Physalis method for heterogeneous mixtures of dielectrics and conductors: Accurately simulating one million particles using a PC

Prosperetti’s seminal Physalis method, an Immersed Boundary/spectral method, had been used extensively to investigate fluid flows with suspended solid particles. Its underlying idea of creating a cage and using a spectral general analytical solution around a discontinuity in a surrounding field as a computational mechanism to enable the accommodation of physical and geometric discontinuities is a general concept, and can be applied to other problems of importance to physics, mechanics, and chemistry. In this paper we provide a foundation for the application of this approach to the determination of the distribution of electric charge in heterogeneous mixtures of dielectrics and conductors. The proposed Physalis method is remarkably accurate and efficient. In the method, a spectral analytical solution is used to tackle the discontinuity and thus the discontinuous boundary conditions at the interface of two media are satisfied exactly. Owing to the hybrid finite difference and spectral schemes, the method is spectrally accurate if the modes are not sufficiently resolved, while higher than second-order accurate if the modes are sufficiently resolved, for the solved potential field. Because of the features of the analytical solutions, the derivative quantities of importance, such as electric field, charge distribution, and force, have the same order of accuracy as the solved potential field during postprocessing. This is an important advantage of the Physalis method over other numerical methods involving interpolation, differentiation, and integration during postprocessing, which may significantly degrade the accuracy of the derivative quantities of importance. The analytical solutions enable the user to use relatively few mesh points to accurately represent the regions of discontinuity. In addition, the spectral convergence and a linear relationship between the cost of computer memory/computation and particle numbers results in a very efficient method. In the present paper, the accuracy of the method is numerically investigated by example computations using one dielectric particle, one isolated conductor particle, one conductor particle connected to an external source with imposed voltage, and two conductor/dielectric particles with strong interactions. The efficiency of the method is demonstrated with one million particles, which suggests that the method can be used for many important engineering applications of broad interest.     

Implementation and investigation of iterative solvers in the Discrete Sources Method

The implementation of iterative methods as solvers for the Discrete Sources Method (DSM) is presented. In this method, light scattering computation linear systems with dense and relative small matrices are generated. The linear systems are traditionally solved using the QR-decomposition method. For large particles or particles with extreme geometries even this commonly stable solver can fail. In these cases, we expect that iterative methods can provide a satisfying solution nevertheless.We will present our investigation in two consecutive papers. Here, we study four different iterative solvers (RGMRES, BiCGStab, BiCGStab(l), and MinRes) considering the performance and the accuracy for typical light scattering problems. Using these iterative methods we increased the quality of a solution, especially for oblate spheroids with a higher aspect ratio. Preconditioning technique is considered in the following paper.     

Controlling of symmetric and asymmetric mode coupling in long-period fiber gratings singe-side induced by long-pulse CO2 laser

We report a simple fabricating approach to control the mode couplings in long-period fiber gratings (LPFGs) through side exposing fiber to long-pulse-10.6-μm laser from a cheap, internally modulated CO₂ tube. By tuning focused-spot size on fibers, not only circularly symmetric mode coupling but also asymmetric mode couplings can be effectively achieved. Simulation of mode profiles in grating cross-section with Finite Element Method (FEM), and LPFG-cladding etching experiment with hydrofluoric acid (HF), support our explanation that asymmetric mode coupling in LPFGs depends on local refractive-index (RI) change within an azimuthally thin cladding layer, resulted from large-spot method induced deep melt flow on fiber surface during CO₂ laser irradiation.     

基于集成最小二乘支持向量机方法的近红外光谱分析

针对近红外（Near Infrared,NIR）光谱测量中的小样本问题。本文提出了一种集成最小二乘支持向量机（Ensemble Least Squares Support Vector Machine,ELS-SVM）新算法。首先使用随机子空间算法（Random Subspace Method,RSM）原始高维变量空间划分为若干个低维度的子空间,然后分别在各个子空间建立最小二乘支持向量机（LS-SVM）模型,最后构造一个集成结果来进行预测。针对一批柴油样本的实验结果表明,本法对柴油十六烷值的预测精度优于传统的LS-SVM方法。     

Sphere-like CuGaS2 nanoparticles synthesized by a simple biomolecule-assisted solvothermal route

