scholarly journals The first-order symmetry operator on gravitational perturbations in the 5D Myers–Perry spacetime with equal angular momenta

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Masataka Tsuchiya ◽  
Tsuyoshi Houri ◽  
Chul Moon Yoo
Keyword(s):  
Field Equation ◽  
Linear Combination ◽  
Symmetry Operator ◽  
First Order ◽  
Gravitational Perturbations ◽  
Angular Momenta ◽  
Mode Decomposition ◽  
Vacuum Spacetime ◽  
Infinitesimal Transformations ◽  
Metric Perturbation

Abstract It has been revealed that the first-order symmetry operator for the linearized Einstein equation on a vacuum spacetime can be constructed from a Killing–Yano 3-form. This might be used to construct all or part of the solutions to the field equation. In this paper, we perform a mode decomposition of a metric perturbation on the Schwarzschild spacetime and the Myers–Perry spacetime with equal angular momenta in 5 dimensions, and investigate the action of the symmetry operator on specific modes concretely. We show that, on such spacetimes, there is no transition between the modes of a metric perturbation by the action of the symmetry operator, and it ends up being the linear combination of the infinitesimal transformations of isometry.

Two-dimensional empirical mode decomposition by finite elements

2006 ◽  
Vol 462 (2074) ◽  
pp. 3081-3096 ◽  
Author(s):  
Y Xu ◽  
B Liu ◽  
J Liu ◽  
S Riemenschneider
Keyword(s):  
Finite Element ◽  
Linear Combination ◽  
Empirical Mode Decomposition ◽  
Spline Interpolation ◽  
Basis Functions ◽  
Two Dimensional ◽  
Element Analysis ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Mode Decomposition

Empirical mode decomposition (EMD) is a powerful tool for analysis of non-stationary and nonlinear signals, and has drawn significant attention in various engineering application areas. This paper presents a finite element-based EMD method for two-dimensional data analysis. Specifically, we represent the local mean surface of the data, a key step in EMD, as a linear combination of a set of two-dimensional linear basis functions smoothed with bi-cubic spline interpolation. The coefficients of the basis functions in the linear combination are obtained from the local extrema of the data using a generalized low-pass filter. By taking advantage of the principle of finite-element analysis, we develop a fast algorithm for implementation of the EMD. The proposed method provides an effective approach to overcome several challenging difficulties in extending the original one-dimensional EMD to the two-dimensional EMD. Numerical experiments using both simulated and practical texture images show that the proposed method works well.

scholarly journals A unified mode decomposition method for physical fields in homogeneous cosmology

2014 ◽  
Vol 26 (03) ◽  
pp. 1430001 ◽  
Author(s):  
Zhirayr G. Avetisyan
Keyword(s):  
Fourier Transform ◽  
Field Equation ◽  
Scalar Field ◽  
Vector Bundle ◽  
Fourier Analysis ◽  
Homogeneous Spaces ◽  
Unified Framework ◽  
Mode Decomposition ◽  
Physical Fields ◽  
Homogeneous Vector Bundle

The methods of mode decomposition and Fourier analysis of classical and quantum fields on curved spacetimes previously available mainly for the scalar field on Friedman–Robertson–Walker (FRW) spacetimes are extended to arbitrary vector bundle fields on general spatially homogeneous spacetimes. This is done by developing a rigorous unified framework which incorporates mode decomposition, harmonic analysis and Fourier analysis. The limits of applicability and uniqueness of mode decomposition by separation of the time variable in the field equation are found. It is shown how mode decomposition can be naturally extended to weak solutions of the field equation under some analytical assumptions. It is further shown that these assumptions can always be fulfilled if the vector bundle under consideration is analytic. The propagator of the field equation is explicitly mode decomposed. A short survey on the geometry of the models considered in mathematical cosmology is given and it is concluded that practically all of them can be represented by a semidirect homogeneous vector bundle. Abstract harmonic analytical Fourier transform is introduced in semidirect homogeneous spaces and it is explained how it can be related to the spectral Fourier transform. The general form of invariant bi-distributions on semidirect homogeneous spaces is found in the Fourier space which generalizes earlier results for the homogeneous states of the scalar field on FRW spacetimes.

Notizen: Quantum Mechanical Calculation of Collision Integrals for HD

1971 ◽  
Vol 26 (11) ◽  
pp. 1926-1928 ◽  
Author(s):  
W. E. Köhler
Keyword(s):  
Scattering Amplitude ◽  
Quantum Mechanical ◽  
Collision Term ◽  
Tensor Polarization ◽  
Collision Integrals ◽  
First Order ◽  
Relaxation Coefficient ◽  
Angular Momenta ◽  
Experimental Values ◽  
Good Agreement

The magnetic Senftleben-Beenakker effect of the viscosity is mainly determined by two collision integrals of the linearized quantum mechanical Waldmann-Snider collision term, viz. by the relaxation coefficient of the tensor polarization of the molecular rotational angular momenta and by the coefficient which couples the friction pressure tensor and the tensor polarization. Starting from a simple nonspherical potential for HD, the scattering amplitude is evaluated analytically in first order distorted wave Born approximation and the two collision integrals are calculated for room temperature. A fairly good agreement with experimental values is found.

