具有稀疏根毛分布的植物根系吸收养分的多尺度分析：非标准尺度
Multiscale analysis of nutrient uptake by plant roots with sparse distribution of root hairs: Nonstandard scaling
摘要：
在本文中，我们进行了多尺度分析的养分吸收的植物根毛，考虑不同的尺度关系的半径和它们之间的距离。我们将形式渐近展开的方法和宏观方程的严格推导结合起来。前者促使我们研究一个杰出的限制（这产生了一个独特的有效方程），使我们能够确定高阶校正和提供动机的建设校正必不可少的严格推导宏观方程。在最后一节中，我们通过与全几何数值模拟的直接比较来验证我们的渐近分析结果。
英文摘要：
In this paper we undertake a multiscale analysis of nutrient uptake by plant root hairs, considering different scale relations between the radius of hairs and the distance between them. We combine the method of formal asymptotic expansions and rigorous derivation of macroscopic equations. The former prompt us to study a distinguished limit (which yields a distinct effective equation), allow us to determine higher order correctors and provide motivation for the construction of correctors essential for rigorous derivation of macroscopic equations. In the final section, we validate the results of our asymptotic analysis by direct comparison with full-geometry numerical simulations.
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