Long Time Behavior of Difference Approximations for the Two-Dimensional Complex Ginzburg–Landau Equation

The finite difference approximations of the dynamical systems governed by two-dimensional complex Ginzburg–Landau equation was considered. For a fully discrete scheme, the solvability, stability and convergence are proved in discrete Sobolev spaces. Furthermore, the existence of global attractors 𝒜 _{h, τ} of the discrete system and the upper semicontinuity dist(𝒜 _{h, τ}, 𝒜) → 0 are obtained.     

On the stability of the spline collocation method for a class of integral equations of the first kind

This paper is concerned with the stability of the spline collocation method for a class of integral equations of the first kind with logarithmic kernels. It is shown that a proper choice of the mesh size can be made in the numerical computation so that one will obtain an optimal rate of convergence for the approximate solutions.     

Periodic finite-genus solutions of the KdV equation are orbitally stable

The stability of periodic solutions of partial differential equations has been an area of increasing interest in the last decade. The KdV equation is known to have large families of periodic solutions that are parameterized by hyperelliptic Riemann surfaces. They are generalizations of the famous multi-soliton solutions. We show that all such periodic solutions are orbitally stable with respect to subharmonic perturbations: perturbations that are periodic with period equal to an integer multiple of the period of the underlying solution.     

The behavior of solutions of second order delay differential equations

In this paper, we study the behavior of solutions of second order delay differential equation

y^″(t)=p₁y^′(t)+p₂y^′(t−τ)+q₁y(t)+q₂y(t−τ),     

Persistence and global stability of positive periodic solutions of three species food chains with omnivory

In this paper, we investigate the existence and global stability of the positive periodic solutions of delayed discrete food chains with omnivory. With the help of continuation theorem in coincidence degree theory and Lyapunov functions, some sufficient conditions are obtained. The results show that, for such a system with omnivory, more conditions are required for the persistence of the positive periodic solutions than that of a linear food chain. On the other hand, omnivory makes no differences on the stability of the solutions.     

Stability for the Multi-Dimensional Borg-Levinson Theorem with Partial Spectral Data

We prove a stability estimate related to the multi-dimensional Borg-Levinson theorem of determining a potential from spectral data: the Dirichlet eigenvalues λ _k and the normal derivatives ?φ _k /?ν of the eigenfunctions on the boundary of a bounded domain. The estimate is of Hölder type, and we allow finitely many eigenvalues and normal derivatives to be unknown. We also show that if the spectral data is known asymptotically only, up to O(k ^?α) with α ? 1, then we still have Hölder stability.     

Explicit and implicit finite difference schemes for fractional Cattaneo equation

In this paper, the numerical solution of fractional (non-integer)-order Cattaneo equation for describing anomalous diffusion has been investigated. Two finite difference schemes namely an explicit predictor–corrector and totally implicit schemes have been developed. In developing each scheme, a separate formulation approach for the governing equations has been considered. The explicit predictor–corrector scheme is the fractional generalization of well-known MacCormack scheme and has been called Generalized MacCormack scheme. This scheme solves two coupled low-order equations and simultaneously computes the flux term with the main variable. Fully implicit scheme however solves a single high-order undecomposed equation. For Generalized MacCormack scheme, stability analysis has been studied through Fourier method. Through a numerical test, the experimental order of convergency of both schemes has been found. Then, the domain of applicability and some numerical properties of each scheme have been discussed.     

Theoretical calculations on the adhesion, stability, electronic structure, and bonding of Fe/WC interface

The adhesion, stability, electronic structure, and bonding of Fe/WC interfaces were studied using first-principles calculations. The preferred stacking sequence is HCP structure that Fe atoms continue the natural stacking sequence of the bulk WC. For two different interfaces with HCP stacking geometry (C-HCP and W-HCP), the work of adhesion of the optimized Fe/WC interfaces are 9.7 J m⁻² for C-HCP and 5.1 J m⁻² for W-HCP, respectively. The effects of the interface on the electronic structures of both the metal Fe and ceramic WC are mainly localized within the first and second layers of the interface. C-HCP interface has strong covalency and W-HCP interface is dominated by metallic bonds. The magnetic moments of Fe atoms at interface are decreased in both interfaces. Calculations of the interfacial energies provide theoretical evidence for the excellent wear behaviors of Fe/WC composites. Besides, the chemical bonding properties for the interfacial atoms are also discussed in this paper based on Milliken population method.     

Cr4+∶YAG被动调Q微晶片激光器重复频率稳定性研究

对连续激光二极管抽运Nd∶YVO4/Cr4+∶YAG被动调Q微晶片激光器输出激光重复频率的稳定性进行了理论和实验研究.结果表明,谐振腔内存在最佳净增益,可以使激光器工作在稳定区.通过优化腔内的净增益,耦合输出镜反射率为85%,饱和吸收体初始透射率为70%,抽运功率从1.05 W到1.20 W的情况下,激光器工作在稳定区.当抽运功率为1.16 W时,获得了重复频率为19.48 kHz,稳定性优于0.68%(RMS)的高重复频率激光输出.进一步分析了抽运功率抖动对输出激光重复频率稳定性的影响.结果表明,激光器进入稳定区之后,抽运功率的抖动是制约输出激光重复频率稳定性进一步提高的最主要因素.针对抽运功率抖动带来的影响,讨论了增益预抽运技术,并比较了其优缺点.     

基于ADS的2.25GHz低噪声放大器的设计与制作

首先介绍用ADS软件仿真设计S波段低噪声放大器的方法,在仿真过程中,采用带封装模型的原理图-版图联合仿真的方法;然后对制作出的放大器在工作频段2.15—2.35GHz内测试,测试结果和电路仿真结果基本一致:输入输出驻波比均小于1.2,增益达到25dB,且带内增益波动为±0.4dB,噪声为0.7dB;最后对放大器进行了低温(液氮环境)测试,结果表明该放大器在低温下也能正常工作。