scholarly journals On center of mass and foliations by constant spacetime mean curvature surfaces for isolated systems in General Relativity

2021 ◽  
Vol 60 (6) ◽  
Author(s):  
Carla Cederbaum ◽  
Anna Sakovich
Keyword(s):  
Initial Data ◽  
Mean Curvature ◽  
Evolution Equations ◽  
Center Of Mass ◽  
Point Particle ◽  
Data Sets ◽  
Data Set ◽  
Definition Of ◽  
Isolated Systems ◽  
Invent Math

AbstractWe propose a new foliation of asymptotically Euclidean initial data sets by 2-spheres of constant spacetime mean curvature (STCMC). The leaves of the foliation have the STCMC-property regardless of the initial data set in which the foliation is constructed which asserts that there is a plethora of STCMC 2-spheres in a neighborhood of spatial infinity of any asymptotically flat spacetime. The STCMC-foliation can be understood as a equivariant relativistic generalization of the CMC-foliation suggested by Huisken and Yau (Invent Math 124:281–311, 1996). We show that a unique STCMC-foliation exists near infinity of any asymptotically Euclidean initial data set with non-vanishing energy which allows for the definition of a new notion of total center of mass for isolated systems. This STCMC-center of mass transforms equivariantly under the asymptotic Poincaré group of the ambient spacetime and in particular evolves under the Einstein evolution equations like a point particle in Special Relativity. The new definition also remedies subtle deficiencies in the CMC-approach to defining the total center of mass suggested by Huisken and Yau (Invent Math 124:281–311, 1996) which were described by Cederbaum and Nerz (Ann Henri Poincaré 16:1609–1631, 2015).

scholarly journals A DYNAMICAL SYMMETRY OF THE QUASI-SPHERICAL (OR SPHERICAL) COLLAPSE

2005 ◽  
Vol 14 (10) ◽  
pp. 1761-1767 ◽  
Author(s):  
UJJAL DEBNATH ◽  
SUBENOY CHAKRABORTY ◽  
NARESH DADHICH
Keyword(s):  
Kinetic Energy ◽  
Initial Data ◽  
Dynamical Symmetry ◽  
Matter Field ◽  
Physical Parameters ◽  
Data Sets ◽  
Type I ◽  
Data Set ◽  
Spherical Collapse ◽  
Scaling Relationship

By linearly scaling the initial data set (mass and kinetic energy functions), it is found that the dynamics of quasi-spherical (or spherical) collapse remains invariant for dust or a general (Type I) matter field, provided the comoving radius is also appropriately scaled. This defines a symmetry of the quasi spherical (or spherical) collapse. That is, the linear transformation identifies an equivalence class of data sets which lead to the same end result as well as its evolution all through. In particular, it is shown that the physical parameters, density and shear remain invariant. What the transformation is exhibiting is an interesting scaling relationship between mass, kinetic energy and the size of the collapsing sphere which is respected not only by the initial data set but remarkably also by the dynamics of collapse.

scholarly journals DEFINITION OF SEDIMENTOLOGICAL MODEL IN LIMITED INITIAL DATA SET CONDITIONS

2018 ◽  
pp. 21-26
Author(s):  
A. V. Podnebesnykh
Keyword(s):  
Initial Data ◽  
Low Cost ◽  
Central Africa ◽  
Main Direction ◽  
Geological Exploration ◽  
Data Set ◽  
Definition Of

The article considers the main procedures which essentially increase the validity of sedimentological models in limited initial data set conditions. The Bentiu formation (Central Africa) is studied as an example of the research. Using simple and low-cost methods it is possible to identify not only the main direction of sedimentary material displacement but also the main characteristics of alluvial systems that will let to plan exploitation of reservoir formation of such type correctly even on geological exploration stage.

scholarly journals Large outlying stable constant mean curvature spheres in initial data sets

2014 ◽  
Vol 197 (3) ◽  
pp. 663-682 ◽  
Author(s):  
Simon Brendle ◽  
Michael Eichmair
Keyword(s):  
Initial Data ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Data Sets

scholarly journals On the Center of Mass of Asymptotically Hyperbolic Initial Data Sets

2015 ◽  
Vol 17 (6) ◽  
pp. 1505-1528 ◽  
Author(s):  
Carla Cederbaum ◽  
Julien Cortier ◽  
Anna Sakovich
Keyword(s):  
Initial Data ◽  
Center Of Mass ◽  
Data Sets ◽  
Asymptotically Hyperbolic

scholarly journals Specifying Angular Momentum and Center of Mass for Vacuum Initial Data Sets

2011 ◽  
Vol 306 (3) ◽  
pp. 785-803 ◽  
Author(s):  
Lan-Hsuan Huang ◽  
Richard Schoen ◽  
Mu-Tao Wang
Keyword(s):  
Angular Momentum ◽  
Initial Data ◽  
Center Of Mass ◽  
Data Sets

scholarly journals A Three-Dimensional Parametric Biomechanical Rider Model for Multibody Applications

2020 ◽  
Vol 10 (13) ◽  
pp. 4509
Author(s):  
Matteo Bova ◽  
Matteo Massaro ◽  
Nicola Petrone
Keyword(s):  
Center Of Mass ◽  
Three Dimensional ◽  
The Body ◽  
Experimental Comparison ◽  
Minor Effect ◽  
Data Sets ◽  
Data Set ◽  
Multibody Model ◽  
Inertial Parameters ◽  
A Minor

