Optimized prefactored compact schemes

The numerical simulation of aeroacoustic phenomena requires high-order accurate numerical schemes with low dispersion and dissipation errors. In this paper we describe a strategy for developing high-order accurate prefactored compact schemes, requiring very small stencil support. These schemes require fewer boundary stencils and offer simpler boundary condition implementation than existing compact schemes. The prefactorization strategy splits the central implicit schemes into forward and backward biased operators. Using Fourier analysis, we show it is possible to select the coefficients of the biased operators such that their dispersion characteristics match those of the original central compact scheme and their numerical wavenumbers have equal and opposite imaginary components. This ensures that when the forward and backward stencils are added, the original central compact scheme is recovered. To extend the resolution characteristic of the schemes, an optimization strategy is employed in which formal order of accuracy is sacrificed in preference to enhanced resolution characteristics across the range of wavenumbers realizable on a given mesh. The resulting optimized schemes yield improved dispersion characteristics compared to the standard sixth- and eighth-order compact schemes making them more suitable for high-resolution numerical simulations in gas dynamics and computational aeroacoustics. The efficiency, accuracy and convergence characteristics of the new optimized prefactored compact schemes are demonstrated by their application to several test problems.     

High-order rogue waves for the Hirota equation

The Hirota equation is better than the nonlinear Schrödinger equation when approximating deep ocean waves. In this paper, high-order rational solutions for the Hirota equation are constructed based on the parameterized Darboux transformation. Several types of this kind of solutions are classified by their structures.     

Higher-order time integration with a local Lax–Wendroff procedure for a central scheme on an overlapping grid

We have implemented a high-order Lax–Wendroff type time integration for a central scheme on an overlapping grid for conservation law problems. Using a local iterative approach presented by Dumbser et al. (JCP, 2008) [12], we extend a local high-order spatial reconstruction on each cell to a local higher-order space–time polynomial on the cell. We rewrite the central scheme in a fully discrete form to avoid volume integration in the space–time domain. The fluxes at cell interfaces are calculated directly via integrating a higher-order space–time reconstruction of the flux. We compare this approach with the corresponding multi-stage Runge–Kutta time integration (RK). Numerical results show that the new time integration is more cost-effective.     

表面增强拉曼光谱研究自组装单分子层在化学接触和纳米隔绝下的分子振动活性变化(英文)

为确定表面增强拉曼光谱中某些有争议的弱振动模式是来自高阶的影响还是分子基团对称性变化的影响,本文以1,4-苯二硫醇作为探针分子提供了一种实验验证的框架方法.光谱实验显示,观测到的有争议的弱振动模式并不是来自高阶的影响,而是分子基团对称性变化所致.我们的实验框架方法很容易拓展开来,如用于研究其它波长激光激发的类似体系或有机分子搭接的分子结.     

Size-dependent resonance and buckling behavior of nanoplates with high-order surface stress effects

This work presents a theoretical study of the resonance frequency and buckling load of nanoplates with high-order surface stress model. A classical thin plate theory based on Kirchhoff–Love assumption is implemented with surface effects. Circular and rectangular nanoplates with simply supported end conditions are exemplified. The size-dependent solutions are compared with the simplified solutions based on simple surface stress model, and also on the classical theory of elasticity. We aim to explore the scope of applicability so that the modified continuum mechanics model could serve as a refined approach in the prediction of mechanical behavior of nanoplates.     

荧光寿命的正弦调制测量法及分析

设计并制作了光强调制度和频率可调的发光二极管驱动电路,应用这种激励源激发荧光样品Eu₂L′3·nH₂O(L′=C₄H₄O₄),测量了激发光和Eu3+离子的5D₀—7F₂发射光的波形。实验得到的数据用按照相位法测量荧光寿命的原理用非线性最小平方曲线拟合,得到Eu3+离子激发态5D₀的寿命约为0.680 ms。讨论了光源调制中的高次谐波分量对测量结果的影响以及寿命具有一定分布的多指数衰减体系的测量和处理方式,提出应用傅里叶级数展开处理数据的修正方法,以扩大相位法测量荧光寿命的适用范围,得到更准确的荧光寿命值。     

叠加态下3色场波形优化增大谐波辐射截止能量及强度

在He~+离子1s态和2s态的叠加态作为初始态时,提出一种优化3束激光场来增大谐波截止能量和强度的方法.结果表明:在叠加初始态下,谐波强度要比基态初始态下增强3个数量级以上.随后,在3色场波形优化下,谐波截止能量又得到增大,进而获得一个高强度、高光子能量的谐波光谱连续区.通过叠加光谱连续区上最后100次的谐波可以获得一个27 as的孤立阿秒脉冲.     

三色圆偏振激光组合脉冲驱动氦原子产生椭圆偏振的阿秒脉冲

我们提出利用频率为ω,3ω和强度较弱的2ω组成的三色圆偏振激光组合脉冲驱动氦原子能够得到椭偏率较大的阿秒脉冲链的一种方法.通过强场近似方法,计算了氦原子在两色和三色圆偏振激光组合脉冲驱动下发射高次谐波谱及其合成阿秒脉冲链,比较了氦原子(初态为s态)在这两种情况下发射高次谐波谱的特点及其合成阿秒脉冲链椭偏率的大小,结果发现,在反旋的两色ω,3ω激光脉冲基础上加入了频率为2ω的第三色激光脉冲联合作用到氦原子上,所得到的阿秒脉冲链的椭偏率相对于双圆场情况下有所增加,通过调整ω,3ω激光的强度比,并且选择适当的第三色激光的强度,对初态为s态的原子,仍能够得到具有较大椭偏率的阿秒脉冲链.     

A high-order finite volume method for systems of conservation laws—Multi-dimensional Optimal Order Detection (MOOD)

In this paper, we investigate an original way to deal with the problems generated by the limitation process of high-order finite volume methods based on polynomial reconstructions. Multi-dimensional Optimal Order Detection (MOOD) breaks away from classical limitations employed in high-order methods. The proposed method consists of detecting problematic situations after each time update of the solution and of reducing the local polynomial degree before recomputing the solution. As multi-dimensional MUSCL methods, the concept is simple and independent of mesh structure. Moreover MOOD is able to take physical constraints such as density and pressure positivity into account through an “a posteriori” detection. Numerical results on classical and demanding test cases for advection and Euler system are presented on quadrangular meshes to support the promising potential of this approach.     

Phase-locking observed among high-order lateral modes of a broad-stripe diode array inside an external cavity

For a laser diode array (LDA) positioned in an external cavity of a certain length, a very strong inter-emitter coupling can be established between the off-axis lateral modes of the broad-stripe emitters. Under these circumstances, the phase-locked operation of the LDA due to couplings between off-axis modes of emitters has been observed, for the first time to our knowledge. The observations suggest that phase locking of a broad-stripe LDA can be achieved among different emitter lateral modes by selecting different cavity lengths.