论文标题
外力场的随机扩散过程
Random diffusivity processes in an external force field
论文作者
论文摘要
最近在许多生物系统中观察到了布朗但非高斯的过程，并且基于随机扩散率模型建立了相应的理论。考虑到随机扩散率的特殊性，本文研究了作用于两种随机扩散率模型的外部力的作用，这些模型在差异化定理是否有效。基于两个随机扩散率模型，我们使用任意外力来得出Fokker-Planck方程，并以恒定力（包括爱因斯坦关系，力矩，峰度，峰度，峰度和粒子粒子位移概率密度函数在不同时间尺度上的概率密度函数的差异性行为）分析各种可观察到的情况。这些可观察结果的理论结果和数值模拟都显示出两种随机扩散率模型之间的显着差异，这意味着波动 - 渗透定理在随机扩散系统中的重要作用。
Brownian yet non-Gaussian processes have recently been observed in numerous biological systems and the corresponding theories have been built based on random diffusivity models. Considering the particularity of random diffusivity, this paper studies the effect of an external force acting on two kinds of random diffusivity models whose difference is embodied in whether the fluctuation-dissipation theorem is valid. Based on the two random diffusivity models, we derive the Fokker-Planck equations with an arbitrary external force, and analyse various observables in the case with a constant force, including the Einstein relation, the moments, the kurtosis, and the asymptotic behaviors of the probability density function of particle's displacement at different time scales. Both the theoretical results and numerical simulations of these observables show significant difference between the two kinds of random diffusivity models, which implies the important role of the fluctuation-dissipation theorem in random diffusivity systems.
