Moving and Interaction of Compact-like Pulses in Klein-Gordon Lattice System

We study the moving and interaction of the compact-like pulses in the system of an anharmonlc lattice with a double well on-site potential by a direct algebraic method and numerical experiments. It is found that the localization of the compact-like pulse is rClated to the nonlinear coupling parameter Cnl and the potential barrier height Vo of the double well potential. The velocity of the moving compact-like pulse is determined by the linear coupling parameter Cl, the localization parameter q (the nonlinear coupling parameter Cnl) and the potential barrier height Vo.Numerical experiments demonstrate that appropriate Cl is not detrimental to a stable moving of the compact-like pulse.However, the head on interaction of two compact-like pulses in the lattice system with comparatively small Cl leads to the appearance of a discrete stationary localized mode and small amplitude nonlinear oscillation background, while moderate Cl results in the emergence of two moving deformed pulses with damping amplitude and decay velocity and radiating oscillations, and biggish Cl brings on the appearing of four deformed kinks with radiating oscillations and different moving velocities.     

Possible Propagating Intrinsic Localized Vibrational Modes for One-Dimensional Klein-Gordon Lattice

A11 possible existed propagating intrinsic localized vibrational modes for the discrete Klein-Gordon lattice are obtained analytically in the whole w(q) space of the system by means of the so-called semidiscrete approximation, with which the carrier wave is treated explicitly while the envelope is described in the continuum approximation. Our investigation shows that, in general, both the pulse-like and kink (antikink) envelope types of the vibrational modes for the system can occur with certain carrier wavenumbers and frequencies in the separated parts of the ω(q) space. And the propagating velocity of the pulse-like modes is either subsonic or nearsonic, abd that of the kink (antikink) modes is either subsonic or supersonic. Our results are similar to or consistent with some results for Klein-Gordon lattice model or other related nonlinear lattice systems by some different methods.     

飞秒光脉冲间相互作用的数值研究

通过数值模拟对飞秒光脉冲间的相互作用进行了研究,结果表明：飞秒孤子的相互作用与常规的皮秒孤子间的相互作用不同。后者在孤子间距较小的情况下,相互作用表现为周期性离合,而前者的相互作用更严重,在初始阶段其相互作用与皮秒孤子一致,而当两孤子合二为一后,一直处于排斥状态,孤子间距传输距离增加而增加,这在通信系统中将造成更大的误码率,传统的不等振幅法在一定程度上可有效地抑制飞秒孤子的相互作用。     

Compact-like discrete breather and its stability in a discrete monatomic Klein--Gordon chain

This paper studies a discrete one-dimensional monatomic Klein--Gordon chain with only quartic nearest-neighbor interactions, in which the compact-like discrete breathers can be explicitly constructed by an exact separation of their time and space dependence. Introducing the trying method, it proves that compact-like discrete breathers exist in this nonlinear system. It also discusses the linear stability of the compact-like discrete breathers, when the coefficient (β) of quartic on-site potential and the coupling constant (K₄) of quartic interactive potential satisfy the given conditions, they are linearly stable.     

格子Boltzmann方法中三维运动边界的统一模型

格子Boltzmann方法(LBM)中边界条件的处理很复杂,在现有的边界条件处理方法中,动力学格式能够精确满足宏观边界条件,但由于要解一个不定方程,必须引入附加假设确保方程非奇异.作为动力学格式和反弹格式的一种扩展,提出一种处理三维任意速度运动边界的统一模型,其中人口速度和固体壁面速度是该模型的特殊情形.给出用于三维15速度的表达式.为了检验该模型,模拟对角顶盖驱动三维空腔流,并将结果与有限差分法计算的结果进行比较,说明所提出的统一模型是合理可行的.     

Fluid-Structure Interaction in Microchannel Using Lattice Boltzmann Method and Size-Dependent Beam Element

Fluid-structure interaction (FSI) problems in microchannels play prominent roles in many engineering applications. The present study is an effort towards the simulation of flow in microchannel considering FSI. Top boundary of the microchannel is assumed to be rigid and the bottom boundary, which is modeled as a Bernoulli-Euler beam, is simulated by size-dependent beam elements for finite element method (FEM) based on a modified couple stress theory. The lattice Boltzmann method (LBM) using D2Q13 LB model is coupled to the FEM in order to solve fluid part of FSI problem. In the present study, the governing equations are non-dimensionalized and the set of dimensionless groups is exhibited to show their effects on micro-beam displacement. The numerical results show that the displacements of the micro-beam predicted by the size-dependent beam element are smaller than those by the classical beam element.     

Klein-Gordon oscillators in noncommutative phase space

We study the Klein-Gordon oscillators in non-commutative (NC) phase space. We find that the Klein-Gordon oscillators in NC space and NC phase-space have a similar behaviour to the dynamics of a particle in commutative space moving in a uniform magnetic field. By solving the Klein-Gordon equation in NC phase space, we obtain the energy levels of the Klein-Gordon oscillators, where the additional terms related to the space-space and momentum-momentum non-commutativity are given explicitly.     

Klein-Gordon oscillators in noncommutative phase space

We study the Klein-Gordon oscillators in non-commutative (NC) phase space.We find that the Klein-Gordon oscillators in NC space and NC phase-space have a similar behaviour to the dynamics of a particle in commutative space moving in a uniform magnetic field.By solving the Klein-Gordon equation in NC phase space,we obtain the energy levels of the Klein-Gordon oscillators,where the additional terms related to the space-space and momentum-momentum non-commutativity are given explicitly.     

Perturbed Coulombic Potentials in Dirac and Klein-Gordon Equations

A relativistic extension of our pseudo-perturbative shifted l-expansion technique is presented to solve for the eigenvalues of Dirac and Klein-Gordon equations. Once more we show the numerical usefulness of its results via comparison with available numerical integration data.     

