Technische Universität Chemnitz, Faculty of Sciences, Institute of Physics, Complex Systems and Nonlinear Dynamics, D-09107 Chemnitz, Germany.
J Chem Phys. 2013 Nov 14;139(18):184105. doi: 10.1063/1.4828860.
Anisotropic diffusion processes emerge in various fields such as transport in biological tissue and diffusion in liquid crystals. In such systems, the motion is described by a diffusion tensor. For a proper characterization of processes with more than one diffusion coefficient, an average description by the mean squared displacement is often not sufficient. Hence, in this paper, we use the distribution of diffusivities to study diffusion in a homogeneous anisotropic environment. We derive analytical expressions of the distribution and relate its properties to an anisotropy measure based on the mean diffusivity and the asymptotic decay of the distribution. Both quantities are easy to determine from experimental data and reveal the existence of more than one diffusion coefficient, which allows the distinction between isotropic and anisotropic processes. We further discuss the influence on the analysis of projected trajectories, which are typically accessible in experiments. For the experimentally most relevant cases of two- and three-dimensional anisotropic diffusion, we derive specific expressions, determine the diffusion tensor, characterize the anisotropy, and demonstrate the applicability for simulated trajectories.
各向异性扩散过程出现在各种领域中，如生物组织中的传输和液晶中的扩散。在这样的系统中，运动由扩散张量描述。对于具有多个扩散系数的过程的适当描述，通常平均平方位移的平均描述是不够的。因此，在本文中，我们使用扩散率分布来研究各向异性均匀环境中的扩散。我们推导出分布的解析表达式，并将其性质与基于平均扩散率和分布的渐近衰减的各向异性度量相关联。这两个量都可以从实验数据中很容易地确定，并揭示了存在多个扩散系数的情况，这允许区分各向同性和各向异性过程。我们进一步讨论了对投影轨迹分析的影响，投影轨迹通常在实验中可以获得。对于二维和三维各向异性扩散的实验最相关情况，我们推导出了具体的表达式，确定了扩散张量，表征了各向异性，并演示了对模拟轨迹的适用性。
