Slow Effects of Fast Harmonic Excitation for Elastic Structures

High-frequency excitation may affect the slow behavior of a dynamical system. For example, equilibria may move, disappear, or gain or loose stability. We consider such slow effects of fast excitation for a simple mechanical system that incorporates features of many engineering structures. The study is intended to contribute to the general understanding of periodically excited linear and nonlinear systems, as well as to the current attempts to utilize high-frequency excitation for altering the low-frequency properties of structures.     

求解二维结构-声耦合问题的一种半数值半解析方法

基于传递矩阵法和虚拟源强模拟技术提出了一种求解在谐激励作用下二维结构-声相互作用问题的半数值半解析法．在足够小的积分步长内，文中对任意形状弹性环沿周向曲线坐标的非齐次状态微分方程组，建立了一种齐次扩容方法．对于外声场，采用多圆形虚拟源强配置方案。并在每一条圆形配置曲线上将源强密度函数用Fourier级数展开，同时结合快速Fourier变换法，提出了一种高精度、高效率求解任意形状二维孔穴Helmholtz外问题的快速算法．在耦合方程的求解方面，根据叠加原理，将外激励和虚拟源强的Fourier级数展开项作为广义力分别作用在弹性环上，借助齐次扩容方法和精细积分法求得弹性环的状态向量，再利用流固交接条件和最小二乘法直接建立了耦合系统的求解方程．文中给出了二个典型弹性环在集中谐激励力作用下声辐射算例，计算结果表明该文方法较通常采用的混合FE-BE法更为有效．     

A spectral element method using the modal basis and its application in solving second‐order nonlinear partial differential equations

We present a high‐order spectral element method (SEM) using modal (or hierarchical) basis for modeling of some nonlinear second‐order partial differential equations in two‐dimensional spatial space. The discretization is based on the conforming spectral element technique in space and the semi‐implicit or the explicit finite difference formula in time. Unlike the nodal SEM, which is based on the Lagrange polynomials associated with the Gauss–Lobatto–Legendre or Chebyshev quadrature nodes, the Lobatto polynomials are used in this paper as modal basis. Using modal bases due to their orthogonal properties enables us to exactly obtain the elemental matrices provided that the element‐wise mapping has the constant Jacobian. The difficulty of implementation of modal approximations for nonlinear problems is treated in this paper by expanding the nonlinear terms in the weak form of differential equations in terms of the Lobatto polynomials on each element using the fast Fourier transform (FFT). Utilization of the Fourier interpolation on equidistant points in the FFT algorithm and the enough polynomial order of approximation of the nonlinear terms can lead to minimize the aliasing error. Also, this approach leads to finding numerical solution of a nonlinear differential equation through solving a system of linear algebraic equations. Numerical results for some famous nonlinear equations illustrate efficiency, stability and convergence properties of the approximation scheme, which is exponential in space and up to third‐order in time. Copyright © 2014 John Wiley & Sons, Ltd.     

Screening acidic zeolites for catalytic fast pyrolysis of biomass and its components

Zeolites have been shown to effectively promote cracking reactions during pyrolysis resulting in highly deoxygenated and hydrocarbon-rich compounds and stable pyrolysis oil product. Py/GC-MS was employed to study the catalytic fast pyrolysis of lignocellulosic biomass samples comprising oak, corn cob, corn stover, and switchgrass, as well as the fractional components of biomass, i.e., cellulose, hemicellulose, and lignin. Quantitative values of condensable vapors and relative compositions of the pyrolytic products including non-condensable gases (NCG's) and solid residues are presented to show how reaction products are affected by catalyst choice. While all catalysts decreased the oxygen-containing products in the condensable vapors, H-ZSM-5 was most effective at producing aromatic hydrocarbons from the pyrolytic vapors. We demonstrated how the Si/Al ratio of the catalysts plays a role in the deoxygenation of the vapors towards the pathway to aromatic hydrocarbons.     

Selective fast pyrolysis of biomass impregnated with ZnCl2: Furfural production together with acetic acid and activated carbon as by-products

Fast pyrolysis of biomass materials impregnated with ZnCl₂ offered a promising way to obtain a liquid product rich in furfural (FF) and acetic acid (AA), and the pyrolytic solids could be used as the precursors to prepare activated carbons (ACs). In this study, a lab-scale fast pyrolysis set was designed and used for the quantitative production of the three chemicals. The maximum FF was produced from the corncob impregnated with at least 15 wt% ZnCl₂ and at the pyrolysis temperature around 340 °C, with the yield of more than 8 wt% compared with only 0.49 wt% from the raw corncob. Meanwhile, AA of around 4 wt% could be obtained. The content of the FF and AA was over 50 wt% and 25 wt% on the water-free basis of the pyrolytic liquids. In addition, ACs were prepared from the pyrolytic solids, and they exhibited similar properties as those prepared from direct activation of ZnCl₂-impregnated biomass materials.     

