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.     

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.     

A second-order accurate numerical method for the two-dimensional fractional diffusion equation

Spatially fractional order diffusion equations are generalizations of classical diffusion equations which are used in modeling practical superdiffusive problems in fluid flow, finance and others. In this paper, we present an accurate and efficient numerical method to solve a fractional superdiffusive differential equation. This numerical method combines the alternating directions implicit (ADI) approach with a Crank–Nicolson discretization and a Richardson extrapolation to obtain an unconditionally stable second-order accurate finite difference method. The stability and the consistency of the method are established. Numerical solutions for an example super-diffusion equation with a known analytic solution are obtained and the behavior of the errors are analyzed to demonstrate the order of convergence of the method.     

Modified Gauss rules for approximate calculation of some strongly singular integrals

The approach we follow consists in transforming the numerical evaluation of hyper-singular integrals into the calculation of a nearly singular integral whose mass is distributed according to a positive parameter ε. To evaluate the latter we apply a Gauss quadrature formula associated with a nearly singular weight function. It is estimated the error in terms of ε. Some numerical results are presented.     

A new thermo‐responsive block copolymer with tunable upper critical solution temperature and lower critical solution temperature in the alcohol/water mixture

The multi‐thermo‐responsive block copolymer of poly[2‐(2‐methoxyethoxy)ethyl methacrylate]‐block‐poly[N‐(4‐vinylbenzyl)‐N,N‐diethylamine] (PMEO₂MA‐b‐PVEA) displaying phase transition at both the lower critical solution temperature (LCST) and the upper critical solution temperature (UCST) in the alcohol/water mixture is synthesized by reversible addition‐fragmentation chain transfer polymerization. The poly[2‐(2‐methoxyethoxy)ethyl methacrylate] (PMEO₂MA) block exhibits the UCST phase transition in alcohol and the LCST phase transition in water, while the poly[N‐(4‐vinylbenzyl)‐N,N‐diethylamine] (PVEA) block shows the UCST phase transition in isopropanol and the LCST phase transition in the alcohol/water mixture. Both the polymer molecular weight and the co‐solvent/nonsolvent exert great influence on the LCST or UCST of the block copolymer. By adjusting the solvent character including the water content and the temperature, the block copolymer undergoes multiphase transition at LCST or UCST, and various block copolymer morphologies including inverted micelles, core‐corona micelles, and corona‐collapsed micelles are prepared. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013, 51, 4399–4412     

Alternants for generalized convex functions

In this paper we consider the problem of best uniform approximation by elements of WT-spaces. In particular, we investigate the structure of the corresponding error function when the function to be approximated is generalized convex with respect to a WT-space. The principal concept involved is that of an alternation element, an element for which the error function takes on its norm with alternating signs a specified number of times. This approach has been employed by Jones, Karlovitz [4], Sommer, Strauss [10], Nurnberger, Sommer [7] and Barrar, Loeb [2]. Much of the material in this paper was inspired by a paper of Amir and Ziegler [1] . A new characterization of WT-spaces in terms of alternation elements is given.