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.

中文翻译：

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通过随机分布的水槽的单向运输的均质化近似

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。出于这种应用的动机，我们研究了一种理想的溶质通过模型的模型，该溶质通过一系列沿点随机分布的点汇阵列，这些点汇通过一级动力学去除溶质。随机的汇点位置会在溶质场中引起长期的空间相关性，并影响平均浓度。我们基于合理地近似合适格林函数的积分，提出了一种非标准的评估这些特征的方法，该方法可以适应短时和长时尺度变化，并且具有确定性和随机性。我们完善了周期水槽阵列的经典两尺度方法的结果（给出了更准确的具有非局部贡献的高阶校正），并找到了浓度和波动性校正的波动的显式预测，以及弱势和均值的均值校正水槽位置严重混乱。我们的预测在很大范围的参数空间中得到了验证。