一类Marangoni对流边界层方程的近似解析解

利用Adomain解析拆分和Padé逼近方法对由Marangoni对流诱发的层流边界层问题进行了研究, 提供了一种求解边界层方程的解析分析方法. 得到了问题的近似解析解并对相应的流动及传热特性进行了探讨. 本文所提出的思想方法可以用于解决其他科学和工程技术问题. 关键词： Marangoni对流 非线性 Adomain拆分法 近似解析解     

六组点堆中子动力学方程组的同伦分析解

鉴于目前六组点堆中子动力学方程仍然无法获得解析解,本文尝试将同伦分析方法应用于六组缓发中子动力方程组的求解,获得了它的级数解析解,并对级数解析解算法的有效性进行了检验.结果表明,该级数解析解算法从计算时间和精度上都能达到工程应用的要求,可适宜于反应堆中子动力学控制的设计分析和仿真计算.     

离轴激光雷达重叠因子解析研究

为了对离轴激光雷达的近场信号进行校正,本文根据离轴激光雷达重叠因子的定义,利用高斯光束光强的解析传输公式,并考虑到离轴激光雷达系统激光分布与望远镜视场的五种关系,得到了利用雷达系统参数表示的离轴激光雷达重叠因子的解析计算公式。基于该公式对澳门地区雷达回波信号进行了校正和反演,所得结果证明了解析公式的有效性。利用解析公式通过数值计算方法详细研究了雷达系统参数对离轴激光雷达重叠因子的影响,该结果对激光雷达系统设计具有一定的参考价值。     

非定常可压等熵流非线性方程显式解析解的推导

本文对作者以前凭试凑、灵感、运气与经验得出的一系列非定常可压流动显式解析解,寻找线索,总结出其可能的推导途径,并以非定常可压等熵一维流为例,具体给出了四种新的求解方法。这些方法会对今后寻找工程热物理领域的非线性主控方程的解析解有所帮助。本文同时还给出了两个新的解析解。     

管内变密度流体流动与换热的充分发展及解析解

本文提出了圆管内变密度流体流动与换热充分发展的概念和相关假设及其推论.在所提出的概念和假设基础上对理想气体在圆管内的流动与换热进行了解析求解,得到了充分发展时的无量纲速度抛物分布及无量纲温度分布.对圆管内密度随温度变化的氩气的流动与换热数值模拟所获得的无量纲速度分布及无量纲温度分布在入口段后与上述解析解非常吻合,从而验证了在本文的计算条件范围内,圆管内变密度流体充分发展流动与换热的概念及其解析解是合理的.     

校验叶轮机械三维数值解的某些解析解

本文给出相对旋转圆柱坐标系中三维不可压位流的某些与叶轮机械内流动相似的解析解、它们的势函数、速度向量和流面方程的数学表达式,并对其中两个分别与离心式和轴流式叶轮机械内流动较相似的解析解进行了讨论,这些解析解可用来验证三维计算程序的可靠性.文中还有验证的示例。     

高温等离子体相对论性平均原子模型中的半解析波函数

半解析求解平均原子模型方法充分利用了已知精确波函数的解析性质,通过对平均原子模型中势函数的数值拟合,就得到仅含一个数值因子的半解析波函数以及相应的能量本征值.本文列出了等离子体中相对论性平均原子模型的诸方程,特别注意方程求解技术和程序设计中的一些细节.与完全数值解以及其他类似模型得到的数值解进行的比较表明,在较高温度条件下半解析结果的精度是相当高的,求解的效率也很高.此外还对物理模型中某些缺陷进行了分析.     

含有高阶参量的生物组织光学漫反射的半经验解析模型

漫反射光谱技术对生物组织快速和无创测量具有非常重要的意义,但缺乏精确的关于漫反射的解析解限制了该技术有效的应用.本文根据光子迁移理论和二阶相似关系推导了半经验公式,然后利用Monte Carlo方法研究了二阶参量γ对半经验公式的影响.研究表明,当小孔径收集漫反射光时,反射率与γ成二次函数关系.与其他含有高阶参量γ的解析模型相比,本文提出的半经验解析模型具有简单的数学形式,这为生物组织光学参量测量和漫反射光谱应用提供了新的理论和技术支持.     

