viscosity, shear rate, and particle configuration. Using a recently introduced sampling technique for nonequilibrium systems, we show that shear thinning can be decoupled from layering, thereby eliminating layering as the driver for shear thinning. In contrast, we find that there is a strong correlation between shear thinning and a two-particle measure of the shear stress. Our results are consistent with a recent experimental study.

We present a theoretical study of the eigenstates of the endohedral fullerene Li@C60 for the case that the C60 cage is assumed to be stationary. These eigenstates represent the three-dimensional nuclear dynamics of a Li atom confined to the interior of the carbon cage. The potential function employed, based on density functional theory calculations that we performed, has a variety of minima corresponding to complex hindered rotations of the Li atom in a shell about 1.5 Å from the cage center. The energies and wave functions of the lowest 1200 states have been calculated, and the characteristic features of selected states and the far-IR spectrum are discussed. An interesting result of the calculations is the finding that the ground-state eigenfunction can become strongly localized when the cage atoms are just slightly perturbed from icosahedral symmetry.