title: Shock wave in a one-dimensional granular chain under Hertz contact.
abstract: The shock wave in one-dimensional bead chain is studied numerically. When the shock wave arrives, the bead velocity oscillates around the piston velocity. It is found that the shock front is composed of several solitary waves and the limitation of the maximum bead velocity is 2 times the piston velocity in the limiting case where the initial overlap is zero. If the initial overlap is not zero, then the maximum bead velocity is less than 2 times the piston velocity but larger than the piston velocity. As the initial overlap increases from zero to the finite value, the shock velocity depends on not only the piston velocity but also the initial overlap. The crossover of the dependence of the shock velocity on the piston velocity from the zero initial prestress to the finite value is obtained in the present manuscript. It is an improvement of the results presented in Phys. Rev. Lett. 108, 058001 (2012)10.1103/PhysRevLett.108.058001. In other words, the dependence of the shock velocity on the parameters of the granular materials is given.
authors.affiliation: Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China.|College of Physics and Electronic Engineering and Joint Laboratory of Atomic and Molecular Physics of NWNU &IMP CAS, Northwest Normal University, Lanzhou 730070, China.
authors.forename: Wen-Shan
authors.initials: WS
authors.lastname: Duan
authors.affiliation: Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China.|College of Physics and Electronic Engineering and Joint Laboratory of Atomic and Molecular Physics of NWNU &IMP CAS, Northwest Normal University, Lanzhou 730070, China.
authors.forename: Zhen-Bin
authors.initials: ZB
authors.lastname: Zhang
authors.affiliation: Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China.|College of Physics and Electronic Engineering and Joint Laboratory of Atomic and Molecular Physics of NWNU &IMP CAS, Northwest Normal University, Lanzhou 730070, China.|Department of Physics, Lanzhou University, Lanzhou 730000, China.
authors.forename: Lei
authors.initials: L
authors.lastname: Yang