Unified Solution of the Expected Maximum of a Discrete Time Random Walk and the Discrete Flux to a Spherical Trap

Two random-walk related problems which have been studied independently in the past, the expected maximum of a random walker in one dimension and the flux to a spherical trap of particles undergoing discrete jumps in three dimensions, are shown to be closely related to each other and are studied using a unified approach as a solution to a Wiener-Hopf problem. For the flux problem, this work shows that a constant c = 0.29795219 which appeared in the context of the boundary extrapolation length, and was previously found only numerically, can be derived analytically. The same constant enters in higher-order corrections to the expected-maximum asymptotics. As a byproduct, we also prove a new universal result in the context of the flux problem which is an analogue of the Sparre Andersen theorem proved in the context of the random walker's maximum.     

Infrared superbroadband emission of Bi ion doped germanium-aluminum-sodium glass

The 96GeO-(3-χ)Al₂O₃-χNa₂O-1NaBiO₃ (χ = 0, 0.5, 1.5 molar percent designated as A1, A2 and A3) and 96GeO-(3.5-ψ)Al₂O₃-ψNa₂O-0.5Bi₂O₃ (ψ = 0.5, 1, 2 molar percent designated as B1, B2 and B3) glasses were prepared by conventional melting method with the measurement of their DTA curve, fluorescence decay curve, transmission, absorption and emission spectra. The near infrared superbroadband emission characteristics of the A1, A2, B1 and B2 glasses peak at ∼1220 nm were observed when pumped by an 800 nm laser diode. The stimulated emission cross section (σ_p) was obtained from the emission spectra. The result indicated that the introduction of Bi⁵⁺ in NaBiO₃ into raw materials could increase the emission intensity of the obtained glasses by 5.6 times than that of Bi³⁺ in Bi₂O₃, and the FWHM (Δλ) and emission lifetime (τ) at 1220 nm increased from 195 nm to 275 nm, and 280 μs to 434 μs. Meanwhile, it was found that the absorption edges were blue-shifted from 486 to 447 nm by comparing those of A1 and B1. The absorption edges were considered to be ascribed to the charge transfer from Bi³⁺ 6s² to Bi⁵⁺ 6s⁰. Therefore we could conclude that the content of Bi⁵⁺ ions in A1 was more than that in B1 glasses. It could be deduced from the emission and absorption spectra that the stronger emission intensity and wider FWHM were due to the higher concentration of Bi⁵⁺ ion in glass. In particular, the increase of Na₂O content was in proportion to the thermal stability and the value of σ_p × τ and σ_p × Δλ of glasses.     

Interfacial spin interactions of ferromagnetic and antiferromagnetic manganite bilayers

A pulsed laser deposition technique was used to grow ferromagnetic La_0.7Sr_0.3MnO₃ (LSMO) films on antiferromagnetic La_0.33Ca_0.67MnO₃ (LCMO) and Pr_0.7Ca_0.3MnO₃ (PCMO) films in bilayer forms. The LSMO film on the PCMO layer had a more elongated out-of-plane lattice than that on the LCMO layer. The former had a lower ferromagnetic transition temperature (320 K) than the latter (350 K). The enhanced low-temperature magnetoresistance of the LSMO/PCMO bilayer suggests that the spin frustration is stronger at this bilayer than in the LSMO/LCMO bilayer. These differences indicate that strain state and defect concentration play important roles in governing interfacial spin interactions.     

Magnetic properties of the bilayer manganese oxide (Pr0.6La0.4)1.2Sr1.8Mn2O7 under pressure

We investigated the effect of pressure on the magnetic properties of a single crystal of the bilayer manganese oxide (Pr_0.6La_0.4)_1.2Sr_1.8Mn₂O₇ by means of DC magnetization measurements under pressure. The ferromagnetic transition, which is accompanied by a metal-insulator transition, is highly sensitive to pressure. The pressure causes a structural variation, which affects the magnetic properties. We discuss the pressure dependence of the 3d electronic state of the Mn ion in this system.     

