Investigations on molecular constants of the CD(X^2Π) radical and elastic collisions between ground-state C and D atoms at low temperatures

The potential energy curve of the CD（X2∏） radical is obtained using the coupled-cluster singles-doublesapproximate-triples [CCSD（T）] theory in combination with the correlation-consistent quintuple basis set augmented with diffuse functions, aug-cc-pV5Z. The potential energy curve is fitted to the Murrell-Sorbie function, which is used to determine the spectroscopic parameters. The obtained Do, De, Re, ωe, ωeXe, αe and Be values are 3.4971 eV, 3.6261 eV, 0.11197 nm, 2097.661 cm^-1, 34.6963 cm^-1, 0.2083 cm^-1 and 7.7962 cm^-1, respectively, which conform almost perfectly to the available measurements. With the potential obtained at the UCCSD（T）/aug-cc-pV5Z level of theory, a total of 24 vibrational states have been predicted for the first time when J = 0 by solving the radial Schrodinger equation of nuclear motion. The complete vibrational levels, the classical turning points, the inertial rotation constants and centrifugal distortion constants are reproduced from the CD（X2∏） potential when J = 0, and are in excellent agreement with the available measurements. The total and the various partial-wave cross sections are calculated for the elastic collisions between the ground-state C and D atoms at energies from 1.0×10^-11 to 1.0 × 10^-4 a.u. when the two atoms approach each other along the CD（X2∏） potential energy curve. Only one shape resonance is found in the total elastic cross sections, and the resonant energy is 8.36×10^-6 a.u. The results show that the shape of the total elastic cross section is mainly dominated by the s partial wave at very low temperatures. Because of the weak shape resonances coming from higher partial waves, most of them are passed into oblivion by the strong total elastic cross sections.

Elastic collisions of sulfur and hydrogen in their ground states at low temperatures and spectroscopic parameters of SH(X^2Π ) radical

This paper constructs the interaction potential of the SH（X^2∏） radical by using the coupled-cluster singlesdoubles-approximate-triples theory combining the correlation-consistent quintuple basis set augmented with the diffuse functions, aug-cc-pV5Z, in the valence range. Employing the potential, it accurately determines the spectroscopic parameters. The present De, Re, ωe, ωeχe, ae and Be values are of 3.7767eV, 0.13424nm, 2699.846 cm^-1, 47.7055 cm^-1, 0.2639cm^-1 and 9.4414 cm^-1, respectively, which are in excellent agreement with those obtained from the measure- ments. A total of 19 vibrational states has been found when J = 0 by solving the radial SchrSdinger equation of nuclear motion. The complete vibrational levels, classical turning points, initial rotation and centrifugal distortion constants when J = 0 are reported for the first time, which are in good accord with the experimental results. The total and various partial-wave cross sections are computed for the elastic collisions of sulfur and hydrogen in their ground states at low temperatures when two atoms approach each other along the SH（X^2∏） potential energy curve. Over the impact energy range from 1.0×10^-11 to 1.0×10^-4 a.u., eight shape resonances have been found in the total elastic cross sections. For each shape resonance, the resonant energy is accurately calculated. Careful investigations have pointed out that these resonances result from the 1 = 0, 1, 2, 3, 4, 6, 7, 8 partial-wave contributions.

Elastic collisions between Si and D atoms at low temperatures and accurate analytic potential energy function and molecular constants of the SiD(X^2Π) radical

