Lattice Model with Traveling Compactons

We introduce a purely anharmonic lattice model with specific double-well on-site potential, which admits traveling compacton-like solitary wave solutions by the inverse method with the help of Mathematica. By properly choosing the shape of the solitary wave solution of the system, we can calculate the parameters of the specific on-site potential. We also found that the localization of the compacton is related to the nonlinear coupling parameter Cnl and the potential parameter V0 of the on-site potential, and the velocity of the propagation of the compacton is determined by the localization parameter q and the potential parameter V0. Numerical calculation results demonstrate that the narrow compacton is unstable while the wide compacton is stable when they move along the lattice chain.     

Moving and Interaction of Compact-like Pulses in Klein-Gordon Lattice System

We study the moving and interaction of the compact-like pulses in the system of an anharmonlc lattice with a double well on-site potential by a direct algebraic method and numerical experiments. It is found that the localization of the compact-like pulse is rClated to the nonlinear coupling parameter Cnl and the potential barrier height Vo of the double well potential. The velocity of the moving compact-like pulse is determined by the linear coupling parameter Cl, the localization parameter q (the nonlinear coupling parameter Cnl) and the potential barrier height Vo.Numerical experiments demonstrate that appropriate Cl is not detrimental to a stable moving of the compact-like pulse.However, the head on interaction of two compact-like pulses in the lattice system with comparatively small Cl leads to the appearance of a discrete stationary localized mode and small amplitude nonlinear oscillation background, while moderate Cl results in the emergence of two moving deformed pulses with damping amplitude and decay velocity and radiating oscillations, and biggish Cl brings on the appearing of four deformed kinks with radiating oscillations and different moving velocities.     

New Similarity Reductions and Compacton Solutions for Boussinesq-Like Equations with Fully Nonlinear Dispersion

In this paper, similarity reductions of Boussinesq-like equations with nonlinear dispersion (simply called B(m,n) equations) u_tt=(uⁿ)_xx+(u^m)_xxxx, which is a generalized model of Boussinesq equation u_tt=(u²)_xx+u_xxxx and modified Bousinesq equation u_tt=(u³)_xx+u_xxxx, are considered by using the direct reduction method. As a result, several new types of similarity reductions are found. Based on the reduction equations and some simple transformations, we obtain the solitary wave solutions and compacton solutions (which are solitary waves with the property that after colliding with other compacton solutions, they re-emerge with the same coherent shape) of B(1,n) equations and B(m,m) equations, respectively.     

Solution of Dirac Equation with Generalized Hylleraas Potential

We employ the parametric generalization of the Nikiforov-Uvarov method to solve the Alhaidari formalism of the Dirac equation with a generalized Hylleraas potential of the form V(r) = V0(a+exp(λr))/(b+ exp(λr)) + V1(d+exp(λr))/(b+exp(λr)).We obtain the bound state energy eigenvalue and the corresponding eigenfunction expressed in terms of the Jacobi polynomials.By choosing appropriate parameter in the potential model,the generalized Hylleraas potential reduces to the well known potentials as special cases.     

Semi-exact Solutions of Konwent Potential

In this work we study the quantum system with the symmetric Konwent potential and show how to find its exact solutions. We find that the solutions are given by the confluent Heun function. The eigenvalues have to be calculated numerically because series expansion method does not work due to the variable z ≥ 1. The properties of the wave functions depending on the potential parameter A are illustrated for given potential parameters V_0 and a. The wave functions are shrunk towards the origin with the increasing |A|. In particular, the amplitude of wave function of the second excited state moves towards the origin when the positive parameter A decreases. We notice that the energy levels ε_i increase with the increasing potential parameter |A| ≥ 1, but the variation of the energy levels becomes complicated for |A| ∈(0, 1), which possesses a double well. It is seen that the energy levels ε_i increase with |A| for the parameter interval A ∈(-1, 0), while they decrease with |A| for the parameter interval A ∈(0, 1).     

