The Theorem of Mather on Generic Projections for Singular Varieties

The theorem of Mather on generic projections of smooth algebraic varieties is also proved for the singular ones.     

High-speed imaging of ultrasonic emulsification using a water-gallium system

Aiming at elucidating ultrasonic emulsification mechanisms, the interaction between a single or multiple acoustic cavitation bubbles and gallium droplet interface was investigated using an high-speed imaging technique. To our best knowledge, the moment of emulsification and formation of fine droplets during ultrasound irradiation were observed for the first time. It was found that the detachment of fine gallium droplets occurs from the water-gallium interface during collapse of big cavitation bubbles. The results suggest that the maximum size of cavitation bubble before collapsing is of prime importance for emulsification phenomena. Previous numerical simulation revealed that the collapse of big cavitation bubble is followed by generation of high-velocity liquid jet directed toward the water-gallium interface. Such a jet is assumed to be the prime cause of liquid emulsification. The distance between cavitation bubbles and water-gallium interface was found to slightly affect the emulsification onset. The droplet fragmentation conditions are also discussed in terms of the balance between (1) interfacial and kinetic energies and (2) dynamic and Laplace pressure during droplet formation.     

Analysis of ultrasound-assisted convective heating/cooling process: Development and application of a Nusselt equation

In this study, the convective heating/cooling process assisted by US irradiation is analyzed with the aims of developing a new convective heat transfer correlation. Heat transfer experiments were conducted with different copper machined geometries (cube, sphere and cylinder), fluid velocities (0.93–5.00 × 10⁻³ m/s), temperatures (5–60 °C), and US intensities (0–6913 W/m²) using water as heat transfer fluid. The Nusselt (Nu) equation was obtained by assuming an apparent Nu number in the US-assisted process, expressed as the sum of contributions of the forced convection and cavitation-acoustic streaming effects. The Nu equation was validated with two sets of experiments conducted with a mixture of ethylene glycol and water (1:1 V/V) or a CaCl₂ aqueous solution (30 g/L) as immersion media, achieving a satisfactory reproduction of experimental data, with mean relative deviations of 17.6 and 17.8%, respectively. In addition, a conduction model with source term and the proposed correlation were applied to the analysis of US-accelerated heating kinetics of dry-cured ham reported in literature. Results demonstrated that US improves heating of ham slices because of the increased heat transfer coefficients and the direct absorption of US power by the foodstuff.     

Simulation and experiment of the cooling effect of trapped ion by pulsed laser

We investigate the process of pulsed laser cooling using a self-constructed molecular dynamics simulation(MDSimulation) program. We simulate the Doppler cooling process and pulsed laser Doppler cooling process of a single ~(40)Ca~+ ion, and the comparison with the experimental results shows that this self-constructed MD-Simulation program works well in the weak laser intensity situation. Furthermore, we analyze the pulsed laser Doppler cooling process of a single ~(27)Al~+ ion. This program can be used to analyze the molecular dynamic process of various situations of Doppler cooling in an ion trap, which could give predictions and experimental guidance.     

Numerical analysis of motional mode coupling of sympathetically cooled two-ion crystals

