论文标题
增强维度分析的理论和应用
Theory and Application of Augmented Dimensional Analysis
论文作者
论文摘要
我们提出了一种创新的方法来进行维度分析，称为增强维度分析，并基于具有比例融合标量表示的完整数量函数的表示定理。这种新定理以纯粹的数量空间代数理论为基础，允许经典的π理论以明确而精确的形式重述，并且其先决条件可以澄清和放松。与经典维度分析相比，增强维度分析可以考虑到所涉及数量之间的所有关系。给出了几个示例，以表明因此获得的信息以及对称性假设可以导致新的或更强大的结果。我们还探讨了维度分析与矩形理论之间的联系，阐明了维度分析的组合方面。有人强调，维度分析基于协方差的原则。
We present an innovative approach to dimensional analysis, referred to as augmented dimensional analysis and based on a representation theorem for complete quantity functions with a scaling-covariant scalar representation. This new theorem, grounded in a purely algebraic theory of quantity spaces, allows the classical πtheorem to be restated in an explicit and precise form and its prerequisites to be clarified and relaxed. Augmented dimensional analysis, in contrast to classical dimensional analysis, is guaranteed to take into account all relations among the quantities involved. Several examples are given to show that the information thus gained, together with symmetry assumptions, can lead to new or stronger results. We also explore the connection between dimensional analysis and matroid theory, elucidating combinatorial aspects of dimensional analysis. It is emphasized that dimensional analysis rests on a principle of covariance.