Interaction potential of the SiD（χ^2П） radical is constructed by using the CCSD（T） theory in combination with the largest correlation-consistent quintuple basis set augmented with the diffuse functions in the wlence range. Using the interaction potential, the spectroscopic parameters are accurately determined. The present Do, De, Re, ωe, αe and Be values are of 3.0956 eV, 3.1863 eV, 0.15223 nm, 1472.894 cm^-1, 0.07799 cm^-1 and 3.8717 cm^-1, respectively, which are in excellent agreement with the measurements. A total of 26 vibrational states is predicted when J = 0 by solving the radial Schroedinger equation of nuclear motion. The complete vibrational levels, classical turning points, initial rotation and centrifugal distortion constants when J = 0 are reported for the first time, which are in good accord with the available experiments. The total and various partial-wave cross sections are calculated for the elastic collisions between Si and D atoms in their ground states at 1.0× 10^-11-1.0×10^-3 a.u. when the two atoms approach each other along the SiD（χ^2П） potential energy curve. Four shape resonances are found in the total elastic cross sections, and their resonant energies are of 1.73×10^-5, 4.0×10^-5, 6.45×10^-5 and 5.5×10^-4 a.u., respectively. Each shape resonance in the total elastic cross sections is carefully investigated. The results show that the shape of the total elastic cross sections is mainly dominated by the s partial wave at very low temperatures. Because of the weakness of the shape resonances coming from the higher partial waves, most of them are passed into oblivion by the strong s partial-wave elastic cross sections.

Elastic Collisions in Minkowski Momentum Space with Lorentz Transformations

We reexamined the elastic collision problems in the special relativity for both one and two dimensions from a different point of view. In order to obtain the final states in the laboratory system of the collision problems, almost all textbooks in the special relativity calculated the simultaneous equations. In contrast to this, we make a detour through the center-of-mass system. The two frames of references are connected by the Lorentz transformation with the velocity of the center-of-mass. This route for obtaining the final states is easy for students to understand the collision problems. For one dimensional case, we also give an example for illustrating the states of the particles in the Minkowski momentum space, which shows the whole story of the collision.

Diagrammatic Approach for Investigating Two Dimensional Elastic Collisions in Momentum Space I: Newtonian Mechanics

We present the usefulness of the diagrammatic approach for analyzing two dimensional elastic collision in momentum space. In the mechanics course, we have two major purposes of studying the collision problems. One is that we have to obtain velocities of the two particles after the collision from initial velocities by using conservation laws of momentum and energy. The other is that we have to study two ways of looking collisions, i.e. laboratory system and center-of-mass system. For those two major purposes, we propose the diagrammatic technique. We draw two circles. One is for the center-of-mass system and the other is for the laboratory system. Drawing these two circles accomplish two major purposes. This diagrammatic technique can help us understand the collision problems quantitatively and qualitatively.

Diagrammatic Approach for Investigating Two Dimensional Elastic Collisions in Momentum Space II: Special Relativity

The diagrammatic approach to the collision problems in Newtonian mechanics is useful. We show in this article that the same technique can be applied to the case of the special relativity. The two circles play an important role in Newtonian mechanics, while in the special relativity, we need one circle and one ellipse. The circle shows the collision in the center-of-mass system. And the ellipse shows the collision in the laboratory system. These two figures give all information on two dimensional elastic collisions in the special relativity.

Laser beam effect on the entanglement of elastic collisions in quantum plasma

In the quantized field formalism, using Kramers-Henneberger unitary transformation as the semi-classical counterpart of Block-Nordsieck transformation, the dynamics of entanglement during the low energy scattering processes in bi-partite systems at the presence of a laser beam fields are studied. The stationary-state Schrodinger equation for the quantum scattering process is obtained for such systems. Then, using partial wave analysis, we introduce a new form of entanglement fidelity considering the effect of high-intensity laser beam fields. The effective potential of hot quantum plasma including plasmon and quantum screening effects is used to obtain the entanglement fidelity ratio as a function of the laser amplitude, and plasmon and Debye length parameters for the elastic electron-ion collisions. It is shown that the plasma free electrons oscillations under interaction with laser beam fields improve the correlations between charged particles and consequently lead to the increase in the system entanglement.

