Spectral collocation and radial basis function methods for one-dimensional interface problems

Differential equations with singular sources or discontinuous coefficients yield non-smooth or even discontinuous solutions. This problem is known as the interface problem. High-order numerical solutions suffer from the Gibbs phenomenon in that the accuracy deteriorates if the discontinuity is not properly treated. In this work, we use the spectral and radial basis function methods and present a least squares collocation method to solve the interface problem for one-dimensional elliptic equations. The domain is decomposed into multiple sub-domains; in each sub-domain, the collocation solution is sought. The solution should satisfy more conditions than the given conditions associated with the differential equations, which makes the problem over-determined. To solve the over-determined system, the least squares method is adopted. For the spectral method, the weighted norm method with different scaling factors and the mixed formulation are used. For the radial basis function method, the weighted shape parameter method is presented. Numerical results show that the least squares collocation method provides an accurate solution with high efficacy and that better accuracy is obtained with the spectral method.     

Stability study and control of helicopter blade flapping vibrations

The response of a two-degree-of-freedom, controlled, autoparametric system to harmonic excitations is studied and solved. The objective of this research is to investigate the effect of linear absorber on the vibrating system and the saturation control of a linear absorber to reduce vibrations due to rotor blade flapping motion. The method of multiple scale perturbation technique is applied to obtain the periodic response equation near the primary resonance in the presence of internal resonance of the system. The stability of the obtained numerical solution is investigated using both phase plane methods and frequency response equations. Variation of some parameters leads to the bending of the frequency response curves and hence to the jump phenomenon occurrence. The reported results are compared to the available published work.     

橄榄石结构磷酸盐脱/嵌锂过程的控制步骤研究

本文详细研究了橄榄石结构磷酸盐脱嵌锂过程的控制步骤,发现就多元橄榄石结构Li(FeMnCo)PO4磷酸盐而言,碳含量比较低时在充放电曲线之间存在非对称现象.充电时与Fe2+/Fe3+电对对应的容量小于理论容量,与Co2+/Co3+电对对应的容量大于理论容量;放电时与Co2+/Co3+电对对应的容量远小于相应的充电容量,但是与Fe2+/Fe3+电对对应的放电容量远大于与该电对对应的充电容量.电极呈现出以Co2+/Co3+电对充电,以Fe2+/Fe3+电对放电的行为.作者认为在充电和放电过程中活性材料颗粒内部存在内界面,充电时内界面内部组成是Fe2+、Co2+、Mn2+和低浓度的Fe3+,而内界面外部组成是Co3+、Mn2+、Fe3+和低浓度的Co2+.非对称现象的主要原因是内界面移动速度缓慢,碳含量低时慢的内界面移动速度是电化学脱嵌锂过程的主要控制步骤.     

Ac electrical conductivity and dielectric relaxation behavior of amorphous Selinum36 Antimony31Cubber33 thin films

ABSTRACT

The alternating-current (Ac) conductivity measurements and dielectric behaviors were observed in the range of temperature (from 303 to 393?K) and in the frequency range from 10² to10⁶?Hz for amorphous films of Selinum₃₆ Antimony₃₁ Cubber₃₃ chalcogenide glass. The ac conductivity has temperature dependency and the frequency dependency. The reduction of the exponent S values with raising temperature was introduced with the correlated barrier hopping model. The maximum height of the barrier W_M for Sellinum₃₆ Antimony₃₁Cubber₃₃ films is reliable with carrier hopping over a potential barrier. The number of localized states per unit volume at the Fermi level enhances with the elevation of ambient temperature of the film sample. Both dielectric constant ε₁ and loss ε₂ increase with the rise of temperature rising and decrease with frequency. The computation of the dielectric modulus M^/ and M^// revealed that the interfacial is the most suitable polarization type.     

