圆管潜射流生成偶极子涡特性实验

利用溢流恒压装置产生具有稳定出流速度的圆管潜射流, 结合染色液流态显示方法, 在多种射流无量纲潜深d/H、雷诺数Re以及限制数C的组合下, 实验研究了该潜射流动量在有限深密度均匀流体中的演化特性, 其中d为射流潜深, H为水深. 研究表明, 当C<1时潜射流表现为深水特征, 而当1≤ C<2时潜射流表现为过渡特征, 在这两种情况下均不产生任何形式的大尺度相干结构; 当2≤ C<10时潜射流表现为浅水特征, 而C≥10时潜射流表现为极浅水特征, 在这两种情况下均产生大尺度的偶极子涡结构. 对极浅水特征潜射流, 在各种无量纲潜深下, 偶极子涡结构的无量纲形成时间t_f^*与无量纲射流时间T_inj^*均满足相同的正比例关系; 对浅水特征潜射流, 当d/H=0.5时, t_f^*与T_inj^*满足某种线性关系, 但对其他无量纲潜深, t_f^*与T_inj^*之间无明显规律. 关键词： 圆管潜射流 限制数 偶极子涡结构 形成时间     

求解非均匀介质中电场反问题的一个新方法

以由R³中多层介质电场的部分数据出发,确定R³中某一区域的形状为例,抽象为最优控制问题,证明了该问题的解的存在性。给出了有限元方法和图论相结合的新算法,根据这个算法,进行多种数值实验,得到了L²下各种计算结果。     

Stokes问题的非协调广义差分法

本文提出解Stokes问题的非协调广义差分法,速度用不连续分片线性函数逼近,压力用分片常数函数逼近。速度近似按‖.‖_h模,压力近似按L²模都具有最优的逼近阶误差估计。本文还给出了数值计算结果。     

LiAl分子基态、激发态势能曲线和振动能级

利用单双激发多参考组态相互作用方法获得了LiAl分子基态X¹∑⁺及七个激发态a³∏, A¹∏, b³∑⁺, c³∑⁺, B¹∏, C¹∑⁺, d³∏的势能曲线, 通过势能曲线得到各态的平衡核间距R_e, 进而求得绝热激发能和垂直激发能.计算结果表明:c³∑⁺ 电子态是一个不稳定的排斥态, A¹∏态是一个较弱的束缚态, 其余6个电子态均为束缚态; b³∑⁺与 c³∑⁺态之间存在预解离现象; 8个电子态分别解离到两个通道, 即Li(²S)+Al(²P⁰)与Li(²P⁰)+Al(²P⁰). 接着将势能曲线拟合到Murrel-Sorbie解析势能函数形式, 据此获得各态的光谱数据:基态X¹∑⁺的平衡键长为0.2863 nm, 谐振频率为316 cm^-1, 解离能D_e为1.03 eV, 激发态a³∏, A¹∏, b³∑⁺, c³∑⁺, B¹∏, C¹∑⁺, d³∏的垂直激发能依次为0.27, 0.83, 1.18, 1.14, 1.62, 1.81, 2.00 eV; 解离能依次为1.03, 0.82, 0.26, 排斥态, 1.54, 1.10, 0.93 eV, 相应谐振频率 ω_e为339, 237, 394, 排斥态, 429, 192, 178 cm^-1. 通过求解核运动的薛定谔方程找到了J=0时 LiAl分子7个束缚电子态的振动能级和转动惯量. 关键词： LiAl 光谱常数 势能曲线 振动能级     

Pb液滴在Ni基底润湿铺展行为的分子动力学模拟

采用分子动力学方法研究了Pb液滴在Ni(100)晶面、(110)晶面和(111)晶面的铺展润湿行为. 结果表明: Pb液滴在Ni(100)及(111)基底上的润湿铺展现象呈各向同性, 而在Ni(110)基底上的润湿铺展现象呈明显的各向异性, 且这种各向异性源于Ni(110)晶面点阵结构上Pb原子沿不同晶向的扩散机制及速度的明显差异; Pb液滴在Ni(111)晶面上铺展时, 未发生表面合金化, 液滴铺展动力学描述近似满足 R² ∝ t, 而液滴在(100)晶面和(110)晶面上铺展时表面产生合金化现象, 铺展动力学关系近似满足 R⁴ ∝ t, 且液滴在(100)晶面上的铺展速度高于(110)晶面上的铺展速度. 关键词： 分子动力学 润湿各向异性 铺展膜 扩散机制     

有限体积元数值方法在大气污染模式中的应用

运用有限体积元方法分析求解大气污染模型问题,分别选取试探函数空间和检验函数空间为一次元函数空间和分片常数函数空间,并且给出L²估计和H¹估计,通过数值实验与有限差分方法进行分析与比较,说明其有效性.为改善大气污染问题的模拟提供实用有效的方法.     

