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：     

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：     

一个分段连续系统中的胖奇异集激变

报道一种有特色的激变.这种激变是在一类分段连续力场作用下的受击转子模型中观察到的.描述系统的二维映象定义域中的函数不连续边界随离散时间发展振荡，从而使这个边界的向前象集构成一个承载混沌运动的胖分形.在控制参数的一个阈值下，一个椭圆周期轨道突然出现在此胖混沌奇异集中，使得迭代向它逃逸，胖混沌奇异集因此突然变为一个胖瞬态集.在这种情况下，有可能根据椭圆周期轨道逃逸孔洞，以及胖分形奇异集的测度随参数变化的规律，估算迭代在奇异集中的平均生存时间所遵循的标度规律.直接数值计算和由此估算所得标度因子值可以很好地互相印证. 关键词： 激变 胖分形 分段连续系统 标度律     

一个强、弱耗散功能可分隔系统中的特征激变

报道一个由保守映象和耗散映象不连续、不可逆地分段描述的系统，以及在其中发生的一例特征激变.激变的独特之处在于逃逸孔洞.由映象的不连续、不可逆性而导致相平面中出现一个胖分形迭代禁区网，它使得一个混沌吸引子突然失稳而发生激变后出现的两个周期吸引子的吸引域边界成为点滴状.仅仅在每个周期点邻近存在这样的一个作为逃逸孔洞的、受到强耗散性支配和禁区边界限制的规则边界吸引域. 关键词： 激变 保守映象 耗散映象 逃逸孔洞     

混合交通流时间序列的去趋势波动分析

应用去趋势波动分析法研究交通流时间序列的复杂性,探讨了混合交通流时间序列演变行为的标度指数.根据标度指数的变化特征,进而揭示交通流时间序列所具有的长程相关性和短程相关性.通过分析发现,存在一密度ρ,当ρ₁<ρ<ρ₂时,交通流时间序列具有长程相关性;而当ρ<ρ₁或ρ>ρ₂时,交通流时间序列具有短程相关性,即密度的变化影响着标度指数的变化.另外分析了在不同慢车比率条件下时间序列的标度指数,发现慢车比率的变化 关键词： 混合交通流 去趋势波动分析 时间序列 长程相关     

具L-近邻键的一维渗流模型临界指数的精确解

应用实空间重正群方法于一维具L-近邻键的点-渗流及键-渗流模型,得到类-温度标度率与类-场标度率,再利用普适标度律得到全部临界指数的精确结果。对于点-渗流模型有α_p=2-L,β_p=0,γ_p=L,δ_p=∞,η_p=1及v_p=L。这与生成函数方法结果一致;对于键-渗流模型有α_p=2-(L(L+1))/2,β_p=0,γ_p=(L(L+1))/2,δ_p=∞,η_p=1及v_p=(L(L+1))/2,其中的“热”临界指数与转移矩阵方法结果一致,磁临界指数是新的结果。由点-渗流及键-渗流模型求出Suzuki的弱普适律的重正化临界指数为φ≡(2-α)/v=1,β≡β/v=0,γ≡γ/v=1,δ≡δ=∞及η≡η=1。即重正化的临界指数不仅与L无关,而且也不依赖于是点抑键的渗流模型,即普适律对Suzuki重正化临界指数仍得以保持。 关键词：     

相对论性氢原子径向算符矩阵元的通项计算公式

给出了相对论性氢原子径向算符矩阵元〈n′₁,K₁,j₁,m_j1|r^p|n′₂,K₂,j₂,m_j2〉的通项计算公式. 关键词：     

Os-Pt区核的基态三轴形状

在偶-偶核基态中寻找稳定的三轴形状,其中最大三轴形变为|γ|≈30°,仍然是核结构的一个主要主题。在本工作中,使用推转Woods-Saxon(WS)壳模型来研究Os-Pt区基态和集体转动态中可能的三轴形状。为寻找核态可能存在的三轴形变,具体用对力-形变-转动频率自洽推转壳模型对偶-偶^176-202Os和^182-204Pt同位素进行了总Routhian面计算。计算是在四极形变(β₂,γ)网格中进行的,而十六极形变β₄可变。事实上,在四极形变(β₂,γ)的每个网格点上,计算的能量相对于十六极形变β₄最小化。发现某些核的基态譬如¹⁹⁶Os和^188-194Pt既非扁椭球亦非长椭球,而是在这些核中基态极小值是形状非轴对称的,即三轴形变。同时,我们把从实验数据提取出的转动惯量与我们的计算结果作比较,显示实验数据不能很好地与转动假定相一致,说明有振动行为。此外,我们使用一种辅助的方法提取了平衡γ₀值,该值...     

