三维空间二阶精度流体体积界面重构方法

给出三维空间网格模板含81个单元的最小二乘流体体积界面重构方法,并和Youngs方法及网格模板含125个单元的最小二乘流体体积界面重构方法进行比较.静态和动态的测试例子均表明:该方法能精确重构任意方向的平面界面,对C²光滑曲面它能达到二阶收敛精度.和网格模板含125个单元的最小二乘流体体积界面重构方法相比,在达到同样网格精度的条件下,减少了计算量,节省了计算时间,提高了计算效率.     

滑移边界对二维Rayleigh-Bénard热对流流态和传热特性的影响

采用并行直接数值模拟（PDM-DNS）计算无滑移和滑移边界二维Rayleigh-Bénard热对流.与无滑移边界形成的随机羽流运动的湍流热对流不同,滑移边界热对流最终形成湍流特征消失,且温度仅分布于四壁的一个大尺度环流的流动形态.平均场近底板的温度分布特性,无滑移边界逐渐变化而滑移边界出现过冲现象.宽高比Γ=1时,Nusselt数（Nu）随Rayleigh数（Ra）的变化具有相同标度指数,Nu~Ra^0.3.滑移边界热对流具有传热增强作用.滑移边界热对流Nu随Γ变化明显,并分为两个阶段,在Γ=0.5时出现Nu_max≈250,是无滑移边界热流Nu的5倍.     

三维枝晶生长的相场法数值模拟研究

基于薄界面限制、耦合界面能各向异性的相场模型,采用动态计算区域的加速算法,对纯物质的三维枝晶生长进行了定量模拟,真实再现了枝晶的生长过程.对枝晶尖端进行了剖切分析,表明主枝截面上各向异性没有主枝方向各向异性明显;对枝晶尖端生长速度、尖端半径、Peclet数及临界稳定性参数σ^*进行模拟计算,并与同条件下报道值进行了对比分析,两者符合良好,并得到了与结晶理论相一致的枝晶生长规律,证实了相场方法模拟三维空间枝晶生长可行有效. 关键词： 相场方法 枝晶生长 微观组织 三维数值模拟     

可向量计算的块预条件迭代算法

提出一种类似于PE算法的实用并行迭代算法(VPE),可以克服M^-1r^(s)向量或并行化处理的困难.这种算法格式简单明了,收敛速度快.并证明了当矩阵A是M-阵和H-阵时,该算法是收敛的。计算实例显示该算法很有效.     

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     

定常不可压Navier-Stokes型方程的非线性Galerkin有限元算法的收敛性

给出数值求解二维定常不可压Navier-Stokes型方程的非线性Galerkin有限元算法,并分析了数值解的正则性和收敛性,当粗网格参数H和细网格参数h满足关系式H=O(h^1/2)时,该算法具有和Galerkin有限元算法同阶的收敛精度,然而在计算上比Galerkin有限元算法更为简单,可以节省可观的计算量.最后给出了数值试验,验证了上述结果。     

MgH分子X2Σ+，A2Π和B2Σ+电子态的势能函数

利用QCISD(T),SAC-CI方法和cc-pVQZ,aug-cc-pVTZ,6-311++G及6-311++G(3df,2pd)基组,对MgH分子的基态X²Σ⁺,第一简并激发态A²Π和第二激发态B²Σ⁺的结构进行优化计算.通过对4个基组计算结果进行比较,得出6-311++G(3df,2pd)基组为最优基组.使用 关键词： 分子结构与势能函数 激发态 Murrell-Sorbie函数 C₆函数')" href="#">Murrell-Sorbie+C₆函数     

块多分裂方法与预条件子空间迭代方法

提出一种块多分裂并行PE迭代算法(MPPE),可以克服M^-1r^(s)并行化处理的困难。这种算法格式简单明了,收敛速度快。并证明了当矩阵A是M-阵和H-阵时,该算法是收敛的。同时把这种分裂作为预处理矩阵,对子空间方法类进行了预处理,并给出的计算实例显示该算法很有效,对子空间方法类的余量光滑和加速都起到了比较好的作用。     

基于多算法优化SVM的粗糙面参数反演

支持向量机（SVM）是粗糙面参数反演中常用的一种反演算法,SVM反演中的惩罚参数C和核函数参数G对反演结果精度的影响较大,若参数取值不当,会使模型产生"过学习"或者"欠学习"的现象,从而降低预测精度.给出几种SVM参数C和参数G的优化算法,如K折交叉验证（K-CV）、遗传算法（GA）和粒子群算法（PSO）,并在此基础上提出一种基于K-CV和GA改进的PSO算法（GA-CV-PSO）.利用矩量法（MoM）获得的粗糙面后向散射系数构造训练集和测试集,通过不同参数反演的仿真结果对比不同优化算法的反演精度和计算时间,表明GA-CV-PSO算法克服了单一优化算法的缺陷,具有更精确的反演精度和更强的泛化能力.     

