Levinson定理及其在相对论量子力学中的推广

本文先用 Green 函数方法证明非相对论量子力学中的 Levinson 定理有如下形式:n_l=1/π[δ_l（0）—δ_l（∞）]—（（—1）^l）/2 sin²δ_l（0）,然后导出了它在 Dirac 方程中的推广形式为:n_k⁺—n_k^-=1/π[δ_k（m）—δ_k（∞）+δ_k（—∞）—δ_k（—m）]—（k/（|k|））（（—1）^x/2）[sin²δ_k（m）+sin²δ_k（—m）].对于 Klein-Gordon 方程,则可以有两种形式:n_l⁺±n_l^-=1/π{δ_l（m）—δ_l（∞）±[δ_l（—m）—δ_l（—∞）]}—（（—1）^l/2）[sin²δ_l（m）±sin²δ_l（—m）].文中对此定理的含义、应用范围及有关问题作了讨论,并就方势阱的 s 态问题,检验了这些公式。     

高速钨杆弹对脆性靶体的侵彻分析

 考虑脆性材料在高速弹体的侵彻下会发生破碎这一特性,将靶体材料划分为弹性-裂纹-破碎三个响应区,利用静态空腔膨胀理论求出了空腔膨胀压力,即修正的流体动力学模型（A-T模型）中的靶体阻力R_t。分析了压剪系数对靶体阻力和靶体应力场的影响。利用A-T模型求出了钨杆弹以1.5~4.5 km/s的速度撞击靶体时的侵彻深度,并与实验结果及其他研究者的结果进行了比较。     

高速弹体对钢筋混凝土靶的侵彻/贯穿效应实验研究

为了研究高速弹体对钢筋混凝土靶的侵彻/贯穿效应,以100 mm口径滑膛炮作为发射平台,驱动10 kg级卵形弹体以820～1195 m/s速度撞击强度为31.0～43.6 MPa的钢筋混凝土靶,获得了弹体侵彻/贯穿钢筋混凝土靶的终点弹道实验数据,并对弹体的侵彻/贯穿深度、靶板侧面自由面效应、弹体的变形进行了详细分析。结果表明:弹体的侵彻/贯穿深度为2.2～2.8 m,部分经验公式预估的侵彻/贯穿深度与实验结果吻合较好;当靶面相对尺寸较小且弹速较高时,靶板侧面自由面效应比较明显;当弹速达到1195 m/s时,弹体开始由刚体向半流体转变。     

从KL0产生（π±μ干）原子

本文求解了自旋是0-1/2的不等质量的库伦原子的Bethe-Salpeter方程。应用所求得的近似的B-S波函数以及近年来发展的复合粒子量子场论微扰展开理论计算了由K_L⁰产生（π^士μ^干）原子的几率。     

多级气隙-光纤探针

 报道了外径为0.8 mm的多级气隙-光纤探针技术。探针接收的弱光信号用变象管相机记录、贮存及数字化处理。该探针嵌入固体炸药TNT/RDX=40/60（ρ₀＝1.70 g/cm³）和液体炸药硝基甲烷内部，测得爆速分别为8.02和6.27 km/s。对光信号的可靠性进行了实验验证。     

秩2紧致单纯李群的不可约表示(I)

本文分析了SU₃群无穷小算子的对易关系,发现SU₃群的8个无穷小算子可以按其在SU₂子群下的交换性质表示为:一个标量算符A,一组角动量算符L₁,L₀,L_-1及两组秩为1/2的不可约张量算符T_±1/2,V_±1/2。利用SU₃群无穷小算子的这个性质,可以容易地求出SU₃群的所有有限维不可约表示,SU₃群的约化系数等等。本文给出了在SU₃群的不可约表示（λμ）中所有的无穷小算子对应的矩阵,从而完全确定了不可约表示（λμ）及其表示空间R^（λμ）。我们还给出了SU₃群约化系数标量因子所满足的方程组和对称关系并给出了（λμ）（?）（10）,（λμ）（?）（01）,（λμ）（?）（20）,（λμ）（?）（11）约化系数标量因子的代数表达式。在本文最后,我们定义了SU₃群的不可约张量算符并证明了相应的Wigner-Eckart定理。本文中所用的方法完全可以推广到其他紧致单纯李群中去,在相继的两篇文章中我们用类似的方法讨论了C₂,B₂,G₂群的不可约表示。     