SiH4激光等离子体内H谱线的线型研究

本工作利用光学多道分析仪(OMA Ⅲ)测量了脉冲TEA CO₂激光诱发的SiH₄等离子体内H Balmer系的H_α,H_σ和H_γ线的线型。结果表明,三条谱线的FWHM(半值全宽度)随跃迁上能级的主量子数的增加而增加,即△λ_1/2(H_α)<△λ_1/2(H_β)<△λ_1/2(H_γ)。通过对等离子体内各类加宽机制的讨论,得出等离子体内谱线的主要加宽机制为Stark加宽。由H_α线的实验线型与Stark加宽理论线型的拟合,得到等离子体的两个重要参量,平均电子密度N≈10¹⁷cm^-3,电子温度T≈40 000K。由H_β线的时间分辨测量得到等离子体的电子密度随时间的演变曲线。 关键词：     

磁控溅射ZnO薄膜的成核机制及表面形貌演化动力学研究

利用原子力显微镜分析了ZnO薄膜在具有本征氧化层的Si(100)和Si(111)基片上的表面形貌 随沉积时间的演化. 通过对薄膜生长形貌的动力学标度表征，研究了射频反应磁控溅射条件 下，ZnO薄膜的成核过程及生长动力学行为. 研究发现，ZnO在基片表面的成核过程可分为初 期成核阶段、低速率成核阶段和二次成核阶段. 对于Si(100)基片，三个成核阶段的生长指 数分别为β₁=1.04，β₂=0.25±0.01，β₃=0.74；对 于Si(11 关键词： ZnO薄膜 磁控溅射 生长动力学 成核机制     

n维格子上Ising模型临界温度的上界

本文利用耦合的技巧,建立了Ising模型与接触过程的联系。由此给出了Ising模型临界温度的上界,即n维Ising模型的临界点β_c(n)应满足 exp{2β_c(n)(2n-1)}·(exp{2β_c(n)}-1)≥2/2n-1。特别是三维Ising模型的临界点β_c(3)>1/2ln1.17。 关键词：     

Analyticity of the partition function for finite quantum systems

The partition functionZ(β,λ)=Tre ^-β(T+λV) for a finite quantized system is investigated. If the interactionV is a relatively bounded operator with respect to the kinetic energyT withT-boundb<1,Z(β,λ) is shown to be a holomorphic function of β and λ for $$\left| {\arg \beta } \right|< arctg\frac{{\sqrt {1 - b^2 \left| \lambda \right|^2 } }}{{b\left| \lambda \right|}}and\left| \lambda \right|< b^{ - 1} .$$ Forb=0Z(β,λ) is an entire function of λ and holomorphic in β for Re β>0.     

Phase transitions in random uniaxial systems with dipolar interactions

The critical behaviour of random uniaxial ferromagnetic (ferroelectric) systems with both short range and long range dipolar interactions is investigated, using the field theoretic renormalization method of Brézin et al. for the free energy above and below the transition pointT _c. The randomness is due to externally introduced fluctuations in the short range interactions (quenched case) or (and) magneto-elastic coupling to the lattice (annealed case). Strong deviations in the critical behaviour with respect to the pure systems are found. In the quenched case e.g. the specific heatC and the coefficientf ₂ (ofM ³ in the equation of state, whereM is the magnetization) change fromC |ln|t^1/3,f ₂ |ln|t^–1 in the pure system toC is the reduced temperature andA _±,C _± are constants) in the random situation. This change should e.g. be experimentally observable by deuterization of the ferroelectric tri-glycine sulfate where the logarithmic behaviour off ₂ has already been detected in the pure case. For nonvanishing magnetoelastic coupling a complex critical behaviour is obtained and discussed. We find the interesting result that if both quenched randomness and a weak magnetoelastic coupling are present the quenched random critical behaviour dominates in the close vicinity ofT _c. Finally the influence of the magnetoelastic coupling on the longitudinal phonons in investigated and it is found that the relative changes in the corresponding elastic constant and structure factor are proportional to the specific heat and the wavevector dependent energy-energy correlation function respectively, suggesting new experiments.     

High-field ENDOR and the sign of the hyperfine coupling

Two different approaches for assigning electron nuclear double resonance (ENDOR) signals to their respectiveM _s manifolds by a controlled generation of asymmetric ENDOR spectra, are described and applied to a number of systems. This assignment then allows a straightforward determination of the sign of the hyperfine coupling. Both approaches rely on a high thermal polarization that is easily achieved at high fields and low temperatures. For high-spin systems, such asS = 5/2 the assignment is afforded by the selective inversion of the | ?3/2〉 → | ?1/2〉 electron paramagnetic resonance (EPR) transition which is highly populated as compared to its symmetric counterpart, the |1/2〉 → |3/2〉 EPR transition, and therefore is easily identified. ForS = 1/2 the determination of the sign of the hyperfine coupling becomes possible when the cross- and nuclear-spin relaxation rates are much slower than the electron-spin relaxation rate and variable mixing time pulse ENDOR is used to measure the spectrum. Under these conditions the signals of theM _s = 1/2 (α) manifold become negative when the mixing time is on order of the electron-spin relaxation time, whereas those of theM _s =?1/2 (β) manifold remain positive. Under partial saturation of the nuclear transitions and short mixing time the opposite behavior is observed. Pulse W-band¹H ENDOR experiments demonstrating these approaches were applied and the signs of the hyperfine couplings of the water ligands in Mn(H₂O) ₆ ²⁺ , the H_α and H_β histidine protons in the Cu(histidine)₂ complex, the imidazole protons in Cu(imidazole) ₄ ²⁺ and the cysteine β-protons in nitrous oxide reductase were determined.     

