绳系小球上升最高点速度参数的设置

在高中阶段学生所学习的曲线运动中,竖直面内的圆周运动比较典型、综合的运动,其运动过程存在较多变数和不确定性.绳系小球或者单轨光滑内侧的物体在竖直面内的圆周运动,是学习圆周运动知识过程中一个难点.其中的变数和不确定性是由设置竖直面内最低点的速度大小不同所决定的.不同的速度大小就会有不同的运动过程,比如是一般的摆动、完整的圆周运动还是圆周运动与斜上抛运动结合,求解最大高度时的方法大不相同.下面通过分析例题,总结求最大高度的方法,讨论不同难易度的题目应如何设置最低点的速度大小.     

气体动理学方法对斜界面不稳定性实验的数值模拟

介绍了基于BGK模型(Bhatnagar-Gross-Krook)的气体动理学数值方法(Gas Kinetic Scheme,GKS),通过计算多组分激波管问题对以GKS方法实现的MBCD程序进行了验证,表明了在接触间断处产生的震荡非常小,网格收敛性好。在多组分问题求解时各组分满足同温和同速的假设条件下,利用该程序开展了Air/SF6斜界面不稳定性实验的数值模拟,得出了不同时刻SF6的密度分布图,并得到交界面宽度、斜界面左右端相对位置在激波穿过斜界面后的变化情况。通过与实验结果的比较可知,GKS方法和程序在网格数为1024×200和512×100时得到的交界面宽度与实验值的最大误差分别为6.1%和7.3%,可用于对界面不稳定性问题的计算。     

带有Fokker-Planck算子的BGK方程 [英文]

本文主要研究带有Fokker-Planck算子的BGK模型,即Fokker-Planck-BGK方程.首先,我们对线性方程?f/?t+v·▽_xf - σ?_vf = g(t, x, v), f (0, x, v) = f_0(x, v).建立了两个基本引理:速度矩引理和速度平均引理.然后通过渐近方法,在初始条件只有二阶矩的情形下得到Fokker-Planck-BGK方程经典解的存在性.     

一类Hamiltion算子的谱分布及其可逆性

本文从Hamilton算子的特征函数与Hamilton算子的内部斜对角块算子之间的关系出发,证明了一类Hamilton算子的谱分布,进而得到这类Hamilton算子可逆的充要条件.最后应用具体的例子说明了所得结论的合理性.     

Evolution of Number State to Density Operator of Binomial Distribution in the Amplitude Dissipative Channel

We show that passing through the amplitude dissipative channel the initial pure number state density operator is evolved into the density operator of binomial distribution （a mixed state）, and the binomial distribution parameter is just equal to e^-2kt, where k is the dissipative parameter of the channel. We solve the corresponding master equation to obtain the operator-sum representation of the density operator by virtue of the entangled state representation, which seems to be a convenient approach.     

Synthesis and Crystal Structure of the Diiron Azadithiolate Complex [（μ-SCH_2）_2NPh]Fe_2（CO）5（Ph_2PCH_2PPh_2）

Reaction of [(μ-SCH2)2NPh]Fe2(CO)6 with Ph2PCH2PPh2 in the presence of Me3NO·2H2O gave the title complex [(μ-SCH2)2NPh]Fe2(CO)5(Ph2PCH2PPh2)(1)in 78% yield.The new complex 1 was characterized by elemental analysis,spectroscopy and X-ray crys-tallography.It crystallizes in triclinic,space group P1 with a = 10.832(2),b = 12.003(2),c = 15.579(3),V = 1785.6(6)3,Z = 2,C32H26Fe2NO5PS2,Mr = 819.40,Dc = 1.524 g/cm3,μ(MoKα)= 1.064 mm-1,F(000)= 840,T = 113(2)K,the final R = 0.0543 and wR = 0.1218 for 6203 observed reflections(I > 2σ(I)).The Ph2PCH2PPh2 ligand resides in an axial position of the square-pyramidal coordination sphere of the Fe atom and trans to the benzene ring in order to reduce the steric repulsion between Ph2PCH2PPh2 and the benzene ring.     

