Numerical representation (computers)

AccessScience ◽  
2015 ◽  
Keyword(s):  
Numerical Representation

Fatigue Investigation of Elastomeric Structures

2010 ◽  
Vol 38 (3) ◽  
pp. 194-212 ◽  
Author(s):  
Bastian Näser ◽  
Michael Kaliske ◽  
Will V. Mars
Keyword(s):  
Fatigue Crack ◽  
Fatigue Crack Growth ◽  
Crack Growth ◽  
Material Behavior ◽  
Period Effect ◽  
Numerical Representation ◽  
Material Force ◽  
Strain Behavior ◽  
Dissipative Effects ◽  
Elastomeric Materials

Abstract Fatigue crack growth can occur in elastomeric structures whenever cyclic loading is applied. In order to design robust products, sensitivity to fatigue crack growth must be investigated and minimized. The task has two basic components: (1) to define the material behavior through measurements showing how the crack growth rate depends on conditions that drive the crack, and (2) to compute the conditions experienced by the crack. Important features relevant to the analysis of structures include time-dependent aspects of rubber’s stress-strain behavior (as recently demonstrated via the dwell period effect observed by Harbour et al.), and strain induced crystallization. For the numerical representation, classical fracture mechanical concepts are reviewed and the novel material force approach is introduced. With the material force approach at hand, even dissipative effects of elastomeric materials can be investigated. These complex properties of fatigue crack behavior are illustrated in the context of tire durability simulations as an important field of application.

On the Positivity of $\mathbf{{a}}$-Linear with Random Finitely

2020 ◽  
Author(s):  
Amanda Bolton
Keyword(s):  
Representation Theory ◽  
Central Problem ◽  
Numerical Representation

Let $\rho$ be an ultra-unique, reducible topos equipped with a minimal homeomorphism. We wish to extend the results of \cite{cite:0} to trivially Cartan classes. We show that $d$ is comparable to $\mathcal{{M}}$. This leaves open the question of uniqueness. Moreover, a central problem in numerical representation theory is the description of irreducible, orthogonal, hyper-unique graphs.

scholarly journals A Note on the Numerical Representation of Surface Dynamics in Quasigeostrophic Turbulence: Application to the Nonlinear Eady Model

2009 ◽  
Vol 66 (4) ◽  
pp. 1063-1068 ◽  
Author(s):  
Ross Tulloch ◽  
K. Shafer Smith
Keyword(s):  
Numerical Models ◽  
Buoyancy Frequency ◽  
Complete Suppression ◽  
Numerical Representation ◽  
Vertical Resolution ◽  
Surface Dynamics ◽  
Coriolis Parameter ◽  
Theoretical Predictions ◽  
Vertical Grid ◽  
Similar Restriction

Abstract The quasigeostrophic equations consist of the advection of linearized potential vorticity coupled with advection of temperature at the bounding upper and lower surfaces. Numerical models of quasigeostrophic flow often employ greater (scaled) resolution in the horizontal than in the vertical (the two-layer model is an extreme example). In the interior, this has the effect of suppressing interactions between layers at horizontal scales that are small compared to Nδz/f (where δz is the vertical resolution, N the buoyancy frequency, and f the Coriolis parameter). The nature of the turbulent cascade in the interior is, however, not fundamentally altered because the downscale cascade of potential enstrophy in quasigeostrophic turbulence and the downscale cascade of enstrophy in two-dimensional turbulence (occurring layerwise) both yield energy spectra with slopes of −3. It is shown here that a similar restriction on the vertical resolution applies to the representation of horizontal motions at the surfaces, but the penalty for underresolving in the vertical is complete suppression of the surface temperature cascade at small scales and a corresponding artificial steepening of the surface energy spectrum. This effect is demonstrated in the nonlinear Eady model, using a finite-difference representation in comparison with a model that explicitly advects temperature at the upper and lower surfaces. Theoretical predictions for the spectrum of turbulence in the nonlinear Eady model are reviewed and compared to the simulated flows, showing that the latter model yields an accurate representation of the cascade dynamics. To accurately represent dynamics at horizontal wavenumber K in the vertically finite-differenced model, it is found that the vertical grid spacing must satisfy δz ≲ 0.3f/(NK); at wavenumbers K > 0.3f/(Nδz), the spectrum of temperature variance rolls off rapidly.

