中空圆柱形边界条件下非线性介质中的晶格孤子

本文采用自相似方法求解中空圆柱形边界贝塞尔晶格中变系数非线性薛定谔方程, 得到了与数值模拟解一致的解析解, 表明由非衍射贝塞尔光束诱导的光子晶格可支持稳定的自相似孤子簇. 精确解ψ_mn是n+2层, 2m极的多极孤立波, 其形状及大小在传播过程中保持不变. 关键词： 空间光孤子 贝塞尔晶格 边界 自相似     

自相似Euler方程的数值方法

Euler方程某些问题的解具有自相似特点，可以使用更准确的方法求解.提出了两种数值方法，分别称为自相似和准自相似方法，新方法可以使用现有守恒律方程的数值格式，无须设计特殊方法.对一维激波管问题、二维Riemann问题、激波反射以及激波折射问题进行了数值计算.对自相似Euler方程，一维计算结果显示数值解基本等同于精确解，二维结果也比现有文献计算的结果有更高的分辨率.对准自相似Euler方程，新方法可以求解不具有自相似性但接近自相似的问题，并在计算时间足够长时可以取得自相似Euler方程的效果.数值求解自相似Euler方程对自相似问题的研究，高分辨率、高精度格式的设计乃至Euler方程的精确解都有重要启示.      

Self-similar tip growth in filamentary organisms

The growth of a family of filamentary microorganisms is described in terms of self-similar growth at the tip which is driven by pressure and sustained by a wall-building growth process. The cell wall is modeled biomechanically as a stretchable elastic membrane using large-deformation elasticity theory. Incorporation of geometry dependent elastic moduli and a self-similar ansatz shows how these equations can generate realistic tip shapes corresponding to a self-similar expansion process.     

Exact self-similar solitary waves and collisions in nonlinear optical media

This paper analyses bright and dark spatial self-similar waves propagation and collision in graded-index nonlinear waveguide amplifiers with self-focusing and self-defocusing Kerr nonlinearities. It finds an appropriate transformation for the first time such that the nonlinear Schrodinger equation （NLSE） with varying coefficients transform into standard NLSE. It obtains one-solitonlike, two-solitonlike and multi-solitonlike self-similar wave solutions by using the transformation. Furthermore, it analyses the features of the self-similar waves and their collisions.     

色散渐减光纤中自相似脉冲传输区域的研究

从非线性薛定谔(NLS)方程出发,用分步傅里叶方法结合对数值解的波形分析,确定了色散渐减光纤(DDF)中能实现自相似脉冲传输的区域,并研究了初始脉冲和光纤参数对自相似区域和演化速度的影响。结果表明,初始脉冲能量的减小有利于扩宽自相似区域,但会使自相似演化进程略为减慢;初始脉宽有一个最佳值,在最佳值上自相似区域最宽,演化较快且输出脉冲和啁啾较为稳定;高斯脉冲比双曲正割脉冲更快转化为自相似脉冲,传输区域也更广。选择具有较小非线性参量的DDF可以获得较广的自相似区域,同时非线性参量的增大可以加快自相似演化,而群速度色散参量和增益系数必须选择在最佳值附近,才能获得最大自相似区域和最快演化速度。     

理想气体一维不定常流自模拟运动的基本微分方程

将一维不定常流自模拟函数推广到一般形式，结合量纲理论和流体力学基本运动方程，导出总能量为常数情况下的理想气体一维不定常流自模拟运动基本微分方程组.该理论模型表明，由流体速率u和自模拟面速率r·〖DD)]组成一个无量纲特性参数L，用L作自变量时理想气体一维不定常流自模拟运动的规律具有常微分方程的最简数学形式.该模型克服了点爆炸Taylor自模拟温度函数原点附近趋于无穷大的问题，具有重要意义. 关键词： 理想气体 自模拟运动 Taylor模型     

Pulse Evolution Characteristics in Self-Similar Mode-locked Fibre Laser

A self-similar mode locked fibre laser is studied based on a numerical model. By introducing a dimensionless factor k to characterize the pulse shape, the self-similar pulse evolution, formation and the temporal and spectral shape changes due to the elements in the cavity are investigated throughout the laser cavity. The results show that in the self-similar mode locked fibre laser, self-similar pulse is first formed in the single-mode fibre, which is then amplified in the gain fibre. Gain bandwidth has a small influence on pulse shape, so high energy self-similar pulse can be obtained after amplification. Because net cavity dispersion directly influences the pulse width as well as peak power after compression by a pair of gratings, which can determine the pulse self-similar evolution, it is very important to control the net cavity dispersion to a certain range to obtain self-similar pulses.     

