An $L^{\infty}$ Second Order Cartesian Method for 3D Anisotropic Interface Problems

A second order accurate method in the infinity norm is proposed for general three dimensional anisotropic elliptic interface problems in which the solution and its derivatives, the coefficients, and source terms all can have finite jumps across one or several arbitrary smooth interfaces. The method is based on the 2D finite element-finite difference (FE-FD) method but with substantial differences in method derivation, implementation, and convergence analysis. One of challenges is to derive 3D interface relations since there is no invariance anymore under coordinate system transforms for the partial differential equations and the jump conditions. A finite element discretization whose coefficient matrix is a symmetric semi-positive definite is used away from the interface; and the maximum preserving finite difference discretization whose coefficient matrix part is an M-matrix is constructed at irregular elements where the interface cuts through. We aim to get a sharp interface method that can have second order accuracy in the point-wise norm. We show the convergence analysis by splitting errors into several parts. Nontrivial numerical examples are presented to confirm the convergence analysis.     

Antiphase States in Coupled Oscillator Systems

Coupled identical oscillators with resistive couplings are investigated. Various antiphase states are observed. The bifurcation threshojds for the antiphase states of coupled van der Pol oscillators and the unstable modes of these systems at the bifurcation points are explicitly compu ted. The dependence of antiphase states on system size and coupling length is investigated in detail. General coupled limit cycle models are also investigated. The realizations of antiphase states can be explained, based on the global potential analysis.     

气候变化对浙江沿海风暴潮的影响

基于浙江沿海多个气象观测站和潮位观测站近50年的气温、潮位及风暴潮的资料,研究了气候变化背景下浙江沿海台风暴潮变化特征.分析表明,随着沿海地区年平均气温的上升,浙江沿海相对海平面、登陆台风、超警戒风暴潮、较大风暴增水、年极值高潮位等都呈现出上升或增多趋势;在此背景下,浙江沿海风暴潮灾害风险也随之增大,特别是2000年以来,登陆浙江沿海的台风个数和最大增水超过300cm的风暴潮次数都显著增多.对气候变化背景下浙江沿海风暴潮灾害的影响分析,将为今后风暴潮预警及防灾、减灾的应对提供重要的启示和参考.     

Luminescence of transparent glass ceramics containing Er<Superscript>3+</Superscript> and Yb<Superscript>3+</Superscript> zirconate-titanate nanocrystals

Luminescence regularities have been studied in new erbium/ytterbium materials based on glasses and glass ceramics of a magnesium-aluminosilicate system containing nanoscale erbium/ytterbium zirconate titanate crystals with the pyrochlore structure. Lifetimes of Yb³⁺ and Er³⁺ ions in the ² F_5/2 state and in the ⁴I_11/2 and ⁴I_13/2 states, respectively, and the efficiency of Yb³⁺ → Er³⁺ energy transfer have been evaluated. The identified spectral-luminescent characteristics of the studied glasses and glass ceramics co-doped with erbium and ytterbium ions show that these materials are promising media for producing laser generation in the spectral range around 1.5 μm.     

Ultrasonic cleavage of thioethers

The rates of DPPH (diphenylpicrylhydrazyl) trapping and the sonolytical products obtained during the sonolysis of thioethers at normal and low temperature are reported. CS2, lower sulfides, thiophene, and sulfurized species are the common products during the ultrasonic irradiations. Hydrocarbons are also obtained during the sonolysis of diallyl sulfide, diethyl disulfide, and dipropyl disulfide. Furthermore, aldehydes are obtained as oxidized species; SO2 is found at 208 K. The principal sonochemical process appears to be the cleavage of C-S or S-S bond with secondary combinations and rearrangements. DPPH has been used to probe the sonolytical potential of thioethers. The results show a good correlation between the rates of DPPH trapping and the vapor pressures of thioethers. In conclusion, a lower vapor pressure results in a higher sonolytical rate. The sonochemical behaviors of thioethers have strong qualitative similarities to the pyrolysis.     

SiO2气凝胶中ZnS∶Mn纳米微晶的发光性质

利用溶胶 凝胶法在SiO2 气凝胶中制得了ZnS∶Mn纳米微晶 ,并对微晶的X射线衍射谱、激发 发射光谱、发光效率、时间分辨光谱进行了研究 ,讨论了发光性质变化的原因。实验表明 ,Mn2 + 在纳米微晶中的发光效率相对于体材料有明显的提高 ,弛豫时间也比在体材料中缩短了约一个数量级     

Electronic structure of the organic semiconductor copper phthalocyanine: experiment and theory

The electronic structure of the organic semiconductor copper-phthalocyanine (CuPc) has been determined by a combination of conventional and resonant photoemission, near-edge x-ray absorption, as well as by the first-principles calculations. The experimentally obtained electronic valence band structure of CuPc is in very good agreement with the calculated density of states results, allowing the derivation of detailed site specific information.     

A direct method for accurate solution and gradient computations for elliptic interface problems

Numerical Algorithms - Recently, an augmented IIM (Li et al. SIAM J. Numer. Anal. 55, 570–597 2017) has been developed and analyzed for some interface problems. The augmented IIM can provide...     

Positive solvability of systems of nonlinear Hammerstein integral equations

The paper deals with the existence of positive continuous solutions to systems of nonlinear Hammerstein integral equations. The main tool used in the proofs is fixed point index theory in a cone. The results obtained here are essentially different from existing ones in the literature.     

ZnS:Eu2+的长余辉发光

Eu2+的5d能级在许多晶体中都低于其4f能级的最低激发态(6P7/2),因此发光呈带状光谱,且发射波长随基质变化很大。由于5L→4f是容许跃迁,所以发光的衰减很快,通常在μs数量级,出人意料的是ZnS:Eu的发光尽管也是Eu2+的5d→4f跃迁,但衰减却极慢,达几十分钟的数量级。弛豫曲线的分析表明,这种长的弛豫是电子陷阱造成的。