论文标题
跨越法律作为一种自相似解决方案的跨界框架：粘弹性板的动态影响
A framework for crossover of scaling law as a self-similar solution : dynamical impact of viscoelastic board
论文作者
论文摘要
在本文中，提出了一个新的缩放定律交叉框架：可以通过自相似的解决方案来描述缩放定律的跨界框架。由于来自自相似性的较高类别的相似性参数的干扰，跨界出现了。该框架已被验证，以使固体球对粘弹性板的动态影响进行验证。所有物理因素（包括球体的大小和速度的影响）都使用原始无量纲数来构建第二种的自相似解，这代表了问题中涉及的动态元素之间的平衡。自相似的解决方案通过描述交叉的扰动方法给出了两个不同的缩放定律。将这些理论预测与实验结果进行比较，以显示良好的一致性。有人认为，相似性的层次结构在跨界方面起着基本作用，这为一般的自相似性提供了基本的见解。
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 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 on crossover, which offers a fundamental insight to self-similarity in general.
