A Galerkin Approach for Power Spectrum Determination of Nonlinear Oscillators

A numerical method to estimate spectral properties of nonlinear oscillators with random input is presented. The stationary system response is expanded into a trigonometric Fourier series. A set of nonlinear algebraic equations, solved by Newtons method, leads to the determination of the unknown Fourier series coefficients of single samples of the response process. For cubic polynomial nonlinearities, closed-form expressions are used to find the nonlinear terms at each step of the solution scheme. Further, a simple procedure yields an approximation of an arbitrary nonlinearity by a cubic polynomial. Power spectral density estimates for the response process are constructed by averaging the square modulus of the computed Fourier coefficients over various samples or by means of well-established smoothing techniques of spectral analysis. Two applications are presented illustrating the effectiveness of the method as compared to statistical linearization and digital Monte-Carlo simulation.     

Shock waves in molecular solids: ultrafast vibrational spectroscopy of the first nanosecond

A novel technique which uses a microfabricated shock target array assembly is described, where the passage of a shock front through a thin (0.5μm) polycrystalline layer and the subsequent unloading process is monitored in real time with ultrafast coherent Raman spectroscopy. Using a high repetition rate laser shock generation technique, high resolution, coherent Raman spectra are obtained in shocked anthracene and in a high explosive material, NTO, with time resolution of ∼ 50 ps. Spectroscopic measurements are presented which yield the shock pressure (up to 5 GPa), the shock velocity (∼ 4 km/s), the shock front risetime (t _r < 25 ps), and the temperature (∼ 400°C). A brief discussion is presented, how this new technique can be used to determine the Hugoniot, the equation of state, the entropy increase across the shock front, and monitor shock induced chemical reactions in real time. Received 28 October 1996 / Accepted 12 November 1996     

ClF-分子离子的结构与势能函数

采用单、双取代包括三重激发的二次组态相互作用[QCISD(T)]方法和单、双取代包括非迭代三重激发的耦合簇理论[CCSD(T)]方法, 结合相关一致基组aug-cc-pVXZ (X=D, T, Q, 5)对基态³⁵ClF^-和³⁷ClF^- (X²Σ⁺)分子离子进行了结构优化计算. 对CCSD(T)方法的计算结果用四种方法分别外推至基组极限, 得到了体系在基组极限的平衡结构常数. 在CCSD(T)/aug-cc-pVXZ (X=D, T, Q, 5)理论水平进行了单点能扫描. 对扫描计算结果进行基组外推并用Murrell-Sorbie 势能函数拟合得到了体系的解析势能函数表达式, 并进一步得到了³⁵ClF^-和³⁷ClF^-的光谱常数. 拟合所得势能曲线准确地再现了其离解能和平衡结构特征. 对ClF 中性自由基采用完全相同的理论方法进行了计算. 所得结果与有关文献中的实验结果符合得很好, 而且在一定程度上证明了将该理论方法应用于ClF^-分子离子的计算是合适而可靠的. ClF 自由基的优化计算结果还被用于计算其电子亲和能.ClF^-的垂直解离能也同时计算得出. 基于ClF^-的结构优化和单点能扫描计算结果, 通过求解核运动的径向薛定谔方程, 得到了无转动³⁵ClF^-和³⁷ClF^-(X²Σ⁺)的全部振动态及相应的分子常数.     

Microstructure and Magnetic Properties of Carbon‐Coated Nanoparticles

Abstract

In the present work, microstructure and superparamagnetic properties of two types of carbon‐coated magnetic Ni and Fe nanoparticles [Ni(C) and Fe(C)] are reviewed. High‐resolution transmission electron microscopy (HRTEM), electron diffraction (SAED), and x‐ray diffraction (XRD) analyses have been used to reveal the distinct structural morphologies of Ni and Fe nanoparticles. Moreover, novel carbon‐coated Ni nanoparticle assemblies offer us great opportunities for studying the mechanism of superparamagnetism in particle assemblies. Magnetization measurements [M(T) and M(H) curves] for assemblies of Ni nanoparticles indicate that modified superparamagnetic properties at T > T _B, have been found in the assemblies of Ni(C) particles. The blocking temperature, T _B, is determined to be near 115K under a certain applied field. Above T _B, the magnetization M(H, T) can be described by the classical Langevin function L using the relation, M/M _s (T = 0) = coth (μH/kT) ? kT/μH. It is suggested that these assemblies of carbon‐coated Ni nanoparticles have typical single‐domain, field‐dependent superparamagnetic relaxation properties. Finally, Mössbauer spectra and hyperfine magnetic fields at room temperature for the assemblies of Fe(C) nanoparticles confirm their distinct nanophases that were detected by structural analysis. Modified superparamagnetic relaxation is observed in the assemblies of Fe(C) nanoparticles, which is attributed to the nanocrystalline nature of the carbon‐coated nanoparticles.     

Copolymerization of 4‐Propanoylphenyl Acrylate with Methyl Methacrylate: Synthesis,Characterization and Reactivity Ratios

The new acrylic monomer 4‐propanoylphenyl acrylate (PPA) was synthesized and copolymerized with methyl methacrylate (MMA) in methyl ethyl ketone at 70±1°C using benzoyl peroxide as a free radical initiator. The copolymers were characterized by FT‐IR, ¹H‐NMR and ¹³C‐NMR spectroscopic techniques. The compositions of the copolymers were determined by ¹H‐NMR analysis. The reactivity ratios of the monomers were determined using Fineman‐Ross (r₁=0.5535 and r₂=1.5428), Kelen‐Tüdös (r₁=0.5307 and r₂=1.4482), and Ext. Kelen‐Tüdös (r₁=0.5044 and r₂=1.4614), as well as by a nonlinear error‐in‐variables model (EVM) method using a computer program, RREVM (r₁=0.5314 and r₂=1.4530). The solubility of the polymers was tested in various polar and non‐polar solvents. The elemental analysis was determined by a Perkin‐Elmer C‐H analyzer. The molecular weights (M_w and M_n) of the copolymers were determined by gel permeation chromatography. Thermogravimetric analysis of the polymers reveals that the thermal stability of the copolymers increases with an increase in the mole fraction of MMA in the copolymers. Glass transition temperatures of the copolymers were found to increase with an increase in the mole fraction of MMA in the copolymers.     

