Some new solutions derived from the nonlinear (2+1)-dimensional Toda equation---an efficient method of creating solutions

This paper presents a new and efficient approach for constructing exact solutions to nonlinear differential--difference equations (NLDDEs) and lattice equation. By using this method via symbolic computation system MAPLE, we obtained abundant soliton-like and/or period-form solutions to the (2+1)-dimensional Toda equation. It seems that solitary wave solutions are merely special cases in one family. Furthermore, the method can also be applied to other nonlinear differential--difference equations.     

分析原子干涉仪的矩阵方法

从原子波包所满足的薛定谔方程出发,从理论上巧妙地推导出了原子干涉仪在重力的影响下所产生的相位差与重力加速度的关系表达式。提出了一种3×3阶的矩阵方法,以此来分析多个元件情况下原子干涉仪中的相位差,可以大大简化计算。利用这种方法不但能得到原子束在重力的影响下在自由空间中的传输矩阵,也可以得到原子束与π/2和π脉冲的相互作用矩阵。作为例子,用3×3阶矩阵方法计算了三脉冲原子干涉仪中的相位差,得出的结果与Wolf等对经典轨迹进行拉格朗日积分所得出的结果完全相符。进一步分析了五脉冲的原子干涉仪中的相位差,以说明3×3阶矩阵方法的简便性。     

Monte Carlo simulations of primitive models for ionic systems using the Wolf method

Thermodynamic and structural properties of primitive models for electrolyte solutions and molten salts were studied using NVT and NPT Monte Carlo simulations. The Coulombic interactions were simulated using the Wolf method [D. Wolf, Phys. Rev. Lett. 68, 3315 (1992); D. Wolf, P. Keblinnski, S. R. Phillpot, and J. Eggebrecht, J. Chem. Phys. 110, 8254 (1999)]. Results for 1?:?1 and 2?:?1 charge ratio electroneutral systems are presented, using the restricted and non-restricted primitive models, as well as a soft PM pair potential for a monovalent salt [J.-P. Hansen and I. R. McDonald, Phys. Rev. A 11, 2111 (1975)] that has also been used to model 2?:?12 and 1?:?20 asymmetric colloidal systems, with size ratios 1?:?10 and 2?:?15, respectively [B. Hribar, Y. V. Kalyuzhnyi, and V. Vlachy, Molec. Phys. 87, 1317 (1996)]. We present the predictions obtained for these systems using the Wolf method. Our results are in very good agreement with simulation data obtained with the Ewald sum method as well as with integral-equation theories results. We discuss the relevance of the Wolf method in the context of variable-ranged potentials in molecular thermodynamic theories for complex fluids.     

Graphite格子光子晶体带隙的数值模拟

采用平面波展开法模拟计算了由锗圆柱构成的Graphite格子二维光子晶体的带隙结构,发现由空气背景中的介质柱构成的二维Graphite格子结构的光子晶体具有完全光子带隙,并得到了使完全带隙最大化的结构参数。数值计算结果表明,Graphite结构二维光子晶体在填充比从f=0.058到f=0.605连续变化的很大范围内都有完全带隙出现,在低能区出现了Δ=0.053(ωa/2πc)的较大带隙。     

一类延迟混沌系统沿主轴方向上Lyapunov指数的计算方法

提出了一种计算延迟混沌系统沿主轴方向上Lyapunov指数的方法：矩阵迭代法.给出了其计算方法的原理及推导过程;同时推导了一类泰勒展开法,介绍了已有的Wolf替代法计算延迟混沌系统的Lyapunov指数.分析了三种不同计算方法的优缺点,最后进行了数值模拟,验证方法的有效性. 关键词： Lyapunov指数 延迟混沌系统 矩阵迭代法 泰勒展开法     

Enhancement of LED light extraction via diffraction of hexagonal lattice fabricated in ITO layer with holographic lithography and wet etching

A novel method for enhancing light extraction efficiency of LEDs via diffraction of the lattice fabricated in ITO layers of LEDs is proposed. The lattice fabrication process includes holographic lithography and wet etching. 3-beam interference holographic approach was used to fabricate large-area hexagonal lattice mask which can cover 2-inch semiconductor wafer, and acid etching was used to transfer the lattice structure into p-contact ITO layer. 1.4 fold enhancement of light output at 20 mA injection current was obtained from GaN-based LEDs in the primary experiment. The lattice fabrication process is rapid and cost-effective thus enabling industrial mass production of high brightness LEDs.     

