Controllable wave propagation in a weakly nonlinear monoatomic lattice chain with nonlocal interaction and active control

The one-dimensional monoatomic lattice chain connected by nonlinear springs is investigated, and the asymptotic solution is obtained through the Lindstedt-Poincar′e perturbation method. The dispersion relation is derived with the consideration of both the nonlocal and the active control effects. The numerical results show that the nonlocal effect can effectively enhance the frequency in the middle part of the dispersion curve.When the nonlocal effect is strong enough, zero and negative group velocities will be evoked at different points along the dispersion curve, which will provide different ways of transporting energy including the forward-propagation, localization, and backwardpropagation of wavepackets related to the phase velocity. Both the nonlinear effect and the active control can enhance the frequency, but neither of them is able to produce zero or negative group velocities. Specifically, the active control enhances the frequency of the dispersion curve including the point at which the reduced wave number equals zero, and therefore gives birth to a nonzero cutoff frequency and a band gap in the low frequency range. With a combinational adjustment of all these effects, the wave propagation behaviors can be comprehensively controlled, and energy transferring can be readily manipulated in various ways.

Dark Solitons in FPU Lattice Chain

Based on multiple scales method, we study the nonlinear properties of a new Fermi-Pasta-Ulam lattice model analytically. It is found that the lattice chain exhibits a novel nonlinear elementary excitation, i.e. a dark soliton. Moreover, the modulation depth of dark soliton is increasing as the anharmonic parameter increases.

Effects of intrinsic decoherence on the entanglement of a two-qutrit 1D optical lattice chain with nonlinear coupling

We have investigated the intrinsic decoherence on the entanglement of a two-qutrit one-dimensional （1D） optical lattice chain with nonlinear coupling. As a measure of the entanglement, the negativity of the system is calculated. It is shown that the influence of intrinsic decoherence on the entanglement varies in different initial systems.

Lattice Dynamics Models to Predict Transmission Properties of Flexural Waves in One-Dimensional Atom Chains with Defects

Flexural waves usually propagate in one-and two-dimensional structures.To further our understanding on their transmission properties from the viewpoint of discrete lattice dynamics,we systematically established analytical atom chain models with mass defects and side branches.Both mechanisms of the Bragg scattering and the local resonance corresponding to mass defects and side branches,respectively,are elucidated by means of the present models.The results from the models show that increasing the number of mass defects or side branches decreases the transmission magnitude gradually,and the finite-width phononic bandgap may form due to the periodical arrangement of defects.The interplay between the local resonance and the Bragg scattering gives rise to the narrow phononic bandgap for lattice chains only with periodical side branches.The width of the bandgap strongly depends on the stiffness of side branches.The transmission is insensitive to the tensile strain considered for both kinds of defects,but significantly decreases with an increase in damping or wave frequency.The present work helps further our understanding on the dynamics of flexural waves.