2022/01/13 by S. Katagiri, Katagiri, S., Y. Matsuo +5
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Computational Physics (physics.comp-ph) #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fractional Differential Equations Solutions #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.2201.04900
openalex publication_date 2022/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.