The dissociated properties of dislocation in two-dimensional triangular lattice

The dissociated core structure of dislocation in two-dimensional triangular lattice is determined by the variational method within lattice theory. The dissociation effect leads to a narrower core width of partial dislocations than the compact one. The equilibrium separation between two partial dislocations is not very sensitive to the intrinsic stacking fault energy and there exists deviation from the intrinsic stacking fault energy criterion in the continuous elastic theory of dislocation. The relationship between the equilibrium separation and intrinsic stacking fault energy is analogous in lattice theory and the Peierls-Nabarro model. But the equilibrium separation obtained in lattice theory is wider than that obtained in the Peierls-Nabarro model for the same intrinsic stacking fault energy.      

On the dynamic Jahn-Teller effect of Er3+ in Pd-Er

The values of the Lea, Leask and Wolf parameters x, W, the off-diagonal matrix element of the vibrational Hamiltonian δ and the three independent coupling constants to Γ₅ lattice modes have been calculated and shown to be consistent with inelastic neutron data and EPR field for resonance results.     

振动纤维捕集颗粒的格子Boltzmann模拟

采用格子Boltzmann方法对振动纤维捕集颗粒进行数值研究.纤维附近采用多块网格加细技术计算,颗粒采用Lagrange跟踪方法模拟.研究雷诺数为200的流向振动纤维绕流的AⅡ、AⅢ、AIV、S四种涡结构下的亚微米煤粉颗粒的捕集问题.结果表明纤维的流向强迫振动能够显著提高颗粒的捕集效率.且迎风面的捕集效率提升不大,背风面的提升则更为显著.颗粒撞击角度的统计反映了背风面捕集效率提升的细节.另外流动处于AⅢ模态时,每个周期内脱落两个正涡一个负涡,被捕集颗粒的初始位置分布不对称.而其它模态基本关于流场中心对称.     

粒子在锥形管中运动的晶格玻尔兹曼方法研究

运用晶格玻尔兹曼方法对单个悬浮粒子在锥形管中的运动进行了数值计算, 给出了锥形管流体的速度分布和压力分布等. 粒子所受的流体作用力分别用动量交换法、改进的动量交换法和压力张量积分法进行计算. 分析了在不同初始位置释放的粒子的运动轨迹和速度变化情况, 结果表明压力张量积分法和改进的动量交换法的计算结果一致, 而没有改进的动量交换法的计算结果和前两者略有不同. 关键词： 晶格玻尔兹曼方法 锥形管 悬浮粒子 改进的动量交换法     

生物过滤器中非均匀性流动的数值研究

生物过滤技术因其具有有效性、低成本和环境友好等优点引起了人们的广泛关注.该技术主要通过生物过滤器去除含有H2S等废气的有毒有害气体.运用格子Boltzmann方法对三种生物过滤器模型中多孔介质的非均匀性流动进行了数值模拟.数值模拟结果表明,多孔介质的性质和进口流动条件对临界Rayleigh数有显著影响,临界Rayleigh数随着多孔介质的孔隙度和Darcy数的增大而逐渐变小,并随着进口Reynolds数的增大而逐渐变大.所得结果可望为生物过滤器的优化设计提供一个合理的理论依据.     

Lattice models of traffic flow considering drivers' delay in response

This paper proposes two lattice traffic models by taking into account the drivers' delay in response. The lattice versions of the hydrodynamic model are described by the differential-difference equation and difference-difference equation, respectively. The stability conditions for the two models are obtained by using the linear stability theory. The modified KdV equation near the critical point is derived to describe the traffic jam by using the reductive perturbation method, and the kink--antikink soliton solutions related to the traffic density waves are obtained. The results show that the drivers' delay in sensing headway plays an important role in jamming transition.     

Three-dimensional lattice Boltzmann method for simulating blood flow in aortic arch

The three-dimensional （3D） lattice Boltzmann models, 3DQ15, 3DQ19 and 3DQ27, under different wall boundary conditions and lattice resolutions have been investigated by simulating Poiseuille flow in a circular cylinder for a wide range of Reynolds numbers. The 3DQ19 model with improved Fillippova and Hanel （FH） curved boundary condition represents a good compromise between computational efficiency and reliability. Blood flow in an aortic arch is then simulated as a typical haemodynamic application. Axial and secondary fluid velocity and effective wall shear stress profiles in a 180° bend are obtained, and the results also demonstrate that the lattice Boltzmann method is suitable for simulating the flow in 3D large-curved vessels.     

