Parameter-uniform hybrid numerical scheme for time-dependent convection-dominated initial-boundary-value problems

In this paper, we propose a numerical scheme which is almost second-order spatial accurate for a one-dimensional singularly perturbed parabolic convection-diffusion problem exhibiting a regular boundary layer. The proposed numerical scheme consists of classical backward-Euler method for the time discretization and a hybrid finite difference scheme for the spatial discretization. We analyze the scheme on a piecewise-uniform Shishkin mesh for the spatial discretization to establish uniform convergence with respect to the perturbation parameter. Numerical results are presented to validate the theoretical results.     

Richardson extrapolation technique for singularly perturbed parabolic convection–diffusion problems

This paper deals with the study of a post-processing technique for one-dimensional singularly perturbed parabolic convection–diffusion problems exhibiting a regular boundary layer. For discretizing the time derivative, we use the classical backward-Euler method and for the spatial discretization the simple upwind scheme is used on a piecewise-uniform Shishkin mesh. We show that the use of Richardson extrapolation technique improves the ε-uniform accuracy of simple upwinding in the discrete supremum norm from O (N ⁻¹ ln N + Δt) to O (N ⁻² ln² N + Δt ²), where N is the number of mesh-intervals in the spatial direction and Δt is the step size in the temporal direction. The theoretical result is also verified computationally by applying the proposed technique on two test examples.     

Spectral characterization and ASTER-based lithological mapping of an ophiolite complex: A case study from Neyriz ophiolite, SW Iran

The Neyriz ophiolite occurs along the Zagros suture zone in SW Iran, and is part of a 3000-km obduction belt thrusting over the edge of the Arabian continent during the late Cretaceous. This complex typically consists of altered dunites and peridotites, layered and massive gabbros, sheeted dykes and pillow lavas, and a thick sequence of radiolarites. Reflectance and emittance spectra of Neyriz ophiolite rock samples were measured in the laboratory and their spectra were used as endmembers in a spectral feature fitting (SFF) algorithm. Laboratory spectral reflectance measurements of field samples showed that in the visible through shortwave infrared (VNIR-SWIR) wavelength region the ultramafic and gabbroic rocks are characterized by ferrous-iron and Fe, MgOH spectral features, and the pillow lavas and radiolarites are characterized by spectral features of ferric-iron and AlOH. The laboratory spectral emittance spectra also revealed a wide wavelength range of SiO spectral features for the ophiolite rock units. After continuum removal of the spectra, the SFF classification method was applied to the VNIR + SWIR 9-band stack, and to the 11-band data set of SWIR and TIR data sets of the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) sensor, using field spectra as training sets for evaluating the potential of these data sets in discriminating ophiolite rock units. Output results were compared with the geological map of the area and field observations, and were assessed by the use of confusion matrices. The assessment showed, in terms of kappa coefficient, that the SFF classification method with continuum removal applied to the SWIR data achieved excellent results, which were distinctively better than those obtained using VNIR + SWIR data and TIR data alone.     

Dimensionality Reduction for Fast Similarity Search in Large Time Series Databases

The problem of similarity search in large time series databases has attracted much attention recently. It is a non-trivial problem because of the inherent high dimensionality of the data. The most promising solutions involve first performing dimensionality reduction on the data, and then indexing the reduced data with a spatial access method. Three major dimensionality reduction techniques have been proposed: Singular Value Decomposition (SVD), the Discrete Fourier transform (DFT), and more recently the Discrete Wavelet Transform (DWT). In this work we introduce a new dimensionality reduction technique which we call Piecewise Aggregate Approximation (PAA). We theoretically and empirically compare it to the other techniques and demonstrate its superiority. In addition to being competitive with or faster than the other methods, our approach has numerous other advantages. It is simple to understand and to implement, it allows more flexible distance measures, including weighted Euclidean queries, and the index can be built in linear time. Received 16 May 2000 / Revised 18 December 2000 / Accepted in revised form 2 January 2001     

An inertia-adaptive particle swarm system with particle mobility factor for improved global optimization

Particle Swarm Optimization (PSO) has recently emerged as a nature-inspired algorithm for real parameter optimization. This article describes a method for improving the final accuracy and the convergence speed of PSO by firstly adding a new coefficient (called mobility factor) to the position updating equation and secondly modulating the inertia weight according to the distance between a particle and the globally best position found so far. The two-fold modification tries to balance between the explorative and exploitative tendencies of the swarm with an objective of achieving better search performance. We also mathematically analyze the effect of the modifications on the dynamics of the PSO algorithm. The new algorithm has been shown to be statistically significantly better than the basic PSO and four of its state-of-the-art variants on a twelve-function test-suite in terms of speed, accuracy, and robustness.     

On the iterated forms of Kalman filters using statistical linearization

The extended Kalman filter (EKF) is a suboptimal estimator of the conditional mean and covariance for nonlinear state estimation. It is based on first order Taylor series approximation of nonlinear state functions. The unscented Kalman filter (UKF) and the ensemble Kalman filter (EnKF) are suboptimal estimators that are termed as Jacobian free because they do not require the existence of the Jacobian of the nonlinearity. The iterated form of EKF is an estimator of the conditional mode that employs an approximate Newton–Raphson iterative scheme to solve the maximization of the conditional probability density function. In this paper, the iterated forms of UKF and EnKF are presented that perform Newton–Raphson iteration without explicitly differentiating the nonlinear functions. The use of statistical linearization in iterated UKF and EnKF is a nondifferentiable optimization method when the measurement function is nonsmooth or discontinuous. All three iterated forms can be shown to be conditional mean estimators after the first iteration. A simple numerical example involving continuous and discontinuous measurment functions is included to evaluate the performance of the algorithms for the estimation of conditional mean, covariance and mode. A batch reactor simulation is shown for estimating both the states and unknown parameters.     

Device performance of transistors with high-/spl kappa/ dielectrics using cross-wafer-scaled interface-layer thickness

A technique has been developed to fabricate transistors using a continuously scaled 0-2.5-nm SiO/sub 2/ interface layer between a silicon substrate and high-/spl kappa/ dielectric, on a single wafer. The transistor results are promising with good mobility values and drive current. The slant-etching process has no detrimental effect on the electrical characteristics of the Si/SiO/sub 2/ interface. This technique provides a powerful tool in examining the effect of the process variations on device performance.     

Optical and electrical properties of ZrSe3 single crystals grown by chemical vapour transport technique

Single crystals of the lamellar compound, ZrSe₃, were grown by chemical vapour transport technique using iodine as a transporting agent. The grown crystals were characterized with the help of energy dispersive analysis by X-ray (EDAX), which gave confirmation about the stoichiometry. The optical band gap measurement of as grown crystals was carried out with the help of optical absorption spectra in the range 700–1450 nm. The indirect as well as direct band gap of ZrSe₃ were found to be 1.1 eV and 1.47 eV, respectively. The resistivity of the as grown crystals was measured using van der Pauw method. The Hall parameters of the grown crystals were determined at room temperature from Hall effect measurements. Electrical resistivity measurements were performed on this crystal in the temperature range 303–423 K. The crystals were found to exhibit semiconducting nature in this range. The activation energy and anisotropy measurements were carried out for this crystal. Pressure dependence of electrical resistance was studied using Bridgman opposed anvils set up up to 8 GPa. The semiconducting nature of ZrSe₃ single crystal was inferred from the graph of resistance vs pressure. The results obtained are discussed in detail.