A two-ion pair in a linear Paul trap is extensively used in the research of the simplest quantum-logic system; however,there are few quantitative and comprehensive studies on the motional mode coupling of two-ion systems yet. This study proposes a method to investigate the motional mode coupling of sympathetically cooled two-ion crystals by quantifying three-dimensional(3 D) secular spectra of trapped ions using molecular dynamics simulations. The 3 D resonance peaks of the ~(40)Ca~+ – ~(27)Al~+ pair obtained by using this method were in good agreement with the 3 D in-and out-of-phase modes predicted by the mode coupling theory for two ions in equilibrium and the frequency matching errors were lower than 2%.The obtained and predicted amplitudes of these modes were also qualitatively similar. It was observed that the strength of the sympathetic interaction of the ~(40)Ca~+ – ~(27)Al~+ pair was primarily determined by its axial in-phase coupling. In addition,the frequencies and amplitudes of the ion pair's resonance modes(in all dimensions) were sensitive to the relative masses of the ion pair, and a decrease in the mass mismatch enhanced the sympathetic cooling rates. The sympathetic interactions of the ~(40)Ca~+ – ~(27)Al~+ pair were slightly weaker than those of the ~(24)Mg~+– ~(27)Al~+ pair, but significantly stronger than those of ~9Be~+ – ~(27)Al~+ . However, the Doppler cooling limit temperature of ~(40)Ca~+ is comparable to that of ~9Be~+ but lower than approximately half of that of ~(24)Mg~+. Furthermore, laser cooling systems for ~(40)Ca~+ are more reliable than those for ~(24)Mg~+and ~9Be~+ . Therefore, ~(40)Ca~+ is probably the best laser-cooled ion for sympathetic cooling and quantum-logic operations of ~(27)Al~+ and has particularly more notable comprehensive advantages in the development of high reliability, compact, and transportable ~(27)Al~+ optical clocks. This methodology may be extended to multi-ion systems, and it will greatly aid efforts to control the dynamic behaviors of sympathetic cooling as well as the development of low-heating-rate quantum logic clocks.     

环形磁场金属等离子体源冷却流场的数值模拟与优化

环形磁场金属等离子体源作为一种全新的等离子体源结构,可用于产生高度离化、无大颗粒、高密度的离子束流,但传统流道结构不能保证其高效、均匀散热,大功率工作时可能引起密封胶圈的烧蚀失效,需对其冷却流场进行优化设计.利用Solidworks Flow Simulation软件对等离子体源冷却流道进行模拟,分析出入水孔分布角度、孔数、孔径以及入水孔高度对冷却效果的影响规律,并对流道结构参数进行优化.结果表明,增大水孔的周向分布范围,有利于提高散热的均匀性;入水孔设置在结构上层有利于减少冷却水的温度分层现象,使铜套和密封胶圈都处于较好的冷却状态;适当减小孔径有利于增大冷却水射流速度,增大湍流程度强化传热,提高换热效率.优化后的流场结构可以提高冷却水的利用率,在相同流量条件下获得更好的冷却效果,改善等离子体源的放电稳定性,为环形磁场金属等离子体源的冷却结构设计提供理论依据.     

纵磁作用下真空电弧单阴极斑点等离子体射流三维混合模拟

真空电弧的特性直接受到从阴极斑点喷射出的等离子体射流的影响,对等离子体射流进行数值仿真有助于我们深入了解真空电弧的内部物理机制.然而,磁流体动力学和粒子云网格仿真方法受限于计算精度和计算效率的原因,无法有效地应用于真空电弧等离子体射流仿真模拟.本文开发了一套三维等离子体混合模拟算法,并在此基础上建立了真空电弧单阴极斑点射流仿真模型,模型中将离子作宏粒子考虑,而电子作无质量流体处理,仿真计算了自生电磁场与外施纵向磁场作用下等离子体的分布运动状态.仿真结果表明,单个阴极斑点情况下真空等离子体射流在离开阴极斑点后扩散至极板间,其整体几何形状为圆锥形,离子密度从阴极到阳极快速下降.外施纵向磁场会压缩等离子体,使得等离子体射流径向的扩散减少并且轴线上的离子密度升高.随着外施纵向磁场的增大,其对等离子体射流的压缩效应增强,表现为等离子体射流的扩散角度逐渐减小.此外,外施纵向磁场对等离子体射流的影响也受到电弧电流大小的影响,压缩效应随电弧电流的增加而逐渐减弱.     

多化学组份反应气体流动的Godunov格式

本文将单介质气体流动的Goduoov方法推广到多化学组份气体流动的计算中,建立了多化学组份气体的间断分解公式以及任意四边形网格下的Godunov方法的差分格式,提出了处理自由边界的虚相法,应用第二类网格,计算了超音速射流及其冲击问题的几个算例,并且同实验结果进行了比较。