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Anisotropic diffusion processes emerge in various fields such as transport inbiological tissue and diffusion in liquid crystals. In such systems, the motionis described by a diffusion tensor. For a proper characterization of processeswith more than one diffusion coefficient an average description by the meansquared displacement is often not sufficient. Hence, in this paper, we use thedistribution of diffusivities to study diffusion in a homogeneous anisotropicenvironment. We derive analytical expressions of the distribution and relateits properties to an anisotropy measure based on the mean diffusivity and theasymptotic decay of the distribution. Both quantities are easy to determinefrom experimental data and reveal the existence of more than one diffusioncoefficient, which allows the distinction between isotropic and anisotropicprocesses. We further discuss the influence on the analysis of projectedtrajectories, which are typically accessible in experiments. For theexperimentally relevant cases of two- and three-dimensional anisotropicdiffusion we derive specific expressions, determine the diffusion tensor,characterize the anisotropy, and demonstrate the applicability for simulatedtrajectories.

Characterizing N-dimensional anisotropic Brownian motion by the distribution of diffusivities