光脉冲传输模拟的快速数值差分递推算法及其应用研究

利用零邻域的马克劳林展开对归一化非线性薛定谔方程的频域差分形式进行分析,得出一个能够同时考虑光学媒质的色散作用以及非线性克尔作用的时域快速数值差分递推公式.选取若干算例,将运用该公式的数值计算结果与已知的解析结果和传统分步傅里叶方法所得的计算结果做了相应的比较,结果表明这种快速数值差分递推公式不但拥有相当快的计算速度,也有很高的计算精度,而且在物理上符合光脉冲在光学媒质中传输时色散和非线性作用同时施加影响的客观实际,这说明它是研究非线性光学媒质中光脉冲传输的一种科学、合理而快速有效的数值计算方法.关键词：快速数值差分递推公式零邻域马克劳林展开非线性薛定谔方程光脉冲传输     

飞秒啁啾Gauss型脉冲在稠密Λ型三能级原子介质中的传播

利用由预估校正(PC)- 时域有限差分(FDTD)法求得的不含慢变包络近似(SVEA)和旋转波近似(RWA)的全波Maxwell-Bloch方程的数值解, 研究了飞秒啁啾Gauss型激光脉冲(以下简称啁啾脉冲)在稠密Λ型三能级原子介质中的传播.研究表明,啁啾系数(C)的正负及大小的变化对脉冲传播特性有显著的影响,而且这个影响与脉冲面积的大小密切相关.面积小于4π的啁啾脉冲,在介质中传播时不发生分裂,且啁啾脉冲逐渐演化为一个近似的无啁啾(C=0)脉冲,这一特点不随啁啾系数的改变而     

波传播计算中的人工边界条件

对无限介质中波传播进行有界区域近似计算时,需要提出人工边界条件.本文分别就连续介质和离散晶格简要介绍一些典型的人工边界条件,包括精确人工边界条件和局部人工边界条件.     

EXACT SOLUTION FOR A TWO-DIMENSIONAL LAMB＇S PROBLEM DUE TO A STRIP IMPULSE LOADING

By applying the integral transform method and the inverse transformation technique based upon the two types of integration, the present paper has successfully obtained an exact algebraic solution for a two-dimensional Lamb＇s problem due to a strip impulse loading for the first time. With the algebraic result, the excitation and propagation processes of stress waves, including the longitudinal wave, the transverse wave, and Rayleigh-wave, are discussed in detail. A few new conclusions have been drawn from currently available integral results or computational results.     

Fish and Plankton Interplay Determines Both Plankton Spatio-Temporal Pattern Formation and Fish School Walks: A Theoretical Study

The fascinating variety of spatio-temporal patterns in aquatic ecosystems and the understanding of the governing mechanisms of its generation and further dynamics requires ongoing experimental and theoretical studies. After introducing a certain hybrid mathematical model, this paper makes an attempt to demonstrate that the predation of a mobile planktivorous fish school on zooplankton can initiate both plankton pattern formation and fish school walks. Nonlinear interactions in the model of a fish-zooplankton-algae trophic chain prevent a simple intuitive understanding of the system dynamics. It is shown that the fish school predation and motion can give rise to plankton spiral waves. In the course of the spiral wave formation, the amplitudes of the spatially averaged plankton density oscillations are decreasing dramatically. Fish school walks are shown to resemble a fractional Brownian motions with a Hurst exponent depending on the fish predation rate.     

Beam propagation factor of partially coherent elegant Hermite-cosh-Gaussian beam through non-Kolmogorov turbulence

Based on the extended Huygens–Fresnel principle and the second moments of the Wigner distribution function, an analytical expression for the propagation factors of partially coherent elegant Hermite-cosh-Gaussian beams (EHChGB) in non-Kolmogorov is derived. The M² factor of partially coherent EHChGB through non-Kolmogorov turbulence is studied analytically and numerically. The results show that partially coherent EHCHGB with higher beam order and longer wavelengths is less affected by non-Kolmogorov turbulence.     

The optical simulation of an air-guide edge-lit

The air-guide edge-lit without a light guide panel has been developed to meet the low manufacturing cost of a surface illuminator. The performance of the light guide inside the air layer between the curved reflector, used as the rear surface, and a flat light diffuse plate, at the front surface, depends on the shape of reflector curve and the BRDF (bidirectional reflectance distribution function) of the material of reflector. The goal of this study is to develop a ray-tracing simulation model in order to design the curve shape of the air-guide edge-lit meeting the luminance uniformity. In the present study, the BRDFs of reflector materials were measured and calibrated. The simulation accuracy in the luminance uniformity of the model was examined, and the influence of BRDF at the high angle of incidence on simulation accuracy was discussed.     

Finite element analysis of quasistatic crack propagation in brittle media with voids or inclusions

A three-level finite element scheme is proposed for simulation of crack propagation in heterogeneous media including randomly distributed voids or inclusions. To reduce total degrees of freedom in the view of mesh gradation, the entire domain is categorized into three regions of different-level meshes: a region of coarse-level mesh, a region of intermediate-level mesh, and a region of fine-level mesh. The region of coarse-level mesh is chosen to be far from the crack to treat the material inhomogeneities in the sense of coarse-graining through homogenization, while the region near the crack is composed of the intermediate-level mesh to model the presence of inhomogeneities in detail. Furthermore, the region very near the crack tip is refined into the fine-level mesh to capture a steep gradient of elastic field due to the crack tip singularity. Variable-node finite elements are employed to satisfy the nodal connectivity and compatibility between the neighboring different-level meshes. Local remeshing is needed for readjustment of mesh near the crack tip in accordance with crack growth, and this is automatically made according to preset values of parameters determining the propagation step size of crack, and so the entire process is fully automatic. The effectiveness of the proposed scheme is demonstrated through several numerical examples. Meanwhile, the effect of voids and inclusions on the crack propagation is discussed in terms of T-stresses, with the aid of three-level adaptive scheme.     

基于流固耦合偏航工况下风力机输出功率的研究

为探索双向流固耦合与未耦合方法对偏航工况风力机输出功率的影响机制,以风力机偏航的Glauert动量定理为基础,基于双向流固耦合方法,采用理论推导与轴向流动过程相结合对输出功率进行分析,揭示了耦合与未耦合数值方法在压力场模拟的差异性、量化了轴向诱导因子对偏航工况输出功率的影响程度、总结了轴向速度分布情况.结果表明:未耦合...     

乙烯基单体正离子聚合中链增长速率常数的研究进展

碳正离子聚合中,聚合速率常数的测定方法通常包括电导法、绝热量热法、胺抑制法、止流光谱法及扩散计时法。在烷基乙烯基醚、苯乙烯及其衍生物和异丁烯等几种常见乙烯基单体的正离子聚合中,本文介绍不同测定方法得到的不同结构碳正离子(包括自由离子和离子对)的链增长速率常数(kp 和kp±)。