关于强子中胶子分布函数的QCD预言

本文对Altarelli-Parisi方程采用Mellin变换方法解析地求得胶子分布函数的级数解析表达式,这个级数收敛得很快,利用它讨论了胶子分布函数的演化行为.     

极端相对论快电子分布等离子体中横振荡色散关系

本文对各向同性极端相对论快电子呈幂律分布等离子体中横振荡色散关系进行了解析和数值研究.得到长波支和短波支色散关系的解析表达式.由于解析近似对波数的限制,无法得到全波数空间色散曲线,因此对色散方程进行了数值求解.研究表明,在满足长波支和短波支条件时,解析色散曲线与数值色散曲线完全符合.此外,利用多项式回归的方法对数值结果进行拟合,得到不同参数下快电子分布等离子体横振荡色散关系近似表达式,该结果为进一步研究快电子分布等离子体的性质提供了重要的理论依据. 关键词： 相对论性等离子体 快电子分布 色散关系 数值计算     

单模光纤中受激喇曼散射对调制不稳定性的影响

基于修正的非线性薛定谔方程，利用线性扰动理论和数值方法研究了单模光纤中的调制不稳定性.由于受激喇曼散射的作用，使得喇曼增益谱叠加到光纤中的调制不稳定性增益谱上.这样，原本调制稳定的光纤正常色散区也出现了调制不稳定性；而在反常色散区，随着初始功率的增加，常规的调制不稳定性增益谱的增益和频谱范围均增大，而喇曼增益谱的增益增大但其频谱范围基本不变，这样导致常规的不稳定区域逐渐侵入并最终掩盖喇曼增益区.数值模拟验证了解析结果的正确性，并证明了利用反常色散情形下的调制不稳定性可以产生超短脉冲序列，但这种脉冲序列的进一步传输将会出现喇曼孤子自频移现象.     

变路径色散管理孤子系统中的调制非稳性研究

本文研究了变路径色散的孤子系统中的调制非稳性.首先采用微扰法对变路径色散的系统中的调制非稳性(MI)进行理论分析,解析出变路径色散系统中的MI特征根表达式,据此得到了色散管理孤子(DMS)系统的特征参数色散管理图强度与MI增益系数关系.研究结果表明,变路径色散系统中的色散管理强度大大影响MI增益的大小以及增益谱范围,而路径平均色散只影响MI增益谱范围.同时,本文结果还表明DMS较普通孤子系统有更强的抑制MI增益的能力.     

Spatiotemporal instability in dispersive nonlinear Kerr medium with a finite response time

We investigated the spatiotemporal modulation instability (MI) in a medium with a non-instantaneous Kerr response in which the nonlinear contribution to the refractive index is governed by a relaxing Debye type equation. The expression for the MI gain spectrum in non-instantaneous Kerr medium is obtained, which clearly reveals the influence of the finite time of the nonlinear response (relaxation effect) on the spatiotemporal MI. It is shown that, due to the relaxation effect, the spatiotemporal MI can appear for the case of anomalous dispersion and defocusing nonlinearity, while it cannot appear in instantaneous Kerr medium for the same case, and a new MI gain spectrum appears, adding to the conventional MI gain spectrum similar to that in an instantaneous Ker medium. In addition, the bandwidth of MI gain spectrum is extended and the maximum MI gain is reduced with increasing of the relaxation time. Interestingly, spatiotemporal MI can appear for any spatial frequencies in non-instantaneous Kerr medium for any combination of dispersion and nonlinearity. We have performed an experiment of MI in carbon disulfide (CS₂), a typical non-instantaneous Kerr medium, which shows quantitative agreement with the theoretical analyses.     

Pressure dependent modulation instability in photonic crystal fiber filled with argon gas

By using the designed photonic crystal fiber filled with argon gas, the effect of gas pressure on modulation instability(MI) gain is analyzed in detail. The MI gain bandwidth increases gradually as the argon gas pressure rises from 1 P_0 to 400 P_0(P_0 is one standard atmosphere), while its gain amplitude slightly decreases. Moreover, the increase of the incident light power also results in the increase of MI gain bandwidth in the Stokes or anti-Stokes region when the incident power increases from 1 W to 200 W. Making use of the optimal parameters including the higher argon gas pressure(400 P_0) and the incident light power(200 W), we finally obtain a 100 nm broadband MI gain. These results indicate that controlling the MI gain characteristic by changing the argon gas pressure in PCF is an effective way when the incident light source is not easy to satisfy the requirement of practical application. This method of controlling MI gain can be used in optical communication and laser shaping.     

