Numerical Representation (numerical + representation)

Distribution by Scientific Domains

Selected Abstracts

Cohesive-zone models, higher-order continuum theories and reliability methods for computational failure analysis,

René de Borst
Abstract A concise overview is given of various numerical methods that can be used to analyse localization and failure in engineering materials. The importance of the cohesive-zone approach is emphasized and various ways to incorporate the cohesive-zone methodology in discretization methods are discussed. Numerical representations of cohesive-zone models suffer from a certain mesh bias. For discrete representations this is caused by the initial mesh design, while for smeared representations it is rooted in the ill-posedness of the rate boundary value problem that arises upon the introduction of decohesion. A proper representation of the discrete character of cohesive-zone formulations which avoids any mesh bias can be obtained elegantly when exploiting the partition-of-unity property of finite element shape functions. The effectiveness of the approach is demonstrated for some examples at different scales. Moreover, examples are shown how this concept can be used to obtain a proper transition from a plastifying or damaging continuum to a shear band with gross sliding or to a fully open crack (true discontinuum). When adhering to a continuum description of failure, higher-order continuum models must be used. Meshless methods are ideally suited to assess the importance of the higher-order gradient terms, as will be shown. Finally, regularized strain-softening models are used in finite element reliability analyses to quantify the probability of the emergence of various possible failure modes. Copyright © 2004 John Wiley & Sons, Ltd. [source]

Inductive Inference: An Axiomatic Approach

ECONOMETRICA, Issue 1 2003
Itzhak Gilboa
A predictor is asked to rank eventualities according to their plausibility, based on past cases. We assume that she can form a ranking given any memory that consists of finitely many past cases. Mild consistency requirements on these rankings imply that they have a numerical representation via a matrix assigning numbers to eventuality,case pairs, as follows. Given a memory, each eventuality is ranked according to the sum of the numbers in its row, over cases in memory. The number attached to an eventuality,case pair can be interpreted as the degree of support that the past case lends to the plausibility of the eventuality. Special instances of this result may be viewed as axiomatizing kernel methods for estimation of densities and for classification problems. Interpreting the same result for rankings of theories or hypotheses, rather than of specific eventualities, it is shown that one may ascribe to the predictor subjective conditional probabilities of cases given theories, such that her rankings of theories agree with rankings by the likelihood functions. [source]

Simplified solution of developing laminar forced flow between parallel plates

Esmail M. A. Mokheimer
Abstract A simplified simulation for developing laminar forced flow in the entrance region between two parallel plates is presented. This simulation is based on an implicit finite difference numerical representation of a boundary layer model describing the flow in the entry region. This boundary layer model comprises the two conservation equations of mass and momentum. A non-iterative implicit numerical scheme is developed to convert the partial differential form of these governing equations into algebraic equations. The resultant algebraic equations have been solved simultaneously via a simplified simulation using spreadsheet programs as well as a Fortran code for the sake of comparison. The numerically obtained developing axial velocity profile at large distance downstream of the entrance shows excellent agreement with the available fully developed analytical profile. Comparison between the abilities of the spreadsheet simulation with other high-level programming languages is outlined. Copyright © 2002 John Wiley & Sons, Ltd. [source]

Intrusiveness of Minorities: Growing Pains for the Majority Group?,

Francine Tougas
In this paper, we examined the impact of the numerical representation and the intrusiveness of immigrants on feelings of group threat voiced by the majority. The present evaluation of group threat differs from previous studies in its inclusion of temporal comparisons. The relationship between feelings of threat and attitudes toward immigration was also evaluated. In all, 221 college students completed a questionnaire. As predicted, results obtained show that numerical representation was positively associated with feelings of group threat resulting from invidious social comparisons. Intrusiveness was positively related to feelings of group threat resulting from temporal comparisons. Contrary to hypotheses, the final model confirms that only feelings of temporal group threat were associated with negative attitudes toward immigration. Practical implications and the important role of temporal comparisons are discussed. [source]

Minorities in Children's Television Commercials: New, Improved, and Stereotyped

Mass media is one means by which consumers learn how to behave as consumers. Consumers' beliefs about minorities as consumers are also influenced by mass media, and the impact is likely highest among young children. A content analysis of 813 commercials in children's television programming reveals that while Caucasians continue to be the predominant models in terms of numbers and in the types of roles they play, the numerical representation of minorities, especially Blacks, has improved. However, the study found that minorities are more likely than Caucasians to have minor roles and to be portrayed in certain product categories, settings, and relationships. Societal impacts and implications for minority consumers are discussed. [source]

Three-dimensional force measurements on oral implants: a methodological study

J. Duyck
This paper describes a methodology that allows in vitro and in vivo quantification and qualification of forces on oral implants. Strain gauges are adapted to the outer surface of 5·5 and 7 mm standard abutments (Brånemark System®, Nobel Biocare, Sweden). The readings of the strain gauges are transformed into a numerical representation of the normal force and the bending moment around the X- and Y- axis. The hardware and the software of the 3D measuring device based on the strain gauge technology is explained and its accuracy and reliability tested. The accuracy level for axial forces and bending moments is 9.72 N and 2.5 N·cm, respectively, based on the current techniques for strain gauged abutments. As an example, an in vivo force analysis was performed in a patient with a full fixed prosthesis in the mandible. Since axial loads of 450 N and bending moments of 70 N·cm were recorded, it was concluded that the accuracy of the device falls well within the scope of our needs. Nevertheless, more in vivo research is needed before well defined conclusions can be drawn and strategies developed to improve the biomechanics of oral implants. [source]

The Logarithmic-To-Linear Shift: One Learning Sequence, Many Tasks, Many Time Scales

Robert S. Siegler
ABSTRACT The relation between short-term and long-term change (also known as learning and development) has been of great interest throughout the history of developmental psychology. Werner and Vygotsky believed that the two involved basically similar progressions of qualitatively distinct knowledge states; behaviorists such as Kendler and Kendler believed that the two involved similar patterns of continuous growth; Piaget believed that the two were basically dissimilar, with only development involving qualitative reorganization of existing knowledge and acquisition of new cognitive structures. This article examines the viability of these three accounts in accounting for the development of numerical representations. A review of this literature indicated that Werner's and Vygotsky's position (and that of modern dynamic systems and information processing theorists) provided the most accurate account of the data. In particular, both changes over periods of years and changes within a single experimental session indicated that children progress from logarithmic to linear representations of numerical magnitudes, at times showing abrupt changes across a large range of numbers. The pattern occurs with representations of whole number magnitudes at different ages for different numerical ranges; thus, children progress from logarithmic to linear representations of the 0,100 range between kindergarten and second grade, whereas they make the same transition in the 0,1,000 range between second and fourth grade. Similar changes are seen on tasks involving fractions; these changes yield the paradoxical finding that young children at times estimate fractional magnitudes more accurately than adults do. Several different educational interventions based on this analysis of changes in numerical representations have yielded promising results. [source]

Regulating hospital use: length of stay, beds and whiteboards

Marie Heartfield
This paper presents part of a larger study of contemporary nursing practice and the rationalisation of hospital length of stay. Informed by Michel Foucault's work on governmentality, length of hospital stay and the re-engineering of surgical services are examined, not in terms of numerical representations of hospital use, but as part of social and political processes through which certain concepts are made susceptible to measurement and practices are organised. Using data generated through fieldwork in a hospital surgical division this analysis offers understandings of how social practices around length of hospital stay are translated and how they pattern contemporary hospital nursing practice. Nursing practice is explored through the reconstitution of hospital beds and the demands of local administration of hospital length of stay. [source]