Simulating gravitational waves passing through the spacetime of a black hole

We investigate how GWs pass through the spacetime of a Schwarzschild black hole using time-domain numerical simulations. Our work is based on the perturbed 3+1 Einstein's equations up to the linear order. We show explicitly that our perturbation equations are covariant under infinitesimal coordinate transformations. Then we solve a symmetric second-order hyperbolic wave equation with a spatially varying wave speed. As the wave speed in our wave equation vanishes at the horizon, our formalism can naturally avoid boundary conditions at the horizon. Our formalism also does not contain coordinate singularities and, therefore, does not need regularity conditions. Then, based on our code, we simulate both finite and continuous initially plane-fronted wave trains passing through the Schwarzschild black hole. We find that for the finite wave train, the wave zone of GWs is wildly twisted by the black hole. While for the continuous wave train, unlike geometric optics, GWs can not be sheltered by the back hole. A strong beam and an interference pattern appear behind the black hole along the optical axis. Moreover, we find that the back-scattering due to the interaction between GWs and the background curvature is strongly dependent on the direction of the propagation of the trailing wavefront relative to the black hole.Comment: 24 pages, 9 figure

High Altitude Steel Roof Truck Crane Installation

In order to solve the problems of crane operating range in blind areas and insufficient weight support of crane for steel structure bubble roof lifting construction, it is a must to design propelling crane on the roof, so that it can move on selected routes, completing the lifting work of steel roofing bubble. Mainly introduce the technical measures and related technical preparation of propelling crane on the roof for steel structure lifting process, to ensure the originality of steel structure during lifting process and safety of construction work,also to guarantee the progress of steel structure lifting work

Competing orders and inter-layer tunnelling in cuprate superconductors: A finite temperature Landau theory

We propose a finite temperature Landau theory that describes competing orders and interlayer tunneling in cuprate superconductors as an important extension to a corresponding theory at zero temperature [Nature {\bf 428}, 53 (2004)], where the superconducting transition temperature $T_c$ is defined in three possible ways as a function of the zero temperature order parameter. For given parameters, our theory determines $T_c$ without any ambiguity. In mono- and double-layer systems we discuss the relation between zero temperature order parameter and the associated transition temperature in the presence of competing orders, and draw a connection to the puzzling experimental fact that the pseudo-gap temperature is much higher than the corresponding energy scale near optimum doping. Applying the theory to multi-layer systems, we calculate the layer-number dependence of $T_c$. In a reasonable parameter space the result turns out to be in agreement with experiments.Comment: 5 pages, 3 figure

Numerical optimization and analysis on vibration characteristics of bicycles based on the novel CA-PSO algorithm

Regarding the published researches on bicycles, they fail to design fatigue characteristics of the bicycle. In addition, dynamics and fatigue characteristics are not further improved by using advanced optimization algorithms. Aiming at these questions, this paper tries to optimize dynamics and fatigue characteristics of the bicycle through combining finite element model with advanced algorithms. The advanced algorithm applies ideas of cellular automation (CA) to Particle Swarm Optimization (PSO), and then a hybrid CA-PSO algorithm is proposed. Moreover, the finite element model is also validated by experimental test. Computational results show that: the maximum stress of bicycles is mainly distributed on the frame, especially on joints of different round pipes at different moments mainly because a dead corner is at the joint, and the dead corner can easily cause stress concentration. Under alternating forces, the stress concentration at joints will cause fatigue damage. Therefore, the service life of this position will be the shortest. As a result, the dynamics and fatigue characteristics of the joint position are taken as the optimized objective. In order to verify the optimized effectiveness of the proposed CA-PSO algorithm in the paper, the widely used PSO algorithm and PSO-GA algorithm are also used to optimize the bicycle. When the traditional PSO algorithm is used to optimize the bicycle, the root-mean-square value and maximum difference of vibration accelerations are decreased by 11.9 % and 14.3 %. When the PSO-GA algorithm is used to optimize the bicycle, the root-mean-square value and maximum difference of vibration accelerations are decreased by 20.3 % and 12.9 %. When the proposed CA-PSO algorithm is used to optimize the bicycle, the root-mean-square value and maximum difference of vibration accelerations are decreased by 27.1 % and 18.6 %. Compared with other two kinds of PSO algorithms, optimized effects of vibration accelerations are very obvious. In addition, the fatigue life of the original structure is 5 years, while the fatigue life of the optimized bicycle is 7 years. Therefore, the fatigue life is improved obviously

A CROSS-SECTIONAL STUDY OF KNEE FLEXION SPEED IN CHINESE CHILDREN DURING GROWTH

INTRODUCTION: In recent years, some research has been done on the relationship between the revolving speed of the adults` knee angles and sports achievements (Sheng, 1992; 1989; 1995). However, there is little information concerning this issue in children. The purpose of this study was to explore the developing regularity of the flexion speed of children’s knee angles across age

(Z)-3-(3-Phenyl­allyl­idene)-1,5-dioxa­spiro­[5.5]undecane-2,4-dione

In the title compound, C18H18O4, the 1,3-dioxane ring adopts a distorted envelope conformation with the C atom common to the cyclo­hexane ring forming the flap. In the crystal, inversion dimers linked by pairs of C—H⋯O hydrogen bonds occur