From crystal steps to continuum laws: Behavior near large facets in one dimension

The passage from discrete schemes for surface line defects (steps) to nonlinear macroscopic laws for crystals is studied via formal asymptotics in one space dimension. Our goal is to illustrate by explicit computations the emergence from step motion laws of continuum-scale power series expansions for the slope near the edges of large, flat surface regions (facets). We consider surface diffusion kinetics via the Burton, Cabrera and Frank (BCF) model by which adsorbed atoms diffuse on terraces and attach-detach at steps. Nearest-neighbor step interactions are included. The setting is a monotone train of N steps separating two semi-infinite facets at fixed heights. We show how boundary conditions for the continuum slope and flux, and expansions in the height variable near facets, may emerge from the algebraic structure of discrete schemes as N→∞. Our technique relies on the use of self-similar discrete slopes, conversion of discrete schemes to sum equations, and their reduction to nonlinear integral equations for the continuum-scale slope. Approximate solutions to the continuum equations near facet edges are constructed formally by direct iterations. For elastic-dipole and multipole step interactions, the continuum slope is found in agreement with a previous hypothesis of ‘local equilibrium’.     

Synthesis, growth, spectral, thermal and photoluminescence properties of a new semiorganic NLO crystal—Thiosemicarbazide lithium chloride [TSLC]

Thiosemicarbazide lithium chloride [TSLC] a new semiorganic nonlinear optical crystal has been synthesized. Single crystals by TSLC have been grown by slow evaporation solution growth technique at room temperature. Chemical composition of the synthesized material was confirmed by elemental analysis. Powder X-ray diffraction (XRD) pattern of the grown crystal has been studied. Functional groups present in the materials were identified by FT IR spectral analysis ranging between 4000 and 450 cm⁻¹. The optical transmission was studied through UV-vis spectrophotometer. Thermal analysis is carried out on the crystal and inferred to be stable at 176 °C. The second harmonic generation (SHG) of the TSLC crystal was confirmed using Nd:YAG laser and also fluorescence spectral analysis is carried out for the TSLC crystal.     

Optical spectroscopy, 1.5 μm emission and up-conversion properties of Er-doped Li3Ba2Gd3(MoO4)8 crystal

Er³⁺:Li₃Ba₂Gd₃(MoO₄)₈ crystal has been grown from a melt of Li₂MoO₄ by the top seeded solution growth method (TSSG). The polarized spectral properties of Er³⁺:Li₃Ba₂Gd₃(MoO₄)₈ crystal were investigated and the spectroscopic parameters were calculated and analyzed based on the Judd-Ofelt (J-O) theory. The emission cross-sections were calculated by the Fuchtbauer-Ladenburg (F-L) equation and the peak values of the emission band at 1535 nm were 9.7×10⁻²¹, 7.9×10⁻²¹ and 8.4×10⁻²¹ cm² for E∥b, E∥D1 and E∥D2, respectively. Under 977 nm excitation five up-conversion fluorescence bands around 490, 530, 550, 660 and 800 nm were observed, and the possible up-conversion mechanisms were proposed.     

Schrödinger Operators with Random Sparse Potentials. Existence of Wave Operators

We consider the connection problem for the Heun differential equation, which is a Fuchsian differential equation that has four regular singular points. We consider the case in which the parameters in this equation satisfy a certain set of conditions coming from the eigenvalue problem of the non-commutative harmonic oscillators. As an application, we describe eigenvalues with multiplicities greater than 1 and the corresponding odd eigenfunctions of the non-commutative harmonic oscillators. The existence of a rational or a certain algebraic solution of the Heun equation implies that the corresponding eigenvalues has multiplicities greater than 1.The research of the author is supported in part by a Grant-in-Aid for Scientific Research (B) (No. 15340005) from the Ministry of Education, Culture, Sports, Science and Technology.Mathematics Subject classifications (2000). primary, 34M35, secondary, 33E20.This revised version was published online in March 2005 with corrections to the cover date.     

驻波腔内电子运动过程的解析分析

考虑了加速电场的高次谐波的影响，解析地分析了电子在驻波腔内的运动过程，给出了电场分布，与数值模拟计算的电场分布比较吻合。讨论了高次谐波对电子束横向运动的影响，利用此解析解可选择高亮度注入器腔的最优电场分布。并得出射频驻波腔内电子束在β趋于１时射频场效应趋于零的结论。     

四模场中单原子系统的新算符求解方法

提出处理腔场与原子、腔场与腔场等系统的较为一般算符方法。基于此方法,通过构造四对时间依赖的产生和湮灭算符,简捷地求解四模腔场或四腔场与二能级原子非共振相互作用系统,得到其本征态、本征值和一般态矢。特别地,在四模场或四腔场和原子的初态分别为真空态和一般叠加态时,给出四场模平均光子数和原子布居数反转的时间演化。该新方法可应用于其它一些量子系统。     

Phase diagram of aqueous solution at high pressure and low temperature

Abstract

This paper presents a constant mass high pressure isothermal calorimeter and describes the range of applications that this type of equipment can deal with. As an example, the thermophysical properties of an aqueous solution of MgSO₄ at low temperature and at high pressure have been investigated. The main results showed that the phase change heat of the solution decreased with increasing pressure and the phase change temperature of the eutectic concentration was depressed under high pressure. Those changes could be related to the MgSO₄ solubility and to water latent heat changes.     

Magneto-Galvanic Resonances in Hollow Cathode Discharge Lamps

The galvanic behavior of a hollow cathode discharge versus an external weak magnetic field is investigated. The application of this field leads to disordering of the self-aligned states, which is detected as a resonance in the discharge current, named the magneto-galvanic signal. A correlation magneto-galvanic signal–operating voltage-current point is established and attributed to Penning ionization. The contribution of the metastable Ne I 1 s₅ to the magneto-galvanic resonance is also verified.     

Numerical Complexiton Solutions of Complex KdV Equation

In this paper, we directly extend the applications of the Adomian decomposition method to investigate the complex KdV equation. By choosing different forms of wave functions as the initial values, three new types of realistic numerical solutions： numerical positon, negaton solution, and particularly the numerical analytical complexiton solution are obtained, which can rapidly converge to the exact ones obtained by Lou et al. Numerical simulation figures are used to illustrate the efficiency and accuracy of the proposed method.     

差分方程解对初值连续性问题

本文讨论了差分方程的解对初值的连续性问题，对较一般的方程给出了保证解对初值连续的充分条件，对线性方程（组）利用系数矩阵的特征值给出其解对初值连续的条件．