Modulation instability in lossy silicon optical waveguide

Taking into account the small linear loss of silicon-on-insulator(SOI) waveguide, conditions and gain spectra of modulation instability(MI) induced by combined effects of self-phase modulation and waveguide dispersions are investigated. The impacts of various parameters to gain spectra of MI are analyzed theoretically. Results show that strong MI takes place even in the existence of low light power. The MI peak gain is 2 to 3 orders of magnitude larger than that achieved in optical fibers with the same light power. The linear loss of waveguide impacts gain spectra of MI, even within ultra-short propagation distance. The peak gain, peak gain frequency and bandwidth of gain spectra decrease to 66.828%, 41.683% and 41.6879% of their maxima at propagation distance z = 5mm, respectively.     

Modulation instability in silicon optical waveguide considering linear loss

Taking into account the linear loss of silicon-on-insulator (SOI) waveguide, modulation instability (MI) induced by combined effects of self-phase modulation and waveguide dispersions is investigated. The impacts of various parameters to gain spectra of MI are analyzed theoretically, and direct numerical simulation of nonlinear Schroedinger equation is performed as well. Results show that strong MI takes place even in the existence of low light power. The linear loss of waveguide obviously impacts gain spectra of MI, even within ultra-short propagation distance. The peak gain frequency and bandwidth of gain spectra decrease to 41.683% and 41.6879% of their maximum at propagation distance z = 5 mm, respectively.     

CdSSe玻璃的光学增益

本文使用放大的自发辐射技术(ASE)测量了CdSSe玻璃(国产JB 510)的光学增益.在波长λ=625nm处,测得增益系数g≈8cm-1.增益出现的波长范围对应样品荧光光谱中陷阱能级的宽带.一个简单的三能级模型,辅之以陷阱能级发光的衰减测量,定性地解释了增益出现的原因.     

基于交叉增益调制效应全光波长变换中半导体光放大器增益与变换光脉冲啁啾分析

对于半导体放大器(SOA),由于连续光注入其有效增益降低,本文提出基于SOA交叉增益调制效应(XGM)全光波长变换(AOWC)简化的系统模型,应用此模型详细分析了信号光功率(P_s)、信号光脉宽(t_p)、泵浦电流和探测光功率(P_cw)对于变换光啁啾的影响.     

Modulational instability in optical fiber with stochastic parameters and noninstantaneous response

We investigate analytically and numerically the modulational instability (MI) in optical fiber, where the effect of noninstantaneous nonlinear response as well as stochastic coefficients are taken into account. Applying the linear stability analysis and stochastic calculus, we show that the MI gain spectrum reads as the maximal eigenvalue of a constant matrix. In the limiting cases of small fluctuations, we give explicit expressions for the MI gain spectra. In the general configurations, we derive an explicit form of the effective matrix and compute numerically the maximal eigenvalue. The moment MI peak is enhanced and the delayed Raman response reduces the maximum MI gain caused by stochasticity both in anomalous and normal dispersion regimes. Numerical simulations of the full stochastic nonlinear Schródinger equation show that, the phenomenon of MI gives rise to periodic pulse arrays of waves train, as well as to a chain of peaks with continuously growing amplitudes.     

含负折射介质的反向定向耦合器的时空不稳定性研究

研究含负折射介质的不对称反向定向耦合器中的时空调制不稳定性(MI),探讨了输入功率、前向波和后向波功率比和通道间的耦合系数等对时空MI的影响。结果表明:在这种新型耦合器中只有当横向波数超过一定阈值时才会产生MI,增加输入功率或减少前向波和后向波的功率比都会扩大MI增益谱的范围并最终使MI区域重合,而降低耦合器通道间的耦合系数可减少MI的增益峰值但拓宽增益谱的范围。负折射介质的电磁参数可调谐特性为实现MI的主动调控和孤子的形成提供了新的方法和手段。