Determination of the Accuracy of Segmented Representations of Cable Shape

1975 ◽  
Vol 97 (2) ◽  
pp. 472-478 ◽  
Author(s):  
H. T. Wang
Keyword(s):  
Finite Number ◽  
Static Case ◽  
Two Dimensional ◽  
Comprehensive Investigation ◽  
Finite Segment ◽  
The Difference ◽  
Number Of Segments

The results of a comprehensive investigation of the accuracy of representing a continuous cable by a finite number of segments are presented. The results are limited to the two-dimensional static case. The accuracy of three different finite-segment models is evaluated for a number of segments ranging from 1 to 40. The difference between the three models lies in the manner in which the inclination of each segment is obtained. The results basically show that relatively few segments are required to accurately obtain the overall geometry and resultant tension of the cable.

scholarly journals Determination of hard X-ray polarization from two-dimensional images

2020 ◽  
Vol 53 (6) ◽  
pp. 1559-1561
Author(s):  
Robert B. Von Dreele ◽  
Wenqian Xu
Keyword(s):  
Incident Beam ◽  
Beam Polarization ◽  
Two Dimensional ◽  
One Dimensional ◽  
X Ray ◽  
Dimensional Image ◽  
Two Dimensional Image ◽  
The Difference ◽  
Two Dimensional Images

An estimate of synchrotron hard X-ray incident beam polarization is obtained by partial two-dimensional image masking followed by integration. With the correct polarization applied to each pixel in the image, the resulting one-dimensional pattern shows no discontinuities arising from the application of the mask. Minimization of the difference between the sums of the masked and unmasked powder patterns allows estimation of the polarization to ±0.001.

Fidelity of the Estimation of the Deformation Gradient From Data Deduced From the Motion of Markers Placed on a Body That is Subject to an Inhomogeneous Deformation Field

2013 ◽  
Vol 135 (8) ◽  
Author(s):  
Vít Průša ◽  
K. R. Rajagopal ◽  
U. Saravanan
Keyword(s):  
Finite Number ◽  
Data Reduction ◽  
Deformation Gradient ◽  
Quantitative Description ◽  
The Body ◽  
Inhomogeneous Deformation ◽  
Actual Error ◽  
The Difference

Practically all experimental measurements related to the response of nonlinear bodies that are made within a purely mechanical context are concerned with inhomogeneous deformations, though, in many experiments, much effort is taken to engender homogeneous deformation fields. However, in experiments that are carried out in vivo, one cannot control the nature of the deformation. The quantity of interest is the deformation gradient and/or its invariants. The deformation gradient is estimated by tracking positions of a finite number of markers placed in the body. Any experimental data-reduction procedure based on tracking a finite number of markers will, for a general inhomogeneous deformation, introduce an error in the determination of the deformation gradient, even in the idealized case, when the positions of the markers are measured with no error. In our study, we are interested in a quantitative description of the difference between the true gradient and its estimate obtained by tracking the markers, that is, in the quantitative description of the induced error due to the data reduction. We derive a rigorous upper bound on the error, and we discuss what factors influence the error bound and the actual error itself. Finally, we illustrate the results by studying a practically interesting model problem. We show that different choices of the tracked markers can lead to substantially different estimates of the deformation gradient and its invariants. It is alarming that even qualitative features of the material under consideration, such as the incompressibility of the body, can be evaluated differently with different choices of the tracked markers. We also demonstrate that the derived error estimate can be used as a tool for choosing the appropriate marker set that leads to the deformation gradient estimate with the least guaranteed error.

scholarly journals Determination of the Homotopy Type of a Morse – Smale Diffeomorphism on a 2-torus by Heteroclinic Intersection

2021 ◽  
Vol 17 (4) ◽  
pp. 465-473
Author(s):  
A. I. Morozov ◽  
Keyword(s):  
Finite Number ◽  
Finite Order ◽  
Homotopy Type ◽  
Orbit Space ◽  
Heteroclinic Orbits ◽  
Two Dimensional ◽  
Homotopy Classes ◽  
Intersection Index ◽  
Homotopic Type

According to the Nielsen – Thurston classification, the set of homotopy classes of orientation-preserving homeomorphisms of orientable surfaces is split into four disjoint subsets. Each subset consists of homotopy classes of homeomorphisms of one of the following types: $T_{1}$) periodic homeomorphism; $T_{2}$) reducible non-periodic homeomorphism of algebraically finite order; $T_{3}$) a reducible homeomorphism that is not a homeomorphism of algebraically finite order; $T_{4}$) pseudo-Anosov homeomorphism. It is known that the homotopic types of homeomorphisms of torus are $T_{1}$, $T_{2}$, $T_{4}$ only. Moreover, all representatives of the class $T_{4}$ have chaotic dynamics, while in each homotopy class of types $T_{1}$ and $T_{2}$ there are regular diffeomorphisms, in particular, Morse – Smale diffeomorphisms with a finite number of heteroclinic orbits. The author has found a criterion that allows one to uniquely determine the homotopy type of a Morse – Smale diffeomorphism with a finite number of heteroclinic orbits on a two-dimensional torus. For this, all heteroclinic domains of such a diffeomorphism are divided into trivial (contained in the disk) and non-trivial. It is proved that if the heteroclinic points of a Morse – Smale diffeomorphism are contained only in the trivial domains then such diffeomorphism has the homotopic type $T_{1}$. The orbit space of non-trivial heteroclinic domains consists of a finite number of two-dimensional tori, where the saddle separatrices participating in heteroclinic intersections are projected as transversally intersecting knots. That whether the Morse – Smale diffeomorphisms belong to types $T_{1}$ or $T_{2}$ is uniquely determined by the total intersection index of such knots.