水绿矾的状态方程和高压熔化

 用阻抗匹配法和压电探针技术测量了初始密度为1.714 g/cm³（孔隙率α=ρ₀/ρ₀₀=1.898/1.714=1.107）的水绿矾（FeSO₄·7H₂O）的冲击压缩线,发现其在0～100 GPa范围内存在两个明显相区：含有部分熔融的低压相和完全熔化的高压相。在两个相区内,冲击波速度D和波后粒子速度u可分别描述为：D=0.59+2.06u（u<3.12 km/s）和D=3.18+1.223u（u≥3.12 km/s）。从冲击压缩数据出发,用欧拉有限应变理论得到了其等熵状态方程。其熔化方程可用p_m(GPa) =0.159(T_m(K)/1000)^6.3371+0.69来近似描述。     

A=15和17原子核单粒能谱的理论计算

根据由格林函数方法导得的满壳层相邻核能谱所满足的方程,在取质量算符（按G矩阵展开）的一级近似下,应用Hamada-Johnston势,计算了A=15核的0s_1/2、0p_3/2、0p（1/2）空穴态和A=17核的0d_5/2、1s_1/2、0d_3/2粒子态能谱与相应的跃迁振幅比,计算中严格顾及了G矩阵的能量相关性。文中对能谱方程自洽求解的收敛速度以及截断近似和选作表象的单粒谐振子势参数对计算结果的影响进行了考察。本文还讨论了质心伪态的消除问题,给出了引入质心谐振子势后计算G矩阵的具体公式。除Os（1/2）态外,本文算得的能谱均消除了质心伪态的影响。与以往重整化的Brueckner-Hartree-Fock（RBHF）计算相比,本文采用的方法计算简单,结果与实验符合颇好。     

23Na（p,α）20Ne反应中几个非孤立共振的研究

本工作测量了²³Na（p,α₀）²⁰Ne_g.s.反应在 E_p=1—2.5MeV 能量范围内和θ_L=30°,150°时的激发函数,还测量了²³Na（p,α₁）²⁰Ne_lst,反应在上述能量范围内和θ_L=30°时的激发函数.对2.171 MeV 共振,在12个角度上测量了（p,α₀）的激发函数,并由激发函数求得了多个角分布,另外在一个固定能量上（150°激发函数的共振峰上）测量了（p,α₀）反应的角分布.对2.117 MeV 共振,在二个固定能量上（150°激发函数的共振峰上和其高能端的半高点处）测量了（p,α₀）反应的角分布.对2.075 MeV 共振,在16个角度上测量了（p,α₀）反应的激发函数,并由激发函数求得了角分布.这三个共振的角分布不是90°对称的,并且共振峰的峰位与角度有关.用复合核理论对它们进行了讨论.     

高压下Al的零温电子结构和物态方程

 用LMTO法（线性Muffin-Tin轨道法），计算了金属铝的超高压电子结构及零温物态方程。Al的压缩比到10，压力达10 TPa。根据第一原理计算结果，在带结构方面，s带总是处于Fermi能以下，随着压力的增加，s、p和d的带宽增加，随后则杂化程度增加，所以s、d轨道的电子占据数连续变化。上述变化对压力的影响也是连续的，换言之，从s→d转变没有理由说明Al在0.5 TPa附近冲击Hugoniot的斜率的拐弯现象。而这一点则是与Altshuler的观点不同。物态方程的第一原理计算结果表明，bcc结构比fcc结构要软，但因差别不很大，即使发生fcc→bcc的转变，也不会引起Hugoniot的质的变化（拐弯）。Al的LMTO物态方程还表明，我们以前所采用的半经验的冷压误差可达30%。为此，根据LMTO结果，给出新的冷压表达式p=∑_i=0⁵a_iδ^i/3，δ=Ω₀/Ω，其中a₀=-7.327 79，a₁=18.754 3，a₂=10.209 7，a₃=-2.523 53，a₄=-4.787 2，a₅=6.065 94，拟合误差小于3%。     