Sphere-like CuGaS₂ nanoparticles were successfully synthesized by a simple biomolecule-assisted solvothermal route using a mixed solution compose of ethylenediamine and distilled water (1:1, v/v), in which l-cystine was used as the sulfide source and complexing molecule. Phase analysis was carried out by X-ray diffraction (XRD) and the results confirmed the as-prepared CuGaS₂ as a single-phase tetragonal structure. Field-emission scanning electron microscope (FESEM) and transmission electron microscope (TEM) showed that the morphologies of CuGaS₂ were sphere-like nanoparticles in shape, and the average diameters was about 600 nm. X-ray photoelectron spectrum (XPS) was used to analyze the composition of CuGaS₂ and the ratio of Cu/Ga/S is 1:0.97:1.98. Raman spectrum of the obtained CuGaS₂ exhibit a high-intensity peak of the A1 mode at 305 cm⁻¹. The influence of reaction temperature, time and solvent was initially investigated. The possible formation mechanism was also discussed.     

Synthesis and photocatalytic property of N-doped TiO2 nanorods and nanotubes with high nitrogen content

Nano N-doped TiO₂ nanotubes were fabricated by hydrothermally treating N-doped TiO₂ nanorods in a 8 M NaOH solution at 110 °C for 20 h. The N-doped TiO₂ nanorods were synthesized by a solvothermal process with precursor solution containing titanium sulfate, urea, and dichloroethane. The N-doped TiO₂ nanorods and nanotubes were characterized with X-ray diffraction, transmission electron microscopy, and UV-vis spectrophotometry. The nitrogen contents of the N-doped TiO₂ nanorods and nanotubes were reached to high values of 36.9 at.% and 25.7 at.%, respectively. The nitrogen doping narrowed the band gap of the N-doped TiO₂ nanorods and nanotubes and introduced indirect band gap to the powders, which respectively extended the absorption edge to visible light and infrared region. The nanotubes showed larger specific surface area and greater degradation efficiency to methyl orange than the nanorods.     

Preparation and mechanism of magnetic carbonaceous polysaccharide microspheres by low-temperature hydrothermal method

In this study, the preparation method for magnetic carbonaceous polysaccharide (Fe₃O₄@CP) microspheres was developed to increase the yield and encapsulation efficiency using a suitable quantity of NaOH as the catalysis. The optimum fabrication condition was identified through a series of experiment, under which the resulting Fe₃O₄@CP microspheres show good magnetic properties. The saturation magnetization was 60.629 emu/g and the magnetite content increased up to 81.7%. The shell of the microspheres was carbonaceous polysaccharide with rich hydroxyl and carbonyl groups located on the surface, and the mean size was less than 300 nm. The formation mechanism of Fe₃O₄@CP was also discussed in this paper.     

Synthetic indicators of mutual funds’ environmental responsibility: An application of the Reference Point Method

Socially Responsible Investing (SRI) is broadly defined as an investment process that integrates not only financial but also social, environmental, and ethical (SEE) considerations into investment decision making. SRI has grown rapidly around the world in the last decades. In the last years, given the causes of the 2008 financial crisis, ethical, social, environmental and governance concerns have become even more relevant investment decision criteria. However, while a diverse set of models have been developed to support investment decision-making based on financial criteria, models including also social responsibility criteria are rather scarce.     

Stabilization via parametric excitation of multi-dof statically unstable systems

The problem of re-stabilization via parametric excitation of statically unstable linear Hamiltonian systems is addressed. An n-degree-of-freedom dynamical system is considered, at rest in a critical equilibrium position, possessing a pair of zero-eigenvalues and n − 1 pairs of distinct purely imaginary conjugate eigenvalues. The response of the system to a small static load, making the zero eigenvalues real and opposite, simultaneous to a harmonic parametric excitation of small amplitude, is studied by the Multiple Scale perturbation method, and the stability of the equilibrium position is investigated. Several cases of resonance between the excitation frequency and the natural non-zero frequencies are studied, calling for standard and non-standard applications of the method. It is found that the parametric excitation is able to re-stabilize the equilibrium for any value of the excitation frequencies, except for frequencies close to resonant values, provided a sufficiently large excitation amplitude is enforced. Results are compared with those provided by a purely numerical approach grounded on the Floquet theory.