Large time behavior of solutions for critical and subcritical complex Ginzburg-Landau equations in H<Superscript>1</Superscript>

Considering the Cauchy problem for the critical complex Ginzburg-Landau equation in H¹(Rⁿ), we shall show the asymptotic behavior for its solutions in C(0, ∖;H¹(Rⁿ)) ∩ L²(0, ∖;H^1,2n/(n-2)(R²)), n≥3. Analogous results also hold in the case that the nonlinearity has the subcritical power in H¹(Rⁿ), n≥1. Dedicated to Professor Zhou Yulin for his 80th birthday.     

成形过程数值模拟的非增量时一空算法*

本文针对计及几何、材料、接触摩擦等耦合作用的高度非线性的加工成形过程数值模拟和计算分析工作,建议了非增量时-空求解算法。本文的非增量算法,系在整个时间域和空间域上迭代求解,与常见的Newton-Raphson算法明显不同。本文所附算例,进一步说明了本算法的正确性和可行性。     

Finite difference scheme for time-space fractional diffusion equation with fractional boundary conditions

In this paper, the finite difference scheme is developed for the time-space fractional diffusion equation with Dirichlet and fractional boundary conditions. The time and space fractional derivatives are considered in the senses of Caputo and Riemann-Liouville, respectively. The stability and convergence of the proposed numerical scheme are strictly proved, and the convergence order is O(τ^2−α+h²). Numerical experiments are performed to confirm the accuracy and efficiency of our scheme.     

基于时空变换恒定磁化的起始磁化曲线推算方法

起始磁化曲线作为铁磁材料磁学特性的重要表征, 研究其获取方法具有重要意义. 现有方法采用随时间变化磁场作为激励磁场, 通过改变激励磁场大小, 逐步改变试件内的磁场及磁感应强度并进行测量以得到起始磁化曲线, 效率较低, 准备繁琐. 为此, 本文从基本的磁学物理定理出发, 提出一种基于时空变换的起始磁化曲线推算方法. 该方法以细长棒状试件或环形试件作为被测试件; 采用恒定磁化在被测试件内产生空间变化磁场作为激励磁场; 通过测量试件表面的磁场值来推算试件内磁场值, 从而获取铁磁材料起始磁化曲线. 直流线圈恒定磁化环形和棒状试件仿真实验验证了该方法的理论正确性. 进一步地, 考虑实际应用限制因素的推算结果表明了该方法在实际应用中是可行的, 可为探索新的起始磁化曲线测量方法提供理论指导.     

Design of a Label Recognition Filter for Crosstalk Suppression in a Label Recognition Unit using Optical Correlation Assuming the Assistance of Optical Time-Gating

To suppress crosstalk caused by matched filtering in label recognition based on optical correlation, we propose the novel design method of a label recognition filter to improve the discrimination performance. Assuming the assistance of optical time-gating, the label recognition filter is designed by a technique of a multiple-object discriminant filter (MODF) so that the crosstalk can be suppressed only at the center of correlation signals. This method can reduce the requirement for the performance of an optical thresholder. Simulation results show that the designed label recognition filter can successfully suppress the crosstalk.     

双掺杂LiNbO3:Fe:Mn体全息光栅的时空衍射特性

通过联立求解两中心带输运物质方程和双光束耦合波方程，建立了研究双掺杂LiNbO_{3< /sub>:Fe:Mn晶体采用双色光记录光折变体全息的时空特性的动力学模型.数值计算表明，该动态体全息光栅的时空衍射特性与晶体中的折射率光栅相对于干涉场的空间相移有关，该空间相移的取值范围为(-π，π)，当空间相移的符号发生变化时，双光束之间的能量耦合方向也相应地发生反转.给出了晶体内的等相位线和光强的重新分布.}     

Large time behavior of solutions for critical and subcritical complex Ginzburg-Landau equations in H~1

Considering the Cauchy problem for the critical complex Ginzburg-Landau equation in H1 (Kn), we shall show the asymptotic behavior for its solutions inAnalogous results also hold in the case that the nonlinearity has the subcritical power in H1(Rn), n≥1.     

时间域有限元法

叙述时间域有限元法在国内外的进展，其中包括协调的、不协调的时间有限元法和时空有限元法，对其中的典型研究成果给出了简要介绍，从而指出这一领域深入研究的必要性．最后简要展望了时间域有限元法的发展前景．     

The Wiener Sequential Testing Problem with Finite Horizon

We present a solution of the Bayesian problem of sequential testing of two simple hypotheses about the mean value of an observed Wiener process on the time interval with finite horizon. The method of proof is based on reducing the initial optimal stopping problem to a parabolic free-boundary problem where the continuation region is determined by two continuous curved boundaries. By means of the change-of-variable formula containing the local time of a diffusion process on curves we show that the optimal boundaries can be characterized as a unique solution of the coupled system of two nonlinear integral equations.     

Novel exact solutions of coupled nonlinear Schrōdinger equations with time-space modulation

We construct various novel exact solutions of two coupled dynamical nonlinear Schrōdinger equations. Based on the similarity transformation, we reduce the coupled nonlinear Schrōdinger equations with time-and space-dependent potentials, nonlinearities, and gain or loss to the coupled dynamical nonlinear Schrrdinger equations. Some special types of non-travelling wave solutions, such as periodic, resonant, and quasiperiodically oscillating solitons, are used to exhibit the wave propagations by choosing some arbitrary functions. Our results show that the number of the localized wave of one component is always twice that of the other one. In addition, the stability analysis of the solutions is discussed numerically.