Vibration of strings with nonlinear supports

The dynamic string motion, which displacement is unilaterally constrained by the rigid termination condition of an arbitrary geometry has been simulated and analyzed. The treble strings of a grand piano usually terminate at a capo bar, which is situated above the strings. The apex of a V-shaped section of the capo bar defines the end of the speaking length of the strings. A numerical calculation based on the traveling wave solution is proposed for modeling the nonlinearity inducing interactions between the vibrating string and the contact condition at the point of string termination. It was shown that the lossless string vibrates in two distinct vibration regimes. In the beginning the string starts to interact in a nonlinear fashion with the rigid terminator, and the resulting string motion is aperiodic. Consequently, the spectrum of the string motion depends on the amplitude of string vibrations, and its spectral structure changes continuously with the passage of time. The duration of that vibration regime depends on the geometry of the terminator. After some time of aperiodic vibration, the string vibrations settle in a periodic regime where the resulting spectrum remains constant.     

Self-Reinforced High-Density Polyethylene Prepared by Low Frequency Vibration-Assisted Injection Molding. II: Microstructure Investigation

Scanning electron microscopy (SEM), differential scanning calorimetry (DSC), and wide angle X-ray diffraction (WAXD) were employed to study the microstructure of self-reinforced high-density polyethylene (HDPE) prepared by conventional injection molding (CIM) and a low frequency vibration-assisted injection molding (VAIM). SEM micrographs following permanganic etching showed the self-reinforcement of HDPE is mainly due to the existence of shish-kebab morphology within the core region for VAIM-processed HDPE samples. Pronounced molecular alignment was identified by the WAXD data. An approximate 9% increase in the crystallinity was confirmed by DSC. Both preferred molecular orientation and increased crystallinity serve to yield stronger VAIM-processed injection moldings.     

Going Off the Grid: Iterative Model Selection for Biclustered Matrix Completion

We consider the problem of performing matrix completion with side information on row-by-row and column-by-column similarities. We build upon recent proposals for matrix estimation with smoothness constraints with respect to row and column graphs. We present a novel iterative procedure for directly minimizing an information criterion to select an appropriate amount of row and column smoothing, namely, to perform model selection. We also discuss how to exploit the special structure of the problem to scale up the estimation and model selection procedure via the Hutchinson estimator, combined with a stochastic Quasi-Newton approach. Supplementary material for this article is available online.     

The resonant secondary emission of the F center in alkali halides

The secondary radiation after resonant excitation of F center and its linear polarization P correlated to the polarization of resonant light have been measured for five alkali halides at low temperatures. In KC1, the spectrum of P over the whole Stokes region is divided into three successive regions, the depolarization range at the one-phonon Raman scattering, the near plateau range, and the depolarization range down to vanishing. The former two have common relevance to resonant energy and symmetries of coupled phonons. These relevances are interpreted adopting a configuration coordinate model for 2s- and 2p-like excited states.     

Solvent‐Free Reactions of Fullerenes with Diethyl Bromomalonate in the Presence of Inorganic Bases Under High‐Speed Vibration Milling Conditions

Abstract

Solvent‐free reactions of C₆₀ and C₇₀ with diethyl bromomalonate in the presence of various inorganic bases were investigated under the high‐speed vibration milling (HSVM) conditions, and are shown to give methanofullerenes 1 and 2 in good to excellent yields based on consumed fullerenes. Several weak inorganic bases were found to be quite effective in promoting the solvent‐free mechanochemical Bingel reactions of C₆₀ and C₇₀ under the HSVM conditions. Among the studied bases, sodium acetate gave the highest yield of monoadducts, while potassium carbonate afforded a considerable amount of bisadducts for both C₆₀ and C₇₀.     

A Raman technique applicable for the analysis of the working principle of promoters and inhibitors of gas hydrate formation

We report a Raman technique applicable for the in situ analysis of the development of hydrogen bonds in the liquid water‐rich phase just before the onset of gas hydrate formation. Herewith, the phase transition as well as the working principle of hydrate formation inhibitors and promoters can be analyzed. © 2015 The Authors. Journal of Raman Spectroscopy published by John Wiley & Sons Ltd.     