Klassische Größen und quantenmechanische Operatoren in allgemeinen Koordinaten

1968 ◽  
Vol 23 (2) ◽  
pp. 199-203 ◽  
Author(s):  
H. Näpfel ◽  
H. Ruder ◽  
H. Volz
Keyword(s):  
Quantum Case ◽  
Angular Momenta ◽  
Translation Rule ◽  
Infinitesimal Transformations

A method is given to find, in general coordinates, expressions for dynamical quantities connected with infinitesimal transformations. The classical and the corresponding quantum case are considered. A simple translation rule between the two cases is derived by comparison. The efficiency of the method is demonstrated in the example of angular momenta.

scholarly journals Reduction of static field equation of Faddeev model to first order PDE

2007 ◽  
Vol 652 (5-6) ◽  
pp. 384-387 ◽  
Author(s):  
Minoru Hirayama ◽  
Chang-Guang Shi
Keyword(s):  
Field Equation ◽  
Static Field ◽  
First Order ◽  
First Order Pde ◽  
Faddeev Model

TOWARDS THE SIEGEL RING IN GENUS FOUR

2008 ◽  
Vol 04 (04) ◽  
pp. 563-586 ◽  
Author(s):  
MANABU OURA ◽  
CRIS POOR ◽  
DAVID S. YUEN
Keyword(s):  
Linear Combination ◽  
Irreducible Component ◽  
Modular Forms ◽  
Quotient Ring ◽  
Siegel Modular Forms ◽  
Weight Enumerators ◽  
New Techniques ◽  
First Order ◽  
The Difference ◽  
Infinite Set

Runge gave the ring of genus three Siegel modular forms as a quotient ring, R3/〈J(3)〉 where R3 is the genus three ring of code polynomials and J(3) is the difference of the weight enumerators for the e8 ⊕ e8 and [Formula: see text] codes. Freitag and Oura gave a degree 24 relation, [Formula: see text], of the corresponding ideal in genus four; where [Formula: see text] is also a linear combination of weight enumerators. We take another step towards the ring of Siegel modular forms in genus four. We explain new techniques for computing with Siegel modular forms and actually compute six new relations, classifying all relations through degree 32. We show that the local codimension of any irreducible component defined by these known relations is at least 3 and that the true ideal of relations in genus four is not a complete intersection. Also, we explain how to generate an infinite set of relations by symmetrizing first order theta identities and give one example in degree 32. We give the generating function of R5 and use it to reprove results of Nebe [25] and Salvati Manni [37].

scholarly journals Examples of linear multi-box splines

2012 ◽  
Vol 15 ◽  
pp. 444-462
Author(s):  
Abdellatif Bettayeb
Keyword(s):  
Linear Combination ◽  
Piecewise Linear ◽  
Linear Functions ◽  
Order Derivative ◽  
Box Splines ◽  
Piecewise Linear Functions ◽  
Finite Linear Combination ◽  
First Order ◽  
Box Spline ◽  
Finite Linear

AbstractLet S1=S1(v0,…,vr+1) be the space of compactly supported C0 piecewise linear functions on a mesh M of lines through ℤ2 in directions v0,…,vr+1, possibly satisfying some restrictions on the jumps of the first order derivative. A sequence ϕ=(ϕ1,…,ϕr) of elements of S1 is called a multi-box spline if every element of S1 is a finite linear combination of shifts of (the components of) ϕ. We give some examples for multi-box splines and show that they are stable. It is further shown that any multi-box spline is not always symmetric

scholarly journals Modeling Dark Sector in Horndeski Gravity at First-Order Formalism

2019 ◽  
Vol 2019 ◽  
pp. 1-8
Author(s):  
F. F. Santos ◽  
R. M. P. Neves ◽  
F. A. Brito
Keyword(s):  
Dark Energy ◽  
Field Equation ◽  
Scalar Field ◽  
Free Choice ◽  
Scalar Potential ◽  
Late Time ◽  
De Sitter ◽  
Dark Sector ◽  
First Order ◽  
Cosmological Scenario

We investigate a cosmological scenario by finding solutions using first-order formalism in the Horndeski gravity that constrains the superpotential and implies that no free choice of scalar potential is allowed. Despite this, we show that a de Sitter phase at late-time cosmology can be realized, where the dark energy sector can be identified. The scalar field equation of state tends to the cosmological scenario at present time and allows us to conclude that it can simulate the dark energy in the Horndeski gravity.

scholarly journals Asymptotic analysis of powers of matrices

2006 ◽  
Vol 2006 ◽  
pp. 1-12
Author(s):  
Diego Dominici
Keyword(s):  
Asymptotic Analysis ◽  
Linear Combination ◽  
Asymptotic Approximation ◽  
First Order

We analyze the representation ofAnas a linear combination ofAj,0≤j≤k−1, whereAis ak×kmatrix. We obtain a first-order asymptotic approximation ofAnasn→∞, without imposing any special conditions onA. We give some examples showing the application of our results.

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