Property-composition correlations and short-range order in bcc and fcc binary solid solutions

The properties of an ordering solid solution are substantially dependent on the long-range and short-range order parameters; a method is given for representing a binary solid solution as a set of cluster components whose short-range order parameters are incorporated out to the second coordination sphere. The scheme is illustrated via the lattice parameter and Debye temperature for Ti-Mo alloys (bcc lattice) and via the magnetic moment of Fe-Pd alloys (fcc lattice). The method allows one to describe nonmonotonic composition-property relationships and to define the values of properties for ordered structures.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 18–24, February 1978.     

纳米云纹法实验研究

结合原子力显微镜技术提出了一种新型纳米云纹方法 ,并应用该方法进行纳米范围的变形。实验中选用原子力显微镜显示屏的扫描线做为参考栅 ,云母和高纯定向石墨的晶格结构做为试件。对纳米云纹形成原理及测量方法进行了详尽讨论。运用该方法对强脉冲激光辐照激光照射之后云母试样的剩余变形进行测量研究。成功的实验结果表明这种方法是可行性的 ,可望在纳米力学行为研究中获得广泛应用。     

有限格点一维Holstein极化子研究

利用相干态正交化展开法,得到了一维Holstein模型基态能量的解析表达式.为了便于比较,将系统的基态试探波函数逐级展开到三级近似,计算了不同格点、不同耦合强度下的基态能量,在展开到3级近似时,所得结果与数值计算一致. 关键词： 相干态正交化展开 极化子 模拟退火方法     

一种基于密度泛函理论计算晶体结合能的变分法

提出了一种基于密度泛函理论计算晶体结合能的变分法，利用该方法初步计算了ＬｉＦ、ＮａＦ、ＫＦ、ＬｉＣｌ、ＮａＣｌ和ＫＣｌ这六种典型离子晶体的结合能、平衡晶格常数和体弹性模量，与实验结果进行了比较，分析了存在的问题，并指出了与其它同类方法相比该方法的优点     

Multi-relaxation-time lattice Boltzmann front tracking method for two-phase flow with surface tension

<正>In this paper,an improved incompressible multi-relaxation-time lattice Boltzmann-front tracking approach is proposed to simulate two-phase flow with a sharp interface,where the surface tension is implemented.The lattice Boltzmann method is used to simulate the incompressible flow with a stationary Eulerian grid,an additional moving Lagrangian grid is adopted to track explicitly the motion of the interface,and an indicator function is introduced to update the fluid properties accurately.The interface is represented by using a four-order Lagrange polynomial through fitting a set of discrete marker points,and then the surface tension is directly computed by using the normal vector and curvature of the interface.Two benchmark problems,including Laplace’s law for a stationary bubble and the dispersion relation of the capillary wave between two fluids are conducted for validation.Excellent agreement is obtained between the numerical simulations and the theoretical results in the two cases.     

Atomic displacements due to interstitial hydrogen in Cu and Pd

The density functional theory (DFT) is used to study the atomic interactions in transition metal-based interstitial alloys. The strain field is calculated in the discrete lattice model using Kanzaki method. The total energy and hence atomic forces between interstitial hydrogen and transition metal hosts are calculated using DFT. The norm-conserving pseudopotentials for H, Cu and Pd are generated self-consistently. The dynamical matrices are evaluated considering interaction up to first nearest neighbors whereas impurity-induced forces are calculated with M₃₂H shell (where M = Cu and Pd). The atomic displacements produced by interstitial hydrogen at the octahedral site in Cu and Pd show displacements of 7.36% and 4.3% of the first nearest neighbors respectively. Both Cu and Pd lattices show lattice expansion due to the presence of hydrogen and the obtained average lattice expansion ΔV/V = 0.177 for Cu and 0.145 for Pd.      

具有振幅调制的光学格子中光束的演化研究

利用变分原理和数值模拟的方法研究了光束在光传输方向的横截面上存在着具有振幅调制的光学格子时的演化,得到了光束宽度、振幅、光束的波阵面曲率随传播距离的演化形式.通过将光束的传输类比于粒子的运动,发现光束参量的条件存在三个区域,在不同的区域光束将在光格子的调制下有不同的传输形式,光格子振幅调制系数在各个区域起到了重要作用.光学格子中周期格子的作用有类似非线性的很好的特性,周期格子的引入提供了更好地控制格子孤子形成和传输的参考条件.