scholarly journals Approximate analytical description of apparent horizons for initial data with momentum and spin

2021 ◽  
Vol 103 (8) ◽  
Author(s):  
Emel Altas ◽  
Bayram Tekin
Keyword(s):  
Initial Data ◽  
Analytical Description ◽  
Apparent Horizons

scholarly journals A NOTE ON THE CYLINDRICAL COLLAPSE OF COUNTER-ROTATING DUST

2002 ◽  
Vol 11 (09) ◽  
pp. 1469-1477 ◽  
Author(s):  
SÉRGIO M. C. V. GONÇALVES ◽  
SANJAY JHINGAN
Keyword(s):  
Cylindrical Shell ◽  
Initial Data ◽  
Analytical Solutions ◽  
Curvature Singularity ◽  
Apparent Horizons ◽  
Long Cylindrical Shell ◽  
Hoop Conjecture ◽  
Cylindrical Collapse

We find analytical solutions describing the collapse of an infinitely long cylindrical shell of counter-rotating dust. We show that — for the classes of solutions discussed herein — from regular initial data a curvature singularity inevitably develops, and no apparent horizons form, thus in accord with the spirit of the hoop conjecture.

scholarly journals Apparent horizons in simplicial Brill wave initial data

1999 ◽  
Vol 16 (6) ◽  
pp. 1979-1985 ◽  
Author(s):  
Adrian P Gentle ◽  
Daniel E Holz ◽  
Warner A Miller ◽  
John A Wheeler
Keyword(s):  
Initial Data ◽  
Apparent Horizons

scholarly journals Bartnik mass via vacuum extensions

2019 ◽  
Vol 30 (13) ◽  
pp. 1940006
Author(s):  
Pengzi Miao ◽  
Naqing Xie
Keyword(s):  
Initial Data ◽  
Scalar Curvature ◽  
Apparent Horizon ◽  
Gauss Curvature ◽  
Positive Mass Theorem ◽  
Data Sets ◽  
Penrose Inequality ◽  
Asymptotically Flat ◽  
Apparent Horizons ◽  
Positive Gauss Curvature

We construct asymptotically flat, scalar flat extensions of Bartnik data [Formula: see text], where [Formula: see text] is a metric of positive Gauss curvature on a two-sphere [Formula: see text], and [Formula: see text] is a function that is either positive or identically zero on [Formula: see text], such that the mass of the extension can be made arbitrarily close to the half area radius of [Formula: see text]. In the case of [Formula: see text], the result gives an analog of a theorem of Mantoulidis and Schoen [On the Bartnik mass of apparent horizons, Class. Quantum Grav. 32(20) (2015) 205002, 16 pp.], but with extensions that have vanishing scalar curvature. In the context of initial data sets in general relativity, the result produces asymptotically flat, time-symmetric, vacuum initial data with an apparent horizon [Formula: see text], for any metric [Formula: see text] with positive Gauss curvature, such that the mass of the initial data is arbitrarily close to the optimal value in the Riemannian Penrose inequality. The method we use is the Shi–Tam type metric construction from [Positive mass theorem and the boundary behaviors of compact manifolds with nonnegative scalar curvature, J. Differential Geom. 62(1) (2002) 79–125] and a refined Shi–Tam monotonicity, found by the first named author in [On a localized Riemannian Penrose inequality, Commun. Math. Phys. 292(1) (2009) 271–284].

scholarly journals Addition and subtraction of integers in codes operands with negative zero

2020 ◽  
Vol 69 (2) ◽  
Author(s):  
O. V. Samoshchenko ◽  
◽  
O. A. Zolotukhina
Keyword(s):  
Initial Data ◽  
Input Data ◽  
Analytical Description ◽  
Negative Numbers ◽  
Source Data ◽  
Computer Representation ◽  
Addition And Subtraction ◽  
Encoding Method ◽  
Positive Properties ◽  
True Values

