Showing papers by "Carnegie Mellon University published in 1973"

The influence of polarization functions on molecular orbital hydrogenation energies

Abstract: Polarization functions are added in two steps to a split-valence extended gaussian basis set: d-type gaussians on the first row atoms C. N, O and F and p-type gaussians on hydrogen. The same d-exponent of 0.8 is found to be satisfactory for these four atoms and the hydrogen p-exponent of 1.1 is adequate in their hydrides. The energy lowering due to d functions is found to depend on the local symmetry around the heavy atom. For the particular basis used, the energy lowerings due to d functions for various environments around the heavy atom are tabulated. These bases are then applied to a set of molecules containing up to two heavy atoms to obtain their LCAO-MO-SCF energies. The mean absolute deviation between theory and experiment (where available) for heats of hydrogenation of closed shell species with two non-hydrogen atoms is 4 kcal/mole for the basis set with full polarization. Estimates of hydrogenation energy errors at the Hartree-Fock limit, based on available calculations, are given.

The mind's eye in chess.

Abstract: Publisher Summary This chapter describes the progress made toward understanding chess skill. It describes the work on perception in chess, adding some new analyses of the data. It presents a theoretical formulation to characterize how expert chess players perceive the chess board. It describes some tasks that correlate with chess skill and the cognitive processes of skilled chess players. It is believed that the demonstration of de Groot's, far from being an incidental side effect of chess skill, actually reveals one of the most important processes that underlie chess skill—the ability to perceive familiar patterns of pieces. In the first experiment discussed in the chapter, two tasks were used. The memory task was very similar to de Groot's task: chess players saw a position for 5 seconds and then attempted to recall it. Unlike de Groot, multiple trials were used—5 seconds of viewing followed by recall—until the position was recalled perfectly. The second task or the perception task for simplicity involved showing chess players a position in plain view.

The Linear Theory of Elasticity

Abstract: Linear elasticity is one of the more successful theories of mathematical physics Its pragmatic success in describing the small deformations of many materials is uncontested The origins of the three-dimensional theory go back to the beginning of the 19th century and the derivation of the basic equations by Cauchy, Navier, and Poisson The theoretical development of the subject continued at a brisk pace until the early 20th century with the work of Beltrami, Betti, Boussinesq, Kelvin, Kirchhoff, Lame, Saint-Venant, Somigliana, Stokes, and others These authors established the basic theorems of the theory, namely compatibility, reciprocity, and uniqueness, and deduced important general solutions of the underlying field equations In the 20th century the emphasis shifted to the solution of boundary-value problems, and the theory itself remained relatively dormant until the middle of the century when new results appeared concerning, among other things, Saint-Venant’s principle, stress functions, variational principles, and uniqueness

Production Systems: Models of Control Structures

Abstract: Publisher Summary This chapter discusses production systems and the way in which they operate. A production system is a scheme for specifying an information processing system. It consists of a set of productions, each production consisting of a condition and an action. It has also a collection of data structures: expressions that encode the information upon which the production system works—on which the actions operate and on which the conditions can be determined to be true or false. The chapter discusses the possibility of having a theory of the control structure of human information processing. Gains seem possible in many forms such as completeness of the microtheories of how various miniscule experimental tasks are performed, the ability to pose meaningfully the problem of what method a subject is using, the ability to suggest new mechanisms for accomplishing a task, and the facilitation of comparing behavior on diverse tasks. The chapter presents a theory of the control structure.

The structural implications of measurement error in sociometry

Abstract: Measurement error, an inherent quality of any empirical data collection technique, is discussed in the context of sociometric data. These data have long been assumed to possess face validity and to be the data of choice in any study of the sentiment structure of small scale social systems. However, it is argued that while methods of sociometric analysis have become increasingly more sophisticated they have failed to yield unequivocal results because they do not distinguish structural complexity from measurement error. Through a discussion of increasingly more complex examples the distortion laden character of most sociometric data is illustrated. This distortion is introduced by the formalities of the sociometric test and it will not be removed by developing increasingly more sophisticated structural models or throwing out some of the data. Instead, when issues concerning the nature of specific relational networks are raised data of much higher quality than those which are commonly available are required....

An FIM-atom probe study of the precipitation of copper from lron-1.4 at. pct copper. Part I: Field-ion microscopy

Abstract: The size and number density of precipitates formed during the early stage of precipitation of copper from Fe-1.4 at. pct Cu at 500°C was determined with the field-ion microscope (FIM). While particles of less than 50 × 10−8 cm remain invisible in the electron microscope (ETM) they are clearly resolved with the FIM; particles as small as 8 × 10−8 cm in diameter could be detected. The growth rate of the particles can be accounted for by normal bulk diffusion. At its peak strength, the alloy contains approximately 1018 particles per cu cm with an average diameter of 24 × 10−8 cm. The alloy reaches its peak strength well before precipitation is complete.