The study of exchange coupling in NiFe/Cu/IrMn trilayer structures by MOKE and FMR measurements

The exchange coupling strength of NiFe/Cu/IrMn trilayer films was examined with both a new magneto optical Kerr effect (MOKE) method developed for the exchange coupling field determination and ferromagnetic resonance (FMR) measurements. We found that the value for exchange coupling field obtained by the MOKE technique coincided with FMR result with high accuracy. Other peculiarities of FMR measurements due to interlayer exchange coupling such as angular dependence of resonance field on Cu spacer thickness are also shown in the article.     

Modulational instability and spatial structures of the Ablowitz-Ladik equation

Spatial structures as a result of a modulational instability are obtained in the integrable discrete nonlinear Schrödinger equation (Ablowitz-Ladik equation). Discrete slow space variables are used in a general setting and the related finite differences are constructed. Analyzing the ensuing equation, we derive the modulational instability criterion from the discrete multiple scales approach. Numerical simulations in agreement with analytical studies lead to the disintegrations of the initial modulated waves into a train of pulses.     

基于密度泛函理论的叶绿素A性质的研究

在液相环境中,采用密度泛函理论(DFT)、含时密度泛函理论(TD-DFT)、Multiwfn波函数分析软件,在pbepbe/6-311g(d)基组水平上,计算并分析了叶绿素A的结构、紫外光谱和电子—空穴分布,结果表明:pbepbe/6-311g(d)方法是计算叶绿素A紫外吸收光谱更精确的方法;叶绿素A分子的吡咯环与取代基相互作用的过程中,吡咯环Ⅳ受侧链"尾巴"的影响最大;理论计算的紫外光谱与实验数据吻合较好,其中635.71 nm和446.87 nm处的两个吸收峰可认为是叶绿素A的特征吸收峰;侧链或取代基团在叶绿素A激发过程中是给电子体,卟啉"头"既是电子供体,也是电子受体.     

The effect of microwave annealing on the electrical characteristics of lanthanum doped bismuth titanate films obtained by the polymeric precursor method

Lanthanum doped bismuth titanate thin films (Bi_3.25La_0.75Ti₃O₁₂ - BLT) were produced by the polymeric precursor method and crystallized in a domestic microwave oven and in conventional furnace. Using platinum coated silicon substrates configuration, ferroelectric properties of the films were determined with remanent polarization P_r and a coercive field E_c of 3.9 μC/cm² and 70 kV/cm for the film annealed in the microwave oven and 20 μC/cm² and 52 kV/cm for the film annealed in conventional furnace, respectively. The films annealed in conventional furnace exhibited excellent retention-free characteristics at low infant periods indicating that BLT thin films can be a promise material for use in non-volatile memories. On the other hand, the pinning of domains wall causes a strong decay at low infant periods for the films annealed in the microwave furnace which makes undesireable the application for future FeRAMS memories.     

Quantitative analysis of multi-element oxide thin films by angle-resolved XPS: Application to ultra-thin oxide films on MgAl substrates

An original procedure has been developed for the quantitative analysis and microstructural interpretation of angle-resolved X-ray photoelectron spectra (AR-XPS) of very thin (<6 nm), multi-element oxide films as grown on metallic binary alloy substrates by, e.g., thermal or plasma oxidation. To this end, first an approach has been given to retrieve the different metallic, oxidic and oxygen primary zero-loss (PZL) intensities from the measured AR-XPS spectra of the bare and oxidized alloy. The principal equations for the determination of the oxide-film thickness, composition and constitution from the resolved PZL intensities have been presented. On this basis, various corresponding calculation routes have been distinguished. The procedure has been applied to the case of very thin (<6 nm), mixed (Mg, Al)-oxide films on bare Mg-based MgAl substrates as grown by dry, thermal oxidation at room temperature. The results obtained on the thickness, composition, defect structure and constitution of the oxide-film have been discussed as function of the bulk Al alloying content and the applied partial pressure of oxygen.