Deep-Sea Nanoscience Research Group, Research Center for Bioscience and Nanoscience, Research Institute for Marine Resource Utilization, Japan Agency for Marine-Earth Science and Technology (JAMSTEC), 2-15 Natsushima-cho, Yokosuka, Kanagawa, 237-0061, Japan.
Advanced Statistical Dynamics, Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto, 606-8502, Japan.
Eur Phys J E Soft Matter. 2023 May 24;46(5):35. doi: 10.1140/epje/s10189-023-00292-9.
In this paper, a new framework for crossover of scaling law is proposed: a crossover of scaling law can be described by a self-similar solution. A crossover emerges as a result of the interference from similarity parameters of the higher class of the self-similarity. This framework was verified for the dynamical impact of a solid sphere onto a viscoelastic board. All the physical factors including the size of spheres and the impact of velocity are successfully summarized using primal dimensionless numbers which construct a self-similar solution of the second kind, which represents the balance between dynamical elements involved in the problem. The self-similar solution gives two different scaling laws by the perturbation method describing the crossover. These theoretical predictions are compared with experimental results to show good agreement. It was suggested that a hierarchical structure of similarity plays a fundamental role in crossover, which offers a fundamental insight into self-similarity in general.
标度律的交叉可以用自相似解来描述。交叉是由于自相似性的更高阶相似参数的干扰而产生的。该框架已通过固体球撞击粘弹性板的动力冲击进行了验证。所有物理因素，包括球体的大小和冲击速度，都成功地用构成第二类自相似解的原始无量纲数来总结，该解代表了所涉及问题的动力要素之间的平衡。自相似解通过描述交叉的微扰方法给出了两个不同的标度律。这些理论预测与实验结果进行了比较，结果吻合较好。结果表明，相似性的层次结构在交叉中起着根本性的作用，为一般的自相似性提供了基本的见解。
