Double Wronskian Solutions for a Generalized Nonautonomous Nonlinear Equation in a Nonlinear Inhomogeneous Fiber

A generalized nonautonomous nonlinear equation, which describes the ultrashort optical pulse propagating in a nonlinear inhomogeneous fiber, is investigated. N-soliton solutions for such an equation are constructed and verified with the Wronskian technique. Collisions among the three solitons are discussed and illustrated, and effects of the coefficients σ₁(x, t), σ₂(x, t), σ₃(x, t) and v(x, t) on the collisions are graphically analyzed, where σ₁(x, t), σ₂(x, t), σ₃(x, t) and v(x, t) are the first-, second-, third-order dispersion parameters and an inhomogeneous parameter related to the phase modulation and gain(loss), respectively. The head-on collisions among the three solitons are observed, where the collisions are elastc. When σ₁(x, t) is chosen as the function of x, amplitudes of the solitons do not alter, but the speed of one of the solitons changes. σ₂(x, t) is found to affect the amplitudes and speeds of the two of the solitons. It reveals that the collision features of the solitons alter with σ₃(x, t)=-1.8x. Additionally, traveling directions of the three solitons are observed to be parallel when we change the value of v(x, t).     

基于4A"势能面研究C(3P)+NO(X2Π)→CO(X1Σ+)+N(4S)反应的立体动力学性质

运用准经典轨线方法(QCT), 基于Abrahamsson等构造的⁴A"势能面(Abrahamsson E Andersson S, Nyman G, Markovic N 2008 Phys. Chem. Chem. Phys. 10 4400), 在碰撞能为0.06 eV时, 对C(³P)+NO(X²Π )→CO(X¹Σ⁺)+N(⁴S)反应立体动力学性质进行了理论研究. 在考虑反应物NO转动和振动激发的条件下, 计算了质心坐标系下k-j'矢量(k与j'分别为反应物速度与产物角动量)相关的P(θ_r)分布和k-k'-j'矢量(k'为产物相对速度)相关的P(φ_r)分布. 此外还计算了该反应的三个极化微分截面(2π/σ)(dσ₀₀/dω_t), (2π/σ)(dσ₂₀/dω_t)以及(2π/σ)(dσ₂₂+dω_t). 计算结果表明转动和振动激发对产物取向影响较大而对定向影响较小; 对于三个极化微分截面, 转动激发的影响不大, 而振动激发的影响则较大.     

一个新的自由能函数对介电高弹薄膜的多组等双轴预拉伸下力电耦合实验的预测

当介电高弹聚合物薄膜被施以面内等双轴预拉伸后, 受到厚度方向的电压作用时, 薄膜在力场和电场共同作用下产生大变形. 电场采用Maxwell应力分析, 力场采用橡胶弹性模型分析. 拟合这类变形的常用橡胶弹性模型主要有Neo-Hookean, Arruda-Boyce, Gent等模型. 这些模型对实验数据的定量拟合存在不同程度的偏差. 通过对实验数据的分析, 结合数学方法, 提出了一个新的自由能函数模型. 通过该模型对VHB4905介电高弹聚合物薄膜的多组等双轴预拉伸电力耦合实验进行拟合, 并以Neo-Hookean, Gent模型作为对照, 结果与实验数据拟合很好, 比对照模型的偏差明显缩小.     

Alternating-current relaxation of a rotating metallic particle

Based on a first-principles approach,we establish an alternating-current(AC) relaxation theory for a rotating metallic particle with complex dielectric constant ε_α=ε_α-iσ_α/ω_0.Here εα is the real part,σ_α the conductivity,ω_0 the angular frequency of an AC electric field,and i=-1~(1/2).Our theory yields an accurate interparticle force,which is in good agreement with the existing experiment.The agreement helps to show that the relaxations of two kinds of charges,namely,surface polarized charges(described by ε_α) and free charges(corresponding to σ_α),contribute to the unusually large reduction in the attracting interparticle force.This theory can be adopted to determine the relaxation time of dynamic particles in various fields.     

High-Order Binary Symmetry Constraints of a Liouville Integrable Hierarchy and Its Integrable Couplings

A 3 × 3 matrix spectral problem and a Liouville integrable hierarchy are constructed by designing a new subalgebra of loop algebra A^-2. Furthermore, high-order binary symmetry constraints of the corresponding hierarchy are obtained by using the binary nonlinearization method. Finally, according to another new subalgebra of loop algebra A^-2, its integrable couplings are established.     

