Least-squares integration of one-dimensional codistributions with application to approximate feedback linearization

We study the problem of approximating one-dimensional nonintegrable codistributions by integrable ones and apply the resulting approximations to approximate feedback linearization of single-input systems. The approach derived in this paper allows a linearizable nonlinear system to be found that is close to the given system in a least-squares (L ₂) sense. A linearly controllable single-input affine nonlinear system is feedback linearizable if and only if its characteristic distribution is involutive (hence integrable) or, equivalently, any characteristic one-form (a one-form that annihilates the characteristic distribution) is integrable. We study the problem of finding (least-squares approximate) integrating factors that make a fixed characteristic one-form close to being exact in anL ₂ sense. A given one-form can be decomposed into exact and inexact parts using the Hodge decomposition. We derive an upper bound on the size of the inexact part of a scaled characteristic one-form and show that a least-squares integrating factor provides the minimum value for this upper bound. We also consider higher-order approximate integrating factors that scale a nonintegrable one-form in a way that the scaled form is closer to being integrable inL ₂ together with some derivatives and derive similar bounds for the inexact part. This allows a linearizable nonlinear system that is close to the given system in a least-squares (L ₂) sense together with some derivatives to be found. The Sobolev embedding techniques allow us to obtain an upper bound on the uniform (L _∞) distance between the nonlinear system and its linearizable approximation. This research was supported in part by NSF under Grant PYI ECS-9396296, by AFOSR under Grant AFOSR F49620-94-1-0183, and by a grant from the Hughes Aircraft Company.     

A dislocation shielding prediction of the toughness transition during cleavage of semibrittle crystals

An interconnected set of observations assesses current equilibrium models of the ductile-brittle-transition temperature (DBTT). This involvesin situ transmission electron microscopy (TEM) studies of crack-tip dislocations in single and polycrystals and bulk fracture toughness tests at various temperatures. Beyond K_I values of 8 MPa · m^1/2 in both iron-base single and polycrystals, large numbers of redundant dislocations are created, as postulated recently by Weertman. [38] Still, the necessary shielding dislocations, as required by equilibrium, can be detected at values as high as 20 and 40 MPa · m^1/2 byex situ TEM and electron channeling, respectively. In addition, the close approach of dislocations to the crack tip in some of the studies, as opposed to others, suggests that large dislocation free zones (DFZ) are a thin-film artifact. However, a failure criterion based partly on the Rice-Thomson model’21 is both consistent with the absence of a large DFZ and observed fracture toughness variations with test temperature. It is emphasized that this toughness transition is entirely in the semibrittle regime where cleavage is the failure mode. Nevertheless,K _lc values increase from 3 to 60 MPa·m^1/2 with an increase in test temperature. This article is based on a presentation made in the symposium “Quasi-Brittle Fracture” presented during the TMS fall meeting, Cincinnati, OH, October 21–24, 1991, under the auspices of the TMS Mechanical Metallurgy Committee and the ASM/MSD Flow and Fracture Committee.     

Scheduling in or-parallel Prolog systems: Survey and open problems

Implementation of or-parallel Prolog systems offers a number of interesting scheduling problems. The main issues are the interaction between memory models and scheduling, ordering of multiple solutions, and scheduling of speculative work. The problems occur partly because of the design choices (e.g. the choice of a memory model), and partly because of the desire to maintain observational equivalence between parallel and sequential implementations of Prolog, while achieving high efficiency. In the first part of this paper a common framework for discussing scheduling in or-parallel systems is introduced, and also a collection of issues that must be addressed in such systems is presented. In the second part of the paper we survey a number of solutions to these problems comparing their efficiency whenever possible. We close the survey with a short discussion of open problems.Current association: Carlstedt Elektronik AB     

Molecular orientation and stress in biaxially deformed polymers. II. Steady potential flow

The development of biaxial segmental orientation and stress in a flexible-chain polymer fluid subjected to steady biaxial extensional flow is analyzed. Closed-formula model based on the Padè approximation of the inverse Langevin function in the non-Gaussian distribution of the chain end-to-end vectors is considered. The approach is free from the limitations related to finite chain extensibility and slow convergence of the series expansion formulations at higher chain deformations.Segmental orientation is characterized by the average orientation tensor, related axial orientation factors and global orientation anisotropy. Orientational behavior and corresponding stresses in the biaxial elongational potential flow are discussed in a wide range of elongation rates. Orientation characteristics calculated for the biaxial flow deformation are much higher than those predicted for the affine biaxial stretch deformation in polymer solids.     

Inhibition of nitrification in the packed bed reactors by selected organic compounds

The effect of methanol, acetone, formalin and glucose on the nitrification process in the packed bed reactors has been investigated. For the utilized compounds the inhibition constant K_i was determined according to Dixon's method. The determined values were as follows: methanol K_i = 116.0 mg l^?1; acetone K_i = 804.2 mg l^?1; formalin K_i = 61.5 mg l^?1. The value of K_i for glucose has not been determined because glucose in applied concentration up to 11,325 mg l^?1 had no effect on the nitrification course.     

AlxGa−xAs/GaAs heterostructure characterization by wet chemical etching

Selective wet chemical etching of the Al_xGa_1−xAs/GaAs system has been applied to heterostructure characterization. Samples of LPE grown AlGaAs/GaAs laser double-heterostructures and separate confinement heterostructures as well as antiresonant reflecting optical waveguides heterostructures were treated with “I2 solution” (I₂:KI:H₂O) and hydrochloric acid. These compounds selectively etch the ternary Al_xGa_1−xAs layers, but with different “threshold composition” x_th values (the x value is that above which the etching rate of a given compound increases sharply). Selectively etched samples have been examined by SEM. The experimental dependence of etching rate on the x value for I2 solution has been derived. From this dependence, the x composition of any ternary layer can be estimated simply. Observations were made of the “microscopic” properties of the heterostructure, such as the smoothness of the interfaces and the uniformity of layers. All imperfections resulting from the growth process, such as interface perturbations or compositional nonuniformity of layers, are clearly seen. An additional advantage of this etching technique is its simplicity. It allows quick examination of grown heterostructure for the selection of wafers for further processing.