SGER / Collaborative Reseach: Multiscale Modeling: Finding Strengths, Avoiding Weaknesses

这个探索性研究的小赠款(SGER)是为了调查多尺度建模的局限性。多尺度建模是一种新的方法，有望在从物理到工程的一系列学科中取得重大进展。通过使用各种聚合方法，将不同物理尺度上发生的事情联系起来，取得了新的进展。然而，在其发展的这个阶段，只有几个一般原则来指导我们对何时应该或不应该使用这种形式的建模的理解。通过应用我们对聚集过程理解的最新进展，这项研究将制定新的指导方针，以理解何时多尺度建模是合适的，何时必须修改通常的多重尺度概念，以及何时使用这种方法不合适。这项研究不仅将对工程学中的建模产生影响，还将对来自物理和数学的问题产生影响。通过为这项技术的适当使用提供指南，这项研究有望促进参与这类建模的越来越多的其他研究人员的研究努力，最终有望增加基于多尺度的工程过程的效率，并有望为将被强调的工程问题类别中的观察到的行为确定新的解释。这个项目还旨在让研究生和本科生接触到一种分析模型的新方法。

This Small Grant for Exploratory Research (SGER) is to investigate the limitations of multiscaling modeling. Multiscaling modeling is a new approach that promises significant advances in an array of disciplines ranging from physics to engineering. By connecting what happens at different physical scales, through the use of a variety of aggregation approaches, new advances have been made. At this stage of its development, however, there are only a few general principles to guide our understanding about when this form of modeling should be, or should not be, used. By applying recent advances in our understanding of aggregation processes, this research will develop new guidelines to understand when multiscaling modeling is appropriate, when the usual notions of multiscaling must be modified, and when using this approach is not appropriate. This research will have an effect not only on modeling within engineering, but also on questions coming from physics and mathematics. By providing guidelines about the appropriate use of this technique, this research can be expected to facilitate the research efforts of the growing number of other researchers who are involved in this type of modeling, it is expected to eventually add to the efficiency of engineering processes that are based on multiscaling, and it is expected to identify new explanations for observed behavior within the class of engineering problems that will be emphasized. This project also is designed to expose graduate and undergraduate students to a new approach for the analysis of models.