基于p1-p2与a1+a2共同本征态的相干纠缠态表象的构建及性质

利用有序算符乘积内的积分技术（IWOP）,建立了一种称之为相干纠缠态的两粒子体系的新表象,研究了这种新表象的性质,从理论上探讨了这种相干纠缠态的产生方法.结果表明：本文建立的这种p₁-p₂与a₁+a₂的共同本征态|p,β〉,既具有相干态的特性,又体现了纠缠态的特征,具有超完备性,完全可以作为一个表象使用. 物理上可以用光分束器来实现|< 关键词： IWOP技术 相干纠缠态表象 分束器     

Random quantum magnets with broad disorder distribution

We study the critical behavior of Ising quantum magnets with broadly distributed random couplings (J), such that P(ln J) ∼ | ln J|^{-1 - α}, α > 1, for large | ln J| (Lévy flight statistics). For sufficiently broad distributions, α < , the critical behavior is controlled by a line of fixed points, where the critical exponents vary with the Lévy index, α. In one dimension, with = 2, we obtained several exact results through a mapping to surviving Riemann walks. In two dimensions the varying critical exponents have been calculated by a numerical implementation of the Ma-Dasgupta-Hu renormalization group method leading to ≈ 4.5. Thus in the region 2 < α < , where the central limit theorem holds for | ln J| the broadness of the distribution is relevant for the 2d quantum Ising model. Received 6 December 2000 and Received in final form 22 January 2001     

Protonic conductivity of β″ and ion-rich β-alumina. II: Ammonium compounds

The conductivity and thermal stability of NH⁺₄, H⁺(H₂O)_nβ″ and ion-rich β-alumina single crystals have been measured by the complex impedance method in the 25–700°C temperature range. Both structures have similar properties, but ion-rich β-alumina shows a higher stability and a lower activation energy (β: 0.18 eV, β″ 0.24 eV below 400°C and 250°C respectively). The room temperature conductivity is about 3×10^-5ω^-1cm^-1. The conducting properties and mechanisms are discussed and compared to other protonic or ionic conductors.     

Characterization of polycrystalline (Na,K)β/β′- alumina ceramics

K β′-alumina is unstable at >1300°C. Mixed alkali β′-alumina has a variable stability depending on the alkali ratio, [K⁺]/([Na⁺]+[K⁺]). For f(β)<[K⁺]/([Na⁺]+[K⁺]), the β′-Al₂O₃ phase decomposes to Kβ-Al₂O₃ 0997 0815 V 3 and a solid solution of Na β′-Al₂O₃ and K β′-Al₂O₃. For f(β)=[K⁺]/([Na⁺]+[K⁺], the ceramic consists of K β-Al₂O₃ and Naβ′-Al₂O₃ and for f(β)>[K⁺]/([Na⁺]+[K⁺]), the excess Na⁺ after Na β′-Al₂O₃ dissolves in the β phase, giving Na β-Al₂O₃/K β-Al₂O₃ solid solution and Na β′-Al₂O₃. These sequences were confirmed by measuring the dependence of the c-axis lattice parameters of β- and β′-Al₂O₃ phases on the f(β), and the change of these parameters during the ion-exchange of Na⁺ and K⁺ ions.     

On the Best Constant in the Moser-Onofri-Aubin Inequality

Let S ² be the 2-dimensional unit sphere and let J _α denote the nonlinear functional on the Sobolev space H ¹(S ²) defined by

Microstructural evolution and phase transformation in the liquid-solid Al/Ni diffusion couple

The liquid-solid Al/Ni diffusion couple was successfully fabricated by annealing at 1373?K for 48?h followed by water-quenching. Cross-sectional scanning and transmission electron microscopic analyses show that the multilayered diffusion zones comprise the following sequence of layers: γ-Ni(Al) | γ′-Ni₃Al | β′-NiAl | Ni-rich β-NiAl | β-NiAl. The Ni-rich β-NiAl upon quenching undergoes a martensitic transformation from β (B2) to β′ (L1₀). The β′ martensite is found to be internally twinned on the {111}<112>system. The volume changes and strains due to martensitic phase transformation, the precipitation of γ′-Ni₃Al from γ-Ni(Al) and lattice mismatch between Ni-rich β-NiAl and β-NiAl in the Al/Ni diffusion couple are quantitatively determined. The cuboidal γ′ phase coherently precipitates cube-on-cube in γ-Ni(Al). Composition fluctuations existing in the supersaturated solid solution γ-Ni(Al), provide sufficient driving force for the precipitation and facilitate nucleation and growth of the γ′ phase under isothermal annealing.