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31.
The statistical distribution of natural phenomena is of great significance in studying the laws of nature. In order to study the statistical characteristics of a random pulse signal, a random process model is proposed theoretically for better studying of the random law of measured results. Moreover, a simple random pulse signal generation and testing system is designed for studying the counting distributions of three typical objects including particles suspended in the air, standard particles, and background noise. Both normal and lognormal distribution fittings are used for analyzing the experimental results and testified by chi-square distribution fit test and correlation coefficient for comparison. In addition, the statistical laws of three typical objects and the relations between them are discussed in detail. The relation is also the non-integral dimension fractal relation of statistical distributions of different random laser scattering pulse signal groups. 相似文献
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Exact projective solutions of generalized nonlinear Schrödinger system with variable parameters
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A direct self-similarity mapping approach is successfully applied to a generalized nonlinear Schrödinger (NLS) system. Based on the known exact solutions of a self-similarity mapping equation, a few types of significant localized excitation with novel properties are obtained by selecting appropriate system parameters. The integrable constraint condition for the generalized NLS system derived naturally here is consistent with the known compatibility condition generated via the Painlev? analysis. 相似文献
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SUN Peng CHEN Shi-Gang WANG Guang-Rui 《理论物理通讯》2009,51(1):149-152
In this paper, the dynamics behaviors on fo-δ parameter surface is investigated for Gledzer-Ohkitani- Yamada model We indicate the type of intermittency chaos transitions is saddle node bifurcation. We plot phase diagram on fo-δ parameter surface, which is divided into periodic, quasi-periodic, and intermittent chaos areas. By means of varying Taylor-microscale Reynolds number, we calculate the extended self-similarity of velocity structure function. 相似文献
35.
Michel L. Lapidus Lũ’ Hùng 《P-Adic Numbers, Ultrametric Analysis, and Applications》2009,1(2):167-180
We develop a geometric theory of self-similar p-adic fractal strings and their complex dimensions. We obtain a closed-form formula for the geometric zeta functions and show
that these zeta functions are rational functions in an appropriate variable. We also prove that every self-similar p-adic fractal string is lattice. Finally, we define the notion of a nonarchimedean self-similar set and discuss its relationship
with that of a self-similar p-adic fractal string. We illustrate the general theory by two simple examples, the nonarchimedean Cantor and Fibonacci strings.
The text was submitted by the authors in English. 相似文献
36.
Based on the kinematic viewpoint, the concept of proportional movement is abstracted to explain the strange behaviors of fractal snowflakes. A transformation group for proportional movement is defined. Under the proportional movement transformation groups, necessary and sufficient conditions for self-similarity of multilevel structures are presented. The characteristic topology of snowflake-like fractal patterns, identical to the topology of ternary-segment fractal line, is proved. Moreover, the topological evolution of N-segment line is explored. The concepts of limit growth and infinite growth are clarified,and the corresponding growth conditions are derived. The topological invariant properties of N-segment line are exposed. In addition, the proposition that the topological evolution of the N-segment line is mainly controlled by the topological invariant N is verified. 相似文献
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采用一种两步化学反应模型对胞格爆轰波的楔面马赫反射过程进行了数值研究,从而澄清和解释胞格不稳定性对马赫反射发展模式和自相似性的影响。考虑到反应欧拉方程源项的刚性问题,本文采用附加RungeKutta方法耦合非刚性对流项和刚性反应源项,对流项的离散采用五阶精度的WENO格式。计算结果表明,对于稳定胞格爆轰波而言,其马赫反射过程本质上与ZND爆轰波的马赫反射是一致的,整体上不存在自相似性,胞格不稳定性只是造成了三波点轨迹线局部小振幅的波动。在楔面顶点附近,由于马赫杆是强过驱的,爆轰波的马赫反射过程是自相似的。在远场,爆轰波马赫反射的三波点轨迹线渐近的趋向于一条直线,说明重新获得了自相似性。对于不稳定的爆轰波,由于自身的不稳定性可以与马赫反射的强度相匹配,定义其三波点的轨迹是困难的,进行自相似性分析没有意义。 相似文献
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Xiaoming Lai Baomin Bian Ling Yang Anzhi He 《力学学报》2010,42(1):122
流体力学自相似运动的外延判据不太完备,对微分方程组做无量纲化处理后,得到以空间相
对坐标\xi和距离$r$为自变量的理想气体一维自相似运动微分方程的基本物理特
征量解函数,它们具有Y(\xi ,r ) = y ( \xi )r^{C_Y }的形式,即对于确定
的\xi, 特征量函数Y ( \xi ,r )具有空间标度不变性. 这种标度不变性是理
想气体一维不定常流自相似运动的存在条件. 相似文献