We discuss the parallel implementation of the Cholesky factorization of a positive definite symmetric matrix when that matrix is block tridiagonal. While parallel implementations for this problem, and closely related problems like the factorization of banded matrices, have been previously reported in the literature, those implementations dealt with the special cases where the block size (bandwidth) was either very large (wide) or very small (narrow). We present a solution that can be used for the entire spectrum of cases, ranging from extremely large (wide) to very small (narrow). Preliminary performance results collected on a Cray T3E-600 distributed memory supercomputer show that our implementation attains respectable performance. Indeed, factorization of a matrix with block size b=1000 and a total dimension of more than 500,000 takes about 3.6 minutes on 128 processors.
This paper develops a theory for geometrically nonlinear waves in strings and presents analytical solutions for a traveling kink, generation of a geometric wave with its accompanying P wave, reflection of a kink at a fixed support and at a smooth sliding support, and interaction of a P wave and a kink. Conditions that must be satisfied for linear wave theory to hold are derived. The nonlinear theory is demonstrated by extending an historically important solution of the barrage balloon problem that was obtained during World War II.
This is the second of two papers describing a procedure for the three-dimensional nonlinear time-history analysis of steel-framed buildings. An overview of the procedure and the theory for the panel zone element and the plastic hinge beam element are presented in part I. In this paper, the theory for an efficient new element for modeling beams and columns in steel frames called the elastofiber element is presented, along with four illustrative examples. The elastofiber beam element is divided into three segments—two end nonlinear segments and an interior elastic segment. The cross sections of the end segments are subdivided into fibers. Associated with each fiber is a nonlinear hysteretic stress-strain law for axial stress and strain. This accounts for coupling of nonlinear material behavior between bending about the major and minor axes of the cross section and axial deformation. Examples presented include large deflection of an elastic cantilever beam, cyclic loading of a cantilever beam, pushover analysis of a 20-story steel moment-frame building to collapse, and strong ground motion analysis of a two-story unsymmetric steel moment-frame building.
Some current investigators have made direct comparisons of recognition performance with cued recall. In other instances, indirect comparisons of recognition and recall have been made by observing the difference in recognition performance with different types of target material, for example, high- and low-frequency words; this difference has been then compared with the difference obtained when recall is used to measure retention of the same type of target materials. Finally, some experimenters have examined how recognition performance is related to the type of target material that is used, for example, words, pictures, and so on. The results obtained from all of these studies have been used to make inferences about the nature of the memorial process. We have attempted to call attention to the generally accepted but neglected finding that performance on any recognition test can be manipulated by changing the characteristics of the distractors, thus casting doubt on the generality of the experimental findings as well as their theoretical implications.
An analysis procedure in the frequency domain for determining the earthquake responses of a dam was developed. The procedure inclides hydrodynamic interaction and water compressibility effects. Linear responses of idealized, two dimensional gravity dams and three dimensional dams, including arch dams were obtained. For an infinite uniform region a finite element discretization provides for a proper transmission of pressure waves. Hydrodynamic effects are equivalent to an added mass and added load in the frequency domain equations of motion of the dam. Complex frequency response functions for acceleration at the dam crest are presented for two dimensional concrete gravity and earth dams and for a three dimensional arch dam. Water compressibility and fluid foundation interaction significantly influence the response of concrete gravity dams and are even more important for each dam.
t-T1HIS IS the first report of work undertaken as the result of a grant | received by the London School of Economics from the Trustees of v the Nuffield Foundation. The purpose of the research is to discover the chief factors responsible for social class differences, for movement and hlndrances to movement from class to class under present conditions) and for the changes that have been taking place in the class structure of the population of England and Wales in recent years. Although the first approach to the problem must be general, because no class in the population is selfcontained and the boundary between neighbounng classes is bluxTed, interest will be centred chiefly in the middle class, for about this class much is surmised and little is known with certainty; past studies have been confined for the most part to the so-called working class. A survey of a large random sample of the population on a nation-wide scale is being camed out in order to discover possible evidence of class mobility by change of occupational grade with changing circumstances, also by comparing the grades of parents and their children and by change of grade on the part of women on mamage if the grade of occupation of the husband differs from that of the fe's father. The grade of occupation first entered is largely detened by educational opportunity, and particulars as to education as well as occupation will be collected in the random sample surveyv A report on this work will be published in due course. Occupational status is of course not the only factor which contributes to the detertnination of class but, being closely linked with economic status, it obviously has a very important beanng on class. If then we are to trace changes in social class by changes in occupation, a preliminary examination of the social grading of occupations is essential.
Forced vibration testing is a well established technique as indicated by references 1 to 8. This paper describes a system for forced vibration testing developed over two years during work performed on dams. The focus of these tests is to investigate the dynamic interaction which takes place between the dam and foundation and between the dam and water. Accurate determination of response in a low signal to noise ratio environment were made. Such responses include motions near and beyond the dam-foundation interface and dynamic pressures in the reservoir. The data set includes complete frequency sweeps at a large number of stations. The volume of data generated necessitates the use of an automated data acquisition and processing system.