Neutron Residual Stress Measurements on Rail Sections for Different Production Conditions

2004 ◽  
Author(s):  
Vladimir Luzin ◽  
Jeffrey E. Gordon ◽  
Thomas Gnaupel-Herold ◽  
Henry J. Prask
Keyword(s):  
Residual Stress ◽  
Stress State ◽  
Residual Stresses ◽  
Two Dimensional ◽  
Strain Measurements ◽  
Stress Measurements ◽  
Triaxial Stresses ◽  
The Difference ◽  
Production Conditions

Rail sectioning with subsequent neutron diffraction experiments has been used to assess residual stresses in the rails. In this study we present the results of neutron stress measurements performed at the NIST Center for Neutron Research (NCNR) on rail sections from rails that were produced under various conditions. Specifically, these are air-cooled, air-cooled and roller-straightened, head-hardened and head-hardened and roller-straightened. More significantly, a head-hardened and roller-straightened rail was also studied after service to elucidate evolution of the service-induced residual stresses. In the latter case both a transverse-cut slice and the central region of a 0.53 m long piece were studied. Measurements on this piece are the first in which triaxial stresses have been determined for an intact rail. Neutron strain measurements with 3×3×3 mm3 spatial resolution were successfully employed for transversally cut slices to verify the difference in the stress state depending on the production process. Although examination of slices allows determination of only two-dimensional stresses in the plane of the slice, additional measurements on obliquely-cut slices, which were also carried out, and utilization of FEM gives the possibility of reconstructing the full triaxial stress distribution. Together, these approaches provide a better understanding of rail fabrication and the possibility of improving the durability and safety of rails in the future.

FRACTIONAL DETERMINATIONS OF URINARY 17-KETOSTEROIDS IN HYPEREMESIS GRAVIDARUM

1962 ◽  
Vol 41 (1) ◽  
pp. 123-128 ◽  
Author(s):  
Pentti A. Järvinen ◽  
Sykkö Pesonen ◽  
Pirkko Väänänen
Keyword(s):  
Hyperemesis Gravidarum ◽  
First Trimester ◽  
Control Group ◽  
Before And After ◽  
Daily Urine ◽  
First Trimester Of Pregnancy ◽  
The Difference

ABSTRACT The fractional determination of 17-ketosteroids in the daily urine was performed in nine cases of hyperemesis gravidarum and in four control cases, in the first trimester of pregnancy both before and after corticotrophin administration. The excretion of total 17-KS is similar in the two groups. Only in the hyperemesis group does the excretion of total 17-KS increase significantly after corticotrophin administration. The fractional determination reveals no difference between the two groups of patients with regard to the values of the fractions U (unidentified 17-KS), A (androsterone) and Rest (11-oxygenated 17-KS). The excretion of dehydroepiandrosterone is significantly higher in the hyperemesis group than in the control group. The excretion of androstanolone seems to be lower in the hyperemesis group than in the control group, but the difference is not statistically significant. The differences in the correlation between dehydroepiandrosterone and androstanolone in the two groups is significant. The high excretion of dehydroepiandrosterone and low excretion of androstanolone in cases of hyperemesis gravidarum is a sign of adrenal dysfunction.

THE SUBJECT FIELD OF INSTITUTIONAL EDUCATION: THE SENSE AND PROSPECTS OF DEVELOPMENT IN UKRAINE

2020 ◽  
pp. 25-38
Author(s):  
Irina Mordous
Keyword(s):  
Decisive Role ◽  
Subject Field ◽  
National Education ◽  
Progressive Development ◽  
Separate Area ◽  
Economic Transformations ◽  
The Difference ◽  
The Individual ◽  
Political Economic

The development of modern civilization attests to its decisive role in the progressive development of institutions. They identified the difference between Western civilization and the rest of the world. Confirmation of the institutional advantages of the West was its early industrialization. The genesis and formation of institutionalism in its ideological and conceptualmethodological orientation occurs as a process alternative to neoclassic in the context of world heterodoxia, which quickly spread in social science. Highlighting institutional education as a separate area of sociocultural activity is determined by the factor of differentiation of institutional theory as a whole. A feature of institutional education is its orientation toward the individual and his/her transformation into a personality. The content of institutional education is revealed through the analysis of the institution, which includes a set of established customs, traditions, ways of thinking, behavioral stereotypes of individuals and social groups. The dynamics of socio-political, economic transformations in Ukraine requires a review of the foundations of national education and determination of the prospects for its development in the 21st century in the context of institutionalism.

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