Research on splitting phenomenon of isochronal martensitic transformation in T91 ferritic steel

T91 steel is a representative type of ferritic heat-resistant steel currently used in power plant components, and is a potential candidate for structural steel in nuclear reactors. The isochronal martensitic transformation behaviors during continuous cooling after austenitization in T91 ferritic steel were systematically investigated by high-resolution dilatometry and microstructure observation. The splitting phenomenon of martensitic transformation is accompanied with the precipitation of needle-like M₃C particles, which is suppressed by rapid cooling after austenitization. The appearance of this splitting is ascribed to the concentration gradient caused by the consumption of alloy element in process of the formation of M₃C. This concentration gradient results in the appearance of wide martensitic laths ahead of the generation of normally narrow laths. These two types of martensitic laths possess different M _s (martensitic start transformation) temperatures, which are attributed to the splitting transformation phenomenon.     

A network approach based on cliques

The characterization of complex networks is a procedure that is currently found in several research studies. Nevertheless, few studies present a discussion on networks in which the basic element is a clique. In this paper, we propose an approach based on a network of cliques. This approach consists not only of a set of new indices to capture the properties of a network of cliques but also of a method to characterize complex networks of cliques (i.e., some of the parameters are proposed to characterize the small-world phenomenon in networks of cliques). The results obtained are consistent with results from classical methods used to characterize complex networks.     

光伏型碲镉汞探测器在波段内连续激光辐照下的两种不同过饱和现象的产生机理

利用连续波段内激光对两批光伏型碲镉汞探测器进行了激光辐照实验, 发现了两种不同的过饱和现象. 实验表明, 光伏型碲镉汞探测器在强光辐照下都会出现开路电压随光强增强而减小的过饱和现象, 明晰了PV型探测器在强光辐照下的一般规律性现象和由探测器个体差异导致的特殊现象. 从等效电路模型出发, 剖析了两种过饱和现象的发生条件, 建立了数值计算的理论模型, 对两种过饱和现象进行了数值模拟, 计算结果与实验结果符合得较好. 研究表明, 光伏型碲镉汞探测器在波段内强光辐照下引起的过饱和现象有两种产生机理, 一种是热效应引起的暗电流增大机理; 另一种是探测器材料中缺陷引起的漏电流增大机理. 关键词： 波段内连续激光 光伏型碲镉汞探测器 过饱和现象     

Numerical study on the effect of the injection pressure on spray penetration length

This paper investigates the fuel spray behavior and variation of the spray characteristics under different injection pressures in internal combustion engines. In diesel engines the fuel spray is affected by the cavitation phenomenon which occurs in the injector orifice. The cavitation is one of the important phenomena which has a significant effect on the fuel spray characteristics. In this paper, for a specified geometry of the nozzle and the combustion chamber, the effect of the cavitation phenomenon on the spray characteristics, i.e. spray penetration length, the Sauter main diameter and evaporation are studied numerically for different values of the injection pressures. High injection pressure causes high velocity of the fuel in the injector orifice which leads to an effective atomization process with small and dispersed fuel droplets. The fluid flow equations are calculated in the combustion chamber to obtain the spray model. Since it is known that, high injection pressure together with low discharge pressure leads to creation of cavitation phenomenon inside the injector orifice, then for having cavitation phenomenon inside the injector orifice and consequently for investigating the cavitation phenomenon effects on the spray characteristics, the injection pressure values of 10–150 MPa are considered while the discharge pressure remains constant. The injector and combustion chamber are simulated in separated regions and the results of the outlet of the nozzle are used as the boundary conditions for solving the fuel flow inside the combustion chamber to achieve the spray simulation. The results of this study show that by increasing the injection pressure, the value of the spray penetration length increases and the Sauter main diameter decreases for constant discharge pressure. The Hydraulic Flip phenomenon occurs after the injection pressure of 120 MPa on the base of the results of this work.     

Schwarz Lemma and Hartogs Phenomenon in Complex Finsler Manifold

The authors prove the Schwarz lemma from a compact complex Finsler manifold to another complex Finsler manifold and any complete complex Finsler manifold with a non-positive holomorphic curvature obeying the Hartogs phenomenon.     

Cryolitic vein XPS imaging from an industrial grade carbon

Aluminium carbide formation and subsequent dissolution is a generally accepted mechanism to explain the cathode wear in the Hall-Héroult industry. Carbide formation is thought to occur inside the cathode pores. Being dependent upon cathodic current density, it is believed to be an electrochemical process. It is also associated with the presence of cryolitic bath species involved in the dissolution of the carbide layer and thus enabling further carbide formation.