平行柱体对平面波/高斯波束电磁散射

基于等效原理和互易性定理，研究了N个相互平行二维柱体对平面波/高斯波束的电磁散射特性，给出了求解N阶散射场公式.一阶散射可通过求解单个柱体的散射场得到，但对于高阶散射场而言，由于耦合散射的复杂性，很难给出精确的解析解.为了解决这一问题，借助等效原理和互易性定理给出了求解N阶散射场的面积分公式.只要给出柱体的i-1阶散射场及相关目标表面上的等效电流和(或)等效磁流，就可应用此公式求解i阶散射场.应用该近似方法计算了相互平行非均匀等离子体涂层导体圆柱的单/双站散射宽度，讨论了束腰半径、等离子体涂层厚度、电子密度、碰撞频率及雷达频率等对散射结果的影响.     

多层“台阶”近似方法中层数与计算误差的关系

多层"台阶"近似方法是将平板波导中折射率随厚度变化的曲线近似地用N层台阶形的折线来代替,使每一个小区域内折射率成为常数,由此得到电磁场分布和传播常数.本文从理论上给出了层数N与计算精度之间的关系.推导出在分割成N层和2N层两种近似下的计算值精度的改进.本文结果适用于任何渐变折射率平板光波导.     

胶体排空相互作用理论与计算

胶体悬浮液由1 nm到1μm大小的颗粒悬浮在液体中构成.胶体颗粒之间具有体积排斥相互作用和其他相互作用,体积排斥导致排空效应.当大硬球处于小球构成的胶体中时,大球周围有小球中心不能进入的排空层.在大的硬球相互接近时,其排空层重合,使小球的自由体积增加,从而熵增加,导致大球之间的等效相互作用,这个相互作用称为排空相互作用.本文介绍了胶体排空相互作用的概念和图像,简要介绍了计算硬球排空相互作用的接受比率方法、Wang-Landau方法、密度泛函理论方法等数值方法;以Asakura-Oosawa模型为例,介绍了Derjaguin近似方法.利用这个近似方法,推导了小硬球胶体中一对硬球、硬球和硬墙之间的排空相互作用,以及一对硬球在细棒胶体和薄盘胶体中的排空相互作用的近似公式.     

虚晶近似法研究AlN-Al2O3固溶体系的力学性能和电子结构

基于密度泛函理论的第一性原理平面波赝势方法, 运用虚晶近似方法计算了AlN-Al₂O₃固溶区内尖晶石相氮氧化铝(Al₂₄O₂₄N₈, Al₂₃O₂₇N₅和Al₂₂O₃₀N₂)和α-Al₂O₃, AlN的力学性能和电子结构. 结果证明虚晶近似法应用到氮氧化铝结构计算中是可行的. 力学常数计算结果和弹性模量B, 剪切模量G, 杨氏模量E反映的材料硬度变化趋势与实验基本一致;Al₂O₃-AlN固 溶区内五种结构均为脆性性质且Al₂₃O₂₇N₅脆性最低, 硬度高、脆性低的特性反映了Al₂₃O₂₇N₅优异的抗弯强度性能. 五种结构满足力学结构上的稳定性, 立方尖晶石相氮氧化铝表现为弹性各向异性. 能带和态密度的计算分析表明这五种结构均为直接宽带隙结构. 在费米能级附近, 氮氧化铝结构中阴离子的2p态和阳离子的3s, 3p态发生了轨道杂化. 理论结果与实验数据基本符合, 为进一步研究提供了一定的理论方法和依据.     

受限于圆柱体内半刚性高分子链的螺旋结构转变

采用非格点珠簧球链模型, 结合Monte Carlo方法, 研究了半刚性高分子链受限于无限长圆柱体的构象性质. 模拟结果表明: 在圆柱体内表面附近具有吸附能的情况下, 当弯曲能b由小到大变化时, 发现半刚性高分子链由开始时的无规则被吸附在圆柱体内表面, 到逐渐出现螺旋结构, 最后伸展成类似棒状的结构. 同时计算了不同弯曲能b时的半刚性高分子链的平均螺旋数N_t, 平均每条链单体的螺旋百分比P_h和能量涨落. 发现高分子链螺旋结构的形成与转变, 不仅与圆柱体半径R的大小有关, 还与弯曲能b的大小有关. 研究结果能有助于加深对受限生物大分子构象的认识.     

多模复共轭奇、偶相干态光场的N次方Y压缩与N次方H压缩

利用新近提出的多模辐射场的广义非线性等阶高阶压缩理论,对多模复共轭奇、偶相干态光场的N次方Y压缩与N次方H压缩特性进行了详细研究.结果发现:①多模复共轭奇相干态光场,压缩阶数N为偶数时,只存在N-Y最小测不准态;而当腔模总数q与压缩阶数的乘积q·N为偶数时,只存在N-H最小测不准态;此外,无论N及q·N为何值,不呈现N次方Y压缩与N次方H压缩效应.②多模复共轭偶相干态光场在一定条件下可呈现出周期性变化的任意阶的N次方Y压缩与N次方H压缩效应.③多模偶相干态光场与多模复共轭偶相干态光场两者的压缩效果和压缩特性完全相同,这种现象称为“压缩简并”.     

