Numerical simulations of systems of PDEs by variational iteration method

In this Letter, a general framework of the variational iteration method (VIM) is presented for solving systems of linear and nonlinear partial differential equations (PDEs). In VIM, a correction functional is constructed by a general Lagrange's multiplier which can be identified via a variational theory. VIM yields an approximate solution in the form of a rapid convergent series. Comparison with the exact solutions shows that VIM is a powerful method for the solution of linear and nonlinear systems of PDEs.     

Max Born and his legacy to condensed matter physics

After a presentation of Max Born's most salient biographical data, we discuss his contributions to science and science policy, with special emphasis on those related to condensed matter physics. Our discussion includes journal articles as well as books. The methodology used is both qualitative and quantitative, including number of items, number of formal and informal citations, and other bibliometric indicators such as the recently proposed Hirsch index (h‐index). The data are mainly based on the Thomson/ISI Web of Science (WoS) which covers a carefully selected set of the more prestigious journals dating back to 1900. Born's books and articles not published in the journals covered by the WoS can also be evaluated, provided they are cited within the WoS journals. Some anecdotic and historical details, which have come to the fore in the course of our bibliometric investigations, are included.     

3H‐1,2‐Dithiole‐3‐thione derivatives as novel solvatochromic dyes

The UV–Vis spectrum of 5‐(1‐butylthio)‐3H‐1,2‐dithiole‐3‐thione (1a) and that of the chromium pentacarbonyl complex of 5‐methyl‐3H‐1,2‐dithiole‐3‐thione (3) present significant changes with the solvent polarity. The two absorption bands shown by the compounds in the region above 300 nm were identified by theoretical calculations. For Compound 1a these are n→π^* and →π^* transitions and for Compound 3 the longest wavelength absorption corresponds to a charge transfer band and shows a remarkably negative solvatochromism. Not only has the wavelength of maximum absorption changed with the solvent but also the ratio of the absorbances at the two wavelengths. The effect of solvents was correlated with solvatochromic parameters such as π^* and α. The spectrum of 5‐(1‐butylthio)‐3H‐1,2‐dithiole‐3‐one ( 2 ) was also measured in different solvents but in this case the changes observed are less significant than for the other two compounds. The spectra of 1a and 3 were also determined in the presence of anionic (SDS), cationic (CTAB), and neutral surfactants (Brig‐35) and it is shown that these compounds can be used as probes for the polarity of the binding sites of organized assemblies. Copyright © 2008 John Wiley & Sons, Ltd.     

Hard magnetic properties in Pr2Fe14B/α-Fe nanocomposite magnets with a combined addition of V and C

Nanostructured Pr₈Fe_86−xV_xB_6−yC_y (x=0, 1; y=0, 1) ribbons composed of Pr₂Fe₁₄B and α-Fe phases with a high coercivity are fabricated by direct melt spinning. The effects of a single addition of V and a combined addition of V and C on the structures and magnetic properties of melt-spun Pr₈Fe₈₆VB_6−xC_x (x=0 and 1) ribbons have been investigated. Compared with addition-free ribbons, 1 at% V addition is found to reduce the grain sizes of the samples and improve their magnetic properties due to a strong exchange coupling between the hard and the soft phase. A remanence ratio of 0.82, a coercive field of 6.2 kOe and a maximum energy product of 23.4 MGOe in melt-spun Pr₈Fe₈₅VB₆ ribbons are obtained at room temperature. The combined addition of V and C is found to lead to the formation of an intermediate phase of VC at grain boundaries, which appears as a pinning barrier during magnetization and results in an increase of the coercivity value to 6.9 kOe for melt-spun Pr₈Fe₈₅VB₅C ribbons.     

基于PIC方法的二维束流动力学模拟程序及其初步应用

为了深入研究强流负氢束在强流质子回旋加速器CYCIAE-100轴向注入线中的传输, 利用split-operator方法分解外场和束流自身的空间电荷场的作用. 对外 场利用单粒子跟踪技术, 采用一阶线性近似; 对空间电荷场采用PIC方法, 利用 快速傅里叶变换求解Poisson方程. 用FORTRAN95语言开发了一个基于面向对象技术的二维宏粒子传输计算程序CYCPIC2D, 本程序可以计算任意分布的强流束在输运线上的传输.最后给出了对CYCIAE-100注入线的模拟计算结果, 并和程序ORBIT, TRACE 3-D的结果进行比对验证, 结果表明: 空间电荷效应在此注入线上有较大的影响, 而且3个程序计算的不同中性化的结果基本上一致; 束流强度达到几十毫安时, 基于PIC方法的两个程序CYCPIC2D和ORBIT的计算结果完全吻合, 而线性近似程序TRACE 3-D有明显差异.     

