单向输运通过随机分布汇点的均匀化近似
Homogenization approximations for unidirectional transport past randomly distributed sinks
摘要：
生物系统中的输运通常发生在涉及随机结构的复杂空间环境中。出于这样的应用程序，我们研究了一个理想化的模型溶质运输过去的一系列点汇，随机分布沿一条线，通过一阶动力学去除溶质。随机汇的位置引起的溶质场的长程空间相关性和影响的平均浓度。我们提出了一个非标准的方法来评估这些功能的基础上合理的近似积分的一个合适的格林函数，它可以容纳不同的贡献，在短期和长期的长度尺度，并具有确定性和随机组件。我们完善的结果，经典的两个尺度的方法为周期性的水槽阵列（更准确的高阶校正与非本地的贡献），并找到明确的预测浓度波动和混乱引起的校正的平均值为弱和强无序的水槽位置。我们的预测在一个大的参数空间区域得到验证。
英文摘要：
Transport in biological systems often occurs in complex spatial environments involving random structures. Motivated by such applications, we investigate an idealised 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 to 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.
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