一类演化方程的高稳定性的差分格式

考虑一类演化方程u_t=au∂_2k+1(其中a是常数,u∂_2k+1=∂^2k+1u/∂x^2k+1,k=1,2……)的有限差分解法。构造了两类具有高稳定性的显式差分格式。并用引入耗散项的方法建立了两类半显式差分格式,它们是无条件稳定的且可显式地进行计算。     

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     

若干高精度恒稳的半显式差分格式

本文构造了解色散方程u₁=au_xxx的若干三层恒稳的半显式差分格式。第Ⅰ、Ⅱ类格式的局部截断误差的阶为O(τ²+h²+(τ²)/(h³));而第Ⅲ、Ⅳ类格式的局部截断误差的阶为O(τ²+h⁴+((τ)/(h))²+τh)。用判别稳定性的Von Neumann准则可证明:第Ⅰ、Ⅱ类格式及当参数α≤1时的第Ⅲ、Ⅳ类格式都是无条件稳定的,并且当必须的边界条件给定时它们可以显式地进行计算。     

类氖CaⅪ和MnXVI2P53L或4L-2P54L1跃迁波长和能级的多组态Dirac-Fock计算

本文用MCDF-EAL计算模式,计算了可能成为超真空紫外区的类氖等离子体激光工作物质的CaⅪ与MnXVI类氖离子的1s²2s²2p⁵3l与1s²2s²2p⁵4l组态的多重态能级的能量值及3l-4l¹和4l-4l¹组态的各多重态能级间的可能的跃迁波长位,3l-4l¹跃迁波长的计算值与实验数据比较符合得很好。文中还预言了4l-4l¹的可能的跃迁波长,     

Ti1－xCrxO2±δ体系的相关系、晶体结构和磁性能研究

采用溶胶凝胶法制备了Ti_1-xCr_xO_2±δ体系系列样品.利用扫描电子显微镜(SEM)，X射线光电子能谱(XPS)，粉末X射线衍射分析(XRD)方法研究了Ti_1-xCr_xO_2±δ系列样品的颗粒尺寸、形貌、组分化学态、相关系和固溶区范围；并利用超导量子干涉磁强计对样品的磁性能进行了研究.采用Rietveld结构精修的方法研究了Cr的不同掺杂量对TiO₂晶体结构的影响，研究表明，1000℃烧结的样品的固溶区范围是x=0—0.03，为金红石单相；随着Cr掺杂量的增加，金红石相晶胞参数规律性地减小；当x>0.03，为金红石相和CrO₂相两相共存.综合XRD和磁性测量结果，500℃烧结的样品的固溶区范围是x=0—0.02，为锐钛矿单相；随着Cr掺杂量的增加，锐钛矿相晶胞参数规律性地减小；当x≥0.04，为锐钛矿相和绿铬矿相(Cr₂O₃)两相共存.XPS实验结果表明，500℃和1000℃退火的样品中Cr都是以Cr⁺³和Cr⁺⁶两种化学态存在，1000℃烧结的样品中可能有更多的Cr³⁺转化为Cr⁶⁺.根据M-H和M-T曲线的测试结果发现，本文500℃烧结的Ti_1-xCr_xO_2±δ体系样品当x=0—0.02时，为室温铁磁性.当x≥0.04时，由铁磁相和顺磁相所组成，在低温下有较强的铁磁性；室温下主要是顺磁相，铁磁相只占据很小的体积分数. 关键词： 1-xCr_xO_2±δ体系')" href="#">Ti_1-xCr_xO_2±δ体系 相关系 固溶区 磁性能     

二维非定常Sine-Gordon方程辛算法及其孤子数值模拟

在矩形域[-a,a]×[-a,a]内对微分算子L=(ə²)/(əx²)+(ə²)/(əy²)用5点差分格式将二维非定常Sine Gordon方程离散化为一个2×799²阶非线性Hamilton系统.对该系统使用Euler中心格式,得到一个非线性方程组.对此方程组建立迭代解法并给出了这个迭代方法的收敛条件和收敛速度.Sine Gordon方程单孤子和双孤子的数值模拟试验显示该辛算法是有效的.     