碱基分子的原子电距矢量表达及核磁共振碳谱模拟

提出以原子电性距离矢量(VAED)描述各种碱基分子中不同等价碳原子的化学环境,结合γ效应校正与碳原子类型,建立核磁共振碳谱(¹³C NMR)化学位移(CS)的五参数线性模型.用于碱基分子中4类不同碳(其中主要是仲叔季碳)的等价碳原子化学位移的估计,复相关系数R和均方根误差RMS[ppm]分别为仲叔季碳:1)对C2n=12,R=0.9998,R²=0.9997,F=2732.2498,EV=0.9994,RMS=0.1804,SD=0.18842)对C3n=41,R=0.9334,R²=0.8712,F=38.3299,EV=0.8528,RMS=9.5268,SD=9.64523)对C4n=23,R=0.9183,R²=0.8433,F=14.3479,EV=0.7972,RMS=6.5304,SD=6.67721)对C2n=12,R=0.9998,R²=0.9997,F=2592.7072,EV=0.9994,RMS=0.1852,SD=0.19342)对C3n=41,R=0.9270,R²=0.8594,F=34.6283,EV=0.8393,RMS=9.548,SD=10.07843)对C4n=23,R=0.9071,R²=0.8229,F=12.3881,EV=0.7708,RMS=6.9425,SD=7.0985经交互校验,模拟稳定性较好.并综合几种处理方法,找到一种较好的建模方法,将它用于4个外部样本化学位移的定量预测,结果良好.     

The angular intensity correlation functions C(1) and C(10) for the scattering of light from randomly rough dielectric and metal surfaces

We study the statistical properties of the scattering matrix S(q|k) for the problem of the scattering of light of frequency ω from a randomly rough one-dimensional surface, defined by the equation x₃=ζ(x₁), where the surface profile function ζ(x₁) constitutes a zero-mean, stationary, Gaussian random process. This is done by studying the effects of S(q|k) on the angular intensity correlation function C(q,k|q',k')=〈I(q|k)I(q'|k')〉-〈I(q|k)〉〈I(q'|k')〉, where the intensity I(q|k) is defined in terms of S(q|k) by I(q|k)=L^-1₁(ω/c)|S(q|k)|², with L₁ the length of the x₁ axis covered by the random surface. We focus our attention on the C⁽¹⁾ and C⁽¹⁰⁾ correlation functions, which are the contributions to C(q,k|q',k') proportional to δ(q-k-q'+k') and δ(q-k+q'-k'), respectively. The existence of both of these correlation functions is consistent with the amplitude of the scattered field obeying complex Gaussian statistics in the limit of a long surface and in the presence of weak surface roughness. We show that the deviation of the statistics of the scattering matrix from complex circular Gaussian statistics and the C⁽¹⁰⁾ correlation function are determined by exactly the same statistical moment of S(q|k). As the random surface becomes rougher, the amplitude of the scattered field no longer obeys complex Gaussian statistics but obeys complex circular Gaussian statistics instead. In this case the C⁽¹⁰⁾ correlation function should therefore vanish. This result is confirmed by numerical simulation calculations.     

Integrable geodesic flows and super polytropic gas equations

The polytropic gas equations are shown to be the geodesic flows with respect to an L² metric on the semidirect product space Diff(S¹)C^∞(S¹), where Diff(S¹) is the group of orientation preserving diffeomorphisms of the circle. We also show that the N=1 supersymmetric polytropic gas equation constitute an integrable geodesic flow on the extended Neveu–Schwarz space. Recently other kinds of supersymmetrizations have been studied vigorously in connection with superstring theory and are called supersymmetric-B (SUSY-B) extension. In this paper we also show that the SUSY-B extension of the polytropic gas equation form a geodesic flow on the extension of the Neveu–Schwarz space.     

