三倍频Nd∶YAG激光抽运氧气中的受激拉曼和布里渊散射

报道了三倍频脉冲Nd∶YAG激光(355 nm)在两种不同带宽模式下抽运氧气中受激拉曼散射(SRS)和受激布里渊散射(SBS)的实验研究。在宽带(约1 cm-1)抽运模式下,只测到了前向受激拉曼散射,而没有观察到后向散射,其一级和二级斯托克斯最大能量转换效率可达22%和8%。在窄带(约0.003 cm-1)模式下,前向、后向受激拉曼散射和受激布里渊散射都测量到了,但大部分抽运能量都转换到受激布里渊散射,其转换效率可达67%。测量了两种带宽模式下各散射组分在它们最佳转换时的波形;窄带情况下后向受激拉曼散射和受激布里渊散射的脉宽分别可压窄至1.5 ns和2.3 ns,不到抽运脉宽的三分之一,使得受激布里渊散射峰值功率可大大高于抽运功率。对氧气中前向、后向受激拉曼散射和受激布里渊散射之间的竞争进行了讨论。     

确定Lotka-Volterra生态系统模型高精度参数的研究

研究确定Lotka-Volterra生态系统模型的高精度参数估计问题.利用周期性,先对测量数据进行预处理;然后用三种不同的方法构造了误差函数,进行非线性最小二乘法参数估计;再用计算机仿真对其进行验证.结果表明该方法能够有效地解决高精度参数估计中消除测量数据误差的问题.     

非线性Schroedinger方程组的精确解组

运用Maple语言程序，在没有假设的条件下，得到了具有耦合特性的非线性Schrfidinger方程组的行波精确解组及其约束条件方程，它们的表达式涵盖了所有的耦合解组与非耦合解组，具有任意性。耦合解组的算例函数及其特性分析，解释了α螺旋蛋白质螺旋链运动模型的行波孤立子解的耦合效应，揭示了增加、稳定和控制蛋白质活性和功能的方向。文章的研究方法，为求解耦合的非线性微分方程组的行波精确解组探索了蹊径。     

超线性与二次收敛序列线性方程组算法

本文,在无严格互补条件下,对非线性不等式约束最优化问题提出了一个新的序列线性方程组(简称SSLE)算法．算法有两个重要特征:首先,每次迭代,只须求解一个线性方程组或一个广义梯度投影阵,且线性方程组可以无解．其次,初始点可以任意选取．在无严格互补条件下,算法仍有全局收敛性、强收敛性、超线性收敛性及二次收敛性．文章的最后,还对算法进行了初步的数值实验．     

(1+2)维强非局域空间光孤子的相互作用

强非局域空间光孤子是指满足强非局域条件的空间孤子.在Snyder和Mitchell工作的基础上，获得了不共面对称斜入射(1+2)维强非局域空间光孤子对相互作用问题的精确解析解.结果表明，光束初始中心距离在大范围尺度内变化时，双孤子的演化都能形成类似DNA结构的稳定缠绕，这种稳定缠绕的结构与双孤子的初始相位差无关；光束中心在横截面上的投影轨迹一般是一个斜椭圆，通过改变两光束的初始中心距离和倾斜度可以控制该椭圆轨迹的变化.指出了利用(1+2)维强非局域空间光孤子的相互作用特性实现平面全光开关和全光互联的潜在可能性. 关键词： (1+2)维非局域非线性介质 空间光孤子的相互作用 全光开关 全光互联     

Algorithms for separable nonlinear least squares with application to modelling time-resolved spectra

The multiexponential analysis problem of fitting kinetic models to time-resolved spectra is often solved using gradient-based algorithms that treat the spectral parameters as conditionally linear. We make a comparison of the two most-applied such algorithms, alternating least squares and variable projection. A numerical study examines computational efficiency and linear approximation standard error estimates. A new derivation of the Fisher information matrix under the full Golub-Pereyra gradient allows a numerical comparison of parameter precision under variable projection variants. Under the criteria of efficiency, quality of standard error estimates and parameter precision, we conclude that the Kaufman variable projection technique performs well, while techniques based on alternating least squares have significant disadvantages for application in the problem domain.     

Interferometric Hetero-Detector Phase Measurement

We present a new method for the measurement of the phase of ultrashort optical pulses with high spectral resolution. This employs an interferometer with a monochromator in one arm. Two detectors operating in single photon and two-photon absorption regimes monitor the output from the interferometer. Comparison of the signals from the two detectors gives a measurement of the phase of the light pulse. The principles underpinning this technique are discussed and the experimental application to picosecond pulses is demonstrated.     

Inner solvers for interior point methods for large scale nonlinear programming

This paper deals with the solution of nonlinear programming problems arising from elliptic control problems by an interior point scheme. At each step of the scheme, we have to solve a large scale symmetric and indefinite system; inner iterative solvers, with an adaptive stopping rule, can be used in order to avoid unnecessary inner iterations, especially when the current outer iterate is far from the solution. In this work, we analyse the method of multipliers and the preconditioned conjugate gradient method as inner solvers for interior point schemes. We discuss the convergence of the whole approach, the implementation details and report the results of numerical experimentation on a set of large scale test problems arising from the discretization of elliptic control problems. A comparison with other interior point codes is also reported. This research was supported by the Italian Ministry for Education, University and Research (MIUR) projects: FIRB Project: “Parallel Nonlinear Numerical Optimization PN ² O” (grant n. RBAU01JYPN, ) and COFIN/PRIN04 Project “Numerical Methods and Mathematical Software for Applications” (grant n. 2004012559, ).