均质化(气候)
有界函数
平流
水槽(地理)
高斯分布
紧凑空间
数学
数学分析
统计物理学
面积二阶矩
物理
几何学
热力学
生物多样性
生态学
地图学
量子力学
生物
地理
作者
George E. Price,Igor L. Chernyavsky,Oliver E. Jensen
标识
DOI:10.1098/rspa.2022.0032
摘要
We investigate the transport of a solute past isolated sinks in a bounded domain when advection is dominant over diffusion, evaluating the effectiveness of homogenization approximations when sinks are distributed uniformly randomly in space. Corrections to such approximations can be non-local, non-smooth and non-Gaussian, depending on the physical parameters (a P\'eclet number Pe, assumed large, and a Damk\"ohler number Da) and the compactness of the sinks. In one spatial dimension, solute distributions develop a staircase structure for large Pe, with corrections being better described with credible intervals than with traditional moments. In two and three dimensions, solute distributions are near-singular at each sink (and regularized by sink size), but their moments can be smooth as a result of ensemble averaging over variable sink locations. We approximate corrections to a homogenization approximation using a moment-expansion method, replacing the Green's function by its free-space form, and test predictions against simulation. We show how, in two or three dimensions, the leading-order impact of disorder can be captured in a homogenization approximation for the ensemble mean concentration through a modification to Da that grows with diminishing sink size.
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