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 We have studied numerically several sequences of period doubling bifurcations of the standard mapping, and found that the sequences also possess universal properties, and obtined the universal constantsδ = 8.721……, α=-4.018…… and β = 16.363……, which agree with thoseobtained from other two dimensional area preserving mappings. 研究标准映象的倍周期分岔序列,发现其具有普适性,得到普适常数δ=8.721…、α=-4.018…及和β=16.363…,和其它二维保面积映象的结果一致。 短句来源 The universal constants obtained in the curve fitting of the experimental data of the three systems are A=-1.8180, A′=3.2215. The difference between the above results and the results obtained from metastable phase separation is also discussed. 这里A、A′是分相普适常数。 本文从这三个系统分相实验值的拟合结果是A=-1.8180,A′=3.2215,并对此结果与从亚稳分相系统得到的普适常数有所不同作了初步分析。 短句来源 Here A andA′are universal constants of immiscible curves. 这里 A、A′为二组元系统分相曲线的普适常数。 短句来源 Universal Properties and Universal Constants in Bifurcation Structure of Nonlinear Mappings 非线性映像分支点结构中的一些普遍规律和普适常数 短句来源 In this paper, the universal functions h(x), D(x), and the universal constants δ, K, which describe the critical behavior of the period-n-tupling sequences, arc discussed and Calculated. 本文讨论与计算了描述高周期序列临界行为的普适函数h(x),D(x)及普适常数δ,κ; 短句来源 更多 “universal constants”译为未确定词的双语例句
 A RENORMALIZATION GROUP APPROACH FOR UNIVERSAL CONSTANTS OF PERIOD DOUBLING SEQUENCES 倍周期分岔序列普适常数的重整化群逼近 短句来源 Physical Meaning about the Universal Constants in Chaos and Fractal 混沌和分形的普适常数的物理意义 短句来源 Futhermore, their phase separation curves at two sides of the critical points can be universally calculated by the following two equations:(x-x_c)/_c=A[(T_c-T)/T_c]~(1/2); (x′-x_c)/x_c=A′[(T_c-T)/T_c]~(1/2), where A and A′ are universal constants of immiscible curves. 相应它们临界点两侧的分相曲线,可普适地由以下两表达式定量表示:(x-x_c)/x_c=A(T_c-T)/T_c)~(1/3),(x′-x_c)/x_c=A′(T_c-T)/T_c)~(1/3)。 短句来源 相似匹配句对
 THE UNIVERSALITY AND UNIVERSAL CONSTANTS OF PHASE SEPARATION IN BINARY SYSTEMS 二元系统分相的普适性及普适常数 短句来源 Physical Meaning about the Universal Constants in Chaos and Fractal 混沌和分形的普适常数的物理意义 短句来源 universal spirit. 天地精神。 短句来源 UNIVERSAL DBMS 通用数据库管理系统 短句来源 All the elastic constants 在整个压力范围内,压缩时表现了良好的弹性各向同性。 短句来源 查询“universal constants”译词为用户自定义的双语例句

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 The main postulates of the quantum electrodynamics of bilocal fields are formulated, the theory containing three universal constants c, h, and k. Each of them corresponds to a saddle solution of the two-dimensional generalization of Feigenbaum-Cvitanovi? equation and is characterized by a set of distinct universal constants analogous to Feigenbaum's α and δ. The boundary of the domain of analyticity of this function is obtained graphically and is shown to be a fractal with self-similar properties obtained by rescaling with the universal constantsα andδ. We propose a new picture of nature in which there are only two fundamental universal constantsè ē (≡e/c) andh(≡?/c). It is emphasized that the coefficients of these models are not universal constants, but rather statistical estimates subject to several sources of error. 更多 The general equations of motion,mass conservation,continuity and energy are de- rived for the aerated turbulent water flow.The equations appear in the paper as Eqs.(6),(7),(8)and(12),where c denotes the air concentration and a_i the rise velo- city of air bubbles.Equation(6)differs significantly from the Reynolds equation by the appearance of the additional turbulent concentration stress The two-dimensional aerated steady uniform open channel flow is studied in detail, for which the stress equation(16)is first... The general equations of motion,mass conservation,continuity and energy are de- rived for the aerated turbulent water flow.The equations appear in the paper as Eqs.