强迫布鲁塞尔振子奇异吸引子的柯尔莫哥洛夫容量和李雅普诺夫维数

本文用周期采样降低吸引子维数的办法,计算和讨论了强迫布鲁塞尔振子的几种典型吸引子的柯尔莫哥洛夫容量d_C和李雅普诺夫维数d_L。结果表明,人们关于d_C和d_L关系的推测是正确的。这些推测是:当最大李雅普诺夫指数λ₁>0时d_C=d_L关系成立,当λ₁=0时d_C=d_L关系不一定成立。文中指出和论证了强迫布鲁塞尔振子的Runge-Kutta差分方程使上述算法给出的d_C不收敛的原因和克服办法。文中还指出:可能是类似的微分方程的差分化的原因,使得用单个观察量的时间系列来计算容量的办法遇到了发散困难。 关键词：     

碱土氟化物离子晶体中点缺陷形成能计算

基于以前通过经验参数化途径得到的碱土氟化物电子壳模型参数和离子间互作用势参数,计算了CaF₂,SrF₂和BaF₂晶体中点缺陷形成能．计算并对比了SrF₂和BaF₂的声子色散曲线与非弹性中子散射实验数据,再一次复验了经验参数集的质量. 关键词：     

Ar-H2(D2, T2)碰撞体系的振转相互作用势及散射截面的理论计算

用量子力学从头算的耦合族CCSD(T)方法, 使用相关一致基组aug-cc-pV5Z并加3s3p2d1f1g高斯键函数计算了Ar原子与H₂分子的振转相互作用和电荷分布, 采用Boys和Bernardi提出的均衡法消除了基组重叠误差(BSSE). 然后用Tang-Toennies势能函数拟合得到Ar-H₂体系相互作用势的解析表达式. 在该相互作用势下, 用密耦方法计算了Ar原子入射能量为83 meV时, Ar-H₂(D₂, T₂)碰撞体系的散射截面. 计算Ar-D₂体系的微分截面与实验值比较符合很好. 计算结果及分析表明, 在长程吸引势的散射中, 色散能起主要作用; 在短程排斥势的散射中, 交换能起重要作用. 当碰撞参数在0.27 nm至0.47 nm的范围时, Ar-H₂(D₂, T₂)碰撞体系的径向偶极发生两次转向.     

β型烧绿石结构氧化物超导体$lt;i$gt;A$lt;/i$gt;Os$lt;sub$gt;2$lt;/sub$gt;O$lt;sub$gt;6$lt;/sub$gt;($lt;i$gt;A$lt;/i$gt;=K,Rb,Cs)电子能带结构的第一性原理计算

用全势线性缀加平面波方法计算β型烧绿石结构氧化物超导体AOs₂O₆ （A=K,Rb,Cs）的电子能带结构及态密度.计算发现电子自旋轨道耦合和在位库仑势U的作用增大了费米面处态密度值.通过计算还得到这三种化合物电子关联常数λ_c分别为1.55,1.12和0.73.由实验测量与能带计算得到的电子比热容系数的比值得到电子质量提高参数.通过分析这三种化合物电子质量提高参数,推算出它们的电声子耦合常数λ_ep分别为1.56,0.78和1.08.由此提出KOs₂O₆为强电子关联和强电声子耦合系统,而RbOs₂O₆和CsOs₂O₆的电子关联性与电声子耦合为中等. 关键词： β型烧绿石超导体 能带结构 电子关联 电声子耦合     

阳离子对Er3+掺杂硼酸盐玻璃结构和发光特性的影响

针对Si/Al掺杂量增大使BaO-(1-x)SiO₂-xAl₂O₃-B₂O₃-0.005Er³⁺(x=0,0.5,1,摩尔分数)玻璃样品的1 540 nm红外发光和540 nm上转换发光强度呈现相反的变化趋势,讨论了阳离子掺杂对稀土离子周边对称性和电负性变化与荧光行为的内在关系。红外傅里叶透射光谱显示,不同掺杂浓度下样品的最大声子能量没有明显变化,说明光谱随掺杂浓度的变化与玻璃体系的最大声子能量无关。根据Judd-Ofelt理论计算了⁴I_13/2和⁴S_3/2能级的光学参数,通过比较两能级的跃迁几率(A)、寿命(τ)、荧光分支比(β)和受激发射截面(σ)等光学参数,发现⁴I_13/2能级和⁴S_3/2能级的相关参数呈现相反的趋势。最后测试了样品⁴I_13/2能级下1 540 nm的寿命,进一步从电负性角度考虑了样品的发光效率。理论计算和实验结果相符。     

