• Hiroaki Katsuragi
Part of the Lecture Notes in Physics book series (LNP, volume 910)


In this book, dimensional analysis and the scaling method were mainly employed to reveal the physics of soft impact phenomena. The scaling approach is very helpful to observe the essence of the underlying physical mechanisms of the considered phenomena. In particular, scaling is very powerful for the order estimate of phenomena whose scale is widely spreading. To conduct assessments with accurate detail, however, we need a complete modeling, including numerical factors. Therefore, the ability of an order estimate based on the scaling should not be overvalued. However, the order estimate is usually appropriate for geophysical or planetary phenomena because the observable information for these phenomena is very limited in most cases. Moreover, most of the geophysical or planetary phenomena occur on an extremely large scale and over a very long time. Scaling is a unique method to discuss such phenomena. Furthermore, scaling and dimensional analysis are important methods in various fields including fluid engineering and astrophysics. These methods are based only on the concept of dimensional homogeneity. Although this concept is very simple, its applicability is extensive. The dimensional homogeneity is only one constraint. In general, it is difficult to obtain a complete physical formulation solely from the dimensional perspective. Thus, additional (real or numerical) experiments are necessary to attain useful scaling expressions, which suggests that dimensional analysis possesses an affinity for experiments. Therefore, we first studied the fundamentals of dimensional analysis and the scaling method. Then, the method was applied to various soft impacts mainly based on experimental results. One of the most important procedures in dimensional analysis and scaling is to find relevant dimensionless numbers. The relevant dimensionless numbers can be obtained using a few methods: nondimensionalization of governing equations, Π-groups method, and intuitive derivation by considering the underlying physical mechanics. These methods are important and have been utilized in various discussions in this book.


Granular Matter Dimensional Analysis Dimensionless Number Planetary Science Soft Matter Physic 
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Copyright information

© Springer Japan 2016

Authors and Affiliations

  • Hiroaki Katsuragi
    • 1
  1. 1.Department of Earth and Environmental SciencesNagoya UniversityNagoyaJapan

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