Sliding of self-similar sets

This paper deals with the Lipschitz equivalence of slidings of self-similar sets by graph-directed construction and martingale theory.     

广义Davey-Stewartson方程组的整体解及自相似解

本文研究Dalvey-Stewartson方程组的整体解与自相似解的存在性.首先,运用Ba- nach不动点定理得到一个关于解整体存在性的一般性定理,然后把一类特殊的初始值用到该存在性结果上去从而得到自相似解存在的结论.     

A nonlinear oblique derivative boundary value problem for the heat equation Part 2: Singular self-similar solutions

This paper continues the study started in [12]. In the upper half-plane, consider the elliptic equation

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, submitted to the nonlinear oblique derivative boundary condition U_x = UU_z on the axis x = 0. The solution of this problem appears to be the self-similar solution of the heat equation with the same boundary condition. As goes to 0, the function U converges to the non trivial solution U of the corresponding degenerate problem. Moreover there exists z₀ > 0 such that U vanishes for z ≥ z₀, is C^∞ on ]0, z₀[× ₊, is continuous on the boundary x = 0 and is discontinuous on the half-axis {z = 0, x> 0}.     

Spatiotemporal self-similar solutions for the nonautonomous （3＋1）-dimensional cubic-quintic Gross-Pitaevskii equation

With the help of similarity transformation,we obtain analytical spatiotemporal self-similar solutions of the nonautonomous(3+1)-dimensional cubic-quintic Gross-Pitaevskii equation with time-dependent diffraction,nonlinearity,harmonic potential and gain or loss when two constraints are satisfied.These constraints between the system parameters hint that self-similar solutions form and transmit stably without the distortion of shape based on the exact balance between the diffraction,nonlinearity and the gain/loss.Based on these analytical results,we investigate the dynamic behaviours in a periodic distributed amplification system.     

自相似业务流建模及其合成性能分析

基于通信网络仿真软件平台OPNET中的RPG模型，本文实现了一个通用的、与协议无关的自相似业务流发生模型，并通过仿真实验和小波分析的方法验证了该模型的正确性和可用性。在此模型的基础上，着重对自相似业务流合成过程的性能和行为特性进行了大量的实验和分析。研究结果表明，自相似业务流的合成过程仍具有自相似性，而且合成流的自相似参数接近于各独立输入业务流中所具有的最大自相似参数。     

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.     

非线性偏振旋转锁模自相似脉冲光纤激光器的研究

利用耦合非线性薛定谔方程（CNLSE）为非线性偏振旋转（NPE）锁模自相似光纤激光器建立了一种新的数值模型.模型中,用CNLSE描述脉冲在单模光纤中的传播,在增益光纤中同时考虑了增益带宽和增益饱和作用,用传输矩阵描述构成NPE锁模的光学元件.优化了腔内净色散和光纤长度等参数,模拟了脉冲在激光腔内的演化特性,得到了典型的自相似脉冲运行区域及特点.在最佳自相似脉冲运行区域内,得到了能量约为7 nJ、脉宽约11 ps、线性啁啾的抛物脉冲.比较了不同腔内净色散条件下输出脉冲的特点,给出了三阶色散对输出脉冲的影响. 关键词： 自相似脉冲 非线性偏振旋转锁模 耦合非线性薛定谔方程 数值模拟     

高阶色散对光纤放大器中自相似脉冲传输的影响

以非线性薛定谔方程为模型,采用分步傅里叶方法对光纤放大器中自相似脉冲的传输特性进行详细的研究,结果表明:抛物型的自相似脉冲可以在不包含高阶色散的光纤放大器系统中稳定传输;当系统的高阶色散(如:三阶色散)不容忽略时,自相似脉冲在光纤放大器中传输时将在脉冲沿出现抖动现象,导致脉冲的抛物线形状产生畸变.     

Spatiotemporal self-similar solutions for the nonautonomous (3+1)-dimensional cubicben quintic Grossben Pitaevskii equation

With the help of similarity transformation, we obtain analytical spatiotemporal self-similar solutions of the nonautonomous (3+1)-dimensional cubic-quintic Gross-Pitaevskii equation with time-dependent diffraction, nonlinearity, harmonic potential and gain or loss when two constraints are satisfied. These constraints between the system parameters hint that self-similar solutions form and transmit stably without the distortion of shape based on the exact balance between the diffraction, nonlinearity and the gain/loss. Based on these analytical results, we investigate the dynamic behaviours in a periodic distributed amplification system.     

非奇异宇宙的理想气体自相似模型

通过引力作用下理想气体运动连续性方程的无量纲化,根据量纲理论Π定理,以尺度因子R(t)为物理量统一度量基准,发现了引力作用下理想气体宇宙模型的自相似性和一系列R(t)的解析解.基于R(t),可建立对应的、具有非欧氏几何特性的均匀膨胀时空坐标系S(t,ξ,θ,φ),并获得一个密度ρ为常数、速度u为零、压强p不为零的理想气体宇宙解.在这个解的形式中,光子红移量z所表现的是光子传播距离r,当红移量z较小时两者成正比(即哈勃定律).由均匀膨胀坐标系还可推导出Robertson-Walker度规(k= 关键词： 宇宙 自相似 哈勃定律