光折变晶体BaTiO3中二波混频的温度效应

研究了光折变晶体钛酸钡中相向传输的二波混频的温度效应,得到在 BaTiO₃中增益耦合系数随温升而增加、并在85℃左右反向.说明其主要载流子的类型在此温度时发生改变.给出了有效陷阱浓度N(T)的温升模型,其理论预期值与实验数据符合较好.     

多模奇相干态光场中的N-Y最小测不准态与N-H最小测不准态

本文根据新近建立的多模辐射场的广义非线性等阶高阶压缩理论,对多模奇相干态光场|Ψ,o〉_q中的N次方Y压缩、N次方H压缩、N-Y最小测不准态以及N-H最小测不准态等进行了详细研究.结果表明:1)当压缩阶数N为偶数时,多模奇相干态|Ψ,o〉_q总是恒处于N-Y最小测不准态;当N为奇数时,态|Ψ,o〉_q既不处于N-Y最小测不准态,也不呈现N次方Y压缩效应.2)当q & #183;N为偶数时,多模奇相干态|Ψ,o〉_q总是恒处于N-H最小测不准态;当q & #183;N为奇数时,态|Ψ,o〉_q既不处于N-H最小测不准态,也不呈现N次方H压缩效应.3)多模奇相干态|Ψ,o〉_q恒处于N-Y最小测不准态与恒处于N-H最小测不准态的条件明显不同,两者存在着严格的区别.     

不同链长二元分子卟啉酞菁(TTP－O－(CH2)n－O－Pc的三阶光学非线

利用简并四波混频(DFWM)方法测量二元分子卟啉酞菁的三阶非线性极化系数X(3)值。得到二元分子卟啉酞菁的X(3)值比它们单元分子卟啉、酞菁的X(3)值大,二元分子卟啉酞菁的X(3)值起初是随链长的增加而增加(Xn=3(3) >Xn=2(3)),链长增至n=3时,X(3)值达到最大值。当链长进一步增加时,二元分子卟啉酞菁的(X(3)值反而下降(Xn=3(3)>Xn=4(3) >Xn=5(3))。这同二元分子中卟啉、酞菁分子由柔性链连接有关。本文对结果给出可能的解释。     

N维各向同性谐振子径向平均值的递推关系和解析表达式

推导出了用于N维各向同性谐振子径向平均值计算的二个递推关系,并在-3≤s≤3的条件下,给出了平均值〈n_rJ_N-2|r^2s|n_rJ_N-2〉的值.二维和三维各向同性谐振子的相关结果均作为特例包含在结论中.     

Binary collision approximation for solitary waves in a Y-shaped granular chain

We implement a binary collision approximation to study solitary wave propagation in a two-dimensional double Y-shaped granular chain. The solitary wave was transmitted and reflected when it met the interface of the bifurcated branches of the Y-shaped granular chains. We obtain the analytic results of the ratios of the transmitted and reflected speeds to the incident speed of the solitary wave, the maximum force between the two neighbor beads in a solitary wave, and the total time taken by the pulse to pass through each branch. All of the analytic results are in good agreement with the experimental observations from Daraio et al. [Phys. Rev. E 82 036603 (2010)]. Moreover, we also discuss the delay effects on the arrival of split pulses, and predict the recombination of the split waves traveling in branches in the final stem of asymmetric systems. The prediction of pulse recombination is verified by our numerical results.     

How hertzian solitary waves interact with boundaries in a 1D granular medium

We perform measurements, numerical simulations, and quantitative comparisons with available theory on solitary wave propagation in a linear chain of beads without static preconstraint. By designing a nonintrusive force sensor to measure the impulse as it propagates along the chain, we study the solitary wave reflection at a wall. We show that the main features of solitary wave reflection depend on wall mechanical properties. Since previous studies on solitary waves have been performed at walls without these considerations, our experiment provides a more reliable tool to characterize solitary wave propagation. We find, for the first time, precise quantitative agreements.     

Highly nonlinear solitary waves in heterogeneous periodic granular media

We use experiments, numerical simulations, and theoretical analysis to investigate the propagation of highly nonlinear solitary waves in periodic arrangements of dimer (two-mass) and trimer (three-mass) cell structures in one-dimensional granular lattices. To vary the composition of the fundamental periodic units in the granular chains, we utilize beads of different materials (stainless steel, brass, glass, nylon, polytetrafluoroethylene, and rubber). This selection allows us to tailor the response of the system based on the masses, Poisson ratios, and elastic moduli of the components. For example, we examine dimer configurations with two types of heavy particles, two types of light particles, and alternating light and heavy particles. Employing a model with Hertzian interactions between adjacent beads, we find good agreement between experiments and numerical simulations. We also find good agreement between these results and a theoretical analysis of the model in the long-wavelength regime that we derive for heterogeneous environments (dimer chains) and general bead interactions. Our analysis encompasses previously-studied examples as special cases and also provides key insights on the influence of heterogeneous lattices on the properties (width and propagation speed) of the nonlinear wave solutions of this system.     

