Characteristics of Raman spectra of natural clinochlore at 200 degrees C and 0.95-7.70 GPa

Variation of crystal structure of natural clinochlore with pressure was investigated by the approach of diamond anvil cell (DAC) and in situ micro-Raman spectroscopic measurement at 200 degrees C and up to 7.7 GPa. The 481 and 786 cm(-1) peaks shift towards high-frequency linearly with increasing pressure at 200 degrees C. The linear relations between Raman shift (N, cm(-1)) and pressure (P, GPa) for the two peaks are: N = 11.136P+482.6 (R2 = 0.987 4) and N = 5.055P+785.7 (R2 = 0.983 7), respectively. The 865 cm(-1) peak arising from the stretching mode of the Si-O(nb) shifts slightly because of the strong repulsion between T cations at the tetrahedral sites and M cations at the octahedral sites in the TOT layer. Raman shift of 481 cm(-1) and 786 means the shortening of the length of M-O(br) and Si-CO(br) bonds since the peaks are contributed by the stretching mode of the M-O(br) and Si-O(br) respectively. No phase transition of clinochlore under the experimental condition was found. The results indicate that chlorite minerals may be stable at least at a depth of 80-90 km in the cold subduction zones, and the fluid derived from chlorite dehydration may be an important fact for earthquake occurrence in the subduction zones.     

O-vacancy and surface on CeO2: A first-principles study

Atomic and electronic structures of CeO₂ (1 1 1), (1 1 0) and (1 0 0) surfaces are investigated using the first-principles density functional theory taking into account the on-site Coulomb interaction. Both the stoichiometric and O-deficient surfaces are examined in order to clarify the overall features. The CeO₂ (1 1 1) is found to be the most stable surface, followed by the (1 1 0) and (1 0 0) surfaces, consistent with experimental observations. Three surfaces exhibit different features of relaxation. Large relaxations are found at the (1 1 0) and (1 0 0) surfaces, while very small changes are observed at the (1 1 1) surface. It is found that the O-vacancy occurs more readily at the (1 1 0) surface as compared with the (1 1 1) surface. Furthermore, the formation energies of the O-vacancy in the surfaces are lower than that in the bulk. The energetically favorable O-vacancy locates in the second O-atomic layer for the (1 1 1) while at the surface layer for the (1 1 0). The excess electrons left with the removal of the O atom are distributed in the first two layers with certain (a considerable) fraction filling the Ce-4f states.     

Thermo-optically tunable silicon photonic crystal light modulator

We designed, fabricated, and characterized a thermo-optically tunable compact (10 μm × 10 μm) silicon photonic crystal (PhC) light modulator that operates at around 1.55 μm for TE polarization. The operational principle of the device is the modulation of the cutoff frequency in a silicon-based line defect PhC. The cutoff frequency is shifted because of the thermo-optic tuning of the silicon refractive index, which is realized by localized heating on the PhC. The modulator is formed by a triangular lattice array of cylindrical air holes on a silicon-on-insulator wafer. Optical characterization was carried out, and the result clearly showed thermo-optic tuning of the cutoff frequency at around 1.55 μm.     

Optimal design of a multilayer diffractive optical element for dual wavebands

A method for optimal design of a multilayer diffractive optical element (MLDOE) for dual-wide-waveband optical systems is presented with consideration of polychromatic integral diffraction efficiency (PIDE) and the weight factors of PIDE for each waveband. The design process and simulation of a MLDOE in mid-wave and long-wave IR are described, and the comparison of diffraction efficiency of the MLDOEs for different design wavelength pairs determined by different methods is given. This method can make the design process more rational and more reasonable and can give a better design result than that with the conventional design method.     

Preparation and electrochemistry of one-dimensional nanostructured MnO2/PPy composite for electrochemical capacitor

One-dimensional nanostructured manganese dioxide/polypyrrole (MnO₂/PPy) composite was prepared by in situ chemical oxidation polymerization of pyrrole in the host of inorganic matrix of MnO₂, using complex of methyl orange (MO)/FeCl₃ as a reactive self-degraded soft-template. The morphology and structure of the composite were characterized by infrared spectroscopy (IR) X-ray diffraction (XRD), scanning electron microscopy (SEM) and transmission electron microscopy (TEM). The results show that the MnO₂/PPy composite consists of α-MnO₂ and PPy with nanotube-like structure. Electrochemical properties of the composite demonstrated the material showed good electrochemical reversibility after 500 charge-discharge cycles in the potential range of −0.4 to 0.6 V, the tube-like nanocomposite has the potential application in electrochemical capacitor.     

Convergence to nonlinear diffusion waves for solutions of Euler equations with time-depending damping

In this paper, we are concerned with the asymptotic behavior of solutions to the system of Euler equations with time-depending damping, in particular, include the constant coefficient damping. We rigorously prove that the solutions time-asymptotically converge to the diffusion wave whose profile is self-similar solution to the corresponding parabolic equation, which justifies Darcy's law. Compared with previous results about Euler equations with constant coefficient damping obtained by Hsiao and Liu (1992) [2], and Nishihara (1996) [9], we obtain a general result when the initial perturbation belongs to the same space, i.e. $H^3(\mathbb{R})\times H^2(\mathbb{R})$. Our proof is based on the classical energy method.     

Global viscosity solutions for eikonal equations on class A Lorentzian 2-tori

On the Abelian cover \(({\mathbb {R}}^{2},g)\) of a class A Lorentzian 2-torus \(({\mathbb {T}}^{2},g)\), we showed the existence of global viscosity solutions to the eikonal equation

$$\begin{aligned} g(\nabla u,\nabla u)=-1 \end{aligned}$$

associated to those homologies in the interior of the stable time cone. Some other related dynamical properties are also considered. As an application of the main results, we study the differentiability of the unit sphere of the stable time separation associated to the class A Lorentzian 2-torus.

     

A second-order space–time accurate scheme for nonlinear diffusion equation with general capacity term

A fully implicit finite difference (FIFD) scheme with second-order space–time accuracy is studied for a nonlinear diffusion equation with general capacity term. A new reasoning procedure is introduced to overcome difficulties caused by the nonlinearity of the capacity term and the diffusion operator in the theoretical analysis. The existence of the FIFD solution is investigated at first which plays an important role in the analysis. It is established by choosing a new test function to bound the solution and its temporal and spatial difference quotients in suitable norms in the fixed point arguments, which is different from the traditional way. Based on these bounds, other fundamental properties of the scheme are rigorously analyzed consequently. It shows that the scheme is uniquely solvable, unconditionally stable, and convergent with second-order space–time accuracy in L^∞(L²) and L^∞(H¹) norms. The theoretical analysis adapts to both one- and multidimensional problems, and can be extended to schemes with first-order time accuracy. Numerical tests are provided to verify the theoretical results and highlight the high accuracy of the second-order space–time accurate scheme. The reasoning techniques can be extended to a broad family of discrete schemes for nonlinear problems with capacity terms.     

离散分红下障碍期权的间接级数展开定价方法

人们投资股票市场的最大动力,除了从股票本身的升值中获利,还包括收益分红.提出了带有离散分红的障碍期权的一种新型的近似方法,以向上敲出看涨障碍期权为例,固定分红的次数,通过泰勒级数展开得到关于关键变量的仿射函数,给出了一个只带有一维积分的定价公式,提高了计算速度.该方法还可以用于回望期权等其它衍生品的定价,对在市场上进行期权交易有一定指导意义.