含高阶非线性效应的薛定谔方程的精确解研究

利用孤子理论,研究了含三次和五次非线性项的非线性薛定谔方程,在参数取不同值时得到了方程的新型亮孤子解、新型暗孤子解和新的三角函数周期解。     

A fast directional algorithm for high-frequency electromagnetic scattering

This paper is concerned with the fast solution of high-frequency electromagnetic scattering problems using the boundary integral formulation. We extend the O(N log N) directional multilevel algorithm previously proposed for the acoustic scattering case to the vector electromagnetic case. We also detail how to incorporate the curl operator of the magnetic field integral equation into the algorithm. When combined with a standard iterative method, this results in an almost linear complexity solver for the combined field integral equations. In addition, the butterfly algorithm is utilized to compute the far field pattern and radar cross section with O(N log N) complexity.     

Femtosecond stimulated Raman spectroscopy

Advances in the field of Femtosecond Stimulated Raman Spectroscopy (FSRS), a new time‐resolved structural technique that provides complete vibrational spectra on the ultrafast timescale, are reviewed. When coupled with a femtosecond optical trigger, the time evolution of a reacting species can be monitored with unprecedented <25 femtosecond temporal and 5 cm^‐1 spectral resolution. New technological and theoretical advances including the development of tunable FSRS and a background‐free FSRS format are discussed. The most recent experimental studies focus on ultrafast reaction dynamics in electronically excited states: isomerization in cyanobacterial phytochrome, ultrafast spin flipping in a solar cell sensitizer, and excited state proton transfer in green fluorescent protein. The use of FSRS to directly map multidimensional reactive potential energy surfaces and to probe the mechanism of reactive internal conversion is prospectively discussed.     

Moment equations for a spatially extended system of two competing species

The dynamics of a spatially extended system of two competing species in the presence of two noise sources is studied. A correlated dichotomous noise acts on the interaction parameter and a multiplicative white noise affects directly the dynamics of the two species. To describe the spatial distribution of the species we use a model based on Lotka-Volterra (LV) equations. By writing them in a mean field form, the corresponding moment equations for the species concentrations are obtained in Gaussian approximation. In this formalism the system dynamics is analyzed for different values of the multiplicative noise intensity. Finally by comparing these results with those obtained by direct simulations of the time discrete version of LV equations, that is coupled map lattice (CML) model, we conclude that the anticorrelated oscillations of the species densities are strictly related to non-overlapping spatial patterns.     

Exact solutions for nonlinear Schr?dinger equation in phase space: applications to Bose－Einstein condensate

The stationary-state nonlinear Schr?dinger equation, which models the dilute-gas Bose－Einstein condensate, is introduced within the framework of the quantum phase-space representation established by Torres-Vega and Frederick. The exact solutions of equation are obtained in the phase space, by means of the wave-mechanics method. The eigenfunctions in position and momentum spaces are obtained through the ‘Fourier-like' projection transformation from the phase space eigenfunctions. The eigenfunction with a hypersecant part is discussed as an example.     

Upshot of Chemical Species and Nonlinear Thermal Radiation on Oldroyd-B Nanofluid Flow Past a Bi-directional Stretched Surface with Heat Generation/Absorption ina Porous Media

A three-dimensional mathematical model is developed to examine the flow of nonlinear thermal radiation Oldroyd-B nanofluid past a bidirectional linearly stretched surface in a porous medium. The flow is induced by temperature dependent thermal conductivity, chemical reaction and convective heat and mass conditions. Novel characteristics of Brownian motion and thermophoresis are accompanied by magnetohydrodynamic and heat generation/absorption. Self-similar transformations are employed to convert the system of nonlinear partial differential equations to a system of ordinary differential equations with high nonlinearity and are solved by strong analytic technique named as Homotopy Analysis method (HAM). Effects of varied arising parameters on involved distributions are reflected through graphical illustrations. From this study, it is perceived that strong magnetic field hinders the fluid's motion and leads to rise in temperature that eventually lowers heat transfer rate from the surface. Further, decrease in heat transfer rate is also observed for enhanced values of thermal radiation parameter. To validate our results, a comparison with already published paper in limiting case is also given and results are found in excellent oncurrence; hence reliable results are being presented.     

用于下一代传感和光源的新型材料、光纤及器件

制造技术与复杂模型、设计工具的进步使微纳结构光学器件的实现成为可能。微纳结构光学器件可用于导光与光的相互作用,液态或气态新型光源和传感器件。IPAS致力于新型光学材料研究与开发,将玻璃工艺和光纤开发有机结合,重点研究微纳结构光纤,光纤表面功能处理和器件开发。介绍了IPAS的研究实力和近年的发展概况,其中包括中红外光学材料、纳米粒子嵌入玻璃材料、新型化学和生物传感器(适用于超低量样本及/或体内样本)、激光器件,以及用于光数据处理的新型高非线性光纤。     

氧化石墨烯/壳聚糖复合薄膜材料的制备及其非线性光限幅效应的研究

石墨烯及其衍生物作为新型碳纳米结构,由于其优异的光限幅性能而受到广泛关注,但现有的工作多侧重于其在液相体系中光限幅效应及其起因研究.本文以壳聚糖为成膜基质,将氧化石墨烯(GO)与壳聚糖(CS)在液相中均匀共混后成膜,对比研究GO溶液和GO-CS复合膜的光限幅效应及其起因.结果表明在线性透过率相同的情况下,GO在固相基质中表现出比液相基质更强的光限幅效应和更弱的非线性散射.这说明不同于碳纳米管简单的非线性散射,在GO中可能存在多种非线性光学效应.     

具时变刚度的相对转动非线性动力系统的周期解问题

建立了一类具有时变刚度,非线性阻尼力和强迫周期力项的相对转动非线性动力系统. 运用Mawhin重合度理论,得到了该模型的周期解存在唯一性结果,推广了已有的结果, 并且列举了具体的例子来说明本文的结果是新的. 关键词： 相对转动非线性动力系统 时变刚度 周期解 存在唯一性     

Tripartite Nonlinear Entangled State Representations in Quantum Mechanics

Based on the technique of integral within an ordered product of nonlinear bosonic operators we construct a kind of tripartite nonlinear entangled states, which can make up a complete set. As its application, we also derive nonlinear 3-mode charge-related entangled state. The essential point for constructing these states lies in choosing the appropriate charge operator.