Code on the outputs of adder binary numbers described as the remainder of the sum the initial data on the adder module is equal to output carry weight. An original technique for synthesizing a way of operands representation in the addition and subtraction schemes of integers in a code with a negative zero was developed, which is based on the representation the source data in the form a remainder on the adder module. A method of computer representation for integer numbers is proposed, in which the codes of posi-tive and negative numbers are formed by the same procedure. The property of duality the addition and sub-traction operations on the initial data in the code with a negative zero have justified analytically. Areas of allowable results values for the correct input data addition and subtraction operations are determined. It is identified combination of the adder output signals, which determine the presence and polarity the adder bit grid overflow. It is shown that designed fixing scheme bit grid overflow of adder outputs invariant with re-spect to operations of addition and subtraction of source data with a negative zero code. For the analytical description of arithmetic operations on integer numbers represented with the proposed encoding method, a technique of calculating the sum and difference of numbers using the biased supplementary code has been proposed. Analytically substantiated, that the technique makes the scheme of the operational adder homoge-neous. The rules for establishing the correctness of the addition and subtraction operations of the integers given in the proposed encoding form are given. For true values of the initial arguments, the sums and the differences codes ranges are obtained, and the rules for positive and negative overflows identification are proposed. The original usage of a common numerical bias during the operands encoding, that evinces itself in the advantages of basic computer operations technical implementation, predetermines positive properties in practical implementations of more complex arithmetical actions.

Quantitative Analysis Of X-Ray Images From Geological Materials

1990 ◽  
Vol 48 (2) ◽  
pp. 244-245
Author(s):  
J. M. Paque ◽  
R. Browning ◽  
P. L. King ◽  
P. Pianetta
Keyword(s):  
Quantitative Analysis ◽  
Bulk Composition ◽  
Principal Component ◽  
Analytical Description ◽  
Bulk Sample ◽  
Geological Samples ◽  
X Ray ◽  
Software And Hardware ◽  
And Storage ◽  
Insight Into

Geological samples typically contain many minerals (phases) with multiple element compositions. A complete analytical description should give the number of phases present, the volume occupied by each phase in the bulk sample, the average and range of composition of each phase, and the bulk composition of the sample. A practical approach to providing such a complete description is from quantitative analysis of multi-elemental x-ray images.With the advances in recent years in the speed and storage capabilities of laboratory computers, large quantities of data can be efficiently manipulated. Commercial software and hardware presently available allow simultaneous collection of multiple x-ray images from a sample (up to 16 for the Kevex Delta system). Thus, high resolution x-ray images of the majority of the detectable elements in a sample can be collected. The use of statistical techniques, including principal component analysis (PCA), can provide insight into mineral phase composition and the distribution of minerals within a sample.

Remarks on nonlinear elastic waves with null conditions

2020 ◽  
Vol 26 ◽  
pp. 121
Author(s):  
Dongbing Zha ◽  
Weimin Peng
Keyword(s):  
Initial Data ◽  
Global Existence ◽  
Elastic Waves ◽  
Wave Equations ◽  
Alternative Proof ◽  
Classical Solutions ◽  
Small Initial Data ◽  
Hyperelastic Materials ◽  
Variational Structure ◽  
Nonlinear Elastic

For the Cauchy problem of nonlinear elastic wave equations for 3D isotropic, homogeneous and hyperelastic materials with null conditions, global existence of classical solutions with small initial data was proved in R. Agemi (Invent. Math. 142 (2000) 225–250) and T. C. Sideris (Ann. Math. 151 (2000) 849–874) independently. In this paper, we will give some remarks and an alternative proof for it. First, we give the explicit variational structure of nonlinear elastic waves. Thus we can identify whether materials satisfy the null condition by checking the stored energy function directly. Furthermore, by some careful analyses on the nonlinear structure, we show that the Helmholtz projection, which is usually considered to be ill-suited for nonlinear analysis, can be in fact used to show the global existence result. We also improve the amount of Sobolev regularity of initial data, which seems optimal in the framework of classical solutions.

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