A bound on the number of bound states in the Schrödinger equation

A boundS _l is given for the number of bound statesn _i in thelth partial wave corresponding to a spherically symmetric potential in non-relativistic quantum mechanics. This bound is given by whereV _a(l, r) is the attractive part of the effective potentialV(r)+l(l+1)/r ². Extensive comparative study ofS _i and the Bargmann inequality is made.     

激光通道传输热特性对远场光束质量的影响

 通过仿真计算分析了激光在光束控制系统通道内传输所产生的热效应及其对远场光束质量的影响。激光传播由近轴波方程描述，用快速傅里叶变换技术求解；激光热效应引起的流场密度变化采用完全Navier-Stokes方程计算。计算给出了不同波长、不同吸收系数条件下的远场光斑情况。计算结果表明，在典型的工作条件和状态下，较高能量激光在光束控制系统通道内产生的热效应影响不容忽视，它会明显降低远场目标处的能量集中度，增大光斑的发散。     

测量圆盘转动惯量产生误差的曲线研究

结合三线摆实验的基本过程,进行实验数据的采集。利用投影法来测量圆盘的转角大小,借助于matlab的cftool工具箱,对数据进行曲线拟合,对测出来的二组数据拟合,得到转角与百分差曲线图。通过误差的大小比较,得出圆盘转动惯量测量值与理论值的百分差随转角变化最接近于三次曲线。     

Existence and regularity of solution to the generalized Tricomi equation with a singular initial datum at a point

In this paper, we study the existence and regularity of a solution to the initial datum problem of a semilinear generalized Tricomi equation in mixed-type domain. We suppose that an initial datum on the degenerate plane is smooth away from the origin, and has a conormal singularity at this point, then we show that in some mixed-type domain, the solution exists and is conormal with respect to the characteristic conic surface which is issued from the origin and has a cusp singularity.     

Meissner Anisotropy in Deuterated (TMTSF)2Clo4

Both the Meissner-signal (flux expulsion on cooling through T_c) and the shielding signal (obtained by turning on a field in the superconducting state) have been observed in deuterated single crystals for fields oriented both along and normal to the chain axis. A possible isotope effect on T_c is discussed. We find complete diamagnetism in normal fields and incomplete (～ 40 %) diamagnetism in parallel fields. A dramatic drop of the Meissner-effect in parallel fields well below H_c1 is observed and not yet well explained.     

LOCALIZED PATTERNS OF THE CUBIC-QUINTIC SWIFT-HOHENBERG EQUATIONS WITH TWO SYMMETRY-BREAKING TERMS

Homoclinic snake always refers to the branches of homoclinic orbits \mbox{near} a heteroclinic cycle connecting a hyperbolic or non-hyperbolic equilibrium and a periodic orbit in a reversible variational system. In this paper, the normal form of a Swift-Hohenberg equation with two different symmetry-breaking terms (non-reversible term and non-k-symmetry term) are investigated by using multiple scale method, and their bifurcation diagrams are initially studied by numerical simulations. Typically, we predict numerically the existence of so-called round-snakes and round-isolas upon particular two symmetric-breaking perturbations.     

2D Burgers equation with large Reynolds number using POD/DEIM and calibration

Model order reduction of the two‐dimensional Burgers equation is investigated. The mathematical formulation of POD/discrete empirical interpolation method (DEIM)‐reduced order model (ROM) is derived based on the Galerkin projection and DEIM from the existing high fidelity‐implicit finite‐difference full model. For validation, we numerically compared the POD ROM, POD/DEIM, and the full model in two cases of Re = 100 and Re = 1000, respectively. We found that the POD/DEIM ROM leads to a speed‐up of CPU time by a factor of O(10). The computational stability of POD/DEIM ROM is maintained by means of a careful selection of POD modes and the DEIM interpolation points. The solution of POD/DEIM in the case of Re = 1000 has an accuracy with error O(10^?3) versus O(10^?4) in the case of Re = 100 when compared with the high fidelity model. For this turbulent flow, a closure model consisting of a Tikhonov regularization is carried out in order to recover the missing information and is developed to account for the small‐scale dissipation effect of the truncated POD modes. It is shown that the computational results of this calibrated ROM exhibit considerable agreement with the high fidelity model, which implies the efficiency of the closure model used. Copyright © 2016 John Wiley & Sons, Ltd.     

High-order rogue waves for the Hirota equation

The Hirota equation is better than the nonlinear Schrödinger equation when approximating deep ocean waves. In this paper, high-order rational solutions for the Hirota equation are constructed based on the parameterized Darboux transformation. Several types of this kind of solutions are classified by their structures.     

On the temperature Dependence of the orientational Order Parameter in the Nematic Phase of Cyanophenyl Behzoates

The orientational order parameters fot two liquid crystal materials, 4-cyanophenyl 4-butylbenzoate and 4-cyanophenyl 4-pentylbenzoate, have been derived by measuring the change in the refractive index as function of temperature. The order parameters are compared with MaierSaupe theory, and the sharpness of the transitions has been shown using the Haller's plot.     

Observation of defect clustering in Gd-doped calcium fluoride

Abstract

Solid solutions Ca_1-xGd_xF_2+x for 3 × 10^?7≤ x ≤10^?1 have been studied by electron paramagnetic resonance (EPR) and ionic thermal currents (ITC). The EPR experiments show the presence of two single-ion sites a cubic and a tetragonal Gd³⁺ center which co-exist with comparable abundances for intermediate impurity concentrations. The cubic center predominates at very low and high concentrations. Seven different relaxation processes have been identified from the ITC spectra and the variation of their intensity vs. x was measured. The absolute concentrations of the cubic and nn Gd³⁺ dipoles were calculated. The scavenging of interstitial fluorines by the neutral clusters explains both the abundance of cubic sites at high concentration and the variety of orientable clusters detected by ITC.