椭圆最优控制问题分裂正定混合有限元方法的超收敛性分析

首先利用变分原理和最优化理论得到了原问题的等价最优性条件;其次构造了椭圆最优控制问题分裂正定混合有限元方法的逼近格式;再次通过引入一些重要的中间变量和投影算子,并利用投影算子的相关性质,结合分裂正定混合有限元本身的逼近结果,得到了椭圆最优控制问题分裂正定混合有限元方法的超收敛性;最后数值实验结果验证了所得理论结果的正确性.     

共孔径偏振耦合分光系统中反射镜造成的相位延迟差的测量

激光信标共孔径发射接收偏振分光系统的动态相位补偿需要测量望远镜各反射镜对s光和p光的相位延迟差。利用Stokes矢量和Mueller矩阵建立了物理模型,并推导出用测得的回光功率计算相位延迟差的解析式。提出一种通过实验测量回光功率计算反射镜相位延迟差的方法,解决了在0～2p范围内唯一确定反射镜相位延迟差的问题。实际测量了两块反射镜的相位延迟差,并将测量结果用于动态相位补偿偏振分光实验,验证了该方法的正确性。分析了偏振分光棱镜、法拉第旋光器以及近似计算这3个主要的测量误差源,并估计总测量误差约为1°。     

分子轨道波函数相对论效应的高分辨电子动量谱学观测

利用新研制的能量分辨为0.5 eV 的高分辨(e, 2e)谱仪测量了CF3I分子在9—15 eV能区的束缚能谱.新谱仪能较好地分辨该分子碘孤对轨道的自旋轨道劈裂组分5e3/2和5e1/2,并得到了它们各自的电子动量分布以及分支比随动量的变化关系.实验结果清楚地显示了5e3/2和5e1/2态波函数的相对论效应.这是第一个分子轨道波函数相对论效应的直接实验观测.     

First-principles study of two-dimensional van der Waals heterostructure based on ZnO and Mg(OH)2: A potential photocatalyst for water splitting

In this study, the structural, electronic and optical properties of the two-dimensional heterostructure based on ZnO and Mg(OH)₂ are investigated by first-principle calculations. The ZnO/Mg(OH)₂ heterostructure, formed by van der Waals (vdW) interaction, possesses a type-II band structure, which can separate the photogenerated electron–holes constantly. The heterostructure has decent band edge positions for the redox reaction to decompose the water at pH 0 and 7. As for the interfacial properties of the heterostructure, the trend of band bending of the ZnO and Mg(OH)₂ layers in the heterostructure is addressed, which will result a built-in electric field. Besides, the charge-density difference and potential drop across the interface of the ZnO/Mg(OH)₂ vdW heterostructure are also calculated. Finally, the heterostructure is demonstrated that it not only has excellent ability to capture the light near the visible spectrum region, but also can improve the optical performance for the monolayered ZnO and Mg(OH)₂.     

Polynomial coefficients. Application to spin–spin splitting by N equivalent nuclei of spin I > 1/2

The NMR intensity pattern of a nucleus split by N identical nuclei of spin 1/2 is given by the binomial coefficients. These are conveniently obtained from Pascal's triangle, equivalent to the chemist's branching diagram. Much less well‐known is the pattern from splitting by N identical nuclei of spin I > 1/2. This was originally presented in terms of multinomial coefficients, but polynomial coefficients are more convenient. These describe the number of ways that N objects can be distributed to 2I + 1 numbered boxes. They arise in the polynomial expansion and are conveniently obtained from generalizations of Pascal's triangle. Examples and predictions are given.     

An operator splitting algorithm for the three-dimensional advection–diffusion equation

Operator splitting algorithms are frequently used for solving the advection–diffusion equation, especially to deal with advection dominated transport problems. In this paper an operator splitting algorithm for the three-dimensional advection–diffusion equation is presented. The algorithm represents a second-order-accurate adaptation of the Holly and Preissmann scheme for three-dimensional problems. The governing equation is split into an advection equation and a diffusion equation, and they are solved by a backward method of characteristics and a finite element method, respectively. The Hermite interpolation function is used for interpolation of concentration in the advection step. The spatial gradients of concentration in the Hermite interpolation are obtained by solving equations for concentration gradients in the advection step. To make the composite algorithm efficient, only three equations for first-order concentration derivatives are solved in the diffusion step of computation. The higher-order spatial concentration gradients, necessary to advance the solution in a computational cycle, are obtained by numerical differentiations based on the available information. The simulation characteristics and accuracy of the proposed algorithm are demonstrated by several advection dominated transport problems. © 1998 John Wiley & Sons, Ltd.     

Phosphating-induced charge transfer on CoO/CoP interface for alkaline H2 evolution

Designing non-noble metal electrocatalysts toward alkaline hydrogen evolution reaction (HER) with high performance at a large current density is urgent. Herein, a CoO/CoP heterostructure catalyst (termed POZ) was designed by a phosphating strategy. The strong electron transfer on the interface of CoO/CoP was experimentally and theoretically proven. POZ showed a low overpotential of 236 mV at 400 mA/cm², which was 249 mV lower than non-phosphated sample. It also exhibited a remarkable solar-to-hydrogen conversion efficiency of 10.5%. In this work, the construction of CoO/CoP interface realized by a simple phosphating strategy could provide an important reference to boost the HER performance on those materials not merely metal oxides.     

Explicit finite volume non‐oscillatory schemes for 2D transient free‐surface flows

A class of high‐resolution non‐oscillatory shock‐capturing Roe, TVD and ENO explicit schemes in finite volume approach are presented for the computation of 2D unsteady rapidly varied open channel flows. In order to apply these schemes to simulate the hydraulic phenomena in field, the Strang‐type operator splitting technique is adopted to treat the flow with bottom slope and friction terms. Verifications of the proposed schemes are made by comparison with analytical solutions or experimental data, and very good agreements are obtained. To illustrate the efficiency and stability of the present algorithms, four typical problems of rapidly varied flows are solved and the results of different schemes are compared. It is demonstrated that the proposed method is accurate, robust and highly stable even in the flows with very strong discontinuites, which need no tuning of any adjustable parameter, such as artificial viscosity coefficient, as other methods do, and is a reliable mathematical modeling for 2D practical hydraulic engineering applications. Copyright © 1999 John Wiley & Sons, Ltd.     

Non-persistence of Homoclinic Connections for Perturbed Integrable Reversible Systems

The dynamics of an analytic reversible vector field (X,) is studied in with one real parameter close to 0; X=0 is a fixed point. The differential D_x (0,0) generates an oscillatory dynamics with a frequency of order 1—due to two simple, opposite eigenvalues lying on the imaginary axis—and it also generates a slow dynamics which changes from a hyperbolic type—eigenvalues are —to an elliptic type—eigenvalues are —as passes trough 0. The existence of reversible homoclinic connections to periodic orbits is known for such vector fields. In this paper we study a particular subclass of such vector fields, obtained by small reversible perturbations of the normal form. We give an explicit condition on the perturbation, generically satisfied, which prevents the existence of a homoclinic connections to 0 for the perturbed system. The normal form system of any order admits a reversible homoclinic connection to 0, which then does not survive under perturbation of higher order. It will be seen that normal form essentially decouples the hyperbolic and elliptic part of the linearization to any chosen algebraic order. However, this decoupling does not persist arbitrary reversible perturbation, which finally causes the appearance of small amplitude oscillations.