Second-order bounds on the domain of attraction and the rate ofconvergence of nonlinear dynamical systems and neural networks

We present a method for analyzing the convergence properties of nonlinear dynamical systems yielding second-order bounds on the domain of attraction of an asymptotically stable equilibrium point and on the time of convergence in the estimated domain. We show that under certain conditions on the system, there exists an analytic solution to the corresponding optimization problem. The method is applied in analyzing the dynamics of a neural network model.     

Intergranular films at Au-sapphire interfaces

The existence of nanometer-thick amorphous equilibrium films at metal-ceramic interfaces has been experimentally verified for the Au–Al₂O₃ system. The films were formed using a novel experimental approach, in which thin sputtered films of Au were dewetted on a sapphire substrate which was previously partially wetted with drops of anorthite glass (CaO–2SiO₂–Al₂O₃). High-resolution transmission electron microscopy and qualitative analytical transmission electron microscopy were used to confirm the existence of the amorphous films. In addition, positive and relatively large Hamaker constants were calculated for the Au-film-Al₂O₃ interface, which indicates the existence of an attractive van der Waals force which stabilizes the film, similar to equilibrium films at grain boundaries in ceramics. A ∼ 1 nm thick surface film was also detected on the (0001) surface of sapphire substrates partially wetted by anorthite glass. The refractive index required to stabilize the surface films, via a positive Hamaker constant, is explored.     

Consistent estimation on finite parameter sets with application to linear systems identification

The consistency of maximum likelihood and related Bayesian estimates for a general class of observation sequences is treated, following a result by P. E. Caines. The condition for consistency is then interpreted in terms of the statistics associated with linear systems driven by white Gaussian inputs, to establish a verifiable condition for the identifiability of such systems on finite sets of mathematical representations.     

A mathematical model for metal flow and heat transfer in centrifuge melt spinning

Centrifuge melt spinning (CMS) is a technique used for the production of rapidly solidified metallic ribbons, in which the liquid metal is ejected centrifugally from a rotating crucible onto a quenching copper rim which rotates in the direction opposite the crucible. A numerical model has been developed to describe the hydraulic features of the alloy melt stream, together with the heat flow in the solidifying melt. The model takes into account, among other things, the dragging mechanism caused by the counter-rotation of the casting crucible and the quenching rim, the additional spreading velocity imparted to the melt by centrifugal forces developing on the rotating rim, the increase of heat transfer in the melt due to convection, and the changes of the viscosity of the melt with temperature. Comparison of the mathematical model with experimental results obtained for an Al-12 at. pct Ge alloy indicates that CMS is characterized by heat-transfer coefficients ranging from 3 to 11 * 10⁶ W m⁻² K⁻¹ depending mainly on the velocities of the casting crucible and the rim. The effect of various process parameters, such as crucible and rim velocities, on the dimensions of the obtained ribbons and the effect of the enhanced heat flow in the melt on the reduction of thermal gradients in the ribbon are presented.     

Closed forms for the Levinson coefficients of polynomialcompensators and inverse systems

The least-squares transformation of a discrete-time multivariable linear system into a desired system by convolving the first with a polynomial system yields optimal polynomial solutions to the problems of system compensation, inversion, and approximation. The polynomial coefficients are obtained from the solution of a normal linear matrix equation whose coefficients are shown to be the weighting patterns of certain linear systems. These can then be used in the recursive solution of the normal equation     

A geometric approach to stochastic model reduction by canonical variables

The reduced-order representation of possibly nonstationary observations of Markovian processes with additive measurement noise is considered. A canonical variable model reduction scheme is derived in a geometric setting.