scholarly journals Operational Significance of the Deviation Equation in Relativistic Geodesy

2018 ◽  
pp. 1-6
Author(s):  
Dirk Puetzfeld ◽  
Yuri N. Obukhov
Keyword(s):  
Deviation Equation

scholarly journals Dimensional reduction of the 5D Kaluza–Klein geodesic deviation equation

2009 ◽  
Vol 42 (2) ◽  
pp. 359-366
Author(s):  
V. Lacquaniti ◽  
Giovanni Montani ◽  
F. Vietri
Keyword(s):  
Dimensional Reduction ◽  
Geodesic Deviation ◽  
Deviation Equation ◽  
Geodesic Deviation Equation ◽  
Kaluza Klein

scholarly journals k-Jet field approximations to geodesic deviation equations

2018 ◽  
Vol 15 (12) ◽  
pp. 1850199
Author(s):  
Ricardo Gallego Torromé ◽  
Jonathan Gratus
Keyword(s):  
Differential Equations ◽  
Tangent Bundle ◽  
Jacobi Equation ◽  
Smooth Manifold ◽  
Specific Class ◽  
Coordinate Transformations ◽  
Geodesic Deviation ◽  
Deviation Equation ◽  
Geodesic Deviation Equation ◽  
Deviation Functions

Let [Formula: see text] be a smooth manifold and [Formula: see text] a semi-spray defined on a sub-bundle [Formula: see text] of the tangent bundle [Formula: see text]. In this work, it is proved that the only non-trivial [Formula: see text]-jet approximation to the exact geodesic deviation equation of [Formula: see text], linear on the deviation functions and invariant under an specific class of local coordinate transformations, is the Jacobi equation. However, if the linearity property on the dependence in the deviation functions is not imposed, then there are differential equations whose solutions admit [Formula: see text]-jet approximations and are invariant under arbitrary coordinate transformations. As an example of higher-order geodesic deviation equations, we study the first- and second-order geodesic deviation equations for a Finsler spray.

scholarly journals Simulating the complexity of the dark matter sheet I: numerical algorithms

2020 ◽  
Vol 495 (4) ◽  
pp. 4943-4964
Author(s):  
Jens Stücker ◽  
Oliver Hahn ◽  
Raul E Angulo ◽  
Simon D M White
Keyword(s):  
Dark Matter ◽  
Numerical Algorithms ◽  
Linear Structure ◽  
Small Scale ◽  
Deviation Equation ◽  
Unknown Amplitude ◽  
Low Mass ◽  
Force Resolution ◽  
Force Calculation ◽  
Matter Phase

ABSTRACT At early times, dark matter has a thermal velocity dispersion of unknown amplitude which, for warm dark matter (WDM) models, can influence the formation of non-linear structure on observable scales. We propose a new scheme to simulate cosmologies with a small-scale suppression of perturbations that combines two previous methods in a way that avoids the numerical artefacts which have so far prevented either from producing fully reliable results. At low densities and throughout most of the cosmological volume, we represent the dark matter phase sheet directly using high-accuracy interpolation, thereby avoiding the artificial fragmentation which afflicts particle-based methods in this regime. Such phase-sheet methods are, however, unable to follow the rapidly increasing complexity of the denser regions of dark matter haloes, so for these we switch to an N-body scheme which uses the geodesic deviation equation to track phase-sheet properties local to each particle. In addition, we present a novel high-resolution force calculation scheme based on an oct-tree of cubic force resolution elements which is well suited to approximate the force field of our combined sheet+particle distribution. Our hybrid simulation scheme enables the first reliable simulations of the internal structure of low-mass haloes in a WDM cosmology.

scholarly journals Relativistic top deviation equation and gravitational waves

2003 ◽  
Vol 312 (3-4) ◽  
pp. 175-186 ◽  
Author(s):  
J.A. Nieto ◽  
J. Saucedo ◽  
V.M. Villanueva
Keyword(s):  
Gravitational Waves ◽  
Deviation Equation

scholarly journals Erratum to: Geodesic deviation equation in f(R) gravity

2015 ◽  
Vol 47 (10) ◽  
Author(s):  
Alejandro Guarnizo ◽  
Leonardo Castañeda ◽  
Juan M. Tejeiro
Keyword(s):  
Geodesic Deviation ◽  
Deviation Equation ◽  
Geodesic Deviation Equation

A coordinate‐free derivation of a generalized geodesic deviation equation

1983 ◽  
Vol 24 (4) ◽  
pp. 883-885 ◽  
Author(s):  
N. S. Swaminarayan ◽  
J. L. Safko
Keyword(s):  
Geodesic Deviation ◽  
Deviation Equation ◽  
Geodesic Deviation Equation

scholarly journals Geodesic deviation equation in Bianchi cosmologies

2010 ◽  
Vol 229 ◽  
pp. 012076 ◽  
Author(s):  
D L Cáceres ◽  
L Castañeda ◽  
J M Tejeiro
Keyword(s):  
Geodesic Deviation ◽  
Deviation Equation ◽  
Geodesic Deviation Equation ◽  
Bianchi Cosmologies

scholarly journals QUANTUM MECHANICS OF A CHARGED PARTICLE IN A BACKGROUND MAGNETIC FIELD INTERACTING WITH LINEARIZED GRAVITATIONAL WAVES

2012 ◽  
Vol 27 (35) ◽  
pp. 1250192 ◽  
Author(s):  
SUNANDAN GANGOPADHYAY ◽  
ANIRBAN SAHA
Keyword(s):  
Charged Particle ◽  
Gravitational Waves ◽  
Quantum Dynamics ◽  
Resonance Condition ◽  
Close Association ◽  
Wave Length ◽  
Geodesic Equation ◽  
Low Velocity ◽  
Deviation Equation ◽  
Background Magnetic Field

We present the quantum dynamics of a charged particle interacting simultaneously with background electromagnetic field and linearized gravitational waves in the long wave-length and low-velocity limit. We start from the geodesic deviation equation, considering its close association with the proper detector frame, rather than the usual geodesic equation which is solved classically in the existing literature. The Hamiltonian is obtained, quantized and solved by using algebraic iterative methods. The solution shows conformity with the classical analysis by exhibiting the same resonance condition.

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