重费米子超导PuMGa5(M=Co,Rh)结构、电子和热力学性质的第一性原理研究

基于第一性原理的PBEsol+U方法研究PuCoGa₅和PuRhGa₅的晶体结构、弹性、电子性质、声子谱以及热力学性质。PBEsol+U方法考虑Pu-5f的库伦排斥作用U和Hund交换相关作用J。计算结果表明,PuCoGa₅和PuRhGa₅在PBEsol+U方法下的基态性质（包括晶格参数和原子占位）与实验数据吻合较好,且力学判据和声子谱均表明在零温和零压条件下PuCoGa₅和PuRhGa₅的基态结构是稳定的;特别地,PuRhGa₅的5f电子在费米能级附近的定域性明显强于PuCoGa₅,这可能是PuCoGa₅的超导临界转变温度高于PuRhGa₅的重要原因。此外,还研究了PuCoGa₅与PuRhGa₅的赫姆霍兹自由能、熵、内能和等容摩尔热容随温度的变化。     

GaAs和AlAs光学声子形变势的第一性原理研究

本文以冻结声子近似模型,采用空球随原子球位移的冻结势近似的LMTO-ASA计算方案,研究了GaAs和AlAs布里渊区Λ轴的光学声子形变势的计算,得到Γ点和Λ轴光学声子形变势d₀,d₃₀,d₁₀(val)和d₁₀(comd)的第一性原理的计算结果。研究中着重从GaAs和AlAs的Λ轴光学声子形变势随k点的变化趋势,从光学声子形变势在Γ点附近满足的关系,以及从不同计算方法对d₀的计算结果与实验结果的比 关键词：     

六方系InAlGaN晶体的长波长光学声子研究

利用拉曼散射实验方法对六方系InAlGaN晶体的光学声子进行了测量,同时利用修正随机元素同向位移模型对其光学声子与组分的关系进行了理论模拟。结果表明InAlGaN晶体的E₁与A₁光学声子分支都表现为单模行为,测量得到的In_xGa_0.45-xAl_0.55N晶体的A₁(LO)声子与计算结果一致。对In_xAl_0.42-xGa_0.58N晶体的A₁(LO)声子的计算结果与Cros的测量结果进行了对比,两者也相符。     

PbTiO3铁电相及顺电相的声子色散理论计算

用统一的、参数物理意义明确的刚性离子模型研究了铁电体PbTiO₃铁电相和顺电相的声子色散关系和布里渊区中心有关相变的振动模,用比以往计算少得多的参数得到了比较好的结果,并提出了研究软模的简化模型构想. 关键词： 3')" href="#">PbTiO₃ 刚性离子模型 Born-Mayer势 声子色散     

LiNH2 的晶格动力学、介电性质和热力学性质第一性原理研究

采用基于密度泛函理论的平面波赝势方法,在局域密度近似下采用线性响应的密度泛函微扰理论计算了LiNH₂的晶格动力学、介电性质和热力学性质,得到了布里渊区高对称方向上的声子色散曲线和相应的声子态密度,分析了 LiNH₂的红外和拉曼活性声子频率,同时给出它的介电张量和玻恩有效电荷张量. 研究表明,LiNH₂存在小的各向异性,计算所得结果与实验值和其他理论值符合较好.最后,利用得到的声子态密度进一步预测了LiNH₂的热力学性质 关键词： 密度泛函理论 晶格动力学 热力学性质 第一性原理计算     

Special electronic structures of inverse spinels LiMVO<Subscript>4</Subscript>(M = Ni and Cu): a first-principles study

We use the Ulam method to study spectral properties of the Perron-Frobenius operators of dynamical maps in a chaotic regime. For maps with absorption we show numerically that the spectrum is characterized by the fractal Weyl law recently established for nonunitary operators describing poles of quantum chaotic scattering with the Weyl exponent ν = d-1, where d is the fractal dimension of corresponding strange set of trajectories nonescaping in future times. In contrast, for dissipative maps we numerically find the Weyl exponent ν = d/2 where d is the fractal dimension of strange attractor. The Weyl exponent can be also expressed via the relation ν = d₀/2 where d₀ is the fractal dimension of the invariant sets. We also discuss the properties of eigenvalues and eigenvectors of such operators characterized by the fractal Weyl law.     

Scale-invariant Lyapunov exponents for classical hamiltonian systems

The Lyapunov exponent for classical hamiltonian systems is made dimensionless by introducing a characteristic time τ_c. This modification yields an energy-independent exponent for systems with scale invariance.     

