Numerical Simulation of Anisotropic Preheating Ablative Rayleigh-Taylor Instability

The linear growth rate of the anisotropic preheating ablative Rayleigh-Taylor instability （ARTI） is studied by numerical simulations. The preheating model κ （T）=κSH [1＋f（T）] is applied, where f（T） is the preheating function interpreting the preheating tongue effect in the cold plasma ahead of the ablative front. An arbitrary coefficient D is introduced in the energy equation to study the influence of transverse thermal conductivity on the growth of the ARTI. We find that enhancing diffusion in a plane transverse to the mean longitudinal flow can strongly reduce the growth of the instability. Numerical simulations exhibit a significant stabilization of the ablation front by improving the transverse thermal conduction. Our results are in general agreement with the theory analysis and numerical simulations by Masse [Phys. Rev. Lett. 98 （2007） 245001].     

He,Ne,Ar,Kr和Xe原子电子的动量密度分布研究

对He,Ne,Ar,Kr和Xe原子体系中电子在动量空间的性质进行了系统的理论计算研究.采用自洽场HFR方法计算了坐标空间He,Ne,Kr和Xe原子体系单电子径向波函数,动量空间的单电子波函数由坐标空间原子体系单电子径向波函数通过运用傅立叶变换计算得到.在冲量近似条件下,进一步计算研究了这些原子的单电子动量密度分布和原子体系总的Compton轮廓.计算结果与已有的实验实验值和其他文献的理论计算结果比较表明,本文计算的结果是准确的.     

聚(2-甲氧基-5-辛氧基)对苯乙炔/Y_2O_3:Eu~(3+)纳米复合材料的光致电子转移效应

采用原位脱氯化氢缩合聚合法制备了聚(2-甲氧基-5-辛氧基)对苯乙炔/Y_2O_3:E~(3+)(PMOCOPV/Y_2 O_3:Eu~(3+))纳米复合材料。红外光谱证实了在Y_2O_3:Eu~(3+)表面的包覆层为PMOCOPV。紫外-可见吸收光谱表明与PMOCOPV相比,PMOCOPV/Y_2O_3:Eu~(3+)的最大吸收峰发生红移且强度提高。荧光光谱研究表明PMOCOPV/Y_2O_3:Eu~(3+)的最大发射波长发生红移且强度提高,荧光寿命得到增强,Y_2O_3:Eu~(3+)与PMOCOPV之间形成了光致电子转移体系,使得π电子离域程度增加,并且导致荧光量子效率提高。根据E_g与入射光子能量hv的关系,拟合了PMOCOPV/Y_2O_3:Eu~(3+)薄膜的光学禁带宽度,发现E_g减小。采用简并四波混频方法测试它们的三阶非线性极化率x~((3)),结果发现与PMOCOPV相比,PMOCOPV/Y_2O_3:Eu~(3+)纳米复合体的非线性光学响应逐渐增强,进一步说明PMOCOPV与Y_2O_3:Eu~(3+)之间形成了分子间光致电子转移体系,产生了复杂的分子间离域π电子非线性运动。     

Non-Markovian relaxation of a three-level system: quantum trajectory approach

The non-Markovian dynamics of a three-level quantum system coupled to a bosonic environment is a difficult problem due to the lack of an exact dynamic equation such as a master equation. We present for the first time an exact quantum trajectory approach to a dissipative three-level model. We have established a convolutionless stochastic Schr?dinger equation called the time-local quantum state diffusion (QSD) equation without any approximations, in particular, without Markov approximation. Our exact time-local QSD equation opens a new avenue for exploring quantum dynamics for a higher dimensional quantum system coupled to a non-Markovian environment.     

Efficient one-pot synthesis of Ag nanoparticles loaded on N-doped multiphase TiO2 hollow nanorod arrays with enhanced photocatalytic activity

The simultaneous Ag loaded and N-doped TiO₂ hollow nanorod arrays with various contents of silver (Ag/N-THNAs) were successfully synthesized on glass substrates by one-pot liquid phase deposition (LPD) method using ZnO nanorod arrays as template. The catalysts were characterized by Raman spectrum, field-emission scanning electron microscopy (FESEM), high-resolution transmission electron microscope (HRTEM), ultraviolet-vis (UV-vis) absorption spectrum and X-ray photoelectron spectroscopy (XPS). The results suggest that AgNO₃ additive in the precursor solutions not only can promote the anatase-to-rutile phase transition, but also influence the amount of N doping in the samples. The photocatalytic activity of all the samples was evaluated by photodegradation of methylene blue (MB) in aqueous solution. The sample exhibited the highest photocatalytic activity under UV light illumination when the AgNO₃ concentration in the precursor solution was 0.03 M, due to Ag nanoparticles acting as electron sinks; When the AgNO₃ concentration was 0.07 M, the sample performed best under visible light illumination, attributed to the synergetic effects of Ag loading, N doping, and the multiphase structure (anatase/rutile).     

Nonlinear Maps Preserving the Jordan Triple *-Product on Factor von Neumann Algebras

Let A and B be two factor von Neumann algebras. For A, B ∈ A, define by [A, B]_*= AB-BA~*the skew Lie product of A and B. In this article, it is proved that a bijective map Φ : A → B satisfies Φ([[A, B]_*, C]_*) = [[Φ(A), Φ(B)]_*, Φ(C)]_*for all A, B, C ∈ A if and only if Φ is a linear *-isomorphism, or a conjugate linear *-isomorphism, or the negative of a linear *-isomorphism, or the negative of a conjugate linear *-isomorphism.     

Recovering a space-dependent source term in a time-fractional diffusion wave equation

This work is concerned with identifying a space-dependent source function from noisy final time measured data in a time-fractional diffusion wave equation by a variational regularization approach. We provide a regularity of direct problem as well as the existence and uniqueness of adjoint problem. The uniqueness of the inverse source problem is discussed. Using the Tikhonov regularization method, the inverse source problem is formulated into a variational problem and a conjugate gradient algorithm is proposed to solve it. The efficiency and robust of the proposed method are supported by some numerical experiments.     

Well-posedness and analyticity of the Cauchy problem for the multi-component Novikov equation

In this paper, we are concerned with the Cauchy problem of the multi-component Novikov equation. We establish the local well-posedness in a range of the Besov spaces by using Littlewood–Paley decomposition and transport equation theory. Moreover, with analytic initial data, we show that its solutions are analytic in both variables, globally in space and locally in time.     

The monoid of $$2 \times 2$$2×2 triangular boolean matrices under skew transposition is non-finitely based

Semigroup Forum - Let $$\mathscr {T\!B}_n$$ be the involution semigroup of all upper triangular boolean $$n\times n$$ matrices under the ordinary matrix multiplication and the skew transposition....     

面内功能梯度三角形板等几何面内振动分析

基于平面应变理论,利用等几何有限元方法分析了弹性边界条件下面内功能梯度三角形板的面内振动特性.板的材料属性沿厚度方向呈均匀分布,而在面内方向呈任意指数梯度变化.采用非均匀有理B样条(NURBS)基函数对三角形结构进行等几何建模和位移描述,实现了三角形板几何设计和振动分析的无缝衔接.在三角形板边界上引入虚拟弹簧约束并通过调节虚拟弹簧刚度,实现任意边界条件的施加.通过不同的单元细化方案和对比算例,验证了等几何方法的灵活性、准确性和快速收敛性.系统研究了边界条件、材料属性和几何参数对三角形板振动特性的影响.同时给出了弹性边界条件下面内功能梯度三角形板的振动特性解,具有重要参考价值.