Moving breather collisions in Klein-Gordon chains of oscillators

We investigate the collisions of moving breathers, with the same frequency, in three different Klein-Gordon chains of oscillators. The on-site potentials are: the asymmetric and soft Morse potential, the symmetric and soft sine-Gordon potential and the symmetric and hard φ⁴ potential. The simulation of a collision begins generating two identical moving breathers traveling with opposite velocities, they are obtained after perturbing two identical stationary breathers which centers are separated by a fixed number of particles. If this number is odd we obtain an on-site collision, but if this number is even we obtain an inter-site collision. Apart from this distinction, we have considered symmetric collisions, if the colliding moving breathers are vibrating in phase, and anti-symmetric collisions, if the colliding moving breathers are vibrating in anti-phase. The simulations show that the collision properties of the three chains are different. The main observed phenomena are: breather generation with trapping, with the appearance of two new moving breathers with opposite velocities, and a stationary breather trapped at the collision region; breather generation without trapping, with the appearance of new moving breathers with opposite velocities; breather trapping at the collision region, without the appearance of new moving breathers; and breather reflection. For each Klein-Gordon chain, the collision outcomes depend on the lattice parameters, the frequency of the perturbed stationary breathers, the internal structure of the moving breathers and the number of particles that initially separates the stationary breathers when they are perturbed.     

基于FDTD算法研究超短脉冲与二能级原子系统的相互作用

以往对于超短脉冲与二能级原子系统的研究大多基于一些近似方法(慢变包络近似和旋转波近似等),从而求得解析的近似解。但是,由于忽略掉一些有用的光场中的信息,就会造成光场导数项所产生的非线性性质的缺失。本文基于FDTD算法和预测-校正法相结合,建立了预测-校正FDTD算法,用于研究超短脉冲与二能级原子系统的相互作用,以准确地描述光场与原子系统相互作用的特征,验证了面积定理的部分规律;进一步构建了能够实现完全反转原子系统上下能级粒子的短脉冲。相关研究可为目标的特征分析提供参考。     

Quark potentials for mesons in the Klein-Gordon equation

Two relativistic potential models are applied to describe meson spectroscopy in a unified way, encompassing both light and heavy quark systems. A combination of linear and coulomb potentials has been investigated for Klein-Gordon equation using the WKB approximation. A power-like phenomenological potential model has also been studied in the Klein-Gordon framework. Meson masses calculated for both the potentials give a good agreement with the corresponding experimental values.     

具有线性型标量势和矢量势的Klein-Gordon的束缚态

给出了当线性型标量势大于或等于其矢量势时的Klein-Gordon方程的s波束缚态解，其解可 用合流超几何函数表示. 关键词： 线性势 Klein-Gordon方程 束缚态     

Phase Formulation and Exact Solutions for the Relativistic Klein-Gordon Field with a Time-Dependent Hamiltonian

On the basis of the phase formulation, we find the quantum and classical exact solutions and corresponding total phases for the Klein-Gordon (KG) field with a time-dependent Hamiltonian. The total phase includes both the dynamical and geometric phases (Abaronov-Anandan phase). The connection between the quantum and classical solutions is then obtained. From this connection, we discuss the condition under which the geometric phase for the KG field can be defined.     

Moving bright solitons in a pseudo-spin polarization Bose-Einstein condensate

We study the moving bright solitons in the weak attractive Bose–Einstein condensate with a spin–orbit interaction. By solving the coupled nonlinear Schr ?dinger equation with the variational method and the imaginary time evolution method,two kinds of solitons(plane wave soliton and stripe solitons) are found in different parameter regions. It is shown that the soliton speed dominates its structure. The detuning between the Raman beam and energy states of the atoms decides the spin polarization strength of the system. The soliton dynamics is also studied for various moving speed and we find that the shape of individual components can be kept when the speed of soliton is low.     

光子晶体光纤中自相位调制效应对超高斯脉冲传输的影响

为了研究光子晶体光纤的微结构对其非线性光传输特性的影响,利用超格子法和光子晶体光纤中的光传输方程,计算了光子晶体光纤中的高斯光脉冲和超高斯脉冲的自相位调制谱.计算结果表明：高斯光脉冲和超高斯光脉冲的高频端比低频端均有较大的频谱展宽,而高斯光脉冲的频谱比超高斯光脉冲的频谱具有更大的中心峰值;超高斯光脉冲较高斯光脉冲有较广的频谱范围,它们的自相位调制展宽范围均随着传输距离的增加而增大.这些现象均可以利用自陡峭效应的理论加以解释.与传统光纤相比,高斯光脉冲在传统光纤中所受自相位调制效应的影响较小.     

Lattice Gas with Finite-Range Interaction Under Gravity

Existence of a phase separation is proved for a classical lattice gas with finite-range pair potential under the action of a weak gravitational field.     

Lattice Green's Function for Infinite Square Lattice in the Second Nearest-Neighbour Interaction Approximation

In dealing with the square lattice model,we replace the traditionally needed Born-Von Karmann periodic boundary condition with additional Hamiltonian terms to make up a ring lattice.In doing so,the lattice Green's function of an infinite square lattice in the second nearest-neighbour interaction approximation can be derived by means of the matrix Green's function method.It is shown that the density of states may change when the second nearest-neighbour interaction is turned on.     

在赝自旋对称性势场中运动的相对论粒子的束缚态

在赝自旋对称性条件下,分别求解了在Kratzer型、Hulthén型和Poschl-Teller型标量势与矢量势场中运动的相对论粒子的Klein-Gordon方程和Dirac方程,给出了它们的束缚态能谱和相对论性波函数.