受限一维无自旋费米子系统的性质研究

本文借助于一维自旋1/2-XXZ模型的Bethe-ansatz精确解, 利用局域密度近似(LDA), 讨论了谐振势中一维无自旋费米子的密度分布, 得出了ρ-u相图(这里的ρ为无量纲的粒子数密度 变量u为相互作用强度)对相图的分析表明, 随着原子密度和近邻相互作用的变化, 系统出现五个不同的混合量子相通过对热力学硬度S_ρ的计算, 发现其可作为体系的序参量, 其奇异点可用以度量受限体系中量子相变的发生     

有限深两层流体中内孤立波造波实验及其理论模型

将置于大尺度密度分层水槽上下层流体中的两块垂直板反方向平推, 以基于 Miyata-Choi-Camassa (MCC)理论解的内孤立波诱导上下层流体中的层平均水平速度作为其运动速度, 发展了一种振幅可控的双推板内孤立波实验室造波方法. 在此基础上, 针对有限深两层流体中定态内孤立波 Korteweg-de Vries (KdV), 扩展KdV (eKdV), MCC和修改的Kdv (mKdV)理论的适用性条件等问题, 开展了系列实验研究.结果表明, 对以水深为基准定义的非线性参数ε 和色散参数μ, 存在一个临界色散参数μ₀, 当μ < μ₀ 时, KdV理论适用于ε ≤μ 的情况, eKdV理论适用于μ < ε ≤√μ 的情况, 而MCC理论适用于ε > √μ 的情况, 而且当μ ≥μ₀ 时MCC理论也是适用的.结果进一步表明, 当上下层流体深度比并不接近其临界值时, mKdV理论主要适用于内孤立波振幅接近其理论极限振幅的情况, 但这时MCC理论同样适用.本项研究定量地表征了四类内孤立波理论的适用性条件, 为采用何种理论来表征实际海洋中的内孤立波特征提供了理论依据. 关键词： 两层流体 内孤立波 双板造波 临界色散参数     

氯化钠晶体在高温高压下热物理参数的分子动力学计算

用分子动力学方法和优化的Tosi-Fumi有效两体势函数计算了NaCl晶体温度从298?K到773?K的等温压缩线和体积模量、热膨胀系数和格临爱森系数等热物理参量.计算结果表明，NaCl晶体在温度从298?K到1073?K、压力从0到80?GPa范围内的格临爱森系数γ=γ ₀(V/V₀)^q的近似公式成立，且q≈1078. 关键词： 分子动力学计算 格临爱森系数 氯化钠晶体     

First-Principle Calculations for Thermodynamic Properties of LiBC Under High Temperature and High Pressure

The thermodynamic properties of LiBC are investigated by using the full-potential linearlzed muffin-tin orbital method （FP-LMTO） within the frame of density functional theory （DFT） and using the quasi-harmonic Debye model. The dependencies of the normalized lattice parameters a/a0 and c/c0, the ratio （c/a）/2, the normalized primitive volume V/V0 on pressure and temperature are successfully obtained. It is found that the interlayer covalent interactions （Li-B bonds or Li-C bonds） are more sensitive to temperature and pressure than intralayer ones （B-C bonds）, as gives rise to the extreme lattice anisotropy in the bulk hop LiBC.     

C-15结构(Hf,Zr,Ta)V2和(Hf,Zr,Nb)V2合金超导转变的压力效应研究

本文研究了C-15结构化合物(Zr_0.5Hf_0.5-xTa_x)V₂(x≤0.2)和(Hf_0.5Zr_0.5-xNb_x)V₂(x≤0.2)的超导转变温度T_c及其压力效应?T_c/?P。报道了实验方法与结果。与(Hf_1-xTa_x)V₂和(Zr_1-xTa_x)V₂的情况不同,在(Zr_0.5Hf_0.5-xTa_x)V₂中Ta的引入使常压下的T_c下降,然而(?)T_c/(?)P却大为提高。因此高压下Zr_0.5Hf_0.45Ta_0.05V₂的T_c反而比Hf_0.5Zr_0.5V₂更高。导出了一个基于角动量分波表象能带论方法的描述压力效应的新关系式。它指出导带电子波函数中的高角动量成分变化对T_c的压力效应影响比较重要。这个公式有助于理解上述复杂的实验现象,并能合理地解释某些元素(如Cs,Ba,La等)的T_c随压力剧增的事实。 关键词：     

用不变本征算符法求晶面吸附原子的振动模

晶体表面的扩散和缺陷对晶体振动模式的影响是表面物理学研究的一个重要和基本的课题.晶格振动的频率对应于系统的能带.由于晶格中原子的振动不是孤立的,并且晶格具有周期性,所以在晶体中形成格波.格波代表晶体中所有原子都参与的频率相同的振动,又常称为一种振动模.本文讨论在表面吸附位势系数β_0与晶体内部原子的周期位势系数β不同的情况下,晶体表面吸附一个质量为m_0(与晶格原子质量m不同)的原子以后晶格的振动模.采用不变本征算符方法,严格地导出此振动模为ω=((2β(1-coshα))/(hm))~(1/2),其中α=ln[-(mβ_0+m_0(-2β+β_0)+(β_0)~(1/2)((-4mm_0β+(m+m_0)~2β_0))~(1/2)/2m_0β].此结果表明,ω不但取决于吸附位势与吸附原子的质量,也与晶格原子的质量与内位势有关.     