Cosmological Redshift Caused by Head-On Collisions with CMB Photons, Not by Expansion of Space

The Big Bang model was first proposed in 1931 by Georges Lemaitre. Lemaitre and Hubble discovered a linear correlation between distances to galaxies and their redshifts. The correlation between redshifts and distances arises in all expanding models of universe as the cosmological redshift is commonly attributed to stretching of wavelengths of photons propagating through the expanding space. Fritz Zwicky suggested that the cosmological redshift could be caused by the interaction of propagating light photons with certain inherent features of the cosmos to lose a fraction of their energy. However, Zwicky did not provide any physical mechanism to support his tired light hypothesis. In this paper, we have developed the mechanism of producing cosmological redshift through head-on collision between light and CMB photons. The process of repeated energy loss of visual photons through n head-on collisions with CMB photons, constitutes a primary mechanism for producing the Cosmological redshift z. While this process results in steady reduction in the energy of visual photons, it also results in continuous increase in the number of photons in the CMB. After a head-on collision with a CMB photon, the incoming light photon, with reduced energy, keeps moving on its original path without any deflection or scattering in any way. After propagation through very large distances in the intergalactic space, all light photons will tend to lose bulk of their energy and fall into the invisible region of the spectrum. Thus, this mechanism of producing cosmological redshift through gradual energy depletion, also explains the Olbers’s paradox.

Collisions, or Reflections and Rotations, Leading to the Digits of π

We analyze a problem of elastic collisions between elements of a system composed of two balls and a wall. Thanks to a change of variables, the problem is reduced to a sequence of reflections and rotations. Moreover, the total number of collisions is easily found. For specific ratios of ball weights, the number of collisions is related to the first successive digits of π.

Collective flow and nuclear stopping in heavy ion collisions in Fermi energy domain

The effects of the in-medium nucleon-nucleon(NN) elastic cross section on the observables in heavy ion collisions in the Fermi energy domain are investigated within the framework of the ultrarelativistic quantum molecular dynamics model. The results simulated using medium correction factors of F=σ_(NN)^(in-medium)/σ_(NN)^(free)=0.2,0.3,0.5,and the density-and momentum-dependent factor obtained from the FU3 FP1 parametrization are compared with the FOPI and INDRA experimental data. It is found that the calculations using the correction factors F=0.2 and 0.5 reproduce the experimental data(i.e.,collective flow and nuclear stopping) at 40 and 150 MeV/nucleon, respectively. Calculations with the FU3 FP1 parametrization can best fit these experimental data. These conclusions can be confirmed in both^(197)Au+^(197)Au and^(129)Xe+^(120)Sn.

Collision efficiency of two nanoparticles with different diameters in Brownian coagulation

The collision efficiency of two nanoparticles with different diameters in the Brownian coagulation is investigated. The collision equations are solved to obtain the collision efficiency for the dioctyl phthalate nanoparticle with the diameter changing from 100 nm to 750 nm in the presence of the van der Waals force and the elastic deformation force. It is found that the collision efficiency decreases as a whole with the increase of both the particle diameter and the radius ratio of two particles. There exists an abrupt increase in the collision efficiency when the particle diameter is equal to 550 nm. Finally, a new expression is presented for the collision efficiency of two nanoparticles with different diameters.

Elastic scattering of two H(~2S_g) and N(~4S_u) atoms at low temperatures and accurate spectroscopic parameters of NH (X^3Σ^-) radical

This paper reports that the interaction potential for the X3Z- state of NH radical is constructed at the CCSD（T）/ cc-PV6Z level of theory. Using this potential, this paper calculates the spectroscopic parameters （De, Re, ωe, ωeχe, αe and Be） and their values are of 3.578eV, 0.10368nm, 3286.833cm^-1, 78.433cm^-1, 0.6469cm^-1 and 16.6735cm^-1 respectively, which are in excellent agreement with the experiments. Then the total of 14 vibrational states has been found when J=0 by solving the radial Schrodinger equation of nuclear motion. For each vibrational state, the vibrational manifolds are reported for the first time. And last, the total cross sections, s-wave, p-wave and d-wave cross sections are computed for the elastic collisions between two ground-state atoms （hydrogen and nitrogen） at low temperatures. It finds that the total elastic cross sections are dominated by s-wave scattering when the collision energy is below 10^-6a.u. The pronounced shape resonance is found at energy of 6.1 × 10^-6a.u. Calculations have shown that the shape resonance comes from the p-wave contributions.

