Propagation dynamics on the Fermi-Pasta-Ulam lattices  

作　　者：Zong-Qiang Yuan Zhi-Gang Zheng 

机构地区：[1]Department of Physics and the Beijing Hong Kong-Singapore Joint Centre for Nonlinear and Complex Systems (Beijing), Beijing Normal University, Beijing 100875, China

出　　处：《Frontiers of physics》2013年第3期349-355,共7页物理学前沿（英文版）

基　　金：Acknowledgements Project supported by the National Natural Science Foundation of China （Grant No. 11075016）, the Fundamental Research Funds for the Central Universities of China （Grant No. 201001）, and the Research and for the Doctoral Program of Higher Education of China （Grant No. 20100003110007）.

摘　　要：The spatiotemporal propagation of a momentum excitation on the finite Fermi-Pasta-Ulam lattices is investigated. The competition between the solitary wave and phonons gives rise to interesting propagation behaviors. For a moderate nonlinearity, the initially excited pulse may propagate co- herently along the lattice for a long time in a solitary wave manner accompanied by phonon tails. The lifetime of the long-transient propagation state exhibits a sensitivity to the nonlinear parameter. The solitary wave decays exponentially during the final loss of stability, and the decay rate varying with the nonlinear parameter exhibits two different scaling laws. This decay is found to be related to the largest Lyapunov exponent of the corresponding Hamiltonian system, which manifests a transition from weak to strong chaos. The mean-free-path of the solitary waves is estimated in the strong chaos regime, which may be helpful to understand the origin of anomalous conductivity in the Fermi-Pasta Ulam lattice.The spatiotemporal propagation of a momentum excitation on the finite Fermi-Pasta-Ulam lattices is investigated. The competition between the solitary wave and phonons gives rise to interesting propagation behaviors. For a moderate nonlinearity, the initially excited pulse may propagate co- herently along the lattice for a long time in a solitary wave manner accompanied by phonon tails. The lifetime of the long-transient propagation state exhibits a sensitivity to the nonlinear parameter. The solitary wave decays exponentially during the final loss of stability, and the decay rate varying with the nonlinear parameter exhibits two different scaling laws. This decay is found to be related to the largest Lyapunov exponent of the corresponding Hamiltonian system, which manifests a transition from weak to strong chaos. The mean-free-path of the solitary waves is estimated in the strong chaos regime, which may be helpful to understand the origin of anomalous conductivity in the Fermi-Pasta Ulam lattice.

关 键 词：Fermi-Past-Ulam model solitary wave low-dimensional heat conduction 

分 类 号：O4-09[理学—物理] TN011[电子电信—物理电子学]