Positivity of energy in five dimensional classical unified field theories, II

Five dimensional classical unified field theories as well as Yang-Mills theory with gauge group U(1), are described in terms of a Lorentzian five dimensional space V₅ with metric tensor γβ which admits a space-like Killing vector ζ. It is assumed that: (1) V₅ has the topology of V₄ x S¹, S¹ is a circle and V₄ is a four dimensional Lorentzian space that is asymptotically flat and (2) the Einstein tensor Γ_β of V₅ satisfies Γ_β Uυ^{β 0} where U and υ are future oriented time-like vectors with γ_βυζ^β = 0. The spinor approach of Witten [4], Nester [3] and Moreschi and Sparling [5] is used to show that the conserved five dimensional energymomentum vector P = ifΓ_β = 0 then V₅ must admit a time-like Killing vector. Lichnerowicz's results [1] then imply that V₅ must be flat. A lower bound for P⁴ (the mass) similar to that found by Gibbons and Hull [6] is obtained.     

Bifurcations and Single Peak Solitary Wave Solutions of an Integrable Nonlinear Wave Equation

Dynamical system theory is applied to the integrable nonlinear wave equation $u_t±(u^3−u^2)x+(u^3)xxx=0$. We obtain the single peak solitary wave solutions and compacton solutions of the equation. Regular compacton solution of the equation corresponds to the case of wave speed $c$=0. In the case of $c^6$≠0, we find smooth soliton solutions. The influence of parameters of the traveling wave solutions is explored by using the phase portrait analytical technique. Asymptotic analysis and numerical simulations are provided for these soliton solutions of the nonlinear wave equation.     

非自治物质畸形波的传播操控

研究了(1+1)维的变系数Gross-Pitaevskii方程, 获得了该方程的精确畸形波解. 基于该精确畸形波解, 深入研究了非自治物质畸形波在随时间指数变化的相互作用下的传播动力学行为, 发现非自治畸形波除具有“来无影、去无踪”的不可预测特性外, 也可实现完全激发、抑制激发以及维持激发等操控. 研究表明, 畸形波操控的关键是对累积时间的最大值T_max 与峰值位置T₀ (或T_I,T_II)值大小关系的调节. 当T_max > T₀ (或T_I,T_II)时畸形波被快速地完全激发, 热原子团中的原子增加到凝聚体中. 当T_max = T₀ (或T_I,T_II) 时畸形波激发到最大振幅, 可以维持相当长的时间而不消失, 热原子团中的原子增加到凝聚体中. 当T_max < T₀ (或T_I,T_II)时畸形波没有充足的时间来激发而被抑制甚至消失, 凝聚体中的原子减少. 这些结果在理论和实际应用上具有启迪意义.     

MGNETOSONIC SOLITARY WAVES IN HOT PLASMAS

In this paper, a magnetosonic solitary wave in hot plasma is considered both analytically and numerically,taking account of the charge separation. The two-direction one-dimension Maxwell-two-fluid equations are obtained,.It is shown that there.exist solitary wave. solutions of these equations when 1+B₀²/4πn₀T_e < (C/C_S)² <2.6, where C is the-wave velocity. The distributions of density and of magnetic intensity both have the shape of single peak. The effect of the magnetic field is to depress the amplitudes and to widen the widths of the solitary waves; and when B_O→0 the magnetosonic solitary wave turn to sonic solitary wave. It is found that for large C the charge separation may be remarkable, so the assumption of quasineutrality is incorrect.     