含运动副间隙的6-RSS并联机器人弹性动力学建模与分析

为了提高空间六自由度并联机器人动力学模型的精度,以6-RSS并联机器人(R:转动副,S:球面副)为研究对象,提出一种将支链弹性变形和运动副间隙随机变化相结合的动力学建模方法。首先,根据几何结构与初始状态,开展理想条件下的运动学分析。利用数理统计原理和符号函数建立含间隙的转动副与球面副运动学模型,进而计算杆件虚长度和各个运动副处的碰撞接触力。然后,将相关参数结合到弹性动力学模型中,建立含运动副间隙的6-RSS并联机器人弹性动力学模型。最后,分析不同状态下支链弹性变形和运动副间隙各自产生误差的原因以及两者综合产生误差的原因。结果表明:改进后的动力学建模方法充分考虑了支链弹性变形和运动副间隙的耦合性与瞬时性,较其他动力学建模方法更加精确。

简谐激励下碰弹强化吸振器的特性试验研究

为了提升传统纯立方吸振器的吸振效果并避免由高分支响应造成的失效,在纯立方吸振器的质量块两侧安装由碰撞板和弹簧组成的小型装置,构造出一种新型的碰弹强化吸振器。首先,设计并加工了由单自由度线性主振子和该吸振器构成的试验平台;其次,对比研究了在简谐激励下连接碰弹强化吸振器与连接纯立方吸振器的主振子加速度响应的差异;最后,试验分析了吸振器的弹簧刚度和碰弹间隙两个参数对主振子加速度响应的影响。结果表明:碰弹强化吸振器具有优越的减振性能,可以改变整个系统的稳定性,并且能够抑制分岔的发生,消除系统在较大激励下的高分支响应;通过合理控制两个参数,碰弹强化吸振器可以得到更好的振动抑制效果。

固体火箭发动机真实热环境下EPDM绝热层烧蚀计算与试验研究

基于Hertz弹性碰撞理论和Thornton弹塑性假设,导出了粒子碰撞炭层过程中的压痕硬度理论表达式,根据弯管试验数据和试件扫描电镜分析提出了临界速度模型,对于三元乙丙橡胶(EPDM)炭化后形成的多孔炭化结构,结合裂纹侵蚀理论提出了两相流非完全弹性碰撞多孔炭化层体烧蚀计算模型。设计了用于验证烧蚀计算模型的模拟发动机旋转过载试验,保证了模拟发动机和真实发动机的天地一致性。结果表明:在模拟发动机真实飞行过程的热环境下,计算结果与实测结果能够基本吻合。研究结果对固体火箭发动机绝热结构的设计具有工程指导意义。

G54钢的动高压性能实验研究

G54钢是我国自主研制的一种新型超高强度钢,具有较高的潜在应用价值。为了研究该材料的动高压性能,为应用推广提供数据支撑,采用火炮作为加载手段,开展了G54钢的飞片对称碰撞实验。实验飞片速度为600~1400 m/s,通过测量G54钢样品的背表面粒子速度-时间历史,获得了典型的冲击相变及层裂信号。通过对粒子速度进行分析,结合材料密度及声速测试结果,获得了冲击压力为13~23 GPa下G54钢的Hugoniot弹性极限、层裂强度、冲击波速度-粒子速度(D-u)关系以及冲击相变点等动高压性能参数。对实验样品进行回收及金相分析发现,随着飞片速度的增加,材料层裂面的损伤机制逐渐从微孔洞聚合主导的韧性断裂向绝热剪切主导的韧性断裂转变。

