Three-Wave Resonant Interaction in Optical Fibres on a Continuous-Wave Background

We predict that a three-wave resonant interaction (TWRI) for the excitations created from a continuous-wave background is possible in nonlinear optical fibres with a centro-symmetry. We show that in normal dispersion regime and near the zero-dispersion point of a single-mode optical fibre, the phase-matching condition for the TWRI can be satisfied by suitably choosing the wavevectors and frequencies of the exciting waves. The nonlinear envelope equations for the TWRI are derived by using a method of multiple-scales, and their explicit solutions for sum- and difference-frequency mixing are provided and discussed.     

Resonant Voice: Spectral and Nasendoscopic Analysis

Although resonant voice therapy is a widely used therapeutic approach, little is known about what characterizes resonant voice and how it is physiologically produced. The purpose of this study was to test the hypothesis that resonant voice is produced by narrowing the laryngeal vestibule and is characterized by first formant tuning and more ample harmonics. Videonasendoscopic recordings of the laryngeal vestibule were made during nonresonant and resonant productions of /i/ in six subjects. Spectrums of the two voice types were also obtained. Spectral analysis showed that first formant tuning was exhibited during resonant voice productions and that the degree of harmonic enhancement in the range of 2.0 to 3.5 kHz was related to voice quality: nonresonant voice had the least amount of energy in this range, whereas a resonant-relaxed voice had more energy, and a resonant-bright voice had the greatest amount of energy. Visual-perceptual judgments of the videoendoscopic data indicated that laryngeal vestibule constriction was not consistently associated with resonant voice production.     

光学Maxwell-Bloch方程的数值算法研究及其应用

建立了高准确度快速求解均匀展宽二能级体系光学Maxwell-Bloch耦合方程的数值算法.通过与特定条件得到的解析解的比较,验证了算法所具有的高收敛性和稳定性,并可保持算法的误差阶数,因此算法是可靠并实用的.应用该算法数值求解了一般条件下的MB方程,并由计算结果分析了失谐量、弛豫时间、初始光强对光脉冲在介质中的传播及对Bloch矢量演化的影响.所建立的数值算法对MB方程以及修正的这类偏微分方程组具有普适性.     

辐射扩散计算方法若干研究进展

辐射流体力学研究辐射的传输对流体运动的影响,并在此条件下研究流体的运动规律.实际应用问题中辐射流体力学所描述的是非常复杂的物理过程,数值模拟是主要的研究手段之一.模拟通常采用流体计算和辐射计算分裂求解的方法.讨论求解辐射扩散方程时迫切需要解决的一些计算方法问题,包括大变形网格上扩散计算格式与非线性迭代方法,并简要介绍部分研究进展.     

自相似Euler方程的数值方法

Euler方程某些问题的解具有自相似特点，可以使用更准确的方法求解.提出了两种数值方法，分别称为自相似和准自相似方法，新方法可以使用现有守恒律方程的数值格式，无须设计特殊方法.对一维激波管问题、二维Riemann问题、激波反射以及激波折射问题进行了数值计算.对自相似Euler方程，一维计算结果显示数值解基本等同于精确解，二维结果也比现有文献计算的结果有更高的分辨率.对准自相似Euler方程，新方法可以求解不具有自相似性但接近自相似的问题，并在计算时间足够长时可以取得自相似Euler方程的效果.数值求解自相似Euler方程对自相似问题的研究，高分辨率、高精度格式的设计乃至Euler方程的精确解都有重要启示.      

Difference-Frequency Generation of THz Radiation via Parametric Three-Wave Interaction in CdTe and ZnTe Crystals

Difference-frequency generation of terahertz (THz) radiation in a collinear single-crystal scheme with distributed feedback implemented by means of parametric interaction of counterpropagating optical waves in a periodically inhomogeneous medium exhibiting quadratic nonlinearity is investigated. Using ZnTe and CdTe crystals optically pumped at λ = 0.77 and 1.06 μm, respectively, as an example, the possibility of obtaining parametric generation of THz radiation with an optical-to-THz conversion efficiency exceeding 10^–3 (with an extremely narrow line of oscillation of less than 4 GHz for ZnTe and less than 9 GHz for CdTe at 1 THz) is demonstrated in the undepleted-pump-intensity approximation. The obtained results can be used for construction of narrow-band lasers in the THz frequency range with an output power (in the quasicw regime of oscillation) of about 10⁵ W/cm².     

铜(Ⅱ)配合物与DNA作用的光谱法研究

采用紫外光谱和荧光光谱研究了配离子[Cu(A)₂]2＋(其中A=邻菲络啉(phen),联吡啶(bpy),乙二胺(en))与小牛胸腺DNA的相互作用。实验发现配合物的存在使DNA碱变性的pH增大,变性后增色效应减小。EB-DNA体系的荧光强度随[Cu(phen)₂]2＋的加入迅速减弱。在DNA存在下,配离子被猝灭剂[Fe(CN)₆]4-的发光猝灭程度减小。进一步研究了配体分子平面的大小对配合物与DNA作用的影响。结果表明,铜配合物与DNA之间发生了插入作用,且该作用随配体芳环平面的减小而减弱, 即[Cu(phen)₂]2＋＞[Cu(bpy)₂]2＋＞[Cu(en)₂]2＋。     

光谱法研究芹菜素与牛血清白蛋白的相互作用

在模拟人体的生理条件下（pH=7.40,Tris-HCl）,采用荧光光谱研究了牛血清白蛋白与芹菜素的相互作用。研究结果表明牛血清白蛋白与较小浓度的芹菜素间的相互作用属于静态猝灭过程;随着芹菜素浓度的增加,与牛血清白蛋白间的相互作用为静态猝灭和动态猝灭共同作用,但仍以静态猝灭为主。进一步求出了在287K和310K温度条件下静态猝灭的猝灭常数,由求得的热力学参数,证明了芹菜素与牛血清白蛋白之间主要依靠静电引力结合,采用同步荧光光谱技术探讨了芹菜素对牛血清白蛋白构象的影响。     

