立方氮化硅及其冲击波合成

 立方氮化硅是高温高压研究近期合成得到的一种新物相，与已经在工业上普遍使用的氮化硅的两种六方物相（α相和β相）相比，新物相的密度增加了26%，预期是一种新型功能材料。简要综述了立方氮化硅的研究进展和存在的问题，讨论了立方氮化硅的人工合成和相关物性研究、Ⅳ(A)族氮化物（Ge₃N₄、Sn₃N₄、C₃N₄）的高密度物相研究，以及后尖晶石相氮化物的实验和理论探索等问题。介绍了作者最近利用炸药爆轰加载技术开展的冲击波合成实验结果，以α相氮化硅为冲击压缩前驱体，实现了在单次冲击波压缩实验中合成出了克量级立方氮化硅粉体，为进一步开展立方氮化硅的性能研究奠定了基础。     

NaF薄膜的脉冲激光沉积法制备与结构研究

 采用脉冲激光沉积(PLD)方法在Si(100)衬底上制备了NaF薄膜。在激光重复频率2 Hz，能量密度3 J/cm²，本底真空度5×10^-5 Pa的条件下，研究衬底温度对薄膜沉积速率及结构的影响。台阶仪分析表明：薄膜的沉积速率随衬底温度增加呈指数函数增加，算出NaF薄膜的反应激活能为48.67 kJ/mol。原子力显微镜分析表明：薄膜致密而光滑，均方根粗糙度为0.553 nm。扫描电镜截面微观形貌分析表明：薄膜呈现柱状结构。X射线衍射分析表明：NaF薄膜为面心立方晶体结构，并具有显著的择优取向；当衬底温度约为400 ℃时，平均晶粒尺寸最大(129.6 nm)，晶格微应变最小(0.225%)。     

Critical Behavior of the Blume-Emery-Griffiths Model for a Simple Cubic Lattice on the Cellular Automaton

The spin-1 Ising model with the nearest-neighbour bilinear and biquadratic interactions and single-ion anisotropy is simulated on a cellular automaton which improved from the Creutz cellular automaton (CCA) for a simple cubic lattice. The simulations have been made for several k=K/J and d=D/J in the 0≤d<3 and −2≤k≤0 parameter regions. We confirm the existence of the re-entrant and the successive re-entrant phase transitions near the phase boundary. The phase diagrams characterizing phase transitions are presented for comparison with those obtained from other calculations. The static critical exponents are estimated within the framework of the finite-size scaling theory at d=0, 1 and 2 in the interval −2≤k≤0. The results are compatible with the universal Ising critical behavior.     

立方非线性Schr?dinger方程的Weierstrass椭圆函数周期解

利用Weierstrass椭圆函数展开法对非线性光学、等离子体物理等许多系统中出现的立方非线性 Schr(o)dinger方程进行了研究.首先通过行波变换将方程化为一个常微分方程,再利用Weierstrass椭圆函数展开法思想将其化为一组超定代数方程组,通过解超定方程组,求得了含Weierstrass椭圆函数的周期解,以及对应的Jacobi椭圆函数解和极限情况下退化的孤波解.该方法有以下两个特点:一是可以借助数学软件Mathematica自动地完成;二是可以用于求解其它的非线性演化方程(方程组).     

THE UNIQUENESS OF LIMIT CYCLE AND THE STRUCTURE OF CRITICAL POINT AT INFINITY FOR A CLASS OF CUBIC SYSTEM

A class of cubic system, which is an accompany system of a quadratic differential one, is studied. It is proved that the system has at most one limit cycle, and the critical point at infinity is a higher order one. The structure and algebraic character of the critical point at infinity are obtained.     

A new volume of fluid method in three dimensions—Part II: Piecewise‐planar interface reconstruction with cubic‐Bézier fit

A new interface reconstruction method in 3D is presented. The method involves a conservative level‐contour reconstruction coupled to a cubic‐Bézier interpolation. The use of the proposed piecewise linear interface calculation (PLIC) reconstruction scheme coupled to a multidimensional time integration provides solutions of second‐order spatial and temporal accuracy. The accuracy and efficiency of the proposed reconstruction algorithm are demonstrated through several tests, whose results are compared with those obtained with other recently proposed methods. An overall improvement in accuracy with respect to other recent methods has been achieved, along with a substantial reduction in the central processing unit time required. Copyright © 2008 John Wiley & Sons, Ltd.     

Envelopes of splines in the projective plane

In this paper a family of curves—Riemannian cubics—inthe unit sphere and the real projective plane is investigated.Riemannian cubics naturally arise as solutions to variationalproblems in Riemannian spaces. It is remarkable to find thatan envelope of lines generated by a Riemannian cubic in onespace is (nearly) a Riemannian cubic in another space.     

Bifurcations and chaos in parametrically excited single-degree-of-freedom systems

The behavior of single-degree-of-freedom systems possessing quadratic and cubic nonlinearities subject to parametric excitation is investigated. Both fundamental and principal parametric resonances are considered. A global bifurcation diagram in the excitation amplitude and excitation frequency domain is presented showing different possible stable steady-state solutions (attractors). Fractal basin maps for fundamental and principal parametric resonances when three attractors coexist are presented in color. An enlargement of one region of the map for principal parametric resonance reveals a Cantor-like set of fractal boundaries. For some cases, both periodic and chaotic attractors coexist.     

Crossover Peng-Robinson equation of state with introduction of a new expression for the crossover function

In this research, we use the original Peng-Robinson (PR) equation of state (EOS) for pure fluids and develop a crossover cubic equation of state which incorporates the scaling laws asymptotically close to the critical point and it is transformed into the original cubic equation of state far away from the critical point. The modified EOS is transformed to ideal gas EOS in the limit of zero density. A new formulation for the crossover function is introduced in this work. The new crossover function ensures more accurate change from the singular behavior of fluids inside the regular classical behavior outside the critical region. The crossover PR (CPR) EOS is applied to describe thermodynamic properties of pure fluids (normal alkanes from methane to n-hexane, carbon dioxide, hydrogen sulfide and R125). It is shown that over wide ranges of state, the CPR EOS yields the thermodynamic properties of fluids with much more accuracy than the original PR EOS. The CPR EOS is then used for mixtures by introducing mixing rules for the pure component parameters. Higher accuracy is observed in comparison with the classical PR EOS in the mixture critical region.     

A new finite difference scheme for a dissipative cubic nonlinear Schr"odinger equation

This paper considers the one-dimensional dissipative cubic nonlinear Schrödinger equation with zero Dirichlet boundary conditions on a bounded domain. The equation is discretized in time by a linear implicit three-level central difference scheme, which has analogous discrete conservation laws of charge and energy. The convergence with two orders and the stability of the scheme are analysed using a priori estimates. Numerical tests show that the three-level scheme is more efficient.