论文标题
非本地相互作用的严格建模决定了宏观对流扩散PDE
Rigorous modelling of nonlocal interactions determines a macroscale advection-diffusion PDE
论文作者
论文摘要
一个缓慢变化或薄的多尺度假设使宏观的理解能力理解从管道和河流中分散的许多物理场景，包括梁，壳和非线性波的调节，以及微观结构的同质化。在这里，我们开始对特定物理学具有非本地微观相互作用的方案进行新的探索。我们严格分析了剪切分散剂的基本示例的动力学。在每个横截面附近，动力学在微观非本地效应的局部力矩中表达。然后，中心歧管理论支持系统动力学的局部建模，并将耦合与相邻的横截面作为非自主强迫。然后，所有横截面的联盟为在大型，有限的大小，域中的宏观模型对流扩散PDE全球的存在和出现提供了强大的新支持。该方法量化了宏观对流扩散近似的准确性，并有可能向新见解打开以前棘手的多尺度问题。
A slowly-varying or thin-layer multiscale assumption empowers macroscale understanding of many physical scenarios from dispersion in pipes and rivers, including beams, shells, and the modulation of nonlinear waves, to homogenisation of micro-structures. Here we begin a new exploration of the scenario where the given physics has non-local microscale interactions. We rigorously analyse the dynamics of a basic example of shear dispersion. Near each cross-section, the dynamics is expressed in the local moments of the microscale non-local effects. Centre manifold theory then supports the local modelling of the system's dynamics with coupling to neighbouring cross-sections as a non-autonomous forcing. The union over all cross-sections then provides powerful new support for the existence and emergence of a macroscale model advection-diffusion PDE global in the large, finite-sized, domain. The approach quantifies the accuracy of macroscale advection-diffusion approximations, and has the potential to open previously intractable multiscale issues to new insights.
