Geometrization of linear perturbation theory for diffeomorphism-invariant covariant field equations. I. The notion of a gauge-invariant variable

1997 ◽  
Vol 36 (8) ◽  
pp. 1787-1816 ◽  
Author(s):  
Zbigniew Banach ◽  
Slawomir Piekarski
Keyword(s):  
Perturbation Theory ◽  
Linear Perturbation ◽  
Field Equations ◽  
Gauge Invariant ◽  
Invariant Variable ◽  
Linear Perturbation Theory ◽  
Covariant Field

Analytical linear perturbation theory for highly eccentric satellite orbits

1995 ◽  
Vol 61 (4) ◽  
pp. 369-387 ◽  
Author(s):  
Eugene Brumberg ◽  
Victor A. Brumberg ◽  
Thomas Konrad ◽  
Michael Soffel
Keyword(s):  
Perturbation Theory ◽  
Linear Perturbation ◽  
Satellite Orbits ◽  
Linear Perturbation Theory

Stability Features of the Saucer-Shaped Blend-Wing-Body Aircraft

2013 ◽  
Vol 712-715 ◽  
pp. 1307-1311
Author(s):  
Lin Lin Wang ◽  
Ge Gao
Keyword(s):  
Perturbation Theory ◽  
Longitudinal Mode ◽  
Flight Dynamics ◽  
Aerodynamic Characteristics ◽  
Linear Perturbation ◽  
Low Speed ◽  
Similarities And Differences ◽  
Linear Perturbation Theory ◽  
Dutch Roll ◽  
Directional Flight

The saucer-shaped aircraft is a novel aircraft adopting blend-wing-body configuration. The linear perturbation theory based on the classic flight dynamics was used to analyze the longitudinal, lateral and directional flight qualities of the saucer-shaped aircraft under low speed conditions. The flight qualities were given. Meanwhile the aerodynamic characteristics of the saucer-shaped aircraft, the conventional aircraft and the flying wing aircraft were also contrasted to discuss their similarities and differences. The results show that the saucer-shaped aircraft has stable longitudinal mode, rollover mode and Dutch roll mode. The spiral mode is unstable. The saucer-shaped aircraft exhibits superior flight qualities and excellent comprehensive performances.

scholarly journals Re-examination of Large Scale Structure & Cosmic Flows

2014 ◽  
Vol 11 (S308) ◽  
pp. 310-317
Author(s):  
Marc Davis ◽  
Adi Nusser
Keyword(s):  
Perturbation Theory ◽  
Velocity Field ◽  
Gravity Field ◽  
Inverse Method ◽  
Large Scale ◽  
Linear Perturbation ◽  
Data Set ◽  
Galaxy Distribution ◽  
Standard Values ◽  
Linear Perturbation Theory

AbstractComparison of galaxy flows with those predicted from the local galaxy distribution ended as an active field after two analyses came to vastly different conclusions 25 years ago, but that was due to faulty data. All the old results are therefore suspect. With new data collected in the last several years, the problem deserves another look. The goal is to explain the 640 km/s dipole anisotropy of the CMBR. For this we analyze the gravity field inferred from the enormous data set derived from the 2MASS collection of galaxies (Huchra et al. 2005), and compare it to the velocity field derived from the well calibrated SFI++ Tully-Fisher catalog (Springob et al. 2007). Using the “Inverse Method” to minimize Malmquist biases, within 10,000 km/s the gravity field is seen to predict the velocity field (Davis et al. 2011) to remarkable consistency. This is a beautiful demonstration of linear perturbation theory and is fully consistent with standard values of the cosmological variables.

scholarly journals The Lynden-Bell bar formation mechanism in simple and realistic galactic models

2020 ◽  
Vol 498 (3) ◽  
pp. 3368-3373
Author(s):  
E V Polyachenko ◽  
I G Shukhman
Keyword(s):  
Perturbation Theory ◽  
Angular Momentum ◽  
Formation Mechanism ◽  
Linear Perturbation ◽  
Matrix Approach ◽  
Precession Rate ◽  
Secular Evolution ◽  
The Matrix ◽  
Linear Perturbation Theory ◽  
Bar Formation

ABSTRACT Using the canonical Hamilton–Jacobi approach we study the Lynden-Bell concept of bar formation based on the idea of orbital trapping parallel to the long or short axes of the oval potential distortion. The concept considered a single parameter – a sign of the derivative of the precession rate over angular momentum, determining the orientation of the trapped orbits. We derived a perturbation Hamiltonian that includes two more parameters characterizing the background disc and the perturbation, which are just as important as the earlier known one. This allows us to link the concept with the matrix approach in linear perturbation theory, the theory of weak bars, and explain some features of the non-linear secular evolution observed in N-body simulations.

scholarly journals In-vivo tissue optical properties derived by linear perturbation theory for edge-corrected time-domain mammograms

2005 ◽  
Vol 13 (21) ◽  
pp. 8571 ◽  
Author(s):  
B. Wassermann ◽  
A. Kummrow ◽  
K. T. Moesta ◽  
D. Grosenick ◽  
J. Mucke ◽  
...  
Keyword(s):  
Optical Properties ◽  
Perturbation Theory ◽  
Time Domain ◽  
Linear Perturbation ◽  
Tissue Optical Properties ◽  
Linear Perturbation Theory

scholarly journals SCALAR DEFORMATIONS OF SCHWARZSCHILD HOLES AND THEIR STABILITY

1998 ◽  
Vol 13 (05) ◽  
pp. 741-764 ◽  
Author(s):  
HELGE DENNHARDT ◽  
OLAF LECHTENFELD
Keyword(s):  
Scalar Field ◽  
Energy Condition ◽  
Linear Perturbation ◽  
Dominant Energy Condition ◽  
Stability Criteria ◽  
Field Equations ◽  
Effective Potentials ◽  
Scalar Hair ◽  
Linear Perturbation Theory ◽  
Scalar Field Equations

We construct two solutions of the minimally coupled Einstein-scalar field equations, representing regular deformations of Schwarzschild black holes by a self-interacting, static, scalar field. One solution features an exponentially decaying scalar field and a triple-well interaction potential; the other one is completely analytic and sprouts Coulomb-like scalar hair. Both evade the no-hair theorem by having partially negative potential, in conflict with the dominant energy condition. The linear perturbation theory around such backgrounds is developed in general, and yields stability criteria in terms of effective potentials for an analog Schrödinger problem. We can test for more than half of the perturbation modes, and our solutions prove to be stable against those.

scholarly journals Simulation of the loss-cone instability in spherical systems – I. Dominating harmonic potential

2019 ◽  
Vol 492 (1) ◽  
pp. 645-650 ◽  
Author(s):  
E V Polyachenko ◽  
P Berczik ◽  
A Just ◽  
I G Shukhman
Keyword(s):  
Perturbation Theory ◽  
Star Clusters ◽  
Spherical Geometry ◽  
Oort Cloud ◽  
Harmonic Potential ◽  
Linear Perturbation ◽  
Stellar Systems ◽  
Physical Processes ◽  
Loss Cone ◽  
Linear Perturbation Theory

ABSTRACT A new so-called ‘gravitational loss-cone instability’ in stellar systems has recently been investigated theoretically in the framework of linear perturbation theory and proved to be potentially important in understanding the physical processes in centres of galaxies, star clusters, and the Oort Cloud. Using N-body simulations of a toy model, we confirm previous findings for the dominating harmonic potential and go beyond the linear theory. Unlike the well-known instabilities, the new one shows no notable change in the spherical geometry of the cluster, but it significantly accelerates the speed of diffusion of particles in phase space leading to an early instability saturation.

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