高阶色散效应常系数Ginzburg-Landau方程自相似脉冲演化的解析分析

采用自相似分析方法,基于常系数高阶色散的Ginzburg-Landau方程,通过分离变量法得出了高阶色散效应自相似脉冲演化的解析解,给出了自相似脉冲的振幅、相位、啁啾以及脉冲宽度的一般表达式.研究表明,在增益光纤的二阶正常色散区域,同时考虑高阶色散和增益色散双重效应影响下演化的自相似孤子脉冲仍然保持线性啁啾;振幅解析解的三阶色散效应显著.这与数值计算的结果非常一致. 关键词： 三阶色散 Ginzburg-Landau方程 自相似脉冲 二阶正常色散     

自由剪切流动中颗粒扩散的自相似特性

为了研究自由剪切流动中颗粒扩散的统计特性,对空间发展模式的三维气固两相射流和时间发展模式的三维气固两相混合层进行了直接数值模拟.其中对气相不可压缩Navier-Stokes方程的求解分别采用有限容积方法和拟谱方法,对离散惯性颗粒的跟踪采用单向耦合的拉格朗日方法.统计结果显示,当流场进入自相似状态后,以流场速度梯度二阶不变量Q为自变量的颗粒数的概率分布函数也呈现出与颗粒尺寸和时间发展无关的自相似特性.     

利用非线性脉冲预整形实现脉冲快速自相似放大

报道了一种通过预先对信号光脉冲非线性整形, 进而在光纤放大器中实现自相似演化的方法. 利用透射光栅对和普通单模光纤组成被动脉冲整形装置, 预先优化脉冲的时域宽度和光谱质量, 使脉冲在光纤放大器中快速演化到自相似子. 研究中首先通过数值模拟对比, 说明了非线性整形对脉冲实现快速自相似放大的关键作用, 提高了放大器输出脉冲质量, 减小了去啁啾脉冲宽度. 实验中, 通过优化非线性整形输出, 在2.2 m 长的掺Yb³⁺光纤中, 在一定抽运功率范围内均实现了脉冲自相似放大, 去啁啾后得到脉冲宽度60 fs 的变换极限脉冲输出. 这种非线性脉冲预整形方法有效减小了 自相似演化所需光纤长度, 同时降低了自相似放大对种子源质量的要求, 首次将全正色散光纤锁模激光器成功用于自相似放大, 促进了当前自相似放大系统的全光纤化. 关键词： 非线性整形 光纤放大器 自相似放大 飞秒激光     

Self-affine analysis of multiparticle production in pp collisions at 400 GeV/c with continuously varying scale

A self-affine analysis of multiparticle production in pp collisions at 400 GeV/c was performed by using the method of continuously varying scale. Comparing with the results obtained from self-similar analysis, the self-affine analysis shows a better power-law behavior. The fractality in multiparticle production is self-affine rather than self-similar.     

Self-similar counter-propagating beams of electromagnetic waves in nonlinear cubic media

We study the structure of the self-similar beams of counter-propagating electromagnetic waves in nonlinear cubic media. Eigenfrequencies of two-mirror quasi-optical resonators, whose eigen-modes are self-similar beams of counter-propagating waves, are found.     