The solid-fluid interface: a comparison and further description using the layer model

The profiles of the concentration and the exchange enthalpy at the solid-fluid interface are investigated with the framework of a layer model (or inhomogeneous cell model). It is shown that for systems consisting of isotropic units, concentration distributions in the interfacial phase obey an exponential law. This is in agreement with results obtained from other theories or computer simulations. Subsequently, a characteristic thickness δ^* (or n^*d) is defined. This factor, together with the surface characterist scaling factor C_ℓ^* and the value of bulk concentrations, will determine the shape of distribution profiles of the concentration and the exchange energy in the interfacial phase. As a result, it is found that this factor δ^* is associated with C_ℓ^*. This is empl estimate C_ℓ^* from δ^*. Finally, the connection between the attachment energy E^att and C_ℓ^* is discussed f crystal.     

Ti/Al p-GaN Schottky barrier height determined by C–V measurements

Data are presented on the rigorous method of capacitance–voltage (C–V) measurements to the barrier height of Ti/Al p-GaN Schottky junction. For a sample with Hall concentration of 5.5 × 10¹⁶/cm³ the upper limit of the modulation frequency leading the full response of the activated carriers is defined as 1.5 kHz from the capacitance versus modulation frequency (C–f) plot. The activation energy of the Mg acceptors determined from the temperature-dependent C–f plot is 0.12 eV. The barrier height estimated with this activation energy and the intercept voltage of the 1/C²–V plot drawn with the 1.5 kHz C–V data is 1.43 eV at 300 K and 1.41 eV at 500 K. This is the most reliable barrier height ever reported. A reliable room temperature C–V doping profile is demonstrated using the 1.5 KHz modulation, which is sensitive enough to resolve the presence of a 15 nm thin highly doped (8 × 10¹⁸/cm³) layer formed near the surface.     

Noncommutative lattices and their continuum limits

We consider finite approximations of a topological space M by noncommutative lattices of points. These lattices are structure spaces of noncommutative C^*-algebras which in turn approximate the algebra C(M) of continuous functions on M. We show how to recover the space M and the algebra C(M) from a projective system of noncommutative lattices and an inductive system of noncommutative C^*-algebras, respectively.     

Nonergodicity and dynamical approach to the anharmonic oscillator

General lower bounds for the time average C^AA(∞)≡lim_T→∞(1/T)∝^T₀ C^AA(t) dt of the correlation C^AA(t)≡A(t)A(0)−A² of an arbitrary variable A are derived, which depend only on the temperature derivatives of the canonical averages of A and the Hamiltonian of the system. The bounds may be used to give good estimations for C^AA(∞) which is different from zero when A is nonergodic. It is important to take care of these terms when dynamical theories made for interacting systems are applied to isolated systems. We show explicitely that our recently developed dynamical approach to phonon systems with quartic anharmonicity yields excellent results for the corresponding isolated system, the anharmonic single well oscillator, when nonvanishing time averages are taken into account.     

Electron spectroscopy observation of the 1s2s2p(S) state in atomic fluorine by means of electron impact excitation of the hf molecule

The energy of the 1s2s²2p⁶²S) core excited state in atomic fluorine is determined by studying a satellite in the electron beam excited KVV Auger electron spectrum of HF. The satellite is assigned to an atomic autoionization transition 1s2(²2p⁶(²S) → 1ss²2p⁴ (¹D). The energy of the 1s2s²2P⁶(²s) initial state has been determined to be 676.5 eV. Transitions to the 1s²2s²2p⁴³p(³P)and 1s²2s²2P⁴(¹S) states are also observed. The intensity for these transitions is very low.     

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|.     

Unintegrated CCFM parton distributions and transverse momentum of gauge bosons

Transverse momentum distribution of gauge bosons W^± and Z⁰ is calculated using unintegrated parton distributions obtained by solving leading order CCFM equation(s) in the impact parameter space. For illustration we compare the results of the fixed-order collinear, soft-gluon resummation and CCFM approaches. A parameter of a nonperturbative form factor is adjusted to the D0 data. In contrast to the collinear approach, the leading order calculation based on the unintegrated CCFM parton distributions generates transverse momentum distributions of gauge bosons, which are almost consistent with experimental data provided the parameter of the nonperturbative form factor is appropriately adjusted. The W⁺–W⁻ asymmetry is calculated as a function of the boson rapidity and transverse momentum. Predictions are given for RHIC and LHC.