标准映象的周期分岔及其向混沌的过渡

本文研究了标准映象的周期轨道在其余数R=1和R=0附近的行为,对于前者出现倍周期分岔序列,其分岔率δ及标度因子α和β与其它二维保面积映象的结果一致;对于后者发生同周期分岔,这与标准映象的奇对称性有关。文中还计算了混沌轨道的李雅普诺夫指数,发现在倍周期分岔序列的聚点k_∞附近,存在标度关系: λ=λ_∞+A(k—k_∞)+B(k—k_∞)^τ, 其中因子τ=0.32。这与理论推断的结果τ=(ln(2))/(l 关键词：     

一维单峰映象的拓扑熵

在对Logistic映象数值计算的基础上,我们分析了一维单峰映象的逆轨道结构,证明了不同参数处逆轨道总数N(n)随求逆次数n而变化的递推公式。借此解析地求得了在倍周期区中h(f)≡0;在U序列RLR²¹的m=3+2l周期点上h(f)=logα_mp,其中α_mp为方程α^m-2α^m-2-1=0的最大实根;在2^j-1常和2j带交界处h_j(f)=(1/2)^jlog2,由此可得聚点μ_∞处拓扑熵的标度指数t=0.449806…。在此基础上,我们还求得了混沌区的周期窗口,U序列RL^aR^b所对应的各点处的拓扑熵,以及h_R*Q(f)=(1/2)h_Q(f)的关系。证明是在M.S.S.规则和“*”乘法则的基础上进行的。所以本文的结果对一维单峰映象是普适的。 关键词：     

一类位于加周期分岔中的貌似混沌的随机神经放电节律的识别

识别非周期神经放电节律是混沌还是随机一直是一个重要的科学问题. 在神经起步点实验中发现了一类介于周期k和周期k+1(k=1,2)节律之间非周期自发放电节律, 其行为是长串的周期k簇和周期k+1簇的交替. 确定性理论模型Chay模型展示出了周期k和周期k+1节律的共存行为. 噪声在共存区诱发出了与实验结果类似的非周期节律, 说明该类节律是噪声引起的两类簇的跃迁. 非线性预报及其回归映射揭示该节律具有确定性机理; 将两类簇分别转换为0和1得到一个二进制序列, 对该序列进行概率分析获得了两类簇跃迁的随机机理. 这不仅说明该节律是具有确定性结构的随机节律而不是混沌, 还为深入识别现实神经系统的混沌和随机节律提供了典型示例和有效方法.     

振动筛系统的两类余维三分岔与非常规混沌演化

建立了振动筛系统的动力学模型,推导出了其周期运动的Poincaré 映射,基于Poincaré 映射方法着重研究了系统Flip-Hopf-Hopf余维三分岔、三次强共振条件下的Hopf-Hopf余维三分岔以及三种非常规的混沌演化过程.研究结果表明,此两类余维三分岔点附近的动力学行为变得更加复杂和新颖,在分岔点附近出现了三角形吸引子、3T²环面分岔以及“五角星型”、“轮胎型”概周期吸引子,揭示了环面爆破、环面倍化以及T²环面分岔向混沌演化的过程,这些结果对于振动筛系统的动力学优化设计提供了理论参考. 关键词： 余维三分岔 非常规混沌演化 T²环面分岔')" href="#">T²环面分岔     

一类分段光滑映象中有新特征的激变

讨论了描述一类电子张弛振子的分段光滑映象中的两种不连续性导致激变的特性.一种激变发生的机理是一个混沌吸引子吸引域内的不稳定周期轨道与映象的不连续区碰撞;而另一种激变的机理是一个混沌吸引子与两个映象的不连续区构成的“映孔”碰撞.发现第一种激变的平均层流相长度的标度律为〈τ〉∝^-1.8,层流相长度分布的标度律为P(τ)=1〈τ〉·exp-τ〈τ〉,而第二种激变的标度律分别为〈τ〉∝exp(k^-1/2)和P(τ)=1〈τ〉exp-τ〈τ〉. 关键词：     