Dip-coated silver-doped V2O5 xerogels as host materials for lithium intercalation

Vanadium pentoxide xerogels have shown high electrochemical performance in terms of energy content. The high specific energy and high intercalation capability make the materials promising for thin film lithium battery and electrochromic device applications. In order to enhance the rate capabilities of the host we increased the electronic conductivity by doping the V₂O₅ xerogels with silver. Samples were prepared by mixing various amounts of silver powder with V₂O₅ hydrogel. We were able to prepare silver-doped vanadium pentoxide dip-coated thin films with a molar ratio (Ag/V) ranging from 0.005 to 0.5 (Ag_yV₂O₃ with y = 0.01, 0.1 and 1). With the successful doping, the electronic conductivity of V₂O₅ was increased by 2 to 3 orders of magnitude. The insertion capacity of the material was maintained and up to 4 moles of lithium per mole of silver-doped V₂O₅ (XRG) were found to be reversibly intercalated.     

A density-wave-like transition in the polycrystalline V3Sb2 sample with bilayer kagome lattice

Recently,transition-metal-based kagome metals have aroused much research interest as a novel platform to explore exotic topological quantum phenomena.Here we report on the synthesis,structure,and physical properties of a bilayer kagome lattice compound V₃Sb₂.The polycrystalline V₃Sb₂ samples were synthesized by conventional solid-state-reaction method in a sealed quartz tube at temperatures below 850℃.Measurements of magnetic susceptibility and resistivity revealed consistently a density-wave-like transition at Tdw≈160 K with a large thermal hysteresis,even though some sample-dependent behaviors were observed presumably due to the different preparation conditions.Upon cooling through Tdw,no strong anomaly in lattice parameters and no indication of symmetry lowering were detected in powder x-ray diffraction measurements.This transition can be suppressed completely by applying hydrostatic pressures of about 1.8 GPa,around which no sign of superconductivity was observed down to 1.5 K.Specific-heat measurements revealed a relatively large Sommerfeld coefficientγ=18.5 mJ·mol^-1·K^-2,confirming the metallic ground state with moderate electronic correlations.Density functional theory calculations indicate that V₃Sb₂ shows a non-trivial topological crystalline property.Thus,our study makes V₃Sb₂ a new candidate of metallic kagome compound to study the interplay between density-wave-order,nontrivial band topology,and possible superconductivity.     

Analytic Results in the Position-Dependent Mass Schrödinger Problem

We investigate the Schrödinger equation for a particle with a nonuniform solitonic mass density. First, we discuss in extent the (nontrivial) position-dependent mass V(x)=0 case whose solutions are hypergeometric functions in tanh²x. Then, we consider an external hyperbolic-tangent potential. We show that the effective quantum mechanical problem is given by a Heun class equation and find analytically an eigenbasis for the space of solutions. We also compute the eigenstates for a potential of the form V(x)=V₀ sinh²x.     

硅纳米线/氧化钒纳米棒复合材料的制备与气敏性能研究

采用纳米球光刻和金属辅助刻蚀法以p型单晶硅片制备了硅纳米线阵列, 并以此作为基底, 通过溅射不同时长的金属钒薄膜并进行热退火氧化处理, 制备出硅纳米线/氧化钒纳米棒复合材料. 采用扫描电子显微镜和X射线衍射仪表征了该复合材料的微观特性, 结果表明该结构增大了材料的比表面积, 有利于气体传感, 并且镀膜时间对后续生长的氧化钒纳米棒形貌有明显影响. 采用静态配气法在室温下测试了该复合材料对NO₂的气敏性能, 气敏测试结果表明沉积钒膜的时间对复合材料的气敏性能影响较大. 当选择合适的镀膜时间时, 适量氧化钒纳米棒增加了材料表面积并形成大量pn结结构, 相比纯硅纳米线对NO₂气体的灵敏度有明显提升, 且在室温下表现出优良的选择性. 同时, 对气敏机理做了定性解释, 认为硅纳米线与氧化钒纳米棒之间形成的pn结及能带结构在接触NO₂ 时的动态变化是其气敏响应提升的主要机制.     

考虑频散效应的一维非线性地震波数值模拟

非线性理论是解决地学问题的重要手段, 充分认识非线性波动特征有助于解释实际观测资料中的一些特殊地震现象. 本文基于Hokstad改造的非线性本构方程, 利用交错网格有限差分法实现了固体介质中一维非线性地震波数值模拟; 采用通量校正传输方法消除非线性数值模拟中波形振荡, 提高模拟精度. 通过与解析解的对比验证了模拟结果的正确性. 研究结果显示了非线性系数对地震波的传播有重要影响, 并且当取适当的非线性和频散系数时, 地震波表现出孤立波的传播特性. 最后分析了不同的非线性地震波在固体介质中的传播演化特征.