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.

LARGE DYNAMICAL SYMMETRY OF QUASI-SPHERICAL GRAVITATIONAL COLLAPSE WITH RADIAL AND TANGENTIAL PRESSURES AND ANISOTROPY AND INHOMOGENEITY OF SPACE–TIME

2006 ◽  
Vol 15 (09) ◽  
pp. 1531-1544 ◽  
Author(s):  
SUBENOY CHAKRABORTY ◽  
SANJUKTA CHAKRABORTY
Keyword(s):  
Initial Data ◽  
Gravitational Collapse ◽  
Naked Singularity ◽  
Dynamical Symmetry ◽  
Physical Parameters ◽  
Data Sets ◽  
Final State ◽  
Data Set ◽  
Higher Dimensional

A detailed study of higher-dimensional quasi-spherical gravitational collapse with radial and tangential stresses has been done and the role of initial data, anisotropy and inhomogeneity has been investigated in determining the end state of collapse. By linear scaling the initial data set and the area radius, it is found that the dynamics of quasi-spherical collapse remains invariant. In other words, the linear transformation identifies an equivalence class of data sets for which physical parameters like density, pressures (radial and tangential), shear remain invariant and the final state of collapse is identical (black hole or naked singularity). Finally, the role of anisotropy and inhomogeneity has been studied by proving some propositions.

DYNAMICAL SYMMETRY IN GRAVITATIONAL COLLAPSE WITH GENERAL INITIAL AREA RADIUS

2006 ◽  
Vol 21 (18) ◽  
pp. 1467-1479 ◽  
Author(s):  
SUBENOY CHAKRABORTY ◽  
SANJUKTA CHAKRABORTY
Keyword(s):  
Initial Data ◽  
Gravitational Collapse ◽  
Linear Transformation ◽  
Arbitrary Function ◽  
Dynamical Symmetry ◽  
Matter Content ◽  
Anisotropic Pressure ◽  
Physical Parameters ◽  
Data Set ◽  
Initial Area

In this work, gravitational collapse has been studied for quasi-spherical spacetime with dust or anisotropic pressure as the matter content. A linear transformation on the initial data set and of the area radius shows the invariance of the physical parameters as well as the final fate of collapse, considering an arbitrary function of r as the initial area radius.

scholarly journals Intention, Principle, Outputs and Aims of the Experimental Pavilion Research of Building Envelopes Including Windows for Wooden Buildings

2017 ◽  
Vol 13 (1) ◽  
pp. 42-51 ◽  
Author(s):  
Daniela Štaffenová ◽  
Ján Rybárik ◽  
Miroslav Jakubčík
Keyword(s):  
Experimental Research ◽  
Climatic Conditions ◽  
Point Of View ◽  
Physical Parameters ◽  
Data Sets ◽  
Data Set ◽  
Building Envelopes ◽  
Climate Conditions ◽  
Time Period

AbstractThe aim of experimental research in the area of exterior walls and windows suitable for wooden buildings was to build special pavilion laboratories. These laboratories are ideally isolated from the surrounding environment, airtight and controlled by the constant internal climate. The principle of experimental research is measuring and recording of required physical parameters (e.g. temperature or relative humidity). This is done in layers of experimental fragment sections in the direction from exterior to interior, as well as in critical places by stable interior and real exterior climatic conditions. The outputs are evaluations of experimental structures behaviour during the specified time period, possibly during the whole year by stable interior and real exterior boundary conditions. The main aim of this experimental research is processing of long-term measurements of experimental structures and the subsequent analysis. The next part of the research consists of collecting measurements obtained with assistance of the experimental detached weather station, analysis, evaluation for later setting up of reference data set for the research locality, from the point of view of its comparison to the data sets from Slovak Hydrometeorological Institute (SHMU) and to localities with similar climate conditions. Later on, the data sets could lead to recommendations for design of wooden buildings.

scholarly journals Modeling Insulin-Glucose Dynamics during Insulin Induced Hypoglycemia. Evaluation of Glucose Counterregulation