一维单峰映象中高周期序列的普适常数与普适函数

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,(RL²)^*n,(RLR²)^*n,(RL²R)^*n和(RL³)^*n序列的δ,κ,h(x),D(x)的计算结果。 关键词：     

Mn离子取代M型钡铁氧体的研究

本文对Mn离子取代M型钡铁氧体BaFe_12-xMn_xO₁₉作了较系统的研究。主要结论如下:(1)在我们的实验条件下,Mn的取代量x可达4,其中约有0.1—0.3的Mn²⁺存在,其余Mn为三价。(2)Mn离子主要进入12k和2a晶位。(3)BaFe_12-xMn_xO₁₉的各向异性常数K₁₉,居里温度T_c和饱和磁化强度σ_s均随x的增加而下降。(4)Mn引起BaFe_12-xMn_xO₁₉的非共线自旋结构。(5)Mn³⁺在12k和2a晶位中的平均零场劈裂因子D^h比尖晶石中八面体B位上的Mn³⁺之D^c值小近一个数量级。 关键词：     

Co2+-Ti4+和Cu2+-Nb5+离子取代BaFe12O19单晶体中Fe3+离子的研究

本文对用Co²⁺-Ti⁴⁺和Cu²⁺-Nb⁵⁺离子取代BaFe₁₂O₁₉单晶体中Fe³⁺离子进行了研究,以Bi₂O₃作为助熔剂生长出了BaFe_12-2xCo_x²⁺Ti_x⁴⁺O₁₉(x=0;0.04;0.09;0.13;0.27和0.68)以及BaFe_12-x[Nb_1/3⁵⁺Cu_2/3²⁺]_xO₁₉(x=0;0.28;0.44和0.60)这两系列的单晶体,测定了100—300K温度范围内样品的磁化强度σ与单轴各向异性常数K₁,我们发现,对Co²⁺-Ti⁴⁺取代的样品,当x≤0.09时,其σ与K₁随x的增加而缓慢增加;当x>0.09时,其σ与K₁随x的增加而迅速降低,至x=1.1时,K₁变为零,对Nb⁵⁺-Cu²⁺取代的样品,其σ值在整个成份范围内基本保持不变,且有缓慢增加趋势;而K₁值则随x增加而单调下降,提出了取代离子在M型六角铁氧体中可能的分布模型来解释我们的结果。 关键词：     

基于TD-ERCS混沌系统的伪随机数发生器及其统计特性分析

为了进一步分析切延迟椭圆反射腔映射系统(TD-ERCS)混沌系统的密码学意义上的安全性， 采用TD-ERCS并行方式构造了一个结构简单的伪随机序列发生器.用户密码不再是固定不变的 ，可在［2⁶⁴，2⁶⁷²］区域内任意取值.对所产生的二值伪随机 序列（即TD-ERC S序列）进行了均衡性、游程特性、相关性等基本统计特性初步测试，并与m序列、logistic 序列、Chebyshev混沌序列、SCQC序列作了对比分析.实验表明，TD-ERCS序列有更好的统计 特性. 关键词： 混沌 TD-ERCS PRNG 统计特性     

14—20 eV范围内CO的Rydberg系列

利用同步辐射和多级光电离吸收池,在14—20 eV (890—620 Å)范围内测量了CO绝对光吸收谱,得到了CO离子态的电离能. 根据CO绝对光吸收谱,结合理论计算,分别识别了收敛到CO⁺三个电子态(Χ²Σ⁺, Α²Π和B ²Σ⁺)的Rydberg系列. 不仅扩充了前人识别的Rydberg系列和振动序列,而且探索性地识别了收敛到CO^{+关键词： 同步辐射 多级光电离吸收池 Rydberg系列 振动序列}     

三方晶系的非线性磁光克尔谱及其表面磁化强度取向的效应

本文计算了三方结构不同表面和不同磁化强度取向下的χ⁽²⁾、SHG、MSHG及非线性克尔旋转角Φ_k,a⁽²⁾.结果表明,SHG和Φ_k,a⁽²⁾值非常灵敏地依赖于薄膜的表面及磁化强度的取向;三方结构的SHG、Φ_k,a⁽²⁾与fcc、bcc和hcp结构的相比有很大的差异,这表明结构对非线性磁光效应有重要的影响;当M//X、Y轴时,MSHG信号很明显,这表明可通过A值的测量来研究磁性薄膜表面的磁畴结构以及取向.     