Zn(NCN)单轴的负热膨胀性及机理研究

负热膨胀(NTE)是一种反常的物理现象, 已在合金和框架结构化合物等材料中被观察到, 但NTE材料的种类仍然有限. 本文合成了一种单轴NTE材料Zn(NCN), 该材料在c轴方向及在100~475 K下的热膨胀系数为-3.35×10^?6 K^?1, 而a轴和b轴方向则呈低热膨胀性, 体积具有低的热膨胀系数[6.13×10^?6 K^?1(100~475 K)]. 通过同步辐射X射线衍射、 扩展X射线吸收精细结构和拉曼光谱等方法, 研究了Zn(NCN)的NTE机理. 结果表明, Zn—N键具有明显的横向振动, 一些低频振动模Grüneisen参数为负值. 直接的实验证据表明, N=C=N的横向振动以及准刚性ZnN₄四面体的耦合旋转和扭摆导致了c轴方向的NTE.     

Built-in piezoelectric field improved photocatalytic performance of nanoflower-like Bi2WO6 using low-power white LEDs

Photocatalysis technology has been proved to be a potential strategy for removal of organic dyes, however high-power light sources are generally necessary to initiate photocatalytic reaction. In this work, we employed an excellent photocatalyst of Bi₂WO₆ with visible light harvest and meanwhile an intrinsic ferroelectricity, which realized the efficient degradation of organic dye via the synergetic photopiezocatalysis. Through coupling the illumination by a low-power (9 W) LED and the ultrasonic vibration (120 W) by an ultrasonic cleaner, the nanoflower-like Bi₂WO₆ composed of ultrathin nanosheets showed a much more enhanced photopiezocatalysis performance for purification of organic dye than the individual photocatalysis and piezocatalysis. Furthermore, the high mineralization efficiency and the good durability of the Bi₂WO₆ catalyst were demonstrated. The possible mechanism of photopiezocatalysis was finally proposed, where the ultrasound-induced piezoelectric field in Bi₂WO₆ drove photo-generated electrons and holes to diffuse along opposite directions, consequently promoting the separation efficiency of charge carriers. This work indicates that the synergetic photopiezocatalysis by coupling irradiation and ultrasonic vibration is a promising strategy to purify organic pollutants in wastewater.     

纳米表面相互作用及振动测头模型

如何实现高精度的测量是现代制造业及微电子技术领域的热点问题之一. 基于微纳米测头的三坐标测量机是当前实现高精度测量的重要手段. 随着测量尺寸的减小, 常用的纳米/微纳尺度的测头与待测表面之间形成静态接触, 其表面相互作用成为了影响其测量精度和可靠性的关键因素之一. 本文基于一种触发式振动测头, 研究了其动力学模型, 并通过对测头纳米尺度表面相互作用的理论分析及数值模拟, 确立了测头振动参数与表面相互作用之间的关联. 实验研究表明, 参数优化后的谐振微纳测头能有效抑制表面作用带来的干扰, 提高测量精度.     

Conservative numerical methods for the Full von Kármán plate equations

This article is concerned with the numerical solution of the full dynamical von Kármán plate equations for geometrically nonlinear (large‐amplitude) vibration in the simple case of a rectangular plate under periodic boundary conditions. This system is composed of three equations describing the time evolution of the transverse displacement field, as well as the two longitudinal displacements. Particular emphasis is put on developing a family of numerical schemes which, when losses are absent, are exactly energy conserving. The methodology thus extends previous work on the simple von Kármán system, for which longitudinal inertia effects are neglected, resulting in a set of two equations for the transverse displacement and an Airy stress function. Both the semidiscrete (in time) and fully discrete schemes are developed. From the numerical energy conservation property, it is possible to arrive at sufficient conditions for numerical stability, under strongly nonlinear conditions. Simulation results are presented, illustrating various features of plate vibration at high amplitudes, as well as the numerical energy conservation property, using both simple finite difference as well as Fourier spectral discretizations. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1948–1970, 2015