On Collisions Times of ‘Self-Sorting’ Interacting Particles in One-Dimension with Random Initial Positions and Velocities

We investigate a one-dimensional system of N particles, initially distributed with random positions and velocities, interacting through binary collisions. The collision rule is such that there is a time after which the N particles do not interact and become sorted according to their velocities. When the collisions are elastic, we derive asymptotic distributions for the final collision time of a single particle and the final collision time of the system as the number of particles approaches infinity, under different assumptions for the initial distributions of the particles’ positions and velocities. For comparison, a numerical investigation is carried out to determine how a non-elastic collision rule, which conserves neither momentum nor energy, affects the median collision time of a particle and the median final collision time of the system.     

类氢离子的电荷剥离截面

使用双撞近似和托马斯－费米近似计算了类氢离子Ｌｉ＾２＋和Ｃ＾５＋与中性原子Ｈ和Ｈｅ碰撞的电荷剥离截面。计算结果表明,总截面主要处在０．３５－１０的速度范围,这些载面与ＴｏｓｈｚｏＳｈｉｒａｉ等人计算的结果符合得较好。     

驻波声场中单分散细颗粒的相互作用特性

利用外加声场促进悬浮在气相中的细颗粒发生相互作用,进而引起颗粒的碰撞和凝并,使得颗粒平均粒径增大、数目浓度降低,是控制细颗粒排放的重要技术途径.为探究驻波声场中单分散细颗粒的相互作用,建立包含曳力、重力、声尾流效应的颗粒相互作用模型,采用四阶经典龙格-库塔算法和二阶隐式亚当斯插值算法对模型进行求解.将数值模拟得到的颗粒声波夹带速度和相互作用过程与相应的解析解和实验结果进行对比,验证模型的准确性.进而研究颗粒初始条件和直径对相互作用特性的影响.结果表明,初始时刻颗粒中心连线越接近声波波动方向、颗粒位置越接近波腹点,颗粒间的声尾流效应就越强,颗粒发生碰撞所需要的时间就越短.研究还发现,颗粒直径对颗粒相互作用的影响取决于初始时刻颗粒中心连线偏离声波波动方向的程度.当偏离较小时,颗粒直径越大,颗粒发生碰撞所需要的时间越短;当偏离很大时,直径较小的颗粒能够发生碰撞,而直径较大的颗粒则无法发生碰撞.     

Nonlinear waves in dry and wet Hertzian granular chains

A one-dimensional dry granular medium, a chain of beads which interact via the nonlinear Hertz potential, exhibits strongly nonlinear behaviors. When such an alignment further contains some fluid in the interstices between grains, it may exhibit new interesting features. We report some recent experiments, analysis and numerical simulations concerning nonlinear wave propagation in dry and wet chains of spheres. We consider first a monodisperse chain as a reference case. We then analyze how the pulse characteristics are modified in the presence of an interstitial viscous fluid. The fluid not only induces dissipation but also strongly affect the intergrain stiffness: in a wet chain, wave speed is enhanced and pulses are shorter. Simple experiments performed with a single sphere colliding a wall covered by a thin film of fluid confirm these observations. We demonstrate that even a very small amount of fluid can overcome the Hertzian potential and is responsible for a large increase of contact stiffness. Possible mechanisms for wet contact hardening are related to large fluid shear rate during fast elastohydrodynamic collision between grains.     

相对论离子与氦二聚体碰撞电离的理论研究

基于对称程函近似,从理论角度研究了相对论离子与氦二聚体碰撞双电离的直接碎裂通道:由入射离子与两个原子的作用造成的双电离。从不同的近似角度出发,建立了两个理论模型,第一个模型将氦二聚体的两个原子看做一个整体,而另外一个模型完全忽略了两个氦原子之间的相互作用。模型的数值计算结果表明,总截面与氦二聚体的空间取向有很强的依赖关系,当氦二聚体与入射离子束流平行时,总截面达到最大值,在垂直时为最小值。进一步研究发现,模型一的结果在氦二聚体核间距较小时更为合理,核间距较大时,模型二更为精确。     

Polarization-multiplexed x((2)) solitary-wave interactions

We investigate interactions between vectorial solitary waves through typeII second-harmonic generation. We demonstrate that one can tune the collision distance of two initially codirectional solitary waves changing their polarization state. Moreover, by adiabatic perturbation analysis, it is possible to predict such a collision distance as a function of solitary-wave separation, in good agreement with numerical simulations.