Intermediate asymptotics on dynamical impact of solid sphere on militextured surface

Complex phenomena incorporating several physical properties are abundant while they are occasionally revealing the variation of power-law behavior depending on the scale. In the present work, the global scaling behavior of the dynamical impact of a solid sphere onto an elastic surface is described. Its fundamental dimensionless function was successfully obtained by applying dimensional analysis combined with a solution by energy conservation complementally. It demonstrates that its power-law behavior is given by the competition between two power-law relations representing inertial and elastic properties respectively, which is strengthened by the scale size of the sphere. These factors are successfully summarized by the newly defined dimensionless parameters, which give two intermediate asymptotics in a different scale range. These power-law behaviors given by the theoretical model were compared with experimental results, showing good agreement. This study supplies the insights to dimensional analysis and self-similarity in general.