弛张筛面大挠度非线性弹性变形分析及负载理论研究

针对弛张筛面大挠度变形理论缺少对筛面材料弹性属性的分析及矿物冲击对筛面挠度变化影响规律的研究,考虑弛张筛面材料的可伸缩性,建立了筛面大挠度非线性弹性变形理论模型,并结合外激励正弦位移函数,首次提出了筛面在不同振幅和频率下的时域表达式;搭建了弛张筛面动力学特性测试平台,验证了理论模型在描述筛面挠曲变化过程中的准确性,通过响应面优化法明晰了大挠度弹性变形理论在描述筛面动态特性时的最优振动参数;结合空载筛面大挠度弹性变形理论提出了颗粒与筛面碰撞时筛面挠曲变化理论,求出了颗粒冲击力下筛面不同运动状态时的挠度曲线,揭示了筛面与矿物颗粒碰撞时不同物理参数对碰撞点局部变形程度的影响规律,并利用仿真试验验证了颗粒碰撞筛面挠曲变化理论表达式在不同初始约束下描述筛面动力学特性的准确性。研究结果表明:静态下筛面大挠度弹性变形理论与实验误差率在6%以下,动态下筛面大挠度弹性变形理论与实验误差率随着振幅与频率的增大而减小,且这种变化是非线性的;当振幅为7.33 mm、频率为11.75 Hz时各测点理论值与实验值误差率达到最低,筛面中点的平均误差率低于3%;颗粒入射角、撞击点位置、筛面安装倾角和运行状态是影响筛面撞击局部变形程度的重要因素,理论证明了在较大筛面安装倾角和颗粒入射角以及筛面靠近中点位置运动到最高点时,颗粒与筛面碰撞可获得最大初始动能,且碰撞后筛面挠曲变形理论表述撞击点位置与仿真试验结果的平均误差在4 mm以下。

基于落锤-弹簧碰撞系统的燃气爆炸载荷模拟加载方法研究

为避免燃气爆炸实验带来的危险,可通过载荷模拟装置产生燃气爆炸载荷替代传统燃气爆炸实验。本文设计开发了一种基于落锤-弹簧碰撞系统的燃气爆炸载荷模拟装置及加载方法,通过一维弹性碰撞理论建立起了系统响应过程的运动方程,并推导得到了载荷与时间之间的函数关系;根据压力时间函数特征以正弦函数和指数函数乘积形式对燃气爆炸实测压力时程曲线进行拟合,建立了模拟燃气爆炸载荷落锤-弹簧碰撞系统参数快速计算方法;该装置及实验方法表明调整阻尼器的阻尼系数、弹簧的刚度和落锤的质量,可获得与燃气爆炸载荷特征相符的压力加载作用时长和载荷峰值。落锤-弹簧碰撞系统可以对燃气爆炸载荷进行多工况多场景的有效模拟。

一维理想弹塑性体的SPH-HLLC耦合算法

通过弹塑性波分析求得HLLC(Harten-Lax-van Leer-contact)近似黎曼解,提出了SPH(smoothed particle hydrodynamics)与一维理想弹塑性体模型下近似的HLLC黎曼求解器耦合的一种构造简单的算法。在SPH计算中,支持域内每个粒子对都存在一个黎曼间断问题,它的黎曼解被代入控制方程中计算。其中一维理想弹塑性体的HLLC近似黎曼解的思想是:先假设整体处于弹性状态计算黎曼解,然后对计算结果进行塑性条件修正,最后用修正后的物理变量计算HLLC近似黎曼解。将提出的SPH-HLLC耦合算法与传统SPH算法在一维算例下的计算结果进行对比,结果表明,该算法能有效模拟一维理想弹塑性体材料的碰撞,并能有效抑制在不同材料之间的压强和偏应力震荡,这是传统SPH方法很难做到的。

基于圆柱体骰子三面概率落地均匀性探究

传统硬币正反面落地概率分别趋近于1/2,而侧面落地概率几乎为0.本文为了探究新型圆柱形骰子三面落地概率均匀的影响因素,从力学角度对圆柱形骰子发生弹性碰撞和非弹性碰撞的运动过程进行了理论分析,将影响落地概率均匀性的因素分为圆柱形骰子自身的物理和几何特征以及外部影响因素,通过建立各类圆柱形骰子模型,采用控制变量法进行实验,并应用软件进行仿真模拟,所得实验结论和仿真结论与理论分析吻合.研究表明骰子厚度直径比、接触面材质硬度、抛掷高度及圆柱体重心线与竖直方向向量夹角是影响落地概率均匀性的主要因素.