Syntheses, Crystal Structures and Properties of Two Supramolecules Assembled from Weak Interactions

Two complexes, [Cu2(Htdb)4(H2O)2] (1) and [Cd(bipy)2(Hmcmbc)2] (2) (H2tdb = 2,2-thiodibenzoic acid, H2mcmbc = m-(carboxyl-methyloxy)-benzenecarboxylic acid, bipy = 4,4'-bipyridine), have been prepared, and were characterized by elemental analysis, FT-IR and single-crystal X-ray diffraction. Structures indicate that complex 1 is a single molecule, and 2 is a one-dimensional chain. Their two-and three-dimensional frameworks are constructed through hydrogen bonding, π…π or C–H…π stacking, and such other weak interactions. The cyclic voltametric behavior of complex 1 and luminescence property of complex 2 were investigated. 1 belongs to the triclinic system, space group P with a = 7.8607(6), b = 11.7619(9), c = 15.3481(12) , α = 109.3670(10), β = 92.4420(10), γ = 92.0450(10)°, V = 1335.65(18) 3, Mr = 1256.26, Dc = 1.5619(2) g/cm3, F(000) = 642, μ = 1.029 mm–1, Z = 1, the final R = 0.0289 and wR = 0.0763 for 5199 observed reflections with I > 2σ(I). Complex 2 crystallizes in triclinic, space group P with a = 9.6378(10), b = 9.7508(10), c = 19.055(2) , α = 88.7020(10), β = 80.5260(10), γ = 69.2000(10)o, V = 1649.9(3) 3, Mr = 815.07, Dc = 1.641 g/cm3, μ = 0.732 mm-1, F(000) = 828, Z = 2, the final R = 0.0511 and wR = 0.1149 for 4729 observed reflections (I > 2σ(I)).     

Mo_8~ⅤW_2~ⅥO_(26)(C_5H_5N)_8·2H_2O: A Novel Mixed-valence Heterometal Polyoxometalate

A new mixed-valence heterometal cluster Mo8VW2VIO26(C5H5N)8·2H2O has been synthesized under solvothermal conditions and characterized by X-ray single-crystal diffraction, IR, UV-vis and XPS spectroscopy. The title compound crystallizes in the triclinic system, space group P1 with a = 11.708(3), b = 12.018(4), c = 13.316(4) , a = 112.184(4), β = 97.844(4), r = 110.043(3)o, V = 1551.9(8) 3 and Z = 1 at 293(2) K. The final full-matrix least-squares refinement converged to R = 0.0414 for 4460 observed unique reflections with I 2σ(I) and w R = 0.1290 for all data(5352) and S = 1.015. In addition, its thermal stability and fluorescent property have also been investigated.     

基于线性算子的广义逆矩阵的几何表示北大核心

广义逆矩阵是矩阵理论的重要内容.由于广义逆矩阵的定义众多,计算较为繁杂,使得初学者很难理解和掌握其本质.基于线性方程组求解问题的等价表示,从线性算子的角度展示多种广义逆矩阵定义的背景及其几何直观意义.通过对一个特殊算例的分析与求解,实现了对多种广义逆矩阵的几何解释及其在线性方程组求解中的作用,淡化了广义逆矩阵计算的繁杂,加深初学者对广义逆矩阵的理解与掌握.     

钨球对高硬度钢斜侵彻效应

为研究高硬度钢板抗不同着角钨球的侵彻性能及破坏模式,通过弹道枪进行了?8 mm、?11 mm钨合金球形破片以0°、20°、40°着角撞击厚度为6 mm、8 mm的高硬度钢板试验,得到了极限贯穿速度v₅₀;分析了钨球轴向径向变形及靶板失效模式与撞击速度的关系,发现高硬度钢板失效模式主要为压缩开坑破坏和沿厚度方向剪切破坏。采用有限元方法对试验进行了模拟,验证了数值模型及参数的合理性,并运用数值模拟方法研究了撞击着角对靶板吸能模式影响,结合试验数据,修正已有极限贯穿速度计算公式。结果表明:随侵彻着角增大,极限贯穿速度提高,且着角越大,极限贯穿速度增长越快;随着角增大,靶板吸能模式逐渐由压缩开坑向剪切冲塞过渡,且着角大于50°时,剪切冲塞耗能将超过压缩开坑耗能;修正后极限贯穿速度计算公式适用范围更广、精度更高,具有较好工程应用价值。