title: Friction phenomena in the overdamped three-layer model.
abstract: An overdamped three-layer model consisting of two harmonic chains of interacting particles, representing the upper and the middle layers, which move over the substrate potential, is studied in the present paper. A dc+ac force is applied only on the upper harmonic chain, and dynamics of both layers are investigated. The results show that the dynamical mode locking and Shapiro steps appear not only in the upper layer but also in the middle one. It is noted that the motion of particles in the upper layer corresponds to the standard Frenkel-Kontorova model. The dependence of the Shapiro steps of the middle layer on the system parameters are determined. It is shown that the height of the first Shapiro step of the upper layer is unrelated to the interaction parameters of the particles of both the upper and the middle layers, while the height of the first Shapiro step of the middle layer depend only on the interaction parameters of the particles of the middle layers. Two critical forces which transfer from locked state to the sliding one of both the upper and the middle layers are also studied. They depend on the amplitude and the frequency of the external ac driving force.
authors.affiliation: College of Physics and Electronic Engineering and Joint Laboratory of Atomic and Molecular Physics of NWNU & IMP CAS, Northwest Normal University, Lanzhou 730070 and Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China.
authors.forename: Li-Ping
authors.initials: LP
authors.lastname: Jia
authors.affiliation: "Vinča" Institute of Nuclear Sciences, Laboratory for Theoretical and Condensed Matter Physics 020, University of Belgrade, Post Office Box 522, 11001 Belgrade, Serbia.
authors.forename: Jasmina
authors.initials: J
authors.lastname: Tekić
authors.affiliation: College of Physics and Electronic Engineering and Joint Laboratory of Atomic and Molecular Physics of NWNU & IMP CAS, Northwest Normal University, Lanzhou 730070 and Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China.
authors.forename: Yang
authors.initials: Y
authors.lastname: Yang
authors.affiliation: College of Physics and Electronic Engineering and Joint Laboratory of Atomic and Molecular Physics of NWNU & IMP CAS, Northwest Normal University, Lanzhou 730070 and Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China.
authors.forename: Cang-Long
authors.initials: CL
authors.lastname: Wang
authors.affiliation: College of Physics and Electronic Engineering and Joint Laboratory of Atomic and Molecular Physics of NWNU & IMP CAS, Northwest Normal University, Lanzhou 730070 and Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China.|State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China.
authors.forename: Wen-Shan
authors.initials: WS
authors.lastname: Duan
authors.affiliation: College of Physics and Electronic Engineering and Joint Laboratory of Atomic and Molecular Physics of NWNU & IMP CAS, Northwest Normal University, Lanzhou 730070 and Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China.|Department of Physics, Lanzhou University, Lanzhou 730000, China.
authors.forename: Lei
authors.initials: L
authors.lastname: Yang