3,923 research outputs found
Energetics and switching of quasi-uniform states in small ferromagnetic particles
We present a numerical algorithm to solve the micromagnetic equations based on tangential-plane minimization for the magnetization update and a homothethic-layer decomposition of outer space for the computation of the demagnetization field. As a first application, detailed results on the flower-vortex transition in the cube of Micromagnetic Standard Problem number 3 are obtained, which confirm, with a different method, those already present in the literature, and validate our method and code. We then turn to switching of small cubic or almost-cubic particles, in the single-domain limit. Our data show systematic deviations from the Stoner-Wohlfarth model due to the non-ellipsoidal shape of the particle, and in particular a non-monotone dependence on the particle size
Influence of the coorbital resonance on the rotation of the Trojan satellites of Saturn
The Cassini spacecraft collects high resolution images of the saturnian
satellites and reveals the surface of these new worlds. The shape and rotation
of the satellites can be determined from the Cassini Imaging Science Subsystem
data, employing limb coordinates and stereogrammetric control points. This is
the case for Epimetheus (Tiscareno et al. 2009) that opens elaboration of new
rotational models (Tiscareno et al. 2009; Noyelles 2010; Robutel et al. 2011).
Especially, Epimetheus is characterized by its horseshoe shape orbit and the
presence of the swap is essential to introduce explicitly into rotational
models. During its journey in the saturnian system, Cassini spacecraft
accumulates the observational data of the other satellites and it will be
possible to determine the rotational parameters of several of them. To prepare
these future observations, we built rotational models of the coorbital (also
called Trojan) satellites Telesto, Calypso, Helene, and Polydeuces, in addition
to Janus and Epimetheus. Indeed, Telesto and Calypso orbit around the L_4 and
L_5 Lagrange points of Saturn-Tethys while Helene and Polydeuces are coorbital
of Dione. The goal of this study is to understand how the departure from the
Keplerian motion induced by the perturbations of the coorbital body, influences
the rotation of these satellites. To this aim, we introduce explicitly the
perturbation in the rotational equations by using the formalism developed by
Erdi (1977) to represent the coorbital motions, and so we describe the
rotational motion of the coorbitals, Janus and Epimetheus included, in compact
form
Numerical approach for high precision 3-D relativistic star models
A multi-domain spectral method for computing very high precision 3-D stellar
models is presented. The boundary of each domain is chosen in order to coincide
with a physical discontinuity (e.g. the star's surface). In addition, a
regularization procedure is introduced to deal with the infinite derivatives on
the boundary that may appear in the density field when stiff equations of state
are used. Consequently all the physical fields are smooth functions on each
domain and the spectral method is absolutely free of any Gibbs phenomenon,
which yields to a very high precision. The power of this method is demonstrated
by direct comparison with analytical solutions such as MacLaurin spheroids and
Roche ellipsoids. The relative numerical error reveals to be of the order of
. This approach has been developed for the study of relativistic
inspiralling binaries. It may be applied to a wider class of astrophysical
problems such as the study of relativistic rotating stars too.Comment: Minor changes, Phys. Rev. D in pres
Algorithmic Verification of Continuous and Hybrid Systems
We provide a tutorial introduction to reachability computation, a class of
computational techniques that exports verification technology toward continuous
and hybrid systems. For open under-determined systems, this technique can
sometimes replace an infinite number of simulations.Comment: In Proceedings INFINITY 2013, arXiv:1402.661
Normal gravity field in relativistic geodesy
Modern geodesy is subject to a dramatic change from the Newtonian paradigm to
Einstein's theory of general relativity. This is motivated by the ongoing
advance in development of quantum sensors for applications in geodesy including
quantum gravimeters and gradientometers, atomic clocks and fiber optics for
making ultra-precise measurements of the geoid and multipolar structure of the
Earth's gravitational field. At the same time, VLBI, SLR, and GNSS have
achieved an unprecedented level of accuracy in measuring coordinates of the
reference points of the ITRF and the world height system. The main geodetic
reference standard is a normal gravity field represented in the Newtonian
gravity by the field of a Maclaurin ellipsoid. The present paper extends the
concept of the normal gravity field to the realm of general relativity. We
focus our attention on the calculation of the first post-Newtonian
approximation of the normal field that is sufficient for applications. We show
that in general relativity the level surface of the uniformly rotating fluid is
no longer described by the Maclaurin ellipsoid but is an axisymmetric spheroid
of the forth order. We parametrize the mass density distribution and derive the
post-Newtonian normal gravity field of the rotating spheroid which is given in
a closed form by a finite number of the ellipsoidal harmonics. We employ
transformation from the ellipsoidal to spherical coordinates to deduce the
post-Newtonian multipolar expansion of the metric tensor given in terms of
scalar and vector gravitational potentials of the rotating spheroid. We compare
these expansions with that of the normal gravity field generated by the Kerr
metric and demonstrate that the Kerr metric has a fairly limited application in
relativistic geodesy. Finally, we derive the post-Newtonian generalization of
the Somigliana formula for the gravity field on the reference ellipsoid.Comment: 39 pages, no figures, accepted to Physical Review
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