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Yongshuai Zhang Xiangxing Tao Tengteng Yao Jingsong He 《Studies in Applied Mathematics》2020,145(4):812-827
Based on the inverse scattering method, the formulae of one higher-order pole solitons and multiple higher-order poles solitons of the nonlinear Schrödinger equation (NLS) equation are obtained. Their denominators are expressed as , where is a matrix frequently constructed for solving the Riemann-Hilbert problem, and the asterisk denotes complex conjugate. We take two methods for proving is invertible. The first one shows matrix is equivalent to a self-adjoint Hankel matrix , proving . The second one considers the block-matrix form of , proving . In addition, we prove that the dimension of is equivalent to the sum of the orders of pole points of the transmission coefficient and its diagonal entries compose a set of basis. 相似文献
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高速激光通信中接收机与光斑中心很难处于精对准状态,导致水下光通信链路难以稳定建立.首先采用蒙特卡洛仿真统计法分析激光光子在海水中传输的接收光强分布规律,再通过实验对接收端的光斑图像进行采样分析,利用曲线拟合得到接收器位置与接收光强的关系.仿真与实验结果表明:光束经过25 m的水下传输,接收光强分布仍近似为高斯分布.采用非线性估计算法(扩展卡尔曼滤波)与基本状态控制反馈理论,根据接收光强度估计接收器当前位置与最大光强处的距离,通过反馈算法实现接收端与光斑中心的主动跟踪对准.算法仿真结果显示,接收端对准误差在2 mm以下,稳定后接收效率超过98%. 相似文献
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提出了一种基于像差特征分析的变焦系统共轴性装调方法。针对某型20倍变焦光学系统的装调,在分析变焦光学系统装调要求的基础上,通过采用光学定心加工技术,提高变焦系统各镜组内光学元件的同轴度;采用Zygo干涉仪,检测变焦系统在长短焦位置的像差特性分布;借助CodeV软件仿真计算各光学元件在系统中的公差灵敏度分布,并确定产生像差影响的敏感光学元件;在中心偏测量仪上,完成最终光学系统像质的调整。此外,还设计了一种变焦光学系统各动组间同轴度调试装置,对变焦相机主镜筒机械内孔轴线与直线导轨的平行性进行了精确测量,保证了动组组元光轴的同轴精度。装调结果表明:变焦系统成像质量有明显改善,像面一致性得到保证,长短焦轴上传递函数值分别优于技术要求值0.45和0.55,长短焦轴外0.7视场传递函数值优于0.25和0.35,实现了高精度装调,验证了该方法的可靠性。 相似文献
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A. E. ABOUELREGAL 《应用数学和力学(英文版)》2020,41(12):1805-1820
The bending of the Euler-Bernoulli micro-beam has been extensively modeled based on the modified couple stress (MCS) theory. Although many models have been incorporated into the literature, there is still room for introducing an improved model in this context. In this work, we investigate the thermoelastic vibration of a micro-beam exposed to a varying temperature due to the application of the initial stress employing the MCS theory and generalized thermoelasticity. The MCS theory is used to investigate the material length scale effects. Using the Laplace transform, the temperature, deflection, displacement, flexure moment, and stress field variables of the micro-beam are derived. The effects of the temperature pulse and couple stress on the field distributions of the micro-beam are obtained numerically and graphically introduced. The numerical results indicate that the temperature pulse and couple stress have a significant effect on all field variables. 相似文献
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《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2020,37(5):1185-1209
We establish the existence of solutions of the Cauchy problem for a higher-order semilinear parabolic equation by introducing a new majorizing kernel. We also study necessary conditions on the initial data for the existence of local-in-time solutions and identify the strongest singularity of the initial data for the solvability of the Cauchy problem. 相似文献
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Shie-Chang Jeng 《Liquid crystals》2020,47(8):1223-1231
ABSTRACT The Tamm-plasmon-polariton (TPP) occurs at the interface between a metallic film and the photonic-crystal (PC) substrate. Unlike conventional surface-plasmon-polariton (SPP), TPP can be directly excited by both the transverse electric (TE) and transverse magnetic (TM) electromagnetic waves without using additional coupling optics. The fact that the optical functionality of most plasmonics devices is determined after fabrication limits their applications. Tunable SPP devices by applying liquid crystals (LCs) have been widely demonstrated due to their large birefringence and easy controllability via external stimuli. However, actively tuning TPP is difficult because the localised electric field is between the metallic film and PC substrate, the change of refractive index above the metallic film has only small influences on TPP. This article is intended to briefly review recent progress towards using LCs for actively tuning TPP devices. Not only TPP devices can gain benefits from LCs, we will also discuss the applications of TPP for measuring the anisotropy of the alignment films of LC devices. The sensitivity of the proposed scheme will be discussed. 相似文献
10.
Dr. Si-Yong Qin Yan Jiang Dr. Han Sun Han Liu Prof. Ai-Qing Zhang Prof. Xinxiang Lei 《Angewandte Chemie (Weinheim an der Bergstrasse, Germany)》2020,132(39):17245-17251
Residual dipolar coupling (RDC), a robust anisotropic NMR parameter for structural elucidation of organic molecules, is only accessible in an anisotropic environment. Herein, we introduce a novel alignment medium based on the molecular self-assembly of oligopeptide amphiphile (OPA). This medium is compatible with different intermediate and polar solvent systems, such as CD3OD, [D6]DMSO, and D2O. The preparation of the OPA-based medium is simple and rapid, while only very weak background signals were observed from OPAs. Furthermore, we show that the purity of OPA has only a minor influence on the quality of the RDC data. These advantages allow RDC measurements of organic molecules with different polarities and solubilities with high efficiency and accuracy. 相似文献