Random diffusivity from stochastic equations: comparison of two models for Brownian yet non-Gaussian diffusion
Random diffusivity from stochastic equations: comparison of two models for Brownian yet non-Gaussian diffusion
复制标题
DOI：
10.1088/1367-2630/aab696
复制
发表时间：
2018-04
影响因子：
3.3
通讯作者：
V. Sposini;A. Chechkin;F. Seno;G. Pagnini;R. Metzler
中科院分区：
文献类型：
--
作者：
V. Sposini;A. Chechkin;F. Seno;G. Pagnini;R. Metzler
最近有相当多的系统被报道，在其中观察到了布朗但非高斯动力学。这些过程的特征是均方位移在时间上呈线性增长，但粒子位移的概率密度函数明显是非高斯的，并且通常具有指数(拉普拉斯)形状。这种在非常不同的物理系统中观察到的明显普遍的行为被解释为是非均匀环境中扩散的结果，并通过一个可变的随机扩散系数在数学上表示。事实上，已经研究了描述波动扩散系数的不同模型。在这里，我们提出了一种描述广泛分布范围内随时间变化的随机扩散系数的随机基的新观点。具体地说，我们的研究是基于广义伽玛分布的非常一般的类别。研究了在这种随机扩散系数设置下粒子扩散的两种模型。第一类属于广义灰布朗运动，第二类源于扩散系数的概念。这两个过程表现出显著的特点，复制了来自不同生物和物理系统的实验结果。我们提出了这两个物理模型来描述复杂环境中的随机粒子运动。
A considerable number of systems have recently been reported in which Brownian yet non-Gaussian dynamics was observed. These are processes characterised by a linear growth in time of the mean squared displacement, yet the probability density function of the particle displacement is distinctly non-Gaussian, and often of exponential (Laplace) shape. This apparently ubiquitous behaviour observed in very different physical systems has been interpreted as resulting from diffusion in inhomogeneous environments and mathematically represented through a variable, stochastic diffusion coefficient. Indeed different models describing a fluctuating diffusivity have been studied. Here we present a new view of the stochastic basis describing time-dependent random diffusivities within a broad spectrum of distributions. Concretely, our study is based on the very generic class of the generalised Gamma distribution. Two models for the particle spreading in such random diffusivity settings are studied. The first belongs to the class of generalised grey Brownian motion while the second follows from the idea of diffusing diffusivities. The two processes exhibit significant characteristics which reproduce experimental results from different biological and physical systems. We promote these two physical models for the description of stochastic particle motion in complex environments.