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 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.

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 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.

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.

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.

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。

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.

2023年高考全国乙卷理综第25题赏析

2023年高考落下帷幕,高考题目是高中物理教师的风向标,针对高考物理命题的热点,用3种方法对2023年高考全国乙卷理综第25题进行多角度赏析,最后对思路总结分析,培养学生核心素养能力.

弹性碰撞振动系统相邻周期运动的转迁规律分析

针对弹性碰撞振动系统全局动力学的研究,稳定与不稳定周期运动的转迁规律是揭示系统的关注要点,通过建立系统动力学模型,并计算系统运动解析解表达式,利用改进胞映射法刻画不同Poincaré截面上系统的吸引域形状轮廓和细节特征,进一步揭示系统多态共存分布区域及其转迁形成机理。利用单自由度弹性碰撞振动系统验证该方法的有效性,得到系统不同周期运动的吸引子和吸引域共存的情况。多态共存区内系统受到鞍结分岔、擦边分岔和倍化分岔的诱导,出现不同形式周期运动的共存,包括稳定和不稳定周期运动。

脉冲非均匀电场下水滴运动及碰撞特性研究

为了提高油包水(W/O)乳液的破乳脱水效率,采用高压方波脉冲非均匀电场,并基于显微试验研究水滴极化后的碰撞行为及微观破乳过程(水滴液膜破裂后聚结)。结果表明:非电解质促进水滴弹/塑性碰撞行为,电解质削弱偶极作用而减小碰撞速度;加入非电解质,电参数对水滴塑性碰撞的影响大于直径比和体积,而加入电解质,直径比对塑性碰撞的影响最大,其次是体积和电参数;不同电压和频率下,乳液B(含非电解质)中水滴塑性碰撞速度极大值分别为9.451μm/s和8.577μm/s,远大于乳液A(对照组)和乳液C(含电解质),其中乳液C最小。研究得到的水滴碰撞聚结规律可为提高静电聚结器的脱水效率和研制高效电脱水器提供借鉴。

融合排序弹性碰撞的改进麻雀搜索算法

为了改善麻雀搜索算法(SSA)种群初始化结果不充分导致多样性丧失,勘探和开采过程中易受到个别位置信息干扰影响寻优精度等缺点,提出了融合排序弹性碰撞的新型麻雀搜索算法(XSSA)。首先,采用改进的无限折叠迭代混沌映射(ICMIC)初始化种群,提升了初始种群分布的分散程度;其次,使用高斯随机游走策略平衡算法的探勘和开发能力;此外,在发现者更新后对所有个体执行排序弹性碰撞策略,避免算法过早地收敛到局部极值;最后,根据不同阶段的寻优特点制定多策略边界处理机制,保留住种群数量,避免多样性的丧失。同时,结合重要的位置信息对超出边界的个体进行位置再更新,使得处理后的位置更加合理,为接下来的迭代搜索提供质量保证。对12个基准函数进行仿真实验,并画出收敛精度图直观展示算法性能。借助各策略的贡献测试、Wilcoxon秩和检验、Friedman检验的综合排名等证明了XSSA的有效性、独特性和具有较好的寻优性能。

基于Lankarani赫兹接触模型的弓网动力学仿真研究

该文通过有限元方法建立简单链型悬挂接触网模型并对其进行模态分析,通过使用Lankarani赫兹接触模型,运用显式中心差分法对弓网耦合动力学方程进行求解,基于上述理论创建弓网动力学仿真平台,采用模块化的思想进行弓网动力学的仿真分析。在此基础上,采用EN50318标准对弓网仿真平台的正确性进行验证。最后,通过对考虑迟滞阻尼效应的Lankarani赫兹接触模型进行动力学仿真,分析Lankarani赫兹接触模型中重要参数对仿真结果的影响。

弹性波传播对列车撞击动力学特性影响研究

在列车撞击动力学中,简化的刚体模型被广泛应用于研究列车耐撞性,以及进一步优化列车在冲击载荷下的能量分布。然而忽略弹性波传播对列车耐撞性能的影响尚不清楚。为了解决这一问题,本文建立了简化的一维弹性车体模型,并研究了弹性波传播对列车能量耗散以及动力学特性的影响。基于经典的弹性波传播理论,提出了一种密度及弹性模量缩比准则,使一维弹性车体的运动特性与其横截面积无关。讨论了弹性波传播速度对不同冲击速度下三节编组列车在冲击工况下的能量吸收、弹性能储存以及车体最终的等效平衡速度的影响。研究发现,当弹性波的传播速度约为3500 m/s时,一维弹性车体与实际列车模型的一致性最好。在初始冲击速度为10、15和20 m/s时,简化的一维弹性模型吸能量与实际列车模型相比误差仅为2.56%、1.84%和1.45%,而简化的刚性模型能量吸收量比实际列车模型高10.7%、12.4%和14.8%,刚性模型显著高估了列车的能量吸收量。我们的研究结果可以促进列车在碰撞条件下的耐撞性设计和优化。