Dynamics of generalized tachyon field

We investigate the dynamics of generalized tachyon field in FRW spacetime. We obtain the autonomous dynamical system for the general case. Because the general autonomous dynamical system cannot be solved analytically, we discuss two cases in detail: $\beta=1$ and $\beta=2$. We find the critical points and study their stability. At these critical points, we also consider the stability of the generalized tachyon field, which is as important as the stability of critical points. The possible final states of the universe are discussed.Comment: 9 pages, 5 figures, published versio

Investigation and visualization of the stability boundary for stressed power systems

Present interconnected power systems are being pushed to their limits due to heavier loading of the transmission network and delay in facility construction. The resultant vulnerability in withstanding system disturbances requires a more accurate understanding of system stability behavior. This dissertation presents the use of real normal form of vector fields, a comparatively new analysis tool in the area of power systems, combined with the use of XGobi, an effective graphic package for multi-dimensional visualization, to investigate and visualize the stability boundary of the stressed system. It also depicts the structural characteristics for the stressed power system corresponding to specific fault scenarios by computing the participation factors and the nonlinear indices along the actual fault trajectory which is obtained from time simulation of the equations governing system dynamics. The objective of this research is to analyze and explain the nonlinear phenomena in stressed power systems and characterize the stability boundary of the power system when subjected to large disturbances. The structural information provided by the method of normal forms will also be utilized in explaining the mechanism of instability near the stability boundary and will be used to determine the critical interactions involved;The main idea of this dissertation is to characterize the stability boundary of the stressed power system by obtaining the nonlinear structural information through the visualization of the stability boundary in multiple dimensions, and by utilizing the analytical measures of nonlinear interaction indices and nonlinear participation factors obtained using the method of normal forms;The proposed approach has been tested on the IEEE 4-generator system and 11-generator system. The stability boundary of the system is approximated by a second order stable manifold of the controlling unstable equilibrium point. The stable manifold is constructed by spanning all stable directions. The effective graphic tool XGobi is used to visualize the approximated stability boundary in all dimensions of the system, which helps to obtain a global structural information of the system. The shape and curvature of the stability boundary are detected. An extended approach to deal with large sized power systems is studied, which provide an effective method to study large sized power systems. The computation of linear and nonlinear participation factors, together with the nonlinear indices of the fault trajectory obtained by the time simulation provides the basis to study the structural characteristics of the system. The structural information helps the tuning of control action, which is valuable for maintaining the stability of practical power systems

Experimental and numerical investigation of stress-relaxation age forming of AA6082

This thesis presents a comprehensive experimental and modelling investigation of stress-relaxation ageing of AA6082. Based on this investigation, successful manufacture of a typical industrial component with large and complex curvatures and with high dimensional accuracy has been achieved through the stress-relaxation age forming (SRAF) process. The 12 hr stress-relaxation ageing behaviour in both the elastic and plastic regions of AA6082-T6 at 160 °C has been experimentally investigated for the first time, including stress-relaxation ageing tests, tensile tests, and microstructural observations. It has been observed that the total stress relaxed after a 12 hr test increases significantly with increasing initial strain levels, while the initial strain levels contribute little effect to the yield strength evolution during stress-relaxation ageing. Microstructural observation results and the stress exponent method have been used to analyse the stress-relaxation mechanisms of the material, and a decreasing threshold stress with increasing initial strain is proposed for stress-relaxation ageing in the plastic region. A new unified constitutive model has been proposed and calibrated to accurately predict both the stress-relaxation behaviour and the yield strength evolutions of AA6082-T6 during the SRAF process in both the elastic and plastic regions. FE simulations of the SRAF process have been carried out using the FE solver ABAQUS, in which the developed material model has been implemented through the user-defined CREEP subroutine, and their effectiveness has been validated by SRAF tests of a singly-curved plate. A springback compensation strategy has been developed for tool shape compensation and its effectiveness proved by SRAF tests of a doubly-curved plate. Finally, an industrial component with large and complex curvatures, which was selected from an in-service high-speed train, has been successfully manufactured through the SRAF process with the integrated numerical technologies developed in this thesis, including material and FE simulation models, and a springback compensation strategy. The successful production of the industrial component has proven the feasibility of the developed technologies, which can be used as an effective tool to guide the future industrial applications of the SRAF process with AA6082 alloy.Open Acces