An FIM-atom probe study of the precipitation of copper from lron-1.4 at. pct copper. Part II: Atom probe analyses

Abstract: Chemical analyses of individual precipitates found during the initial stages of precipitation of copper from Fe-1.4 at. pct Cu at 500°C were made with the FIM-atom probe. Precipitates as small as 8 × l0−8cm in diam were analyzed. The results indicate that the precipitate nuclei contain much less copper than the equilibrium e phase and that most of the particle-matrix boundaries are less than 10−7 cm wide. The average copper content of the precipitates increases with aging time until well after the alloy reaches its peak strength. Thermodynamic calculations show that it is reasonable to expect the precipitate compositions that were experimentally observed.

Global variable considered harmful

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Does Scientific Discovery Have a Logic

Abstract: It is unusual for an author, less than one-tenth of the way through his work, to disclaim the existence of the subject matter that the title of his treatise announces. Yet that is exactly what Karl Popper does in his classic, The Logic of Scientific Discovery, [4], announcing in no uncertain terms on p. 31 that scientific discovery has no logic. The disclaimer is so remarkable that it deserves to be quoted at length: I said above that the work of the scientist consists in putting forward and testing theories.

Hydrodynamic Model of the Condensation of a Vapor near Its Critical Point

Abstract: A hydrodynamic model is used to describe the condensation of a supersaturated vapor near its critical point. Calculations are based on a statistical theory of nucleation previously developed by one of the authors (J.S.L.). The method permits careful study of various statistical corrections and a quantitative treatment of the thermal nonaccommodation effect. Although the theory developed here is based on assumptions which are quite different from the classical Becker-D\"oring theory, numerical predictions of the critical supersaturation in Xe and C${\mathrm{O}}_{2}$ turn out to be very nearly the same as the classical results.

Abstracts of Contributed Papers

Abstract: The strength of the K line of singly ionized calcium has been measured for several hundred A-type stars within a few hundred parsecs of the Sun and for the A stars in several galactic star clusters. The derived abundance of calcium varies from star to star by up to a factor of 2, and there is no correlation of abundance with the space motion of the stars.

The Development of Empathy in Chinese and American Children Between Three and Six Years of Age: A Cross-Cultural Study.

Abstract: A series of social interaction situations representing the four emotions of happy, afraid, sad, and angry were administered to 288 American children and 288 Chinese children. Twenty-four girls and 24 boys, half from middleclass families and half from disadvantaged families, were tested at 6-month intervals between 3 and 6 years of age. Children from both cultural groups exhibited similar overall trends in their ability to recognize other people's emotional responses. By 3 years of age, the majority of American and Chinese children could differentiate between happy and unhappy reactions in other people. Perception of afraid, sad, and angry feelings developed somewhat later and appeared to be influenced by social learning. This cross-cultural study confirms the results of a previous investigation that very young children are capable of empathic responses. The awareness of other people's feelings by young children from very different cultural backgrounds suggests that empathy may be a basic human characteristic related to social adaptation.

Proposal for Notation at Tricritical Points

Abstract: A notation for critical exponents at a tricritical point is proposed on the basis that the line of critical points observed experimentally in metamagnets, N${\mathrm{H}}_{4}$Cl, or ${\mathrm{He}}^{3}$-${\mathrm{He}}^{4}$ mixtures defines a special direction in the space of thermodynamic parameters. Scaling at a tricritical point implies certain relations among the exponents which are summarized in a table.

Benefit-Cost Analysis of Coding Techniques for the Primal Transportation Algorithm

Abstract: A computer code for the transportation problem that is even more efficient than the primal-dual method is developed. The code uses the well-known (primal) MODI method and is developed by a benefit-cost investigation of the possible strategies for finding an initial solution, choosing the pivot element, finding the stepping-stone tour, etc. A modified Row Minimum Start Rule, the Row Most Negative Rule for choice of pivot, and a modified form of the Predecessor Index Method for locating stepping-stone tours were found to perform best among the strategies examined. Efficient methods are devised for the relabeling that is involved in moving from one solution to another. The 1971 version of this transportation code solves both 100 × 100 assignment and transportation problems in about 1.9 seconds on the Univac 1108 Computer, which is approximately the same time as that required by the Hungarian method for 100 × 100 assignment problems.An investigation of the effect on mean solution time of the number of significant digits used for the parameters of the problem indicates that the cost parameters have a more significant effect than the rim parameters and that the solution time “saturates” as the number of significant digits is increased. The Minimum Cost Effect, i.e. the fact that total solution time asymptotically tends to the time for finding the initial solution as the problem size is increased (keeping the number of significant digits for the cost entries constant), is illustrated and explained. Detailed breakup of the solution times for both transportation and assignment problems of different sizes is provided. The paper concludes with a study of rectangular shaped problems.