波动方程辛算法的迭代求解

对(∂²)/(∂x²)利用中心差商算子,对expt作对角Padé逼近,由波动偏微分方程可得到两类具有O(Δx²+Δt^2l)和O(Δx⁴+Δt^2l)精度的辛格式.对由此类辛格式产生的线性方程组构造了两种迭代解法,并对l=1,2,3,4给出了它们的收敛条件.并进行了数值实验.     

一类广义强阻尼Sine-Gordon方程的整体解

同时考虑黏性效应及外阻尼作用研究了一类广义强阻尼Sine-Gordon方程-利用Galerkin方法,首先证明了该方程在初值u(x,0)∈H¹₀(Ω),u_t(x,0)∈L²(Ω)的条件下初边值问题存在整体弱解u(x,t),并证明了整体弱解关于初始条件具有 关键词： Sine-Gordon型方程 强阻尼 Galerkin方法 整体解     

三角对称晶场下d8电子组态的EPR参量的普遍公式及其应用

本文考虑到d⁸电子组态中所有自旋三重态和自旋单态对基态的影响,用高阶微扰法导出了d⁸电子组态在三角对称晶场下光谱和基态EPR普遍公式。发现在三角对称晶场下,d⁸电子组态离子的g_⊥ > g_‖或g_⊥ < g_‖和D > 0或D < 0是以立方对称晶场为界,晶体中顺磁离子的配体沿C₃轴伸长或压缩所致。利用所得公式计算了NiCl₂和NiSiF₆·6H₂O晶体的EPR参量,其结果与实验吻合较好。     

AlC分子 X4∑-和B4∑-电子态的光谱性质

采用Davidson修正的内收缩多参考组态相互作用方法(MRCI+Q) 结合Dunning等的相关一致基aug-cc-pVnZ (n=D,T,Q,5,6) 计算了AlC分子X⁴∑^-和B⁴∑^-态的势能曲线, 并利用总能量外推公式将这两个态的总能量分别外推至完全基组极限. 对势能曲线进行核价相关修正及相对论修正, 并详细讨论了基组、核价相关和相对论修正 等对X⁴∑^-和B⁴∑^-电子态的能量和光谱常数的影响. 拟合核价相关及相对论效应修正的外推势能曲线, 得到了AlC分子X⁴∑^- 和B⁴∑^-电子态的主要光谱常数T_e, R_e, ω_e, ω_ex_e, ω_ey_e, B_e和α_e. 它们与实验结果符合较好. 求解双原子分子核运动的径向Schrödinger方程, 找到了无转动的AlC分子两个电子态的全部振动态. 针对每一振动态, 还分别计算了其相应的振动能级和惯性转动常数等分子常数. 它们与已有的实验结果一致. 关键词： 光谱常数 分子常数 核价相关修正 相对论修正     

Light-enhanced reactivation of passivated boron in hydrogen treated silicon

The thermal reactivation of the boron acceptor in hydrogenated silicon is strongly enhanced if the anneals are performed under illumination. The changes of the inactive boron concentration R versus annealing time t satisfy the equation dR/dt = -rR²/(N_A − R)², where N_A is the total boron concentration. Under strong illumination the annealing parameter r is proportional to the light intensity.     

The ΔNγ electromagnetic transition form factors GM(q) and GE(q)

A parameter-free, nonperturbative calculation of the ΔNγ electromagnetic transition amplitudes GM*(q2), GE*(q2), and the resonant multipole ratio REM(q2)≡E1+3/2(q2)/M1+3/2(q2) is performed in terms of the well-known nucleon isovector Sachs form factor GMV. Our methods are fully relativistic with conservation of the electromagnetic current guaranteed. We find that GM*(q2) decreases more rapidly than the nucleon dipole form factor when −q21 GeV2/c2 and that REM(q2) remains small even for very high four-momentum transfer implying that the perturbative QCD prediction REM(q2)→1 is purely asymptotic and is valid only for extremely high |q2|.     

