一种求解抛物型方程的Monte Carlo并行算法

1 引言有限差分法是求解抛物型偏微分方程的一种主要的数值方法,用隐格式求解是绝对稳定的,但是如果直接用传统的方法(如Gauss消去法,超松弛迭代法等)求解相应的差分方程组,运算量很大,计算时间很长,对于高维情况,问题更显得突出．因而寻求可对其     

Soliton Solutions,B/icklund Transformations and Lax Pair for a （3 ＋ 1）-Dimensional Variable-Coefficient Kadomtsev-Petviashvili Equation in Fluids

Under investigation in this paper is a （3 q- 1）-dimensional variable-coefficient Kadomtsev-Petviashvili equation, which describes the propagation of surface and internal water waves. By virtue of the binary Bell polynomials, symbolic computation and auxiliary independent variable, the bilinear forms, soliton solutions, Backlund transformations and Lax pair are obtained. Variable coefficients of the equation can affect the solitonic structure, when they are specially chosen, while curved and linear solitons are illustrated. Elastic collisions between/among two and three solitons are discussed, through which the solitons keep their original shapes invariant except for some phase shifts.     

三氧化钨表面氢吸附机理的第一性原理研究

采用基于密度泛函理论的第一性原理平面波超软赝势方法,在广义梯度近似下,研究了立方WO_3,WO_3(001)表面结构及其氢吸附机理.计算结果表明立方晶体WO_3理论带隙宽度为0.587 eV.WO_3(001)表面有WO终止(001)表面和O终止(001)表面两种结构,表面结构优化后W—O键长和W—O—W键角改变,从而实现表面弛豫;WO终止(001)表面和O终止(001)表面分别呈现n型半导体特征和p型半导体特征.分别计算了H原子吸附在WO终止(001)表面和O终止(001)表面的H—O_(2c)—H,H—O_(2c)…H—O_(2c),H—O_(1c)—H和H—O_(1c)…H—O_(1c)四种吸附构型,其中H—O_(1c)—H吸附构型的吸附能最小,H—O键最短,H失去电子数最多,分别为-3.684 eV,0.0968 nm和0.55e,此吸附构型最稳定.分析其吸附前后的态密度,带隙从吸附前的0.624 eV增加到1.004 eV,价带宽度基本不变.H的1s轨道电子与O的2p,2s轨道电子相互作用,在-8和-20 eV附近各形成了一个较强的孤立电子峰,两个H原子分别与一个O_(1c)原子形成化学键,最终吸附反应生成了一个H_2O分子,同时产生了一个表面氧空位.     

Lax pair and vector semi-rational nonautonomous rogue waves for a coupled time-dependent coefficient fourth-order nonlinear Schrodinger system in an inhomogeneous optical fiber

Optical fibers are seen in the optical sensing and optical fiber communication. Simultaneous propagation of optical pulses in an inhomogeneous optical fiber is described by a coupled time-dependent coefficient fourth-order nonlinear Schr?dinger system, which is discussed in this paper. For such a system, we work out the Lax pair, Darboux transformation, and corresponding vector semi-rational nonautonomous rogue wave solutions. When the group velocity dispersion(GVD) and fourth-order dispersion(FOD) coefficients are the constants, we exhibit the first-and second-order vector semirational rogue waves which are composed of the four-petalled rogue waves and eye-shaped breathers. Both the width of the rogue wave along the time axis and temporal separation between the adjacent peaks of the breather decrease with the GVD coefficient or FOD coefficient. With the GVD and FOD coefficients as the linear, cosine, and exponential functions, we respectively present the first-and second-order periodic vector semi-rational rogue waves, first-and second-order asymmetry vector semi-rational rogue waves, and interactions between the eye-shaped breathers and the composite rogue waves.     

基于多体摄动理论的CaO电子能带结构及光吸收谱的研究

使用多体摄动理论研究了碱土金属氧化物CaO的电子激发态和光吸收谱. 运用GW近似方法来改进DFT对电子交换关联的处理, 并计算了CaO电子能带结构. 考虑到电子与空穴的相互作用, 运用二粒子格林函数理论来求解Bethe-Salpeter方程, 计算电子-空穴激发态, 并在此基础上计算光吸收谱. 计算结果CaO能隙为7.0eV, 与实验结果7.1eV符合很好; 并且CaO光吸收谱的理论结果与实验数据也相符合.     

Painlevé Analysis,Soliton Collision and B?cklund Transformation for the (3+1)-Dimensional Variable-Coefficient Kadomtsev–Petviashvili Equation in Fluids or Plasmas

In this paper, we investigate a(3+1)-dimensional generalized variable-coefficient Kadomtsev–Petviashvili equation, which can describe the nonlinear phenomena in fluids or plasmas. Painlev′e analysis is performed for us to study the integrability, and we find that the equation is not completely integrable. By virtue of the binary Bell polynomials,bilinear form and soliton solutions are obtained, and B¨acklund transformation in the binary-Bell-polynomial form and bilinear form are derived. Soliton collisions are graphically discussed: the solitons keep their original shapes unchanged after the collision except for the phase shifts. Variable coefficients are seen to affect the motion of solitons: when the variable coefficients are chosen as the constants, solitons keep their directions unchanged during the collision; with the variable coefficients as the functions of the temporal coordinate, the one soliton changes its direction.     

基于数据驱动的舵面结构优化设计

在航空航天领域,基于结构拓扑优化理论的轻量化设计需求逐步增加;而一些高端装备的空气舵通常服役于严酷的热力耦合环境中,对其进行高效地轻量化设计兼具挑战和重要意义.对于给定的载荷,薄壁结构的刚度特性可以通过增加肋或加强筋而得到显著增强,这与空气舵结构的设计需求高度一致.然而,传统隐式拓扑优化框架下的加筋设计存在设计变量数目多、计算效率较低、不易保证筋条几何特征以及不便直接将优化设计结果导入CAD系统等问题.本研究采用了全新的显式拓扑优化方法-移动可变形组件法(MMC),并结合数据驱动对具有异形封闭几何特征的空气舵进行高效加筋设计.该方法直接对筋条骨架的几何信息进行优化,具有设计变量少、计算效率高、优化结果可与CAD软件无缝衔接等优势,从而解决了采用隐式拓扑优化方法及后续模型重构、参数优化等冗余步骤所面临的优化周期长、对设计人员经验依赖性强等问题.进一步,建立了加筋布局与关键力学性质映射的人工神经网络模型;将其作为代理模型进行优化可极为高效地得到高质量的初始设计,从而显著提升了舵面结构优化设计的效率.文章设计框架融合了结构拓扑优化算法与人工神经网络技术,可以推广应用于其他高端装备的智能设计.     

单颗粒电感耦合等离子体飞行时间质谱测定生物样品中掺金属微塑料

建立了单颗粒电感耦合等离子体飞行时间质谱（SP-ICP-TOF-MS）分析生物样品中掺金属聚苯乙烯颗粒的新方法。采用四甲基氢氧化铵和过氧化氢消解含有聚苯乙烯微塑料颗粒的小鼠肝脏样品；采用离心浓缩的方法消除消解液中的基体，以满足SP-ICP-TOF-MS分析要求。本方法对聚苯乙烯颗粒的回收率为102%±11%，微塑料颗粒中Ce、Eu、Ho和Lu的检出限为0.004～0.026 fg，颗粒数量浓度检出限为37 particles/mL。本方法为研究微塑料的环境污染和毒理提供了新途径。