1999 ◽  
Vol 1 (4) ◽  
pp. 313-323 ◽  
Author(s):  
Boris P. Kovatchev ◽  
Leon S. Farhy ◽  
Daniel J. Cox ◽  
Martin Straume ◽  
Vladimir I. Yankov ◽  
...  
Keyword(s):  
Temporal Pattern ◽  
Type I Diabetes ◽  
Coefficient Of Determination ◽  
Data Sets ◽  
Type I ◽  
Euglycemic Hyperinsulinemic Clamp ◽  
Data Set ◽  
Utilization Coefficient ◽  
History Of ◽  
Glucose Dynamics

A dynamical network model of insulin-glucose interactions in subjects with Type I Diabetes was developed and applied to data sets for 40 subjects. Each data set contained the amount of dextrose + insulin infused and blood glucose (BG) determinations, sampled every 5 minutes during a one-hour standardized euglycemic hyperinsulinemic clamp and a subsequent one-hour BG reduction to moderate hypoglycemic levels. The model approximated the temporal pattern of BG and on that basis predicted the counterregulatory response of each subject. The nonlinear fits explained more than 95% of the variance of subjects' BG fluctuations, with a median coefficient of determination 97.7%. For all subjects the model-predicted counterregulatory responses correlated with measured plasma epinephrine concentrations. The observed nadirs of BG during the tests correlated negatively with the model-predicted insulin utilization coefficient (r = -0.51,p< 0.001) and counterregulation rates (r= -0.63,p< 0.001). Subjects with a history of multiple severe hypoglycemic episodes demonstrated slower onset of counterregulation compared to subjects with no such history (p< 0.03).

scholarly journals GENERICITY ASPECTS IN GRAVITATIONAL COLLAPSE TO BLACK HOLES AND NAKED SINGULARITIES

2012 ◽  
Vol 21 (08) ◽  
pp. 1250066 ◽  
Author(s):  
PANKAJ S. JOSHI ◽  
DANIELE MALAFARINA ◽  
RAVINDRA V. SARAYKAR
Keyword(s):  
Black Holes ◽  
Initial Data ◽  
Gravitational Collapse ◽  
Naked Singularity ◽  
Matter Field ◽  
Einstein Equations ◽  
Type I ◽  
Naked Singularities ◽  
Physical Conditions ◽  
Perfect Fluids

Here we investigate the genericity and stability aspects for naked singularities and black holes that arise as the final states for a complete gravitational collapse of a spherical massive matter cloud. The form of the matter considered is a general Type I matter field, which includes most of the physically reasonable matter fields such as dust, perfect fluids and such other physically interesting forms of matter widely used in gravitation theory. Here, we first study in some detail the effects of small pressure perturbations in an otherwise pressure-free collapse scenario, and examine how a collapse evolution that was going to the black hole endstate would be modified and go to a naked singularity, once small pressures are introduced in the initial data. This allows us to understand the distribution of black holes and naked singularities in the initial data space. Collapse is examined in terms of the evolutions allowed by Einstein equations, under suitable physical conditions and as evolving from a regular initial data. We then show that both black holes and naked singularities are generic outcomes of a complete collapse, when genericity is defined in a suitable sense in an appropriate space.

Bianchi type I Universe: An extension of ΛCDM model

2021 ◽  
pp. 2150069
Author(s):  
Rajendra Prasad ◽  
Lalit Kumar Gupta ◽  
A. Beesham ◽  
G. K. Goswami ◽  
Anil Kumar Yadav
Keyword(s):  
Bianchi Type ◽  
Hubble Constant ◽  
Model Parameters ◽  
Constant Density ◽  
Data Sets ◽  
Type I ◽  
Data Set ◽  
Bianchi Type I ◽  
Age Of The Universe ◽  
The Universe

In this paper, we investigate a Bianchi type I exact Universe by taking into account the cosmological constant as the source of energy at the present epoch. We have performed a [Formula: see text] test to obtain the best fit values of the model parameters of the Universe in the derived model. We have used two types of data sets, viz., (i) 31 values of the Hubble parameter and (ii) the 1048 Pantheon data set of various supernovae distance moduli and apparent magnitudes. From both the data sets, we have estimated the current values of the Hubble constant, density parameters [Formula: see text] and [Formula: see text]. The dynamics of the deceleration parameter shows that the Universe was in a decelerating phase for redshift [Formula: see text]. At a transition redshift [Formula: see text], the present Universe entered an accelerating phase of expansion. The current age of the Universe is obtained as [Formula: see text] Gyrs. This is in good agreement with the value of [Formula: see text] calculated from the Plank collaboration results and WMAP observations.