Bestimmung des Fluxoidquants in supraleitenden Hohlzylindern. II

Electron interferometric measurements on superconducting hollow cylinders with an inner diameter of about 0.7 μm yielded the fluxoid quantum to Φ_{0, exp}=2.1·10^?7 Gcm² (theoretical value: Φ₀=2.07·10^?7 Gcm²). For this determination a relation between the experimental values and the fluxoid quantum was derived from the thermodynamic potential.     

Gaussian Multiplicative Chaos and KPZ Duality

This paper is concerned with the construction of atomic Gaussian multiplicative chaos and the KPZ formula in Liouville quantum gravity. On the first hand, we construct purely atomic random measures corresponding to values of the parameter γ ² beyond the transition phase (i.e. γ ² > 2d) and check the duality relation with sub-critical Gaussian multiplicative chaos. On the other hand, we give a simplified proof of the classical KPZ formula as well as the dual KPZ formula for atomic Gaussian multiplicative chaos. In particular, this framework allows to construct singular Liouville measures and to understand the duality relation in Liouville quantum gravity.     

Formation of carbonium ions on zeolite surfaces

The adsorption and thermal desorption of carbonium ions from surfaces of zeolites, Al₂O₃ and TiO₂ have been investigated spectroscopically. The formation of stable carbonium ions (Φ₃C⁺) of triphenylmethyl compounds (Φ₃CCl and Φ₃COH) occurred at relatively low temperatures, e.g. 100°C. No Φ₃C⁺ ions could be detected after adsorption of triphenylmethane. These findings are in agreement with prior mass spectrometric results. Intensities of the respective IR bands indicate that the molecules (Φ₃CCl, Φ₃COH, Φ₃CH) penetrate into the interior of the zeolite grains, where they are adsorbed. The experiments show that acidic Lewis sites are responsible for the carbonium ion formation in the present system.     

Theoretical computations of spontaneous vibration-rotation raman scattering from OH(X 2Φ) and NO(X 2Φ)

Absolute values of Q-branch line intensities for OH(X² Φ) and NO(X² Φ) has been calculated, primarily for use in making measurements in flames. The effects of spin-orbit interaction, spin uncoupling, vibration-rotation interaction, and anharmonicity has been included in the calculations simultaneously in a self-consistent fashion. A-doubling is neglected. Multiconfigurational self-consistent field calculations of static polarizabilities are used to approximate the required electronic matrix elements. Complete derivations and discussion of the wave functions and matrix elements are included for clarity and to point out restrictions and approximations. Results of the calculations for NO agree well with room temperature measurements of Raman cross sections. No experimental data are available for OH.     

Multiple fluorescence and the electronic relaxation processes of coronene vapor: The fluorescence from the S1, S2, and S3 states

Fluorescence and excitation spectra of coronene vapor have been measured under different conditions. Weak emission which can be regarded as the fluorescence from the third excited singlet state, S₃(¹E_1u), was observed in addition to the S₁(¹B_2u) and S₂(¹B_1u) fluorescence. The observed S₂ and S₃ fluorescence are substantially different from those reported previously for coronene vapor. Addition of oxygen resulted in significant decrease of the S₁ fluorescence intensity, but did not affect the S₂ fluorescence intensity, indicating the faster decay rate of the S₂ state than that of S₁. Excitation energy dependence of the S₁, S₂ and S₃ fluorescence quantum yields (Φ_F(S₁), Φ_F(S₂) and Φ_F(S₃), respectively) revealed that Φ_F(S₁) decreases with increasing excitation energy, while Φ_F(S₂) and Φ_F(S₃) increase significantly. The quantum yield ratios, Φ_F(S₂)/Φ_F(S₁) and Φ_F(S₃)/Φ_F(S₂), obtained as a function of excitation energy are correlated with the ratios of the relative internal conversion rates.     

