扩展的Jacobi椭圆函数展开法和Zakharov方程组的新的精确周期解

对Jacobi椭圆函数展开法进行了扩展，且利用这一方法求出了Zakharov方程组的一系列新的精确周期解，在极限情况下可得到相应的孤波解，补充了前面研究的结果. 关键词： Jacobi椭圆函数展开法 非线性发展方程 精确解 周期解     

Lagrange系统一类新型的非Noether绝热不变量——Lutzky型绝热不变量

研究了Lagrange系统的Lie对称性摄动与新型的非Noether绝热不变量. 列出了未受扰Lagrange系统的Lie对称性导致的Lutzky型精确不变量；基于力学系统的高阶绝热不变量的定义，研究在小扰动作用下Lagrange系统Lie对称性的摄动，得到了系统的一类Lutzky形式的绝热不变量.举例说明方法和结果的应用.     

非线性演化方程孤立波的同伦分析法求解

利用同伦分析法求解了Burgers方程，得到了其扭结形孤立波的近似解析解，该解非常接近于相应的精确解.结果表明，同伦分析法可用来求解非线性演化方程的孤立波解.同时，也对所用方法进行了一定扩展，得到了Kadomtsev-Petviashvili(KP)方程的钟形孤立子解.经过扩展后的方法能够更方便地用于求解更多非线性演化方程的高精度近似解析解. 关键词： Burgers方程 同伦分析法 KP方程 孤立波解     

非线性Schrodinger方程的Jacobi椭圆函数包络解

通过函数变换和扩展Jacobi椭圆函数展开法,利用吴消元法,借助符号运算软件Maple,得到非线性Schringer方程丰富的包络形式精确解,特别是由两个Jacobi椭圆函数表示的精确解.当模数m→1或m→0时,一部分解退化为双曲函数或三角函数表示的解,F-展开法和扩展的F-展开法得到的精确解是本文结果的特例.     

高维非线性演化方程孤立波的同伦分析法求解

利用同伦分析法求解了修正的Kadomtsev-Petviashvili方程, 得到了它的近似孤立波解, 该解与精确解符合得非常好.结果表明，同伦分析法在求解高维非线性演化方程的孤立波解时, 仍然是一种行之有效的方法. 关键词： 同伦分析法 修正的Kadomtsev-Petviashvili方程 孤立波解     

含相变微粒流体热对流启动的Galerkin解

采用Bubnov-Galerkin方法对有恒壁温条件下,两平板间夹有含相变颗粒流体的自然对流热启动瑞利数进行了近似解析求解,求出了临界瑞利数Racr和波频数kcr随相变物质浓度,以及在相变温度范围内随加热表面温度的解析关系表达式.从而,为实现该类功能性潜热流体的自然对流传热强化,及其优化控制蓄热过程有理论指导意义.     

A modified NaSch model with density-dependent randomization for traffic flow

Based on the Nagel-Schreckenberg (NaSch) model of traffic flow, a modified cellular automaton (CA) traffic model with the density-dependent randomization (abbreviated as the DDR model) is proposed to simulate traffic flow. The fundamental diagram obtained by simulation shows the ability of this modified NaSch model to capture the essential features of traffic flow, e.g., synchronized flow, metastable state, hysteresis and phase separation at higher densities. Comparisons are made between this DDR model and the NaSch model, also between this DDR model and the VDR model. And the underlying mechanism is analyzed. All these results indicate that the presented model is reasonable and more realistic.     

Simple Analytical Model of the Anodic Streamer

In this work, an analytical model is used to study the formation of the anodic streamer in high pressure electrical discharge. This model enabled us to see the space variations of the characteristics of the streamer such as the electric field and the propagation velocity of streamer. The validity of the analytic approach is demonstrated by comparing the model results to the data from the literature. A qualitative concord was found. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effects of co-substitution on the electrical properties of BiFeO3 thin films prepared by chemical solution deposition

Ferroelectric BiFeO₃ thin films with Nd-Cr (or Sm-Cr) co-substitution (denoted by BNdFCr and BSmFCr, respectively) were deposited on the Pt(2 0 0)/TiO₂/SiO₂/Si(1 0 0) substrates by a chemical solution deposition method. X-ray diffraction patterns revealed the formation of BNdFCr and BSmFCr thin films without any secondary phases. The co-substituted BNdFCr (or BSmFCr) thin films, which were annealed at 550 °C for 30 min in N₂ atmosphere, exhibited enhanced electrical properties compared to BFO thin films with the remanent polarization (2P_r) and coercive electric field (2E_c) of 196, 188 μC/cm² and 600, 570 kV/cm with the electric field of 800 kV/cm, respectively. The leakage current densities of BNdFCr and BSmFCr thin films measured at room temperature were approximately three orders of magnitude lower than that of BFO thin film, and the leakage current at room temperature of the thin films exhibited three distinctive conduction behaviors. Furthermore, the values of pulse polarizations [i.e., +(P*-P^{^}) or −(P*-P^{^})] of BNdFCr and BSmFCr thin films were reasonably unchanged up to 1.4 × 10¹⁰ switching cycles.     

Understanding the adsorption of 4H-1,2,4-triazole derivatives on mild steel surface in molar hydrochloric acid

This study examines the use of some 4H-triazole derivatives, namely 3,5-diphenyl-4H-1,2,4-triazole (DHT), 3,5-bis(4-pyridyl)-4H-1,2,4-triazole (4-PHT) and 3,5-bis(4-methyltiophenyl)-4H-1,2,4-triazole (4-MTHT) for corrosion and dissolution protection of mild steel in normal hydrochloric acid solution. The inhibiting efficiency of the different additives is evaluated by means of weight loss and electrochemical techniques such as ac impedance measurements and polarisation curves. The experimental results obtained reveal that 4-MTHT is the best effective inhibitor and the inhibition efficiency is found to be in the following order: 4-MTHT > 4-PHT > DHT. The variation in inhibitive efficiency mainly depends on the type and nature of the substituents present in the inhibitor molecule. Polarisation curves show that theses triazoles are mixed-type inhibitors in 1 M HCl. The inhibition efficiency increases with 4H-triazole derivatives concentration and attains the maximum value of 99.6% in the case of 4-MTHT at 5 × 10⁻⁴ M. The results obtained from weight loss electrochemical studies were in reasonable agreement. The adsorption of 4H-triazole derivatives on the steel surface obeys to the Langmuir isotherm model. The thermodynamic data of adsorption and activation are determined and discussed. The fundamental thermodynamic functions were used to glean important information about the 4H-triazoles inhibitory behaviour. Molecular modeling was used to get better insight, about structural and electronic effects in relation to the inhibition efficiencies.