(6),(7),(8)and(12),where c denotes the air concentration and a_i the rise velo- city of air bubbles.Equation(6)differs significantly from the Reynolds equation by the appearance of the additional turbulent concentration stress The two-dimensional aerated steady uniform open channel flow is studied in detail, for which the stress equation(16)is first derived,making use of Eqs.(6),(7)and(8). It is pointed out that Eq.(16)contains the gravitational force gρ sin θ(y- which increases with the angle θ of inclination,and the concentration stresscos θ,which decreases with θ.As the velocity is influenced by these two quantities,the increase of discharge with θ should be less for the aerated open channel flow than for the nonaerated. As needed for subsequent analysis,the test values of against Y_1~′/d_s obtained from Straub and Anderson's data for the open channel flow are plotted in Figs.(5)and(6).The symbol d_s is the depth from the channel bed(y=0)to the interface(y=d_s)between the water and the air flow; and are the air concentra- tions at the bed and at the interface respectively is the corresponding sectional mean; Y_1~′ is the distance from the center of the entrained air mass to the interface. Following the two figures,the velocity-profile equations are derived by using Eq.(16) and Prandtl's mixing length(l)theory.The plane(y=d_1)of the maximum velocity is considered to divide the open channel flow into two regions:the lower region 0≤y≤d_1 near the bottom wall,and the upper region d_1≤y≤d_s near the interface, both having comparable depths.For the lower region,l=Ky is assumed as usual and a logarithmic velocity profile in the form of Eq.(24)is obtained,where u_1~* is the shear- stress velocity at y=d_1.In Eq.(23),which is used to define u_1~*,k is the ratio of - to gρ(y).For the upper region,however,the turbulence is con- sidered“free”,and the assumption l/d_s=D yields a linear velocity profile with adverse transverse gradient.As shown by Figs.7 and 8,measured velocities such as given by Straub and Lamb for different angles θ can be plotted in accordance with the two velocity equations. Using Eqs.(24)and(26),the resistance equation(30),which contains the universal constants A,K,B,D,k,d_1/d_s and /u_1~*,and expresses Chezy's C as a function of θ,Re,,is finally derived. 本文给出了掺气水流的运动、连续、质量平衡、动量及能量诸基本方程式.考虑了在运动方程式中出现的浓度紊动应力项的重要意义,应用普兰特紊流的混合长度理论,对二元明渠掺气均匀水流的流速分布公式进行了推导.在邻近渠底部分,紊动受底边界约束,混合长度与对底距离成正比,流速分布与通常均质紊流相似,为对数曲线.在邻近水面的部分,紊动自由,混合长度为常值,流速分布为直线的.二分布式均与已有的试验结果符合.文中还继续根据分布式给出了谢才系数依据水流倾角、雷诺数、断面平均掺气浓度及渠底掺气浓度而变的表示式. In this paper, the universal functions h(x), D(x), and the universal constants δ, K, which describe the critical behavior of the period-n-tupling sequences, arc discussed and Calculated. The niumerical results of δ, K, h(x), D(x) for R*n, (RL)*n, (RL2)*n, (RLR2)*n, (RL2R)*n and (RL3)*n are obtaired. 本文讨论与计算了描述高周期序列临界行为的普适函数h(x),D(x)及普适常数δ,κ;给出了R~(*n),(RL)~(*n),(RL~2)~(*n),(RLR~2)~(*n),(RL~2R)~(*n)和(RL~3)~(*n)序列的δ,κ,h(x),D(x)的计算结果。 We have studied numerically several sequences of period doubling bifurcations of the standard mapping, and found that the sequences also possess universal properties, and obtined the universal constantsδ = 8.721……, α=-4.018…… and β = 16.363……, which agree with thoseobtained from other two dimensional area preserving mappings. 研究标准映象的倍周期分岔序列,发现其具有普适性,得到普适常数δ=8.721…、α=-4.018…及和β=16.363…,和其它二维保面积映象的结果一致。 << 更多相关文摘 相关查询

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