标度律交叉的自相似解框架：粘弹性板的动力学冲击
A framework for crossover of scaling law as a self-similar solution : dynamical impact of viscoelastic board
AI总结：
本文提出用自相似解描述标度律交叉的新框架，通过粘弹性板冲击实验验证，理论预测与实验吻合，揭示相似性层级结构在交叉中的基础作用。
摘要：
本文提出了一个标度律交叉的新框架：标度律的交叉可以通过自相似解来描述。交叉现象产生于更高阶自相似性中相似性参数的干涉。该框架通过固体球对粘弹性板的动力学冲击进行了验证。包括球体尺寸和冲击速度在内的所有物理因素，均成功地用原始无量纲数进行了概括，这些无量纲数构成了第二类自相似解，代表了问题中涉及的动力学元素之间的平衡。自相似解通过微扰方法给出了描述交叉的两种不同标度律。这些理论预测与实验结果进行了比较，显示出良好的一致性。研究表明，相似性的层级结构在交叉现象中起着基础性作用，这为一般意义上的自相似性提供了基本见解。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
