Numerical determination of time transfer in general relativity

This paper determines the travel time of a light ray connecting two points in the space-time solving numerically a two-point boundary value problem by means of the shooting method. For the resolution of this problem multiple precision floating-point arithmetic is required. We have studied distinct implementations of the shooting method attending to the way in which the Jacobian appearing at each iteration is approximated. We have shown that by using Magnus expansions to solve the differential equation for the Jacobian, one obtains a better efficiency of the shooting method. Also, a comparison between the numerical results obtained through the application of the shooting method and those derived by Le Poncin-Lafitte et al. (Class Quantum Grav, 21:4463-4483, 2004) from perturbative expansions of the world function is made.     

HOMOTOPY CONTINUATION METHODS FOR STOCHASTIC TWO-POINT BOUNDARY VALUE PROBLEMS DRIVEN BY ADDITIVE NOISES

In this paper the homotopy continuation method for stochastic two-point boundary value problems driven by additive noises is studied. The existence of the solution of the homotopy equation is proved. Numerical schemes are constructed and error estimates are obtained. Numerical experiments demonstrate the effectiveness of the homotopy continu- ation method over other commonly used methods such as the shooting method.     

Periodic traveling wave train and point-to-periodic traveling wave for a diffusive predator–prey system with Ivlev-type functional response

A diffusive predator–prey system with Ivlev-type scheme is investigated in this article. The existences of a small amplitude periodic traveling wave train _Γp${\Gamma }_p$ and the traveling wave solution connecting the boundary equilibrium _Eu(1,0)$E_u(1,0)$ to the periodic traveling wave _Γp${\Gamma }_p$ are obtained. The existence of this point-to-periodic solution reveals that the predator invasion leads to the periodic population densities in the coexistence domain, and thus plays a mild role in the evolution of predator–prey communities. The techniques used here are the Hopf bifurcation theorem, the improved shooting method combining with the geometric singular perturbation method.     

显微拉曼光谱检验射击残留物

建立了一种使用显微拉曼成像光谱仪检验发射火药、火药燃烧后产物和射击残留物的方法。取警用仿9×19巴拉贝鲁姆手枪弹发射药颗粒和“QSZ92式”9毫米手枪发射药燃烧后的产物,同时提取射击者手部射击残留物、枪管内射击残留物和目标靶物上射击残留物。使用显微拉曼成像光谱仪对采集的发射火药、火药燃烧后产物和射击残留物样本进行拉曼检测。实验中发现检测上述样品宜采用455 nm波长激光,此波段激光可有效避开荧光的干扰;激光强度选择6.0 mW,该能量下拉曼强度可达到最大,与其他杂峰有较好的区分;同时观察物镜选择50倍条件,该倍数条件下,可看到待测样本的微观形态特征,也可以最大程度的吸收拉曼信号。采用以上参数,待测样本获得的拉曼信号效果最好。拉曼光谱的检测谱图结果证明发射火药、火药燃烧后成分和其他部位提取的射击残留物主要成分基本一致,这些成分主要来源于待测样品中的有机成分部分。火药燃烧后成分和其他部位提取射击残留物的某些部分拉曼强度相对于发射火药有所下降和变化,实验中荧光现象有所加强,证明了射击后某些特定的成分会发生变化。50倍物镜条件下,微观形态可比性强,发现待测物表面存在表面黑亮、塌陷空洞和裂缝等特点,这些特点可视为不同类型待测样品的典型微观形态特征,也可作为判定射击残留物的有力证据。该方法可利用拉曼光谱对发射火药、火药燃烧后产物和射击残留物进行无损检验,符合当下光谱检验和法庭科学对此类样品的检验要求。同时方法的灵敏度高,分析速度快,操作简便。     

Investigation of distribution of soil antimony using sequential extraction and antimony complexed to soil-derived humic acids molar mass fractions extracted from various depths in a shooting range soil

Trace metal contamination from bullet fragments in shooting ranges is a major environmental concern. In particular, trace metals such as lead, antimony, and copper are toxic and have the potential to enter groundwater supplies and to be absorbed by plants. Soil humic acids can play a critical role in mobilizing some of these released metals through complexation. The purpose of this study is to investigate the antimony complexed to soil-derived humic molar mass fractions extracted from various depths in a shooting range soil and to examine the distribution of antimony in various fractions of shooting range soils using sequential chemical extraction approach. The surface soil and soil core samples from a local shooting range were collected. Soil-derived humic acids were extracted from different depths of the top soil layer and characterized by various spectroscopic methods. Results of sequential chemical extraction demonstrated that Sb was found in shooting range in the upper 30 cm depth of the soil core. Highly elevated Sb is present in the exchangeable and ammonium acetate extracted fractions. Antimony is also present in the residual fraction in both surface and core soil samples, but is most likely present in a lithic phase which may not be readily bio-available. Leached antimony complexed to soil humic acid molar mass fractions was determined by size exclusion chromatography coupled to inductively coupled plasma-mass spectrometry (SEC-ICP-MS). The results demonstrate that Sb is ‘tightly’ bound to humic acid mass molar mass fractions and confined in the top 10 cm of soil-derived humic acids.     

