Covariant boundary conditions in gravitational radiation theory: A new covariant definition of spatially asymptotically flat space-times

1981 ◽  
Vol 23 (2) ◽  
pp. 267-271
Author(s):  
Demetrios Papadopoulos ◽  
Louis Witten
Keyword(s):  
Boundary Conditions ◽  
Gravitational Radiation ◽  
Flat Space ◽  
Asymptotically Flat ◽  
Radiation Theory ◽  
Definition Of

IS THERE CLASSICAL SUPER-RADIANCE ON KERR-NEWMAN-ANTI-DE SITTER BLACK HOLES?

2002 ◽  
Vol 17 (20) ◽  
pp. 2782-2782
Author(s):  
ELIZABETH WINSTANLEY
Keyword(s):  
Black Holes ◽  
Boundary Conditions ◽  
Killing Vector ◽  
De Sitter ◽  
Transparent Boundary Conditions ◽  
Asymptotically Flat ◽  
Ads Black Holes ◽  
Definition Of ◽  
Conditions At Infinity ◽  
Positive Frequency

Since the formulation of the AdS/CFT correspondence 1, there has been great interest in space-times which are asymptotically anti-de Sitter, and the properties of the Kerr-Newman-anti-de Sitter (KN-AdS) space-time in various dimensions have been extensively studied 2. However, the properties of classical or quantum fields propagating on this background have not been widely studied, and, in particular, the question of whether super-radiance occurs has not been addressed. This is an important issue since a detailed understanding of classical super-radiance is necessary before tackling quantum field theory on rotating black hole geometries 3. We considered a classical scalar field on the KN-AdS background 4, and examined the form of the separated field modes. Given the structure of infinity in asymptotically anti-de Sitter space-times, we paid particular attention to the boundary conditions at infinity. Unlike the situation for asymptotically flat Kerr-Newman black holes 5, super-radiance is not inevitable. It depends partly on our choice of boundary condition at infinity. For reflective boundary conditions at infinity, there is no super-radiance. On the other hand, if we consider transparent boundary conditions at infinity, then the presence of super-radiance depends on our choice of positive frequency. For those KN-AdS black holes possessing a globally time-like Killing vector, then the natural definition of positive frequency implies that there are no super-radiant modes. For other KN-AdS black holes, then this same definition of positive frequency again leads to no super-radiance.

The metric and curvature properties of H -space

1978 ◽  
Vol 363 (1715) ◽  
pp. 445-468 ◽  
Keyword(s):  
Taylor Series ◽  
Gravitational Radiation ◽  
Twistor Space ◽  
Flat Space ◽  
Contour Integral ◽  
Integral Expression ◽  
Asymptotically Flat ◽  
Einstein Vacuum Equations ◽  
Einstein Vacuum ◽  
Flat Solution

The space H of asymptotically (left-) shear-free cuts of the J + (good cuts) of an asymptotically flat space-time M is defined. The connection between this space and the asymptotic projective twistor space PJ of M is discussed, and this relation is used to prove that H is four-complex-dimensional for sufficiently ‘calm’ gravitational radiation in M . The metric on H -space is defined by a simple contour integral expression and is found to be complex Riemannian. The good cut equation governing H -space is solved to three orders by a Taylor series and the solution is used to demonstrate that the curvature of H -space is always a self dual (left flat) solution of the Einstein vacuum equations.

scholarly journals Shape Sensing of a Complex Aeronautical Structure with Inverse Finite Element Method

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1388
Author(s):  
Daniele Oboe ◽  
Luca Colombo ◽  
Claudio Sbarufatti ◽  
Marco Giglio
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Strain Field ◽  
Element Analysis ◽  
Inverse Finite Element Method ◽  
Shape Sensing ◽  
Definition Of ◽  
High Level ◽  
Element Method

The inverse Finite Element Method (iFEM) is receiving more attention for shape sensing due to its independence from the material properties and the external load. However, a proper definition of the model geometry with its boundary conditions is required, together with the acquisition of the structure’s strain field with optimized sensor networks. The iFEM model definition is not trivial in the case of complex structures, in particular, if sensors are not applied on the whole structure allowing just a partial definition of the input strain field. To overcome this issue, this research proposes a simplified iFEM model in which the geometrical complexity is reduced and boundary conditions are tuned with the superimposition of the effects to behave as the real structure. The procedure is assessed for a complex aeronautical structure, where the reference displacement field is first computed in a numerical framework with input strains coming from a direct finite element analysis, confirming the effectiveness of the iFEM based on a simplified geometry. Finally, the model is fed with experimentally acquired strain measurements and the performance of the method is assessed in presence of a high level of uncertainty.

scholarly journals Computational Analysis of the Pulmonary Arteries in Congenital Heart Disease: A Review of the Methods and Results

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
M. Conijn ◽  
G. J. Krings
Keyword(s):  
Congenital Heart Disease ◽  
Heart Disease ◽  
Boundary Conditions ◽  
Congenital Heart ◽  
Treatment Options ◽  
Pulmonary Arteries ◽  
Original Research ◽  
Numerical Studies ◽  
Computational Fluid Dynamics Cfd ◽  
Definition Of

