Discrete gap breathers in a two-dimensional diatomic face-centered square lattice

In this paper we study the existence and stability of two-dimensional discrete gap breathers in a two-dimensional diatomic face-centered square lattice consisting of alternating light and heavy atoms, with on-site potential and coupling potential. This study is focused on two-dimensional breathers with their frequency in the gap that separates the acoustic and optical bands of the phonon spectrum. We demonstrate the possibility of the existence of two-dimensional gap breathers by using a numerical method. Six types of two-dimensional gap breathers are obtained, i.e., symmetric, mirror-symmetric and asymmetric, whether the center of the breather is on a light or a heavy atom. The difference between one-dimensional discrete gap breathers and two-dimensional discrete gap breathers is also discussed. We use Aubry＇s theory to analyze the stability of discrete gap breathers in the two-dimensional diatomic face-centered square lattice.

Periodic,quasiperiodic and chaotic discrete breathers in a parametrical driven two-dimensional discrete diatomic Klein-Gordon lattice

We study a two-dimensional （2D） diatomic lattice of anhaxmonic oscillators with only quartic nearest-neighbor interactions, in which discrete breathers （DBs） can be explicitly constructed by an exact separation of their time and space dependence. DBs can stably exist in the 2D discrete diatomic Klein-Gordon lattice with hard and soft on-site potentials. When a parametric driving term is introduced in the factor multiplying the harmonic part of the on-site potential of the system, we can obtain the stable quasiperiodic discrete breathers （QDBs） and chaotic discrete breathers （CDBs） by changing the amplitude of the driver. But the DBs and QDBs with symmetric and anti-symmetric profiles that are centered at a heavy atom are more stable than at a light atom, because the frequencies of the DBs and QDBs centered at a heavy atom are lower than those centered at a light atom.

On band gaps of nonlocal acoustic lattice metamaterials:a robust strain gradient model

We have proposed an"exact"strain gradient(SG)continuum model to properly predict the dispersive characteristics of diatomic lattice metamaterials with local and nonlocal interactions.The key enhancement is proposing a wavelength-dependent Taylor expansion to obtain a satisfactory accuracy when the wavelength gets close to the lattice spacing.Such a wavelength-dependent Taylor expansion is applied to the displacement field of the diatomic lattice,resulting in a novel SG model.For various kinds of diatomic lattices,the dispersion diagrams given by the proposed SG model always agree well with those given by the discrete model throughout the first Brillouin zone,manifesting the robustness of the present model.Based on this SG model,we have conducted the following discussions.(Ⅰ)Both mass and stiffness ratios affect the band gap structures of diatomic lattice metamaterials,which is very helpful for the design of metamaterials.(Ⅱ)The increase in the SG order can enhance the model performance if the modified Taylor expansion is adopted.Without doing so,the higher-order continuum model can suffer from a stronger instability issue and does not necessarily have a better accuracy.The proposed SG continuum model with the eighth-order truncation is found to be enough to capture the dispersion behaviors all over the first Brillouin zone.(Ⅲ)The effects of the nonlocal interactions are analyzed.The nonlocal interactions reduce the workable range of the well-known long-wave approximation,causing more local extrema in the dispersive diagrams.The present model can serve as a satisfactory continuum theory when the wavelength gets close to the lattice spacing,i.e.,when the long-wave approximation is no longer valid.For the convenience of band gap designs,we have also provided the design space from which one can easily obtain the proper mass and stiffness ratios corresponding to a requested band gap width.

Size Dependent Heat Conduction in One-Dimensional Diatomic Lattices

We study the size dependency of heat conduction in one-dimensional diatomic FPU-β lattices and establish that for low dimensional material,contribution from optical phonons is found more effective to the thermal conductivity and enhance heat transport in the thermodynamic limit N →∞.For the finite size,thermal conductivity of 1D diatomic lattice is found to be lower than 1D monoatomic chain of the same size made up of the constituent particle of the diatomic chain.For the present 1D diatomic chain,obtained value of power divergent exponent of thermal conductivity0.428±0.001 and diffusion exponent 1.2723 lead to the conclusions that increase in the system size,increases the thermal conductivity and existence of anomalous energy diffusion.Existing numerical data supports our findings.

