Nonnormality and stochastic differential equations

A highly nonnormal Jacobian may give rise to large transients. This behaviour has been shown to have implications for (a) the relevance of linearising a nonlinear system and (b) the timestep restrictions required to keep a numerical method stable. Here, we show that nonnormality also manifests itself for stochastic differential equations. We give an example of a family of systems that is stable without noise, but can be made exponentially unstable in mean-square by a noise perturbation that shrinks to zero as the nonnormality increases. We then show via finite-time convergence theory that an Euler approximation shares the same property, giving a discrete analogue of the result. In memory of Germund Dahlquist (1925–2005).AMS subject classification (2000) 65C30, 34F05     

竞争-竞争-互惠交错扩散模型的整体解

应用能量估计方法和bootstrap技巧证明了竞争-竞争-互惠交错扩散模型在空间维数小于6时古典解的整体存在性.当反应函数的系数满足一定条件时,应用Lyapunov函数获得了该模型解的收敛性.     

光纤型宽带可调连续波差频产生中红外激光器

报道一种新型光纤化宽带可调连续波中红外激光器系统,该激光系统采用准相位匹配(QPM)的差频产生(DFG)技术,非线性晶体为多周期的周期性极化掺镁铌酸锂晶体(PPMgLN),掺镱光纤激光器(YDFL)用作抽运光源,可调激光器经掺铒光纤放大器(EDFA)功率提升后作为信号光源。利用建立的准相位匹配-差频产生系统,获得了连续波中红外差频光输出;实验发现,温度导致相位失谐的半峰全宽(FWHM)为4.5℃;通过优化选择晶体周期,并结合调节信号光波长和控制温度,该准相位匹配-差频产生系统可在3.1~3.6μm内连续调谐。     

Propagation characteristics of linearly polarized Bessel-Gaussian beams through an annular apertured paraxial ABCD optical system

By means of Collins diffraction integral formula in the paraxial approximation and based on the fact that a hard aperture function can be expanded into a finite sum of complex Gaussian functions, an approximate analytical expression for linearly polarized Bessel-Gaussian beams passing through a paraxial ABCD optical system with an annular aperture has been derived. The results provide more convenient for studying their propagation and transformation than the usual way by using diffraction integral directly. By using the analytical expression and the diffraction integral formula some numerical simulations are done to illustrate for the propagation characteristics of a linearly polarized Bessel-Gaussian beam through an optical system with an annular aperture.     

含超导材料Thue-Morse序列一维光子晶体传输特性研究

超导光子晶体是一类重要的带隙可调谐的光子晶体.利用传输矩阵法研究了含超导材料的Thue -Morse序列准周期结构—维光子晶体在可见光波段的传输特性.数值结果表明在正入射时,光子带隙宽度和位置基本不随序列项数的增加而改变;准周期超导光子晶体的传输特性可以通过改变传统电介质材料的结构参数和环境温度等来进行调节.     

Investigation of 515 nm green-light emission for full color emission LaAlO3 phosphor with varied valence Eu

Photoluminescence and lifetime decay properties of varied valence Eu were employed to investigate the luminescence mechanism of green-light emission positioned at ∼515 nm for full color emission LaAlO₃ phosphor co-doped with Eu²⁺ and Eu³⁺. The enhanced ⁵D₂→⁷F₃ transition emission of Eu³⁺ was assigned for this green emission. Energy transfer between Eu²⁺ and ⁵D₂ level of Eu³⁺ was proposed, which results in the enhancement of ⁵D₂→⁷F₃ transition emission. In addition, energy transfer relations between host-Eu and charge transfer state (CTS)-Eu were also discussed associated with the PLE spectra and band schemes.     

3ω法加热/测温膜中温度波解析及其在微/纳米薄膜导热系数测量中的应用

给出了3ω法测试系统中描述薄膜表面加热/测温膜中温度波动的级数形式解，并将复数温度波动的实部和虚部分开表示.利用该解分析了交流加热频率、加热膜宽度和材料热物性的组合参数对加热膜温度波动幅度的影响.并根据此解对测量原理的数学模型进行了修正，建立了相应的3ω测试系统，首先测定了厚度为500 nm SiO₂薄膜的导热系数，验证了实验系统的合理性.加大了测试频率，利用级数模型在高频段直接得到SiO₂薄膜的导热系数，结合低频段的数据同时确定了Si基体的导热系数.利用级数解分析测试了激光晶体Nd:YAG〈111〉面上多层ZrO₂/SiO₂增透膜的导热系数，测试的ZrO₂薄膜的导热系数比体材料小.进行了不确定度分析.结果表明，提出的分析方法可以有效研究微器件表面薄膜结构的导热性能. 关键词： ω法')" href="#">3ω法 微/纳米薄膜 导热系数 微尺度加热膜     

Melting of dense sodium

High-pressure high-temperature synchrotron diffraction measurements reveal a maximum on the melting curve of Na in the bcc phase at approximately 31 GPa and 1000 K and a steep decrease in melting temperature in its fcc phase. The results extend the melting curve by an order of magnitude up to 130 GPa. Above 103 GPa, Na crystallizes in a sequence of phases with complex structures with unusually low melting temperatures, reaching 300 K at 118 GPa, and an increased melting temperature is observed with further increases in pressure.     

Sobolev-Lorentz范数约束下的次临界型Adams不等式

本文在Sobolev-Lorentz空间W2L2,q(R4)的范数约束下得到了一个最佳的二阶次临界型Adams不等式.进一步,当次临界指标逼近最佳常数时,得到了Adams泛函的上、下界的估计.本文主要采用了Lam和Lu[A new approach to sharp Moser-Trudinger and Adams ...     

Wear resistance of reactive plasma sprayed and laser remelted TiB2-TiC0.3N0.7 based composite coatings against medium carbon steel

Wear resistance of reactive plasma sprayed TiB₂-TiC_0.3N_0.7 based composite coatings and the as-sprayed coating with laser surface treatment was investigated using plate-on-plate tests. Wear tests were performed at different normal loads and sliding speeds under dry sliding conditions in air. The surface morphologies of counterparts against as-sprayed and laser remelted coatings were investigated. The microstructure and chemical composition of wear debris and coatings were studied using scanning electron microscopy (SEM) and energy dispersive X-ray spectroscopy (EDS), respectively. The results show that the wear resistance of the laser remelted coating is improved significantly due to their increased microhardness and reduced flaws. The primary wear mechanism of the remelted coating is oxidation wear and its minor wear mechanisms are grain abrasion and fatigue failure during the course of wear test. In contrast, the primary wear mechanism of the as-sprayed coating is grain abrasion at the low sliding speed (370 rpm) and fatigue failure at the high sliding speed (549 rpm). The oxidation wear mechanism is a minor contributor for the as-sprayed coating.