弱熔体对流对定向凝固中棒状共晶生长的影响

利用渐近方法求出在弱对流熔体中定向凝固棒状共晶生长的浓度场的渐近解,研究了弱熔体对流对定向凝固中棒状共晶生长的影响.结果表明,弱熔体对流对定向凝固中棒状共晶生长有显著的作用;平均界面过冷度不仅与棒状共晶的棒间距、生长速度有关,还与流动强度有关;当生长速度一定时,随着流动强度增大,棒状共晶的平均界面过冷度减小.利用最小过冷原则,获得棒间距与生长速度和流动强度的关系.结果表明,当生长速度比较小时,随着流动强度增大,棒状共晶的棒间距增大;当生长速度比较大时,随着流动强度增大,棒状共晶的棒间距变化减弱;棒状共晶的生长速度越小,流动对棒状共晶生长的影响越大.利用本文的解析结果计算在对流条件下Al-Cu共晶的棒间距,结果显示随着转速增大或径向距离增大,共晶的间距增大,这与Junze等的实验结果相符合.     

Variable fluid properties and variable heat flux effects on the flow and heat transfer in a non-Newtonian Maxwell fluid over an unsteady stretching sheet with slip velocity

The effects of variable fluid properties and variable heat flux on the flow and heat transfer of a non-Newtonian Maxwell fluid over an unsteady stretching sheet in the presence of slip velocity have been studied. The governing differential equations are transformed into a set of coupled non-linear ordinary differential equations and then solved with a numerical technique using appropriate boundary conditions for various physical parameters. The numerical solution for the governing non-linear boundary value problem is based on applying the fourth-order Runge-Kutta method coupled with the shooting technique over the entire range of physical parameters. The effects of various parameters like the viscosity parameter, thermal conductivity parameter, unsteadiness parameter, slip velocity parameter, the Deborah number, and the Prandtl number on the flow and temperature profiles as well as on the local skin-friction coefficient and the local Nusselt number are presented and discussed. Comparison of numerical results is made with the earlier published results under limiting cases.     

Persistence of zero velocity fronts in reaction diffusion systems

Steady, nonpropagating, fronts in reaction diffusion systems usually exist only for special sets of control parameters. When varying one control parameter, the front velocity may become zero only at isolated values (where the Maxwell condition is satisfied, for potential systems). The experimental observation of fronts with a zero velocity over a finite interval of parameters, e.g., in catalytic experiments [Barelko et al., Chem. Eng. Sci., 33, 805 (1978)], therefore, seems paradoxical. We show that the velocity dependence on the control parameter may be such that velocity is very small over a finite interval, and much larger outside. This happens in a class of reaction diffusion systems with two components, with the extra assumptions that (i) the two diffusion coefficients are very different, and that (ii) the slowly diffusing variables has two stable states over a control parameter range. The ratio of the two velocity scales vanishes when the smallest diffusion coefficient goes to zero. A complete study of the effect is carried out in a model of catalytic reaction. (c) 2000 American Institute of Physics.     

钨合金长杆弹侵彻半无限钢靶的数值模拟及分析

 利用显式动力有限元程序ANSYS/LS=DYNA,采用ALE方法和Steinberg本构模型,对钨合金长杆弹侵彻半无限厚钢靶进行了数值模拟,给出了侵彻过程4个阶段的完整图像和相关物理量的时程变化曲线,分析了弹、靶的压力分布、质点速度以及材料的流动特性。结果表明：在较大速度范围内,模拟计算的侵彻深度与实验结果吻合得很好;沿侵彻轴线,弹靶交界面附近的材料行为主要由静水压力控制。     

A Lattice-Boltzmann study of active boundary layer flow control

A Lattice Boltzmann method was employed to simulate active boundary layer flow control by means of a low-temperature surface plasma. Plasma was generated by an AC input voltage over a surface electrode and an embedded electrode, resulting in an uneven distribution of charges and an induced flow near the vicinity of the surface. Simulations were performed to examine the effect of various geometrical parameters on the velocity flow profile and maximum velocity.     