scholarly journals Performance of Portfolios Based on the Expected Utility-Entropy Fund Rating Approach

Entropy ◽  
2021 ◽  
Vol 23 (4) ◽  
pp. 481
Author(s):  
Daniel Chiew ◽  
Judy Qiu ◽  
Sirimon Treepongkaruna ◽  
Jiping Yang ◽  
Chenxiao Shi
Keyword(s):  
Mutual Funds ◽  
Portfolio Selection ◽  
Expected Utility ◽  
Decision Model ◽  
Risky Choice ◽  
Numerical Representation ◽  
Better Than ◽  
The Eu

Yang and Qiu proposed and reframed an expected utility–entropy (EU-E) based decision model. Later on, a similar numerical representation for a risky choice was axiomatically developed by Luce et al. under the condition of segregation. Recently, we established a fund rating approach based on the EU-E decision model and Morningstar ratings. In this paper, we apply the approach to US mutual funds and construct portfolios using the best rating funds. Furthermore, we evaluate the performance of the fund ratings based on the EU-E decision model against Morningstar ratings by examining the performance of the three models in portfolio selection. The conclusions show that portfolios constructed using the ratings based on the EU-E models with moderate tradeoff coefficients perform better than those constructed using Morningstar. The conclusion is robust to different rebalancing intervals.

Should I Stay or Should I Go? The Role of Impostorism in STEM Persistence

2018 ◽  
Vol 43 (2) ◽  
pp. 151-164 ◽  
Author(s):  
Karen W. Tao ◽  
Alberta M. Gloria
Keyword(s):  
Self Efficacy ◽  
Research Training ◽  
Sense Of Self ◽  
Academic Persistence ◽  
Doctoral Degree ◽  
Numerical Representation ◽  
Multiple Mediation ◽  
Training Environment ◽  
Academic Context ◽  
Representation Of Women

Impostor phenomenon or “impostorism” refers to the experience of high-achieving individuals (particularly women) who, despite being successful, attribute their accomplishments to luck, and fear being exposed as frauds. In the current study, we examined the association between impostorism and graduate student self-efficacy, perceptions of the research-training environment, and attitudes toward academic persistence of 224 women completing a science, technology, engineering, and mathematics (STEM)-related doctoral degree. As hypothesized, participants who identified more strongly with impostor characteristics reported a lower sense of self-efficacy, more negative views of their academic context, and more pessimistic outlooks toward attaining their doctorate. However, results from a multiple mediation analysis revealed that women’s levels of self-efficacy and perceptions of their doctoral environment accounted for the effects of impostorism on their attitudes about academic persistence. Also, the relation between impostorism and persistence attitudes strengthened as numerical representation of women in a STEM program increased. Results illuminate the potential role STEM departments can have on students’ persistence by developing early opportunities for research collaborations and fostering an early sense of accomplishment. Parents and teachers might also draw from our findings to develop strategies to inoculate younger students from the insidious effects of gender-based stereotypes. Online slides for instructors who want to use this article for teaching are available on PWQ's website at http://journals.sagepub.com/page/pwq/suppl/index

A Scheme for Numerical Representation of Graph Structures in Engineering Design

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
David F. Wyatt ◽  
David C. Wynn ◽  
P. John Clarkson
Keyword(s):  
Engineering Design ◽  
Design Problem ◽  
Structure Design ◽  
Numerical Representation ◽  
Graph Structure ◽  
Numerical Techniques ◽  
Mathematical Properties ◽  
Conversion Algorithm ◽  
Graph Structures ◽  
Improve Access

Graph structures are fundamental in many aspects of design. This paper discusses a way to improve access to design spaces of graph structures, by converting graph structures into numerical values and vice versa. Mathematical properties of such conversions are described, and those that are desirable are identified. A candidate conversion algorithm, Indexed Stacked Blocks, is proposed. Its use and benefits are illustrated through an example graph-structure design problem. The example demonstrates that such conversions allow design spaces of graph structures to be visualized, sampled, and evaluated. In principle, they also allow other powerful numerical techniques to be applied to the design of graph-structure-based systems.

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