New oxychlorides, T-type CaRCuO3Cl (R=Y, Ho and Er), prepared under high pressure

We synthesized new copper-oxychlorides with the T^* structure CaRCuO₃Cl (R=Y, Ho and Er), using a high pressure technique. X-ray diffraction indicates that samples with nominal compositions of CaRCuO₃Cl (R=Y, Ho and Er) have a tetragonal structure with the a-axis lattice parameters in the range 3.84–3.86 Å, which are comparable to those of typical p-type superconductors. Both the a-axis and c-axis lattice parameters decrease approximately linearly with decreasing ion size R. The range cationic radius ratio of alkaline earth and rare earth elements for these copper-oxychlorides agrees with those previously reported for T^* copper-oxides and -oxychlorides.     

Dynamical spin susceptibility of the d–p model in the over doping region

Dynamical spin susceptibility χ^s(q,ω) of the d–p model in the over doping region is investigated by using the auxiliary boson technique. It includes higher order terms of the 1/N-expansion within the random phase approximation (RPA) of the local vertex, where frequency dependence of the quasi-particle interaction is taken into account. The incommensurate spin fluctuation is obtained due to the nesting effect in the low energy region (ωω^*), whereas the commensurate one in the high energy region (ωω^*), the characteristic energy ω^* is estimated to be about 30 meV. Both of the spin–lattice relaxation rate 1/T₁ and the spin–spin relaxation rate 1/T_g monotonically increase as T decreases, while the spin Knight shift K is almost independent of T.     

Gravitational quasi-normal modes of static R~2 Anti-de Sitter black holes

In this paper, we study the gravitational quasi-normal modes(QNMs) for a static R~2 black hole(BH) in Anti-de Sitter(AdS) spacetime. The corresponding master equation of odd parity is derived and the QNMs are evaluated by the Horowitz and Hubeny method. Meanwhile the stability of such BH is also discussed through the temporal evolution of the perturbation field. Here we mainly consider the coefficient λ, which is related to the radius of AdS black hole, on the QNMs of the R~2 AdS BH. The results show that the Re(ω) and |Im(ω)| of the QNMs increase together as |λ| increases for a given angular momentum number l. That indicates with a larger value of |λ| the corresponding R~2 AdS BH returns to stable much more quickly. The dynamic evolution of the perturbation field is consistent with the results derived by the Horowitz and Hubeny method. Since in the conformal field theory the QNMs can reflect its approach to equilibrium, so our related results could be referential to studies of the AdS/CFT conjecture. The relationship between λ and the properties of the static R~2 BH might be helpful for the development of R~2 gravitational theory.     

Long-time correlation tails in crystals

Nonequilibrium thermodynamics and the Onsager hypothesis are utilized to demonstrate that long-time correlation “tails”, decaying as t^−3/2, should be expected in the velocity autocorrelation function of crystals. In the simplest situation, this behavior is due to the non-propagating (Rayleigh) mode. In the general case, it is argued that “diffusive” modes decaying in wavevector space as exp (−tK²), where is a constant, should lead to the same behavior.     

Effects of encounters on phase separation dynamics from diffusion-controlled growth to coarsening

We investigate the dynamics of phase separations in quenched binary mixtures, such as binary alloys and polymer blends with low mobilities, at higher volume fractions. Computer simulations are performed using simple model equations in the presence of encounters of droplets. Four characteristics stages with three crossovers, including dynamical scaling behavior and temporal power laws, are found beyond a volume fraction of approximately 0.14, where each crossover is attributed to a transition from one growth mechanism to the other. The encounter effect is thus shown to strongly influence a transition from the diffusion-controlled (t^1/2) stage to the coarsening (t^1/3) stage. A simple analytical argument for the simulation results is also presented.     

Remarks on stochastic non-linear birth and death models

The first part of this paper is an attempt to formulate and motivate additional work on the important problem of obtaining global bounds applicable to the controlled truncation of the paper relates specifically to the linear birth, quadratic death model. Asymptotic results are given for the first finite difference ΔT_m where T_m is the exactly known mean time to extinction starting from state m (m= 0,1,…). These results are in terms of the environmental carrying capacity n^* taken to be large. For m near zero ΔT_me^n*/(n^*)²; whereas, for m near n^*ΔT_m ≈ (π/2)^1/2/(n^*)^3/2. This indicates the vastly different time scales in those two regions of state space - with considerably slower action near extinction than near n^*.