2019/12/12 by Alex Hansen, Hansen, Alex, Eirik G. Flekkøy +1
Engineering · Mathematics · Physics and Astronomy · #FOS: Physical sciences #Field-Flow Fractionation Techniques #Fractional Differential Equations Solutions #Phase Equilibria and Thermodynamics #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.1912.05856
10 pages, 10 figures
arxiv created 2019/12/12 · openalex publication_date 2019/12/12 · arxiv updated 2019/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show analytically that there is anomalous diffusion when the diffusion constant depends on the concentration as a power law with a positive exponent or a negative exponent with absolute value less than one and the initial condition is a delta function in the concentration. On the other hand, when the initial concentration profile is a step, the profile spreads as the square root of time. We verify our results numerically using particles moving stochastically.