丁二酰化壳寡糖稀土配合物与鲱鱼精DNA相互作用的电化学及光谱学研究

采用紫外光谱和循环伏安法,研究了丁二酰化壳寡糖稀土配合物（BCS-La、BCS-Nd）与鲱鱼精DNA之间的作用方式。BCS-La、BCS-Nd的存在导致Fe（CN）₆^3-/4-探针分子峰电流下降,式量电位正移,表明BCS-La、BCS-Nd和探针分子与DNA之间存在竞争性作用;BCS-La和BCS-Nd分子都是通过插入方式与DNA相互作用。在一定的扫描速率范围内（0.01~0.2 V/s）,在BCS-La或BCS-Nd参与的条件下,Fe（CN）₆^3-/4-在Au/DNA电极上的反应受吸附控制。BCS-La和BCS-Nd分别使得鲱鱼精DNA的特征峰产生明显的减色效应,最大吸收峰峰位红移,进一步表明BCS-La和BCS-Nd分别以插入方式与鲱鱼精DNA发生相互作用,导 致DNA分子的构象变化。BCS-La与DNA的结合比为：n（BCS-La）：n（DNA）=2：1;n（BCS-Nd）：n（DNA）=6：1。     

Convergence Analysis of the Spectral Methods for Weakly Singular Volterra Integro-Differential Equations with Smooth Solutions

The theory of a class of spectral methods is extended to Volterra integro-differential equations which contain a weakly singular kernel $(t-s)^{-\mu}$ with $0<\mu<1$. In this work, we consider the case when the underlying solutions of weakly singular Volterra integro-differential equations are sufficiently smooth. We provide a rigorous error analysis for the spectral methods, which shows that both the errors of approximate solutions and the errors of approximate derivatives of the solutions decay exponentially in $L^\infty$-norm and weighted $L^2$-norm. The numerical examples are given to illustrate the theoretical results.     

Numerical Analysis and Comparison of Four Stabilized Finite Element Methods for the Steady Micropolar Equations

In this paper, four stabilized methods based on the lowest equal-order finite element pair for the steady micropolar Navier–Stokes equations (MNSE) are presented, which are penalty, regular, multiscale enrichment, and local Gauss integration methods. A priori properties, existence, uniqueness, stability, and error estimation based on Fem approximation of all the methods are proven for the physical variables. Finally, some numerical examples are displayed to show the numerical characteristics of these methods.     

Hyperelliptic Theta-Functions and Spectral Methods: KdV and KP Solutions

This is the second in a series of papers on the numerical treatment of hyperelliptic theta-functions with spectral methods. A code for the numerical evaluation of solutions to the Ernst equation on hyperelliptic surfaces of genus 2 is extended to arbitrary genus and general position of the branch points. The use of spectral approximations allows for an efficient calculation of all characteristic quantities of the Riemann surface with high precision even in almost degenerate situations as in the solitonic limit where the branch points coincide pairwise. As an example we consider hyperelliptic solutions to the Kadomtsev–Petviashvili and the Korteweg–de Vries equations. Tests of the numerics using identities for periods on the Riemann surface and the differential equations are performed. It is shown that an accuracy of the order of machine precision can be achieved.     

Pfaffian Solutions and Resonant Interaction Properties of a Coupled BKP Lattice

In this paper, we give a coupled lattice equation with the help of Hirota operators, which comes from a special BKP lattice. Two-soliton and three-soliton solutions to the coupled system are constructed. Furthermore, resonant interaction of the two-soliton solution is analyzed in detail. Under some special resonant condition, it is shown that low soliton can propagate faster than high one. Finally, the N-soliton solution is presented in the Pfaffian form.     

Pfaffian Solutions and Resonant Interaction Properties of a Coupled BKP Lattice

In this paper, we give a coupled lattice equation with the help of Hirota operators, which comes from a special BKP lattice. Two-soliton and three-soliton solutions to the coupled system are constructed. Furthermore,resonant interaction of the two-soliton solution is analyzed in detail. Under some special resonant condition, it is shown that low soliton can propagate faster than high one. Finally, the N-soliton solution is presented in the Pfaffian form.     

Spectral Resolution and Inversion of the Bloch Equations with Relaxation

It is demonstrated that the linear Bloch equations, describing near-resonant excitation of two-level media with relaxation, can be resolved into a 3n-dimensional nonlinear system associated with a special spectral problem, generalizing the classical Zakharov–Shabat spectral problem. Remarkably, for n = 1 it is the well-known Lorenz system, and for n > 1 several such systems coupled with each other in a manner dependant on the excitation pulse. The unstable manifold of a saddle equilibrium point in this ensemble characterizes possible excitations of the spins from the initial equilibrium state. This enables us to get a straightforward geometric extension of the inverse scattering method to the damped Bloch equations and hence invert them, i.e., design frequency selective pulses automatically compensated for the effect of relaxation. The latter are essential, for example, in nuclear magnetic resonance and extreme nonlinear optics.      

一类非线性发展方程的特征中心差分法

给出一类非线性发展方程的特征中心差分法,分别得到非规则网格上的位移u、速度u_t及其对空间变量x的一阶导数项的差分解和误差估计.所讨论方法的计算量与基于线性插值的特征差分法相当,其近似解与基于二次插值的特征差分法的近似解具有相同阶的误差估计,u,u_t对空间变量x的一阶导数近似均具有超收敛误差估计.数值试验说明了该方法的可行性和有效性.