scholarly journals Initial Data Sets with Ends of Cylindrical Type: I. The Lichnerowicz Equation

2014 ◽  
Vol 16 (5) ◽  
pp. 1231-1266 ◽  
Author(s):  
Piotr T. Chruściel ◽  
Rafe Mazzeo
Keyword(s):  
Initial Data ◽  
Data Sets ◽  
Type I ◽  
Lichnerowicz Equation

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 Evaluating generalised additive mixed modelling strategies for dynamic speech analysis

2020 ◽  
Author(s):  
Marton Soskuthy
Keyword(s):  
Type I Error ◽  
Simulated Data ◽  
Real Data ◽  
Speech Analysis ◽  
Data Sets ◽  
Type I ◽  
Data Set ◽  
Modelling Strategies ◽  
Additive Mixed Models ◽  
Pitch Contours

Generalised additive mixed models (GAMMs) are increasingly popular in dynamic speech analysis, where the focus is on measurements with temporal or spatial structure such as formant, pitch or tongue contours. GAMMs provide a range of tools for dealing with the non-linear contour shapes and complex hierarchical organisation characteristic of such data sets. This, however, means that analysts are faced with non-trivial choices, many of which have a serious impact on the statistical validity of their analyses. This paper presents type I and type II error simulations to help researchers make informed decisions about modelling strategies when using GAMMs to analyse phonetic data. The simulations are based on two real data sets containing F2 and pitch contours, and a simulated data set modelled after the F2 data. They reflect typical scenarios in dynamic speech analysis. The main emphasis is on (i) dealing with dependencies within contours and higher-level units using random structures and other tools, and (ii) strategies for significance testing using GAMMs. The paper concludes with a small set of recommendations for fitting GAMMs, and provides advice on diagnosing issues and tailoring GAMMs to specific data sets. It is also accompanied by a GitHub repository including a tutorial on running type I error simulations for existing data sets: https://github.com/soskuthy/gamm_strategies.

Strategies for solving neighboring-element problems: a case study using resonant X-ray diffraction and pulsed neutron diffraction to examine Sr8Ga16Ge30

2003 ◽  
Vol 36 (5) ◽  
pp. 1182-1189 ◽  
Author(s):  
Yuegang Zhang ◽  
Angus P. Wilkinson ◽  
George S. Nolas ◽  
Peter L. Lee ◽  
Jason P. Hodges
Keyword(s):  
Neutron Diffraction ◽  
Resonant Scattering ◽  
Atomic Displacement ◽  
Scattering Data ◽  
Data Sets ◽  
Type I ◽  
Neighboring Element ◽  
Data Set ◽  
X Ray ◽  
Atomic Displacement Parameters

The distribution of gallium and germanium over the available framework sites in the type-I clathrate Sr8Ga16Ge30(Pm\bar{3}n) has been determined by powder diffraction using several different combinations of resonant scattering data sets, collected at energies close to both the Ga and GeK-edges, and time-of-flight (TOF) neutron diffraction data. Based on a combined refinement using three X-ray data sets and a composition restraint, the fractional occupancies of the 6c, 16iand 24ksites by gallium are estimated to be 0.705 (5), 0.181 (3) and 0.376 (2), respectively. The required resonant scattering factors were determined by Kramers–Kronig transformation from X-ray absorption spectra. The results from refinements using single data sets and various combinations of data sets are compared. The high degree of scattering contrast that resonant diffraction can provide leads to very precise site occupancies. However, systematic errors in the resonant diffraction intensity data can considerably degrade the accuracy of the results. The use of a carefully chosen multiple-data-set strategy can minimize bias in the refinement results by reducing the correlations between site occupancies, atomic displacement parameters and histogram scale factors. The effect of errors in the resonant scattering factors on the refinement results was also examined.

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