Higher-order effects on self-similar parabolic pulse in the microstructured fibre amplifier

By considering higher-order effects, the properties of self-similar parabolic pulses propagating in the microstructured fibre amplifier with a normal group-velocity dispersion have been investigated. The numerical results indicate that the higher-order effects can badly distort self-similar parabolic pulse shape and optical spectrum, and at the same time the peak shift and oscillation appear, while the pulse still reveals highly linear chirp but grows into asymmetry. The influence of different higher-order effects on self-similar parabolic pulse propagation has been analysed. It shows that the self-steepening plays a more important role. We can manipulate the geometrical parameters of the microstructured fibre amplifier to gain a suitable dispersion and nonlinearity coefficient which will keep high-quality self-similar parabolic pulse propagation. These results are significant for the further study of self-similar parabolic pulse propagation.     

Analytic solutions of self-similar pulse based on Ginzburg-Landau equation with constant coefficients

Based on the constant coefficients of Ginzburg-Landau equation that considers the influence of the doped fiber retarded time on the evolution of self-similar pulse, the parabolic asymptotic self-similar solutions were obtained by the symmetry reduction algorithm. The parabolic asymptotic amplitude function, phase function, strict linear chirp function and the effective temporal pulse width of self-similar pulse are given in this paper. And these theoretical results are consistent with the numerical simulations. Supported by the Natural Science Foundation of Guangdong Province of China (Grant No. 04010397)     

高非线性光纤产生自相似抛物线脉冲的特性研究

基于脉冲在光纤中传输所满足的非线性薛定谔方程,采用数值计算的方法对脉冲在高非线性光纤中演化成自相似抛物线脉冲的传输特性进行了研究。结果表明,脉冲在不同初始能量和啁啾参量的情况下,高非线性光纤产生自相似抛物线脉冲,且随着归一化长度的增大,脉冲的自相似指数从0.0796减小到0.0720。进一步的研究表明:啁啾高斯脉冲在光纤传输过程中,脉冲逐渐展宽,同时正啁啾越大,其自相似演化结果越差;参数N=8的正负啁啾脉冲分别演化成平顶自相似抛物线脉冲以及三角形脉冲。     

Self-similar propagation region in passive optical fibers based on low-order approximation

For the first time, we numerically demonstrate that similaritons in passive fibers can only propagate with parabolic profile without oscillations in a limited self-similar propagation region when low-order approximation is applied. Dispersion-decreasing fiber (DDF) and nonlinearity increasing fiber (NIF) are used here to generate self-similar pulse in different passive ways. Moreover, we put forward several self-similar features to judge effective similariton propagation and determine self-similar region by numerical simulations and waveform observation. Finally we compare in DDF and NIF the dependence of these regions on incident pulse and fiber parameters in order to obtain parabolic similariton more effectively and steadily. These results extend the low-order propagation properties in passive fibers and are beneficial for the generation of high-quality similariton pulse by parameter selection in experimental studies and practical applications.     

Spatiotemporal self-similar waves for the (3 + 1)-dimensional inhomogeneous cubic-quintic nonlinear medium

Spatiotemporal self-similar waves of the (3 + 1)-dimensional generalized nonlinear Schrödinger equation, describing propagation of optical pulses in a cubic-quintic nonlinear medium with inhomogeneous dispersion and gain, are derived. A one-to-one correspondence between such self-similar waves and solutions of the constant-coefficient cubic-quintic nonlinear Schrödinger equation exists when two certain compatibility conditions are satisfied. Under these conditions, we discuss dynamical behaviors of self-similar waves in dispersion decreasing fiber.     

Generation of excellent self-similar pulses in a dispersion-decreasing fiber

Pulses compression has been widely studied for a long time. In order to generate excellent self-similar pulses in a dispersion-decreasing optical fiber with normal group-velocity dispersion, the influence of initial pulse parameters on the properties of the self-similar parabolic pulses interaction are firstly investigated in the paper. We find that the phase of sinusoidal fit and asymptotic dark soliton change according to the changing of initial phase difference. Meanwhile, increasing the full-width at half-maximum and input energy or decreasing time-delay properly, the interaction between self-similar pulses enhances accordingly, which makes the interaction length shorter and reduce the lose of energy, resulting in high energy output. The results are beneficial in experimental studies by adjusting the initial parameters of pulses to generate high-quality self-similar pulse. It is important for Dense Wavelength Division Multiplexing (DWDM) transmission system which is in heavy demands of light source in wide-range wavelength.