快离子导体AgxTiS2中Ag+离子－空位的二维基态结构与能量性质研究

根据Ag⁺离子-空位的二维有序结构建立了三维晶胞模型.采用局域密度近似下的平面波赝势方法,对有序Ag_xTiS₂(x=0,1/4,1/3,1/2,2/3,3/4,1)系列进行了几何结构优化和总能量计算,并与Li_xTiS₂系列进行了对比研究.有序Ag_xTiS₂系统的晶格参量增量Δa_{关键词： x}TiS₂')" href="#">Ag_xTiS₂ 有序—无序相变 离子扩散 第一性原理计算     

一类特殊单模压缩态的Wigner函数

本文运用IWOP技术推导出Wigner算符的相干态显式,计算出一类特殊单模压缩态 |z〉_f,g=exp[－(|z|²)/2 +(fz+gz^*)a⁺－fga⁺²]|0〉的Wigner函数解析式,通过数值计算可以看到,参数f和g的任一个取值固定时,另一个参数的旋转取值会使得特殊 关键词： IWOP技术 Wigner算符 Wigner函数     

时间分数阶亚扩散方程的高阶差分方法

提出两差分格式求解时间分数阶亚扩散方程.两个格式都是绝对稳定的,收敛阶均为O(τ^q+h²),其中q(q=2-β或2)与方程解的光滑性有关,β(0 < β < 1)是分数阶导数的阶、τ和h分别是时间和空间方向步长.数值实验验证了理论结果的正确性,并与其他方法进行比较,显示了本文方法的有效性和精确性.     

稀土掺杂镝(Ⅲ)乙酰丙酮邻菲咯啉三元配合物的合成和荧光性质

合成了三个系列稀土掺杂镝乙酰丙酮(Hacac)邻菲咯啉(phen)三元配合物RE_xDy_1-x(acac)₃phen(RE=La,Y,Gd;x=0,0.10,0.20,0.30,0.50,0.70,0.90,1.00),通过紫外光谱、红外光谱、X射线粉末衍射对配合物进行了表征。对各系列配合物进行荧光光谱研究,发现La³⁺、Y³⁺、Gd³⁺对Dy³⁺离子均有荧光增敏作用,它们对Dy³⁺离子的荧光增强顺序为I(La³⁺)>I(Y³⁺)≈I(Gd³⁺)。当x=0.10~0.30,所有掺杂配合物的荧光强度都大于未掺杂的配合物Dy(acac)₃phen的荧光强度。     

Ferromagnetic resonance in Sr doped rare earth orthocobaltites, Ln1−xSrxCoO3†

FMR measurements have been carried out on several members of the Ln_1−xSrxCoO₃ (Ln = Rare earth) system. The results show that g_eff in these systems is around 1.25 independent of x as well as the rare earth ion. It is suggested that this unusual value of g_eff is due to the localized intermediate-spin Co³⁺ ions (t⁵_2g e¹_g) located at the top of the π^* band.     

Analytical result for dimensionally regularized massless master non-planar double box with one-leg off shell

The dimensionally regularized massless non-planar double box Feynman diagram with powers of propagators equal to one, one leg off the mass shell, i.e., with p₁²=q²≠0, and three legs on shell, p_i²=0, i=2,3,4, is analytically calculated for general values of q² and the Mandelstam variables s,t and u (not necessarily restricted by the physical condition s+t+u=q²). An explicit result is expressed through (generalized) polylogarithms, up to the fourth order, dependent on rational combinations of q²,s,t and u, and simple finite two- and three-fold Mellin–Barnes integrals of products of gamma functions which are easily numerically evaluated for arbitrary non-zero values of the arguments.     