某些Cr(Ⅲ)配合物的冷冻溶液或稀释粉末ESR谱研究

报道了三个Cr(Ⅲ)螯合物负离子--［Cr(ox)₃]^3- (1), ［Cr(bipy)(ox)₂］^- (2), ［Cr(phen)(ox)₂］^- (3)(ox为草酸根二价负离子,bipy为2,2′-联吡啶,phen为1,10-邻菲罗啉)在冷冻水溶液中,以及一个粉末样品-稀释在硫酸铝铵中硫酸铬铵（mol比Cr³⁺∶Al³⁺=1∶150 ）(4)于室温下的ESR谱,得到配合物的波谱参数值,并对分子的对称性进行了分析. 1,2,3有相同的g值(1.99),相近的D值(0.42～0.45cm^-1),但相差 很大的E值(分别为0.015, 0.05, 0.11cm^-1),这些值反映了溶液中过渡金 属离子内在对称性的变化.     

Four-Particle Entangled State Representation and Its Squeezing Transformation

The four-particle EPR entangled state | p,χ₂,χ₃,χ₄〉is constructed. The corresponding quantum mechanical operator with respect to the classical transformation p→e^λ₁p, χ₂→ e^λ₂χ₂, χ₃→e^λ₃χ₃, and χ₄→e^λ₄χ₄ in the state |p,χ₂ ,χ₃ ,χ₄〉is investigated, and the four-mode realization of the SU(1,1) Lie algebra as well as the corresponding squeezing operators are presented.     

Symmetries and Infinite Dimensional Lie Algebra of the Variable Coefficient KDV Equation

With the help of the conditional strong symmetry, we obtain the K symmetries, r symmetries, infinite dimensional Lie algebra and the corresponding infinite conservation quantities of the variable coefficient KdV equation u_t = h₁(t)(u_xxx +6uu_x) +4h₂(t)u_x - h₀(t)(2u+ xu_x) with h₀, h₁ and h₂ being three arbitrary functions of t.     

NMR study of monomethylammonium cation in (CH3NH3)5Bi2Cl11 ferroelectric polycrystal

Spin-lattice relaxation times T₁ and T_1ρ are determined for protons in three polycrystals (CH₃NH₃)₅Bi₂Cl₁₁, (CD₃NH₃)₅Bi₂Cl₁₁ and (CH₃ND₃)₅Bi₂Cl₁₁. The temperature dependencies of the relaxation times obtained for (CH₃NH₃)₅Bi₂Cl₁₁ and (CD₃NH₃)₅Bi₂Cl₁₁ are interpreted as a result of correlated motions of the three-proton groups of the monomethylammonium cation. The minimum of the T_1ρ relaxation time is explained as a result of the oscillations of the symmetry axis of the whole cation.     

Convergent-beam electron diffraction of CaZr4O9, a complex zirconia alloy phase

The point-group and space-group symmetry of the controversial fluorite-based stoichiometric superlath phase of ø₁ (CaZr₄O₉: Z=16), considered to be a coherently-intergrown subphase of lime-stabilized zirconia, is examined. Using convergent-beam and selected-area electron diffraction, it is determined that the space group of ø₁ is C2/c, in apparent agreement with earlier studies utilizing other diffraction techniques.     

The Fibre Bundle Formulation of σ-Model and SUSY σ-Model

In this paper, we present an analysis of the general symmetry properties of some physical systems, where especially the method of h_μ(x), k_μ(x) decomposition of connection is used. Then we reformulate the σ-model and the SUSY σ-model in the framework of fibre bundle theory. By comparisons, we obtain the SUSY partner of "linearized" equation or Lax pair of σ-model.     

A Possible Generalization of Jaynes-Cummings Model with Degenerate Spectrum

We propose a generalized Jaynes-Cummings model (JCM) for three two-level atoms and three-mode radiation field with the interaction being H₁=λ(a₁⁺a₂⁺σ_1-σ_2-+a₂⁺a₃⁺σ_2-σ_3-+a₁⁺a₃⁺σ_1-σ_3-+H.C.). This model is characteristic of possessing partly degenerate spectrum. Some transition process of this system is calculated.     

A new 9 K superconducting organic salt composed of the bis (ethylenedithio) tetrathiafulvalene (ET) electron-donor molecule and the tetrakis (trifluoromethyl) cuprate (III) anion, [Cu(CF3)4]

We report the discovery of a second, higher-T_c superconducting organic charge-transfer salt derived from the electron-donor molecule BEDT-TTF (or ET), the novel organometallic anion [Cu(CF₃)₄]⁻, and the neutral solvent molecule 1, 1, 2-trichloroethane (TCE). We have very recently reported that this charge-transfer system yields a new superconducting phase salt, _L- (ET)₂Cu(CF₃)₄·TCE, with inductive onset T_crmc=4.0 K at ambient pressure. This phase salt ( denotes a particular packing arrangement of the ET organic donor molecules) is electrocrystallized in the habit of hexagonal plates. Crystals possessing a needle-like habit electrocrystallize simultaneously with these plates, and we find these needles to be a distinctly different superconducting phase with diamagnetic onset T_c=9.2±0.1 K at ambient pressure. On the basis of our experiments, we denote this new superconducting phase as _H−(ET)₂Cu(CF₃)₄·(TCE)_x,X<1.     

