Search results for " frame"
showing 10 items of 1365 documents
One pendulum to run them all
2013
The analytical solution for the three-dimensional linear pendulum in a rotating frame of reference is obtained, including Coriolis and centrifugal accelerations, and expressed in terms of initial conditions. This result offers the possibility of treating Foucault and Bravais pendula as trajectories of the same system of equations, each of them with particular initial conditions. We compare them with the common two-dimensional approximations in textbooks. A previously unnoticed pattern in the three-dimensional Foucault pendulum attractor is presented.
Observational effects of varying speed of light in quadratic gravity cosmological models
2017
We study different manifestations of the speed of light in theories of gravity where metric and connection are regarded as independent fields. We find that for a generic gravity theory in a frame with locally vanishing affine connection, the usual degeneracy between different manifestations of the speed of light is broken. In particular, the space-time causal structure constant ([Formula: see text]) may become variable in that local frame. For theories of the form [Formula: see text], this variation in [Formula: see text] has an impact on the definition of the luminosity distance (and distance modulus), which can be used to confront the predictions of particular models against Supernovae t…
Relativistic Magnetohydrodynamics: Renormalized eigenvectors and full wave decomposition Riemann solver
2010
We obtain renormalized sets of right and left eigenvectors of the flux vector Jacobians of the relativistic MHD equations, which are regular and span a complete basis in any physical state including degenerate ones. The renormalization procedure relies on the characterization of the degeneracy types in terms of the normal and tangential components of the magnetic field to the wavefront in the fluid rest frame. Proper expressions of the renormalized eigenvectors in conserved variables are obtained through the corresponding matrix transformations. Our work completes previous analysis that present different sets of right eigenvectors for non-degenerate and degenerate states, and can be seen as…
Feynman diagrams as a weight system: four-loop test of a four-term relation
1996
At four loops there first occurs a test of the four-term relation derived by the second author in the course of investigating whether counterterms from subdivergence-free diagrams form a weight system. This test relates counterterms in a four-dimensional field theory with Yukawa and $\phi^4$ interactions, where no such relation was previously suspected. Using integration by parts, we reduce each counterterm to massless two-loop two-point integrals. The four-term relation is verified, with $ = 0 - 3\zeta_3 + 6\zeta_3 - 3\zeta_3 = 0$, demonstrating non-trivial cancellation of the trefoil knot and thus supporting the emerging connection between knots and counterterms, via transcendental number…
The dynamics of bunched laser-cooled ion beams at relativistic energies
2007
We discuss the axial dynamics of laser-cooled relativistic C3+ ion beams at moderate bunching voltages. Schottky noise spectra measured at a beam energy of 122 MeV/u are compared to simulations of the axial beam dynamics. Ions confined in the bucket are addressed by the narrow-band force of a laser beam counter-propagating to the ion beam, while the laser frequency is detuned relatively to the cooling transition frequency in the rest frame of the bucket. At large detuning comparable to the momentum acceptance of the bucket, the axial dynamics can be well explained by the secular motion of individual non-interacting ions. At small detuning, corresponding to a small axial momentum spread Δpax…
APPROXIMATE INERTIAL MANIFOLDS FOR THERMODIFFUSION EQUATIONS
2004
In this paper, we consider the two dimensional equations of thermohydraulics, i.e. the coupled system of equations of fluid and temperature in the Boussinesq approximation. We construct a family of approximate Inertial Manifolds whose order decreases exponentially fast with respect to the dimension of the manifold. We give the explicit expression of the order of the constructed manifolds.
Chiral excitations of magnetic droplet solitons driven by their own inertia
2019
The inertial effects of magnetic solitons play a crucial role in their dynamics and stability. Yet governing their inertial effects is a challenge for their use in real devices. Here, we show how to control the inertial effects of magnetic droplet solitons. Magnetic droplets are strongly nonlinear and localized autosolitons than can form in current-driven nanocontacts. Droplets can be considered as dynamical particles with an effective mass. We show that the dynamical droplet bears a second excitation under its own inertia. These excitations comprise a chiral profile, and appear when the droplet resists the force induced by the Oersted field of the current injected into the nanocontact. We …
Non-linear axisymmetric pulsations of rotating relativistic stars in the conformal flatness approximation
2005
We study non-linear axisymmetric pulsations of rotating relativistic stars using a general relativistic hydrodynamics code under the assumption of a conformal flatness. We compare our results to previous simulations where the spacetime dynamics was neglected. The pulsations are studied along various sequences of both uniformly and differentially rotating relativistic polytropes with index N = 1. We identify several modes, including the lowest-order l = 0, 2, and 4 axisymmetric modes, as well as several axisymmetric inertial modes. Differential rotation significantly lowers mode frequencies, increasing prospects for detection by current gravitational wave interferometers. We observe an exten…
Relativistic positioning: four-dimensional numerical approach in Minkowski space-time
2011
We simulate the satellite constellations of two Global Navigation Satellite Systems: Galileo (EU) and GPS (USA). Satellite motions are described in the Schwarzschild space-time produced by an idealized spherically symmetric non rotating Earth. The trajectories are then circumferences centered at the same point as Earth. Photon motions are described in Minkowski space-time, where there is a well known relation, Coll, Ferrando & Morales-Lladosa (2010), between the emission and inertial coordinates of any event. Here, this relation is implemented in a numerical code, which is tested and applied. The first application is a detailed numerical four-dimensional analysis of the so-called emissi…
Relativistic positioning: errors due to uncertainties in the satellite world lines
2014
Global navigation satellite systems use appropriate satellite constellations to get the coordinates of an user -close to Earth- in an almost inertial reference system. We have simulated both GPS and GALILEO constellations. Uncertainties in the satellite world lines lead to dominant positioning errors. In this paper, a detailed analysis of these errors is developed inside a great region surrounding Earth. This analysis is performed in the framework of the so-called relativistic positioning systems. Our study is based on the Jacobian, J, of the transformation giving the emission coordinates in terms of the inertial ones. Around points of vanishing J, positioning errors are too large. We show …