无序度对一维长程关联无序系统中局域化-退局域化转变的影响

对长程幂律关联能量序列进行了修正，使其能体现出无序度在一维长程关联无序系统中的影响，并利用重正化群方法，计算了能反映该系统局域化-退局域化转变的Lyapunov指数.结果表明，在由于关联指数p的影响而在系统中出现的局域化向退局域化的转变中，无序度起着相反的作用.当关联指数p一定而无序度W增大时，系统中心能区范围内由于长程关联而引起的扩展态逐渐向局域态转变.当无序度W增大到某一临界值W_c时，系统中所有本征态均转变为局 关键词： 长程关联 Lyapunov指数 无序度 局域化-退局域化转变     

二维logistic映射的动力学行为和奇怪吸引子的分形特征

研究了二维logistic映射的动力学行为和奇怪吸引子的分形特征.利用分岔图、相图和Lyapunov指数谱分析系统的分岔过程,研究系统通向混沌的道路并确定系统处于混沌运动的参数区间;采用G-P算法计算奇怪吸引子的关联维数和Kolmogorov熵,对奇怪吸引子的分形特征定量刻画;采用逃逸时间算法构造奇怪吸引子的彩色广义M-J集,对奇怪吸引子的分形特征定性表征.结果表明,这些分析方法的配合使用可以更全面、形象地描述奇怪吸引子的分形特征.     

The role of diffusion in the chaotic advection of a passive scalar with finite lifetime

We study the influence of diffusion on the scaling properties of the first order structure function, S₁, of a two-dimensional chaotically advected passive scalar with finite lifetime, i.e., with a decaying term in its evolution equation. We obtain an analytical expression for S₁ where the dependence on the diffusivity, the decaying coefficient and the stirring due to the chaotic flow is explicitly stated. We show that the presence of diffusion introduces a crossover length-scale, the diffusion scale (L_d), such that the scaling behaviour for the structure function is analytical for length-scales shorter than L_d, and shows a scaling exponent that depends on the decaying term and the mixing of the flow for larger scales. Therefore, the scaling exponents for scales larger than L_d are not modified with respect to those calculated in the zero diffusion limit. Moreover, L_d turns out to be independent of the decaying coefficient, being its value the same as for the passive scalar with infinite lifetime. Numerical results support our theoretical findings. Our analytical and numerical calculations rest upon the Feynmann-Kac representation of the advection-reaction-diffusion partial differential equation. Received 18 March 2002 Published online 31 July 2002     

Analysis and adaptive synchronization of eight-term 3-D polynomial chaotic systems with three quadratic nonlinearities

This paper proposes a eight-term 3-D polynomial chaotic system with three quadratic nonlinearities and describes its properties. The maximal Lyapunov exponent (MLE) of the proposed 3-D chaotic system is obtained as L ₁ = 6.5294. Next, new results are derived for the global chaos synchronization of the identical eight-term 3-D chaotic systems with unknown system parameters using adaptive control. Lyapunov stability theory has been applied for establishing the adaptive synchronization results. Numerical simulations are shown using MATLAB to describe the main results derived in this paper.     

On the dynamics of the Ashkin-Teller-Potts model

The dynamical critical exponent of the s-states Ashkin-Teller-Potts model is found with the help of the linear response theory in the ? = d_c - d expansion (d_c = 4 and 6).     

Chaotic dynamics in the electroconvection system of a nematic liquid crystal

The transition from a steady domain structure to turbulence in the electroconvection system of a nematic under the action of a constant electric field is studied using the methods of optical and acoustic responses. The chaotic dynamics is investigated both by conventional methods (Fourier signal spectrum) and by methods of nonlinear dynamics. From the quantitative estimates of basic characteristics of the chaotic behavior (namely, the correlation dimension, leading Lyapunov exponent, K-entropy, and embedding dimension), one can conclude that temporal chaos arises in the system, giving rise to a strange attractor, as the control parameter increases at ɛ ≥ ɛ _c ≈ 0.5. The fact that the distribution of laminar domains in the liquid-crystal layer depends on their length under the conditions of developed turbulence indicates that the dynamics of the nematic demonstrates the intermittent behavior.     

A special type of attractor and transitions in a delayed system

We discuss strange nonchaotic attractors (SNAs) in addition to chaotic and regular attractors in a quasiperiodically driven system with time delays. A route and the associated mechanism are described for a special type of attractor called strange-nonchaotic-attractor-like (SNA-like) through T² torus bifurcation. The type of attractor can be observed in large parameter domains and it is easily mistaken for a true SNA judging merely from the phase portrait, power spectrum and the largest Lyapunov exponent. SNA-like attractor is not strange and has no phase sensitivity. Conditions for Neimark-Sacker bifurcation are obtained by theoretical analysis for the unforced system. Complicated and interesting dynamical transitions are investigated among the different tongues.