Theoretical analysis of correlation between ionization threshold fluence in IR‐MALDI and IR absorption spectrum of matrix molecules

To investigate the correlation between the wavelength dependence of ionization threshold fluence of target molecule in matrix‐assisted laser desorption/ionization by infrared (IR) laser and the IR absorption spectrum of matrix molecule, we have analyzed the IR absorption spectra of four matrix molecules using density functional theory and correlated ab initio molecular orbital method. The calculated IR absorption spectra of the isolated molecules showed more qualitative correlation with the wavelength dependence of ionization threshold fluence than those of the solid state structures. We can consider that a portion of matrix molecules lost the ordered crystal structure and that the transition to the diluted or isolated state occurred at the early process of IR laser irradiation. © 2012 Wiley Periodicals, Inc.     

LiB6Si: An indirect band gap semiconductor

Using first-principle calculations, mechanical properties, electronic structure, and Raman spectra of LiB₆Si structure were investigated. The band structures calculated by GGA-PBE and HSE06 methods reveal that LiB₆Si is an indirect band gap semiconductor. The band gap estimated by HSE06 method is about 2.24 eV, which is in good agreement with that of experimental value 2.27 eV. The calculated tensile stress-strain curves of LiB₆Si reveal that [010] direction is the cleavage direction under tensile strains. The calculated Raman spectra of LiB₆Si are also in good agreement with that of measured. The position of the band gap may provide a basis for further photocatalysis research on LiB₆Si.     

Additive assisted hydrothermal synthesis,characterization and optical properties of one dimensional DyPO4:Ce3+ nanostructures

One dimensional nanostructures of cerium doped dysprosium phosphate (DyPO₄:Ce³⁺) were synthesized via hydrothermal route in the presence of different surfactants [sodium dodecyl sulfate (SDS), dodecyl sulfosuccinate (DSS), polyvinyl pyrollidone (PVP)] and solvent [ethylene glycol and water]. The prepared nanostructures were characterized by Powder X-ray diffraction (PXRD), Fourier transform infrared spectroscopy (FTIR), Field emission scanning electron microscopy (FE-SEM), Transmission electron microscopy (TEM), energy dispersive spectroscopy (EDS), UV-VIS-NIR absorption spectrophotometer and photoluminescence (PL) studies. The PXRD and FTIR results indicate purity, good crystallinity and effective doping of Ce³⁺ in nanostructures. SEM and TEM micrographs display nanorods, nanowires and nanobundles like morphology of DyPO₄:Ce³⁺. Energy-dispersive X-ray spectra (EDS) of DyPO₄:Ce³⁺nanostructures confirm the presence of dopant. UV-VIS-NIR absorption spectra of prepared compounds are used to calculate band gap and explore their optical properties. Luminescent properties of DyPO₄:Ce³⁺ was studied by using PL emission spectra. The effect of additives and solvents on the uniformity, morphology and optical properties of the nanostructures were studied in detail.     

Mössbauer Spectra of FePS3-Cobaltocene Intercalation Compound

Abstract

Mössbauer spectra of the FePS₃-cobaltocene intercalation compound were measured in the temperature range of 300K to 10K. The spectra, distinct from those of pure FePS₃, suggest the charge transfer from cobaltocene to Fe-S antibonding orbitals of the FePS₃ host lattice.     

Electric field‐induced birefringence,optical rotatory power and conoscopic measurements of a chiral antiferroelectric smectic liquid crystal

Using a photoelastic modulator‐based novel set‐up, the electric field‐induced in‐plane birefringence and the optical rotatory power (ORP) were measured of an antiferroelectric liquid crystalline compound (12OF1M7) in its various phases using 30 µm homeotropic cells. Some specific signatures of the in‐plane birefringence and of the ORP for the various phases are being established. A relatively small threshold field is needed for the unwinding process of the antiferroelectric phase with a unit cell of four layers [SmC_A*(1/2)] compared with that for two layers [SmC_A*(0)]. On application of the electric field on the high temperature side of the SmC_A*(1/2) phase (80.1–81.5°C), a field‐induced phase transition is shown to occur directly to the SmC* phase, whereas on the lower temperature side (79.4–80.1°C) the transition takes place to SmC* via the SmC_A*(1/3) phase. The in‐plane birefringence exhibits a critical power law dependence for the SmC*–SmA transition. The ORP changes sign within the temperature range of the phase with a unit cell of three layers, reflecting a change in the handedness during this phase. Using tilted conoscopy, the results for the biaxiality and the apparent tilt angle for a smectic liquid crystal with a tilt angle greater than 18° in the ferroelectric phase are reported. The biaxiality implies the difference in the refractive indices between the two minor axes of the refractive index ellipsoid. The optical transmittance at visible and IR wavelengths for free‐standing films reveal characteristic reflection bands for these phases. The modulated structures of the reflected bands appear just above the SmC_A* phase and below SmC_A*(1/3); these are possibly due to an easy deformation of the phase by the surfaces.