High—Dimensional Integrable Models with Infinitely Dimensional Virasoro—Type Symmetry Algebra

Using every realization of the Virasoro-type symmetry algebra[σ(f1),σ(f2)]=σ(f1f2-f2f1),we can obtain various high-dimensional integrable models under the meaning that they possess infinitely many symmetries,By means of a concrete realization ,many(3 1)-dimensional equations which possess Kac-Moody-Virasoro-type infinite dimensional symmetry algebras are obtained.     

In2O3晶体电子结构和光吸收机理研究

为了得到准确的In₂O₃晶体电子结构, 本文分别采用GGA, GGA+U, HSE06的方法计算了电子结构, 并进行了G₀W₀修正, 通过比较计算结果, 得到HSE06+G₀W₀方法计算得到的禁带宽带最接近实验结果. 在此基础上使用Hedin的G₀W₀近似方法和Bethe-Salpeter方程计算得到了In₂O₃晶体的光学性质, 计算结果与实验结果吻合很好, 在此基础上通过对准粒子能带结构、光学跃迁矩阵和光学吸收谱的分析, 给出了In₂O₃晶体的光学跃迁机理.     

Equilibrium dynamics of the sub-Ohmic spin-boson model under bias

Using the bosonic numerical renormalization group method, we studied the equilibrium dynamical correlation function C(ω) of the spin operator σ_z for the biased sub-Ohmic spin-boson model. The small-ω behavior C(ω) ∝ω~s is found to be universal and independent of the bias ε and the coupling strength α(except at the quantum critical point α = αc and ε = 0). Our NRG data also show C(ω) ∝χ~2ω~s for a wide range of parameters, including the biased strong coupling regime(ε = 0 and α α_c), supporting the general validity of the Shiba relation. Close to the quantum critical point αc,the dependence of C(ω) on α and ε is understood in terms of the competition between ε and the crossover energy scale ω_0~*of the unbiased case. C(ω) is stable with respect to ε for ε《ε~*. For ε》ε~*, it is suppressed by ε in the low frequency regime. We establish that ε~*∝(ω_0~*)~(1/θ)holds for all sub-Ohmic regime 0≤s 1, with θ = 2/(3s) for 0 s≤1/2 and θ = 2/(1 + s) for 1/2 s 1. The variation of C(ω) with α and ε is summarized into a crossover phase diagram on the α–ε plane.     

镁-锌时效合金中一维过渡相β′2的晶体学研究

采用X射线衍射方法,显示出镁-5Wt％锌合金在165℃时效初期有两种过渡相β′₁和β′₂共存。对细杆状过渡相,β′₂的一维衍射现象进行了详细分析。这种过渡相具有六角点阵结构,其[0001]轴是杆的长轴,它的点阵常数及与母相间的取向关系经测定为:a_(β′2)=13.2?,c_(β′2)=5.25?,[0001]_{(β′2)关键词：}     

Critical Behaviors and Finite-Size Scaling of Principal Fluctuation Modes in Complex Systems

Complex systems consisting of N agents can be investigated from the aspect of principal fluctuation modes of agents. From the correlations between agents, an N×N correlation matrix C can be obtained. The principal fluctuation modes are defined by the eigenvectors of C. Near the critical point of a complex system, we anticipate that the principal fluctuation modes have the critical behaviors similar to that of the susceptibity. With the Ising model on a two-dimensional square lattice as an example, the critical behaviors of principal fluctuation modes have been studied. The eigenvalues of the first 9 principal fluctuation modes have been invesitigated. Our Monte Carlo data demonstrate that these eigenvalues of the system with size L and the reduced temperature t follow a finite-size scaling form λ_n(L, t)=L^γ/ν f_n(tL^1/ν), where γ is critical exponent of susceptibility and ν is the critical exponent of the correlation length. Using eigenvalues λ₁, λ₂ and λ₆, we get the finite-size scaling form of the second moment correlation length ξ(L, t)=Lξ(tL^1/ν). It is shown that the second moment correlation length in the two-dimensional square lattice is anisotropic.     

关于海森堡反铁磁链材料LiVGe2O6有限温度相变的理论研究

自旋s=1的海森堡反铁磁链材料LiVGe₂O₆的磁化率以及 核磁共振实验表明该材料在临界温度约为22 K时由顺磁相转变为反铁磁Néel相, 且低温磁激发谱存在能隙. 本文在已有模型哈密顿量的基础上提出了一个低能场论模型——Ginzburg-Landau理论来描述 这一反铁磁链材料, 并运用这一理论讨论了LiVGe₂O₆由于自发对称性破缺导致的有限温度相变及 相应的磁化率变化情况, 理论计算很好地解释了现有的实验结果. 关键词： 海森堡模型 σ模型')" href="#">O(3)非线性σ模型 有限温度相变