量子混沌系统本征态的统计非遍历性及其半经典极限

讨论半经典极限下circular unitary ensemble(CUE)系综本征态θ_k(j)的非遍历性质.为研究量子系统本征态在统计上的非遍历性,定义了本征态分布ρ_k(j)的一对统计函数：Φ_N(j)=∑N-1k=0ρ_k(j)²和Ψ_N(j)=∑N-1k=0ρ_k(j),以分别体现量子本征态分布的凸起与凹陷.在随机矩阵理论的框架内,数值地计算了由正交归一的 关键词：     

Molecular beam surface ionization detection: II. Field reversal and surface ionization study of Na on Re with adsorbed oxygen

The desorption and surface ionization of Na on a polycrystalline Re surface with various amounts of adsorbed oxygen have been studied by field reversal, surface ionization and thermoelectronic emission methods. In this work the unique properties of the field reversal method are taken advantage of, i.e. that both neutral and ionic desorption rate constants can be determined simultaneously. Absolute ionization coefficients have been measured by field reversal and have been compared with values found by the “oxygen coverage” method and by static surface ionization. The application to beam flux density determinations is discussed. The simultaneous variation of the neutral and ionic desorption rate constants during oxygen adsorption and the temperature dependence of them have been studied. The Re surface in 2 × 10^?8 Torr of oxygen and at 1300–1500 K is shown to be very stable and to behave differently than in studies at higher temperatures. The very rapid change in both desorption rate constants at an effective work function Φ^e = 5.35 V is here correlated with the results of LEED experiments (Gorodetskii and Knysh) and is proposed to indicate a change from a stable Re oxide surface at low Φ^e (and oxygen coverage) to a different surface structure at higher Φ^e. Desorption energies have been determined at various values of Φ^e. The neutral desorption energy at low oxygen pressure is 2.70 ± 0.06 eV, which agress well with earlier, here corrected modulated beam results. The energy (Schottky) cycle for surface ionization is shown to be closed at low Φ^e, which has been difficult to show with other methods in any other case.     

Renormalization problem in nonrenormalizable massless Φ4 theory

Nonrenormalizable massless Φ⁴ theory is made finite by regularization via higher derivatives in the kinetic part of the Lagrangean. The theory is shown to remain finite in the infinite cutoff limit if certain integrals over functions of one variable, with computable Taylor expansion at the origin, are finite. The values of these integrals are the only unknowns in the double series in powers ofg andg ^2/ε obtained for the Green's functions in massless (Φ⁴)_4+ε with generic ε. For ε=1 and ε=2, these series reduce to double series in powers ofg and lng. The problems of extension to (Φ⁴)_4+ε with mass, of causality and unitarity, of the relation to the BPHZ formalism, and of the indeterminacy of the result are discussed.     

Magnetic field effects on electron transfer reactions involving sextet-spin (S = 5/2) intermediates generated on photoexcitation of a Cr(III)-porphyrin complex

The excited trip-sextet (⁶T₁) state of chloro-(3-methylimidazol)-(meso-tetraphenylporphyrinato) chromium(III) (Cr^IIIP) is quenched by 1,1′-dibenzyl-4,4′-bipyridinium (BV²⁺) in acetonitrile through electron transfer to give ⁵(Cr^IIIP^·+) and ²BV^·+. The intermediate is a geminate ion pair in the sextet (Sx) state ⁶[⁵(Cr^IIIP^·+) ²BV^·+], which decays through either the escape from a solvent cage to give the free ions or the spin conversion to the quartet (Qa) state followed by back electron transfer. The free ion yield (Φ_FI) increased with increasing magnetic field from 0 to 4 T and then slightly decreased from 4 T to 10 T. These magnetic field effects are explained as follows. Under low fields where the Zeeman splitting of the spin sublevels is lower than or comparable with the electron spin dipole—dipole interaction within ⁵(Cr^IIIP^·+), this interaction effectively induces the Sx → Qa conversion of [⁵(Cr^IIIP^·+)²BV⁺] to result in low Φ_FI values. Under high fields where the Zeeman splitting is larger than the dipole—dipole interaction, the Sx → Qa conversion is decreased with increasing field to cause higher Φ_FI values. The slight decrease in Φ_FI above 4 T may be due to the Δg mechanism.