Three-dimensional equilibria of nonlinear pre-curved beams using an intrinsic formulation and shooting

This article describes a shooting method for computing three-dimensional equilibria of pre-curved nonlinear beams with axial and shear flexibility using the intrinsic beam formulation. For distributed and concentrated follower loads acting on a cantilevered beam, the method amounts to a direct solution approach requiring only a single shot (zero iterations) to compute the equilibria. This is possible since the system equations are defined in a local coordinate system that rotates and translates with the beam, akin to the follower loads themselves. A general procedure employing nonconservative follower loads, which invokes the Picard–Lindelöf theorem on uniqueness and existence of solutions, is also introduced for finding all solutions for three-dimensional pre-curved beam problems with conservative loading. This is particularly useful in beam buckling problems where multiple stable and unstable solutions exist. Three-dimensional equilibrium solutions are generated for many loading cases and boundary conditions, including three-dimensional helical beams, and are compared to similar solutions where available in the literature. Excellent agreement is documented in all comparison cases. For buckling examples, the stability of the computed solutions is assessed using a dynamic finite element code based on the same intrinsic beam equations. Due to the ability to avoid iteration, the presented approach may find application in model-based control for practical three-dimensional problems such as the control of manipulators utilized in endoscopic surgeries and the control of spacecraft with robotic arms and long cables.     

Nonlinear forced oscillation in a magnetically levitated system: the effect of the time delay of the electromagnetic force

Vibration analysis is important to explain and control the various kinds of vibration problems in magnetically levitated mechanical systems. This study investigates the vibration phenomena of the one-degree-of-freedom magnetically levitated system considering the effect of the nonlinearity of the electromagnet. It is difficult to apply the conventional nonlinear analysis techniques for the magnetically levitated system, since the magnetic force has a strong nonlinear characteristic that varies in inverse proportion to the square of the gap. This paper performs theoretical analyses using the shooting method, clarifies the stability and bifurcation characteristics, and verifies them experimentally. We conclude that the shape of the resonance curve becomes soft-type, superharmonic resonances occur, and period-doubling bifurcations occur at the main resonance and at superharmonic resonances.     

Postbuckling of elastic beam subjected to a concentrated moment within the span length of beam

This paper aims to present the exact closed form solutions and postbuckling behavior of the beam under a concentrated moment within the span length of beam. Two approaches are used in this paper. The nonlinear governing differential equations based on elastica theory are derived and solved analytically for the exact closed form solutions in terms of elliptic integral of the first and second kinds. The results are presented in graphical diagram of equilibrium paths, equilibrium configurations and critical loads. For validation of the results from the first approach, the shooting method is employed to solve a set of nonlinear differential equations with boundary conditions. The set of nonlinear governing differential equations are integrated by using Runge–Kutta method fifth order with adaptive step size scheme. The error norms of the end conditions are minimized within prescribed tolerance (10⁻⁵). The results from both approaches are in good agreement. From the results, it is found that the stability of this type of beam exhibits both stable and unstable configurations. The limit load point existed. The roller support can move through the hinged support in some cases of β and leads to the more complex of the configuration shapes of the beam.     

Measurement and calculation of electrostatically induced voltage generated on an ungrounded metal box

When a charged body passes by the front of an ungrounded metal box such as a box of electronic equipment, an electrostatically induced voltage is generated. The induced voltage can cause malfunctions and failure of the equipment. However, whether a voltage is induced in the metal box by a moving charged body and how much is induced is not clear. In this study, measured induced voltages are compared with values calculated for two capacitance-measuring methods. The results will be helpful to estimate the possibility of malfunction and failure by induced voltage and whether a standard test method should be considered.     

On the parallel version of the successive approximation method for quasilinear boundary value problem

The convergence properties of the successive approximation method to solve a quasilinear two points boundary value problem is studied. The successive approximation method is used to solve the parallel/multiple version of the problem. Conditions which assure the convergence of the method and error bound are given.