Homogenization approximations for unidirectional transport past randomly distributed sinks
Homogenization approximations for unidirectional transport past randomly distributed sinks
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DOI：
10.1093/imamat/hxz004
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发表时间：
2020-04-01
影响因子：
1.2
通讯作者：
Jensen, Oliver E.
中科院分区：
文献类型：
--
作者：
Russell, Matthew J.;Jensen, Oliver E.
生物系统中的运输通常发生在涉及随机结构的复杂空间环境中。受此类应用的启发，我们研究了一种理想化的溶质模型，该模型用于溶质通过一系列沿线随机分布的点汇的传输，这些点汇通过一级动力学去除溶质。随机汇位置会引起溶质场中的长程空间相关性并影响平均浓度。我们提出了一种基于适当格林函数的有理近似积分来评估这些特征的非标准方法，该方法适应短长度尺度和长长度尺度上变化的贡献，并且具有确定性和随机分量。我们改进了周期性汇阵列的经典双尺度方法的结果（通过非局部贡献提供更准确的高阶校正），并找到了对浓度波动的明确预测以及对弱无序汇位置和强无序汇位置均值的无序引起的校正。我们的预测在大范围的参数空间中得到验证。
Transport in biological systems often occurs in complex spatial environments involving random structures. Motivated by such applications, we investigate an idealized model for solute transport past an array of point sinks, randomly distributed along a line, which remove solute via first-order kinetics. Random sink locations give rise to long-range spatial correlations in the solute field and influence the mean concentration. We present a non-standard approach in evaluating these features based on rationally approximating integrals of a suitable Green's function, which accommodates contributions varying on short and long lengthscales and has deterministic and stochastic components. We refine the results of classical two-scale methods for a periodic sink array (giving more accurate higher-order corrections with non-local contributions) and find explicit predictions for the fluctuations in concentration and disorder-induced corrections to the mean for both weakly and strongly disordered sink locations. Our predictions are validated across a large region of parameter space.