各向异性反常扩散的解析物理模型
Analytic physical model of anisotropic anomalous diffusion
摘要：
时间福克-普朗克方程解析积分在任意数量的空间维度，但与二维和三维的结果突出显示。它表明，时间的各向异性扩散系数的幂律分析自然导致一个物理上合理的模型的正常和异常扩散漂移。的漂移和扩散系数的解释提供和分析的增长率的面积和体积的不确定性被确定。它示出的渐近增长的不确定性的体积的空间的平均位置是成比例的平方根的时间提出的幂的总和的各向异性扩散系数的所有指数。
英文摘要：
The temporal Fokker-Planck equation is analytically integrated in an arbitrary number of spatial dimensions but with the 2D and 3D results highlighted. It is shown that a temporal power-law ansatz for the anisotropic diffusion coefficients leads naturally to a physically reasonable model of normal and anomalous diffusion with drift. An interpretation of the drift and diffusion coefficients is provided and the analytic growth rate of the area and volume of uncertainty is determined. It is shown that the asymptotic growth of the uncertainty in the volume of space about the mean position is proportional to the square-root of time raised to the power of the sum over all exponents of the anisotropic diffusion coefficients.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