拟随机选择法

本文针对通常的随机选择法在求Riemann问题基本解上遇到的困难,提出采用拟特征线形式下的各独立标量方程形式,求其简单的Riemann问题组以代替原Riemann问题的解。这样,使方法基本保持了随机选择法的特点,又使方法的实现、应用和推广更加容易,而且可以设计并行算法。最后用激波管和溃坝问题为例作了实算。结果与已知的结果相比也是满意的。     

Spectroscopic study of BixEu1−xVO4 and BiyGd1−yVO4 mixed oxides

The mixed oxides Bi_xEu_1−xVO₄ and Bi_yGd_1−yVO₄ crystallize in a zircon-type structure, for 0 <x < 0.6 and 0 < y < 0.64, and in a fergusonite-type structure, for 0.94 < x < 1 and 0.93 < y < 1. A process of competition between the dominant and the constrained effects of the lone-pair 6s² of Bi³⁺ is discussed. The diffuse reflectance spectroscopic studies of these mixed oxides are presented. The observed broad bands are attributed to charge transfer processes and the sharp peaks in the Bi_xEu_1−xVO₄ spectra are ascribed to intra-configurational 4f – 4ftransitions of the Eu³⁺ ion. The broad absorption shift in BiLnVO₄ (Ln : Eu and Gd) compounds to the longer wavelengths range, when Bi is introduced in the LnVO₄ lattice, is ascribed to charge transfer processes in a Bi-VO₄ center and are interpreted assuming a Jahn-Teller effect in the excited state of Bi³⁺. The concept of an internal pressure of Bi³⁺ ions is also used to explain the broad A-band shifts.     

1/f-type fluctuation of electron transmission in one-dimensional disordered systems

A universal feature of 1/f-type fluctuation is numerically observed in the system-size n dependence of the transmission amplitude t_n in various one-dimensional disordered systems. The power spectrum P(f) of the transmission coefficient T(n)=|t_n|² exhibits the power law of 1/f², irrespective to the type of disorder of the system whether it is of short-range or of long-range correlation. That of the phase θ_t(n) of t_n also does the universal power law of 1/f^1.4.     

Ion-size effects on the structure and superconductivity of La-214 compounds at 1/8 doping

A structural transition to a low-temperature tetragonal (TLT) phase occurs below T_d2≈60 K in La_2−xBa_xCuO₄ only around x=0.125, accompanied by sharp suppression of superconductivity. In this study we investigated the effects of partial substitution of smaller divalent cations for Ba²⁺ ions (Ba²⁺ > Sr²⁺ > Ca²⁺) on these anomalous low-temperature properties. The suppression of superconductivity is strongly affected by the appearance of the TLT phase for this carrier concentration. We also show that the variations of T_d2 and T_c are quantitatively scaled by the averaged size of cations at the La site. This dependence can be interpreted as chemical effects acting effectively as applied pressure. We discuss how our observation is related to recent reports which claim that the TLT structure itself does not necessarily destroy the superconductivity.     

Saturation and BFKL dynamics in the HERA data at small-x

We show that the HERA data for the inclusive structure function F₂(x,Q²) for x10⁻² and 0.045Q²45 GeV² can be well described within the color dipole picture, with a simple analytic expression for the dipole–proton scattering amplitude, which is an approximate solution to the non-linear evolution equations in QCD. For dipole sizes less than the inverse saturation momentum 1/Q_s(x), the scattering amplitude is the solution to the BFKL equation in the vicinity of the saturation line. It exhibits geometric scaling and scaling violations by the diffusion term. For dipole sizes larger than 1/Q_s(x), the scattering amplitude saturates to one. The fit involves three parameters: the proton radius R, the value x₀ of x at which the saturation scale Q_s equals 1 GeV, and the logarithmic derivative of the saturation momentum λ. The value of λ extracted from the fit turns out to be consistent with a recent calculation using the next-to-leading order BFKL formalism.     

悬链曲面上的点粒子动力学及扩展空间约束系统量子化

扩张型正则量子化方案的核心内容是位置、动量以及哈密顿量同时量子化. 通过分析悬链面上粒子的扩张型正则量子化方案, 并且与薛定谔理论进行比较, 发现内禀几何中二维悬链面给不出与薛定谔理论相一致的结果, 而考虑将二维悬链面嵌入在三维欧氏空间之后, 还需要将正则量子化方案进行扩张, 可以得到体系的几何势能和几何动量, 并与薛定谔理论相一致.