Effect of a corona discharge on the gasdynamical flow rate

We have shown experimentally that the application of an electric field to an air stream blowing over a corona point has the additional effect of increasing the air velocity. This result is derived from the interaction of two factors. We have developed a model of the phenomenon which is based on electrostatic and hydrodynamic equations. The model provides an equation which relates the additional air velocity to the basic corona discharge parameters. The resulting function agrees with the experimental results.     

Effect of magnetic and boundary parameters on flow characteristics analysis of micropolar ferrofluid through the shrinking sheet with effective thermal conductivity

Ferrofluids have many applications in mechanical and electrical engineering. In this paper, characteristics of ferrofluid over a shrinking sheet with effective thermal conductivity model are studied by the homotopy perturbation method (HPM) and Akbari-Ganji's method (AGM). Also, the Finite Element Method (FEM) has been applied for numerical solution. The governing equations formulated by the Tiwari-Das model. It is supposed that base fluid and nanoparticles are water and Fe₃O₄respectively. Effect of related parameters of micro-rotation velocity and dimensionless velocity have taken for suction and injection of mass transfer parameter. Results show that the magnetic and boundary parameters, in contrast to the micro-rotation parameter, have the same impact on velocity. Moreover, a comparison has been made between the results of this study with other researchers shows the impressive accuracy and efficiency of these methods.     

Soret and Dufour effects on MHD non-Darcian mixed convection heat and mass transfer over a stretching sheet with non-uniform heat source/sink

An analysis has been carried out to study the effects of thermal-diffusion and diffusion-thermo on non-Darcian mixed convection heat and mass transfer of an incompressible, electrically conducting fluid over a stretching sheet embedded in a porous medium in the presence of an external magnetic field and non-uniform heat source/sink. Similarity transformations are used to convert highly non-linear partial differential equations into ordinary differential equations. Similarity equations are then solved numerically using shooting algorithm with Runge-Kutta-Fehlberg scheme over the entire range of physical parameters. The effects of various physical parameters on the dimensionless velocity, temperature and concentration profiles are depicted graphically. Present results are compared with previously published work on various special cases of the problem and the results are found to be in very good agreement. Numerical results for local skin-friction, local Nusselt number and local Sherwood number are tabulated for different physical parameters.     

受曲面约束弹性细杆的平衡问题

作为DNA等一类生物大分子的力学模型，弹性细杆的非线性力学再次受到关注，形成一个力学与分子生物学的交叉学科.除了不受外界约束的自由弹性细杆外，受曲面约束的弹性细杆静力学具有重要的应用背景.在分析约束、约束方程和约束力的基础上建立了受曲面约束的圆截面弹性细杆的平衡微分方程，即曲面上的Kirchhoff方程，它是以截面主矢和截面姿态坐标以及中心线的Descartes坐标为变量的微分/代数方程.作为应用，讨论了约束是圆柱面的情形.此时平衡的无量纲方程仅含的物理参数是截面对形心的抗扭刚度和对主轴的抗弯刚度的比值，与几何参数无关.由此导出方程的螺旋杆特解.数值计算表明，对弹性细杆中心线的几何形状有显著影响的是截面主矢和姿态坐标及其导数的起始值，而不是物理参数. 关键词： 弹性细杆 DNA超螺旋 曲面约束 螺旋杆     

Thermal radiation and slip effects on MHD stagnation point flow of nanofluid over a stretching sheet

Present model is devoted for the stagnation point flow of nanofluid with magneto-hydrodynamics (MHD) and thermal radiation effects passed over a stretching sheet. Moreover, we have considered the combined effects of velocity and thermal slip. Condition of zero normal flux of nanoparticles at the wall for the stretched flow phenomena is yet to be explored in the literature. Convinced partial differential equations of the model are transformed into the system of coupled nonlinear differential equations and then solved numerically. Graphical results are plotted for velocity, temperature and nanoparticle concentration for various values of emerging parameters. Variation of stream lines, skin friction coefficient, local Nusselt and Sherwood number are displayed along with the effective parameters. Final conclusion has been drawn on the basis of both numerical and graphs results.