A hevein-like protein and a class I chitinase with antifungal activity from leaves of the paper mulberry

Paper mulberry (Broussonetia papyrifera, syn. Morus papyrifera L.) is a Chinese traditional medicine and its low‐molecular‐weight extracts are reported to have antifungal activity. In this study, two proteins (PMAPI and PMAPII) with activity against Trichoderma viride were obtained from paper mulberry leaves with a fast protein liquid chromatography (FPLC) unit. The purification protocol employed (NH₄)₂SO₄ precipitation, ion‐exchange chromatography and hydrophobic‐interaction chromatography on FPLC. Molecular masses were 18,798 Da for PMAPI, and 31,178 Da for PMAPII determined by Matrix‐assisted laser desorption ionization time‐of‐flight mass spectrometry. Peptide mapping fingerprint analysis showed that PMAPI has no peptides similar to PMAPII. N‐terminal amino acid sequencing revealed that PMAPI is a hevein‐like protein, and PMAPII is a class I chitinase. They both had a half‐maximal inhibitory concentration (IC50) of 0.1 µg/µL against T. viride. This is the first report of high‐molecular‐weight extracts with antifungal activity from paper mulberry. Copyright © 2011 John Wiley & Sons, Ltd.     

Al掺杂对正极材料LiNi0.33-xMn0.33Co0.33AlxO2结构和电化学性能的影响

以柠檬酸为螯合剂利用快速湿化学法合成了具有α-NaFeO₂型层状结构的LiNi_0.33-xMn_0.33Co_0.33Al_xO₂(x=0.00,0.01,0.02, 0.04)正极材料,并通过X-射线衍射、充放电测试、循环伏安和交流阻抗对材料的结构和电化学性能进行了系统研究。XRD结果表明此方法合成的材料具有很好的层状结构且阳离子的混排度随着Al³⁺含量的增加而下降。电化学测试表明,LiNi_0.31Mn_0.33Co_0.33Al_0.02O₂具有很好的电化学性能和和循环性能,1C放电倍率下首次放电比容量达到176.9 mAh·g^-1,且Al³⁺的掺杂能有效提高电荷在电极界面间转移并抑制了在高压循环过程中电荷转移阻抗的增加。     

A fast second‐order difference scheme for the space–time fractional equation

In this paper, a fast second‐order accurate difference scheme is proposed for solving the space–time fractional equation. The temporal Caputo derivative is approximated by ?L2 ‐1_σ formula which employs the sum‐of‐exponential approximation to the kernel function appeared in Caputo derivative. The second‐order linear spline approximation is applied to the spatial Riemann–Liouville derivative. At each time step, a fast algorithm, the preconditioned conjugate gradient normal residual method with a circulant preconditioner (PCGNR), is used to solve the resulting system that reduces the storage and computational cost significantly. The unique solvability and unconditional convergence of the difference scheme are shown by the discrete energy method. Numerical examples are given to verify numerical accuracy and efficiency of the difference schemes.     

An Acceleration Technique for the Augmented IIM for 3D Elliptic Interface Problems

A new fast algorithm based on the augmented immersed interface method and a fast Poisson solver is proposed to solve three dimensional elliptic interface problems with a piecewise constant but discontinuous coefficient. In the new approach, an augmented variable along the interface, often the jump in the normal derivative along the interface is introduced so that a fast Poisson solver can be utilized. Thus, the solution of the Poisson equation depends on the augmented variable which should be chosen such that the original flux jump condition is satisfied. The discretization of the flux jump condition is done by a weighted least squares interpolation using the solution at the grid points, the jump conditions, and the governing PDEs in a neighborhood of control points on the interface. The interpolation scheme is the key to the success of the augmented IIM particularly. In this paper, the key new idea is to select interpolation points along the normal direction in line with the flux jump condition. Numerical experiments show that the method maintains second order accuracy of the solution and can reduce the CPU time by 20-50%. The number of the GMRES iterations is independent of the mesh size.