Solution and applications of the Lyapunov equation for controlsystems

Recent advances in control systems analysis and design have implied new uses for the Lyapunov equation of the form AX+XA^T+Q=0. Implementation requirements for the incorporation of the use of Lyapunov equations in practical design, however, point out the need for a set of specialized numerical procedures. This special set of numerical procedures must efficiently solve large, sparse Lyapunov equations, solve sets of Lyapunov equations that differ only in the coefficient matrix Q, and provide good low rank estimates of the Lyapunov equation solution X in the case where low rank approximations are applicable. Discussions of the motivations for the solution of these problems and of candidate solution approaches are provided     

Low-temperature interface reaction in aluminium-silicon carbide particulate composites produced by mechanical alloying

An experimental investigation has been carried out on the reaction that takes place between 3 and 20 μm SiC particles and the aluminium alloy 1050 matrix of composite materials prepared by a mechanical alloying process. The work is different from that undertaken by other researchers in that the SiC-Al interface reaction has been studied in the temperature range 853–933 K, i.e., with the matrix initially in the solid state. Differential thermal analysis, X-ray diffraction and scanning electron microscopy all show that the SiC-Al reaction initiates in the solid state at temperatures as low as 883 K. The reaction produces Al4C3 and Si, the latter entering into solid solution in the aluminium matrix. At temperatures exceeding 903 K, the reaction produces a liquid phase and at this stage the speed of the interface reaction increases significantly. The results are discussed in terms of Al-Si-C metastable equilibrium and the kinetics of the reaction. This revised version was published online in November 2006 with corrections to the Cover Date.     

A new SPICE model of power P-I-N diode based on asymptotic waveformevaluation

A new SPICE subcircuit model for power p-i-n diodes is proposed in this paper. The model is based on a moment-matching approximation of the ambipolar diffusion equation. It is shown that both the quasistatic model and the lumped charge model can be obtained as ion-order moment-matching approximations while new and more accurate models can be obtained from higher-order solutions. The proposed model takes into account emitter recombination in the highly doped end regions, conductivity modulation in the base and the moving-boundaries effect during reverse-recovery, showing good convergence properties and fast simulation times. Comparisons between the results of the SPICE model and both numerical device simulations and experimental results are presented     

Quantitative NMR spectroscopy by matrix pencil methods

The matrix pencil (MP) method, based on the singular value decomposition (SVD), is applied to quantitative NMR spectroscopy. Its relationship to other SVD-based methods is also presented. Simulations and applications are given to demonstrate the capability of superior performance.©1993 John Wiley & Sons Inc     

A mathematical model for the prediction of temperature in a dry snow layer

A mathematical model for predicting the temperature in a homogeneous layer of dry snow is presented. The model, which is physically based, is capable of predicting diurnal temperature behaviour at the snow surface and at any depth within a snow layer given the variation in a limited set of meteorological parameters over that period. A sensitivity analysis is performed to determine the important parameters in the prediction of snow surface temperatures. These are found to be consistent with simple physical reasoning.