Selective membrane transport

Abstract: Cyclic Polyethers acting as mobile carriers in facilitated transport can cause changes of as much as three orders of magnitude in the fluxes of various cations across liquid membranes. The cyclic polyether dibenzo-18-crown-6 (2,3,11,12-dibenzo-1,4,7,10,13,16-hexaoxacyclooctadeca-2,11-diene) was used in this work to achieve such a large selectivity. The results show that a primary factor leading to the selectivity is the ratio of unsolvated cation radius to polyether central ring radius. The implication is that by selecting a polyether with a desired central ring radius, any two cations of slightly different radius can be separated efficiently.

Lectures on the Foundations of Continuum Mechanics and Thermodynamics

Abstract: This is an outline of a series of lectures I delivered at the Technion in Haifa, Israel, in the summer of 1972. This outline gives my view of what the basic concepts of modern continuum mechanics and thermodynamics are and how they should be presented to graduate students of mathematics and theoretical mechanics. This view evolved gradually over the past eight years. A first version was given in a series of lectures I delivered at the Summer Session in Bressanone, Italy, in 1965 (reference [1]). The material was reworked several times for an introductory graduate course repeatedly given at Carnegie-Mellon University and for lecture series given at the University of Karlsruhe, Germany, in 1968 and in Jablonna, Poland, in 1970. This paper is the latest version, and it renders reference [1] obsolete.

Geometric programming with signomials

Abstract: The difference of twoposynomials (namely, polynomials with arbitrary real exponents, but positive coefficients and positive independent variables) is termed asignomial. Each signomial program (in which a signomial is to be either minimized or maximized subject to signomial constraints) is transformed into an equivalent posynomial program in which a posynomial is to be minimized subject only to inequality posynomial constraints. The resulting class of posynomial programs is substantially larger than the class of (prototype)geometric programs (namely, posynomial programs in which a posynomial is to be minimized subject only to upper-bound inequality posynomial constraints). However, much of the (prototype) geometric programming theory is generalized by studying theequilibrium solutions to thereversed geometric programs in this larger class. Actually, some of this theory is new even when specialized to the class of prototype geometric programs. On the other hand, all of it can indirectly, but easily, be applied to the much larger class of well-posedalgebraic programs (namely, programs involving real-valued functions that are generated solely by addition, subtraction, multiplication, division, and the extraction of roots).

Tests for Neutral Currents in Neutrino Reactions

Abstract: Neutral currents predicted by weak-interaction models of the type discussed by Weinberg may be detected in neutrino reactions. Limits on the ratio $R$ of $\ensuremath{\sigma}(\ensuremath{ u}+N\ensuremath{\rightarrow}\ensuremath{ u}+X)$ to $\ensuremath{\sigma}(\ensuremath{ u}+N\ensuremath{\rightarrow}{\ensuremath{\mu}}^{\ensuremath{-}}+X)$ are obtained independent of any dynamical assumption. For the total cross section for high-energy neutrinos, we find $R\ensuremath{\ge}0.18$, provided the Weinberg mixing angle satisfies ${{sin}^{2}\ensuremath{\theta}}_{W}\ensuremath{\le}0.33$. For the production of a single ${\ensuremath{\pi}}^{0}$ we find ${R}^{\ensuremath{'}}\ensuremath{\ge}0.50$ contrasted with the experimental result ${R}^{\ensuremath{'}}\ensuremath{\le}0.14$ using only the assumption of (3,3)-resonance dominance. Applications are also given to antineutrino reactions.

On the Contact Problem of an Inflated Spherical Nonlinear Membrane

Abstract: The contact problem of an inflated spherical nonlinear elastic membrane between two large rigid plates is formulated in terms of three first-order ordinary differential equations for the region where the spherical membrane is not in contact with the rigid plates. The constraint condition introduced by the rigid plate on part of the spherical membrane reduces the number of governing equations to two for the contact region. A general stress-strain relation for the spherical membrane is used in the formulation. The results presented in this paper assume that the material behavior of the spherical membrane is that described by the Mooney model. Nonlinear spring characteristics and the instability phenomena of the inflated membrane are discussed.