With the help of computational fluid dynamics (CFD), hemodynamics of the pulmonary arteries (PA’s) can be studied in detail and varying physiological circumstances and treatment options can be simulated. This offers the opportunity to improve the diagnostics and treatment of PA stenosis in biventricular congenital heart disease (CHD). The aim of this review was to evaluate the methods of computational studies for PA’s in biventricular CHD and the level of validation of the numerical outcomes. A total of 34 original research papers were selected. The literature showed a great variety in the used methods for (re) construction of the geometry as well as definition of the boundary conditions and numerical setup. There were 10 different methods identified to define inlet boundary conditions and 17 for outlet boundary conditions. A total of nine papers verified their CFD outcomes by comparing results to clinical data or by an experimental mock loop. The diversity in used methods and the low level of validation of the outcomes result in uncertainties regarding the reliability of numerical studies. This limits the current clinical utility of CFD for the study of PA flow in CHD. Standardization and validation of the methods are therefore recommended.

scholarly journals Investigating the Effect of Solid Boundaries on the Gas Molecular Mean-Free-Path

2009 ◽  
Author(s):  
Erik J. Arlemark ◽  
Jason M. Reese
Keyword(s):  
Molecular Dynamics ◽  
Boundary Conditions ◽  
Free Path ◽  
Mean Free Path ◽  
Gas Flows ◽  
Standard Temperature ◽  
Binary Collisions ◽  
The Mean ◽  
Temperature And Pressure ◽  
Definition Of

A key parameter for micro-gas-flows, the mean free path, is investigated in this paper. The mean free path is used in various models for predicting micro gas flows, both in the governing equations and their boundary conditions. The conventional definition of the mean free path is based on the assumption that only binary collisions occur and is commonly described using the macroscopic quantities density, viscosity and temperature. In this paper we compare the prediction by this definition of the mean free paths for helium, neon and argon gases under standard temperature and pressure conditions, with the mean free paths achieved by measurements of individual molecules using the numerical simulation technique of molecular dynamics. Our simulation using molecular dynamics consists of a cube with six periodic boundary conditions, allowing us to simulate an unconfined gas “package”. Although, the size of this package is important, since its impact on computational cost is considerable, it is also important to have enough simulated molecules to average data from. We find that the molecular dynamics method using 20520 simulated molecules yields results that are within 1% accuracy from the conventional definition of the mean free paths for neon and argon and within 2.5% for helium. We can also conclude that the normal approximation of only considering binary collisions is seemingly adequate for these gases under standard temperature and pressure conditions. We introduce a single planar wall and two parallel planar walls to the simulated gas of neon and record the mean free paths at various distances to the walls. It is found that the mean free paths affected by molecular collisions with the walls corresponds well with theoretical models up to Knudsen numbers of 0.2.

scholarly journals The Thermodynamic Relationship between the RN-AdS Black Holes and the RN Black Hole in Canonical Ensemble

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Yu-Bo Ma ◽  
Li-Chun Zhang ◽  
Jian Liu ◽  
Ren Zhao ◽  
Shuo Cao
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Flat Space ◽  
Space Time ◽  
Asymptotically Flat ◽  
Time Space ◽  
Ads Black Holes ◽  
Different Types ◽  
Thermodynamic Relationship ◽  
The Relationship

In this paper, by analyzing the thermodynamic properties of charged AdS black hole and asymptotically flat space-time charged black hole in the vicinity of the critical point, we establish the correspondence between the thermodynamic parameters of asymptotically flat space-time and nonasymptotically flat space-time, based on the equality of black hole horizon area in the two different types of space-time. The relationship between the cavity radius (which is introduced in the study of asymptotically flat space-time charged black holes) and the cosmological constant (which is introduced in the study of nonasymptotically flat space-time) is determined. The establishment of the correspondence between the thermodynamics parameters in two different types of space-time is beneficial to the mutual promotion of different time-space black hole research, which is helpful to understand the thermodynamics and quantum properties of black hole in space-time.

REVISITING Xor-IMPLICATIONS: CLASSES OF FUZZY (CO)IMPLICATIONS BASED ON f-Xor (f-XNor) CONNECTIVES

2013 ◽  
Vol 21 (06) ◽  
pp. 899-925 ◽  
Author(s):  
BENJAMÍN BEDREGAL ◽  
RENATA HAX SANDER REISER ◽  
GRAÇALIZ PEREIRA DIMURO
Keyword(s):  
Boundary Conditions ◽  
Unit Interval ◽  
End Points ◽  
Triangular Norms ◽  
Fuzzy Implications ◽  
Classical Definition ◽  
Definition Of ◽  
Exclusive Or ◽  
Intrinsic Definition ◽  
Fuzzy Connectives

The main contribution of this paper is the introduction of an intrinsic definition of the connective “fuzzy exclusive or” E (f-Xor E), based only on the properties of boundary conditions, commutativity and partial isotonicity-antitonicity on the the end-points of the unit interval U = [0,1], in a way that the classical definition of the boolean Xor is preserved. We show three classes of the f-Xor E that can be also obtained from the composition of fuzzy connectives, namely, triangular norms, triangular conorms and fuzzy negations. A discussion about extra properties satisfied by the f-Xor E is presented. Additionally, the paper introduces a class of fuzzy equivalences that generalizes the Fodor and Roubens's fuzzy equivalence, and four classes of fuzzy implications induced by the f-Xor E, discussing their main properties. The relationships between those classes of fuzzy implications and automorphisms are explored. The action of automorphisms on f-Xor E is analyzed.

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