随机调制偶极子反常扩散的解析研究
Analytical Study of Anomalous Diffusion by Randomly Modulated Dipole
摘要：
本文导出了在势场中运动的粒子受随机调制偶极子作用时的Fokker-Planck（FP）方程。FP方程描述了在同伴论文[1]中观察到的反常扩散，并打破了偶极子在奇点处的总几率守恒。它还表现出各向异性扩散，这在流体湍流中是典型的。我们需要通过引入一种机制来恢复粒子，从而修改概率密度。修正后的潜分形维数与相关文献的结果基本一致。我们希望我们的模型给出了一个新的分数扩散的例子，其中随机奇异性触发分数。
英文摘要：
This paper derives the Fokker-Planck (FP) equation for a particle moving in potential by a randomly modulated dipole. The FP equation describes the anomalous diffusion observed in the companion paper [1] and breaks the conservation of the total probability at the singularity by the dipole. It also shows anisotropic diffusion, which is typical in fluid turbulence. We need to modify the probability density by introducing a mechanism to recover the particle. After the modification, the latent fractal dimension matches with the results of the companion paper. We hope that our model gives a new example of fractional diffusion, where the random singularity triggers fractionality.
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