Preference of Chaotic Synchronization in a Coupled Laser System

In a coupled laser system, the dynamics of the receiving laser is investigated when two separate transmitting lasers are injected into the receiving laser with different coupling strengths. It is shown that the phenomenon of preference of chaotic synchronization appears under appropriate coupling conditions. The receiving laser will entrain the pulses of either one or both transmitting lasers when the coupling is strong while it keeps its own dynamics when the coupling is weak.     

On the voltage sensitivity of current in electronic transport

The sensitivity of current-to-voltage is treated by defining an adequate parameter useful for a wide variety of cases within the context of ballistic electron transport. This parameter may be conceived as a normalized conductance which is studied in relation to electronic density of states.     

Facetting and (n × 1) reconstructions of SrTiO3(1 1 0) surfaces

(n × 1) reconstructions and facetting of the (1 1 0) polar surface of SrTiO₃ are studied by means of a combination of shell model and density functional calculations. The polarity compensation can be achieved through the formation of {1 0 0} nano-facets, which play a crucial role in the reconstruction process. The behaviors of various possible terminations (Sr, Ti, and O) are analyzed, as well as their atomic structure and energetics. Their stability in different chemical environments is discussed, with respect to previous formulations and experimental results. The Sr-terminated surface tends to expose large facets, while the TiO and O terminations are marginally stabilized or even destabilized by (n × 1) reconstructions, respectively. Trend to facetting results from a subtle competition between the thermodynamic stability of the ideal non stoichiometric (n × 1) surfaces, and huge atomic relaxations that contribute to the lowering of the surface energy differently for each termination.     

不同酯基结构的棕榈油生物柴油的性能研究

以棕榈油为研究对象,分别与甲醇、乙醇、异丙醇和异丁醇进行酯交换反应制备了不同酯基结构的生物柴油。利用差示扫描量热仪和应力控制流变仪分析了不同酯基结构棕榈油生物柴油的结晶行为和低温流变性能,同时分析了酯基结构对生物柴油的氧化稳定性,40℃时的动力黏度、20℃时的密度等重要性质的影响。结果表明,随着醇的碳链长度的增加,棕榈油生物柴油的析蜡点和胶凝点均降低,特别是棕榈油异丁酯的析蜡点和胶凝点分别降低到了-2.57和-8.09℃,低温流动性得到了明显改善,且氧化诱导期略有延长,氧化稳定性有所改善。生物柴油的密度和黏度随着酯基结构的不同而有所变化,但其数值都符合中国生物柴油标准。     

Molecular dynamics calculations of the hard-sphere equation of state

The equation of state of the hard-sphere fluid is studied by a Monte Carlomolecular dynamics method for volumes ranging from 25V ₀ to 1.6V ₀ , whereV ₀ is the close-packed volume, and for system sizes from 108 to 4000 particles. TheN dependence of the equation of state is compared to the theoretical dependence given by Salsburg for theNPT ensemble, after correction for the ensemble difference, in order to obtain estimates for the thermodynamic limit. The observed values of the pressure are compared with both the [3/2] and the [2/3] Padé approximants to the virial series, using Kratky's value for the fifth virial coefficientB ₅ and choosingB ₆ andB ₇, to obtain a least-squares fit. The resulting values ofB ₆ andB ₇ lie within the uncertainties of the Ree-Hoover-Kratky Monte Carlo estimates for these virial coefficients. The values ofB ₈,B ₉, andB ₁₀ predicted by our optimal [3/2] approximant are also reported. Finally, the Monte Carlo-molecular dynamics equation of state is compared with a number of analytic expressions for the hard-sphere equation of state.Work supported by the Office of Basic Energy Sciences, U.S. Department of Energy.