二维双原子正方晶格振动的色散关系

利用晶格动力学理论推导了二维双原子正方晶格振动的色散关系表达式,得到第一布里渊区中沿Γ-X、Γ-M和X-M 3种对称方向的声子色散曲线,每一对称方向有四支格波,即两支声学波和两支光学波.讨论了原子质量和次近邻原子间作用对色散关系的影响,结果表明:当两原子质量相等时,3个对称方向的声学波与光学波间无频隙;当两原子质量不等时,声学波与光学波间出现频隙.计及次近邻原子间作用,对Γ点声子频率的大小和简并不影响,两声学模频率为零、两光学模频率简并;对X点声子频率的简并也无影响,但相应频率增大;使M点声子频率的简并度降低,高频声学和光学声子的频率增大,而低频声学和光学声子的频率不变;沿Γ-X方向四支格波仍是非简并的,对应的频率增大,但都表现出色散性;沿Γ-M和X-M方向简并格波的简并度消失,除Γ-M方向低频声学支和光学支频率不变之外,其他格波声子的频率都增大,并且四支格波都表现出色散性.

具有在位势的一维双原子链晶格振动的色散关系

在简谐近似下,求解具有在位势的一维双原子链晶格振动运动方程,得到了具有在位势的晶格振动的色散关系.在位势使色散关系声频支在布里渊区中心的振动频率不再为零,并且随在位势的增大而增大.对于原子之间相互作用势不随在位势大小变化的情况下,晶格振动的色散关系的频隙随在位势的增大而变宽.讨论了原子链由只有在位势的不连续极限(AC极限),通过在位势逐渐减弱而原子间相互作用势逐渐增强,最后演变到只有原子间相互作用势的原子链的情况.随着在位势减弱和相互作用势增强,色散关系的频隙由AC极限的孤立轻、重原子简谐振动频率之差逐渐变化到通常的无在位势的色散关系频隙.

一维双原子链中杂质引起的局域振动模

对含杂质的一维双原子链,在链中所有原子之间近邻相互作用力常数均相等的情况下,数值求解晶格振动的运动方程组,得到不同局域振动模的振动图像和产生条件,给出了局域模关于杂质原子质量和原胞中两种晶格原子质量比分布的相图.

一维双原子链晶格振动u_(2n+1)(q)≠u_(2n+1)(q+(2π/2a))谬误的分析

对一维双原子链晶格振动的u2n+1(q)≠u2n+1(q + 2π2a)谬误进行分析 ,给出了正确的关系式 ,进一步给出了一维三原子链晶格振动的波矢q振动模与相差一个倒格矢的振动模等同的有关关系式 .

双原子链中点缺陷引起的局域振动

通过对存在一个点缺陷的一维双原子链振动方程的求解,得到晶格局域模频率的对称解析解和反对称解析解,并对局域模进行了简要讨论.

杂质引起的双原子链晶格振动频率的变化

对含单个杂质的双原子链的晶格振动模型的振动方程进行求解，得到了晶格振动频率和局域模频率的解析解，给出了该模型中杂质对双原子链的光学振动频率和声学振动频率的影响，并对局域模进行简要讨论。

一维双原子链中杂质的局域振动

讨论了一维双原子链中杂质的局域振动,对杂质原子替代大原子和替代小原子的情况进行了分析,分别得到这两种情况下的高频模和隙模的频率.

在位势对于一维双原子链晶格振动长光学模的影响

在简谐近似下,求解具有在位势的一维双原子链晶格动力学方程,得出并分析新的色散关系。讨论了具有在位势的一维双原子链晶格振动的高频支长波模振动图像。

双原子正方晶格光子晶体边界模式的光传输特性（英文）

利用平面波展开法,发现双原子正方晶格光子晶体中ΓM方向边界面存在着快慢两类边界模式,并且通过计算色散关系和电场分布研究了边界参量对这两类边界模式传输特性的影响.依据两种模式的色散关系,计算了群指数和群速度色散参量,结果表明边界参量的变化对第一类边界模式传输特性的影响较小,该模式的平均群指数始终维持在5.0左右;第二类边界模式与第一类模式明显不同,边界参量的变化能够有效地影响到这种模式的传输特性,该模式的最大平均群指数可达178左右.利用时域有限差分法记录了不同时刻电场强度在边界附近的分布及监测点处的电场幅度变化情况,结果表明,两类模式都能够被限制在边界附近并向前传播,时域有限差分法得到的群速度与平面波展开法的结果完全吻合.

不变本征算符方法求解含不同在位势的一维双原子链的色散关系

本文运用全量子化的不变本征算符方法,求解了含有不同简谐在位势的一维双原子链模型,得到其色散关系并讨论了不同在位势系数之比和力常数对于色散关系高频支和低频支的影响,分析发现在位势的存在使得低频支和高频支的频谱都有一定程度的抬高;在一定的条件下,布里渊区边界的高频支与低频支存在交点,意味着在某些在位势下,高频支与低频支的频隙为零.