Bicycles and motorcycles are characterized by large rider-to-vehicle mass ratios, thus making estimation of the rider’s inertia especially relevant. The total inertia can be derived from the body segment inertial properties (BSIP) which, in turn, can be obtained from the prediction/regression formulas available in the literature. Therefore, a parametric multibody three-dimensional rider model is devised, where the four most-used BSIP formulas (herein named Dempster, Reynolds-NASA, Zatsiorsky–DeLeva, and McConville–Young–Dumas, after their authors) are implemented. After an experimental comparison, the effects of the main posture parameters (i.e., torso inclination, knee distance, elbow distance, and rider height) are analyzed in three riding conditions (sport, touring, and scooter). It is found that the elbow distance has a minor effect on the location of the center of mass and moments of inertia, while the effect of the knee distance is on the same order magnitude as changing the BSIP data set. Torso inclination and rider height are the most relevant parameters. Tables with the coefficients necessary to populate the three-dimensional rider model with the four data sets considered are given. Typical inertial parameters of the whole rider are also given, as a reference for those not willing to implement the full multibody model.

scholarly journals The Zeroth Law of Thermodynamics in Special Relativity

2020 ◽  
Vol 50 (11) ◽  
pp. 1554-1586
Author(s):  
L. Gavassino
Keyword(s):  
Special Relativity ◽  
Equivalence Relation ◽  
Thermal Equilibrium ◽  
Center Of Mass ◽  
Experimental Conditions ◽  
Fundamental Level ◽  
Definition Of ◽  
Isolated Systems ◽  
Moving Bodies ◽  
Operational Formulation

AbstractWe critically revisit the definition of thermal equilibrium, in its operational formulation, provided by standard thermodynamics. We show that it refers to experimental conditions which break the covariance of the theory at a fundamental level and that, therefore, it cannot be applied to the case of moving bodies. We propose an extension of this definition which is manifestly covariant and can be applied to the study of isolated systems in special relativity. The zeroth law of thermodynamics is, then, proven to establish an equivalence relation among bodies which have not only the same temperature, but also the same center of mass four-velocity.

scholarly journals Estimating Pay Gaps for Workers With Disabilities: Implications From Broadening Definitions and Data Sets

2014 ◽  
Vol 28 (4) ◽  
pp. 264-290 ◽  
Author(s):  
Kevin F. Hallock ◽  
Xin Jin ◽  
Linda Barrington
Keyword(s):  
Survey Data ◽  
Data Sets ◽  
Full Time ◽  
Data Set ◽  
Pay Gap ◽  
Persons With Disabilities ◽  
Total Compensation ◽  
Individual Level ◽  
Compensation Gap ◽  
Definition Of

Purpose:To compare pay gap estimates across 3 different national survey data sets for people with disabilities relative to those without disabilities when pay is measured as wage and salary alone versus a (total compensation) definition that includes an estimate of the value of benefits.Method:Estimates of the cost to the employers of employee benefits at the occupational level from an employer survey data set are matched to individual-level data in each of the 3 data sets. Multiple regression techniques are applied to estimate wage and salary and total compensation gaps between full-time men with and without disabilities.Results:For full-time working men with disabilities (relative to those without disabilities), there is a consistently larger percentage wage and salary gap than percentage total compensation gap and breadth of the definition of pay affects the size of any estimated pay gap. In addition, there are differences in the estimated pay gaps depending on data source and disability measure.Conclusions:Results obtained from a single data set or definition of key variables may not be broadly generalizable. Studies containing such limitations should be interpreted cautiously. Our research further suggests employers looking to hire persons with disabilities or those offering employment placement services should put substantial weight on the non–base pay component of the total compensation package.

scholarly journals Comparison of radon mapping methods for the delineation of radon priority areas – an exercise

2021 ◽  
Author(s):  
Valeria Gruber ◽  
Sebastian Baumann ◽  
Oliver Alber ◽  
Christian Laubbichler ◽  
Peter Bossew ◽  
...  
Keyword(s):  
Indoor Radon ◽  
Mapping Method ◽  
Data Sets ◽  
Data Set ◽  
Priority Areas ◽  
Eu Member States ◽  
Mapping Process ◽  
Spatial Estimates ◽  
Definition Of ◽  
The Impact

Background: Many different methods are applied for radon mapping depending on the purpose of the map and the data that are available. In addition, the definitions of radon priority areas (RPA) in EU Member States, as requested in the new European EURATOM BSS (1), are diverse. Objective: 1) Comparison of methods for mapping geogenic and indoor radon, 2) the possible transferability of a mapping method developed in one region to other regions and 3) the evaluation of the impact of different mapping methods on the delineation of RPAs. Design: Different mapping methods and several RPA definitions were applied to the same data sets from six municipalities in Austria and Cantabria, Spain. Results: Some mapping methods revealed a satisfying degree of agreement, but relevant differences were also observed. The chosen threshold for RPA classification has a major impact, depending on the level of radon concentration in the area. The resulting maps were compared regarding the spatial estimates and the delineation of RPAs. Conclusions: Not every mapping method is suitable for every available data set. Data robustness and harmonisation are the main requirements, especially if the used data set is not designed for a specific technique. Different mapping methods often deliver similar results in RPA classification. The definition of thresholds for the classification and delineation of RPAs is a guidance factor in the mapping process and is as relevant as harmonising mapping methods depending on the radon levels in the area.

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