343 research outputs found
Equivariant symbol calculus for differential operators acting on forms
We prove the existence and uniqueness of a projectively equivariant symbol
map (in the sense of Lecomte and Ovsienko) for the spaces of differential
operators transforming p-forms into functions. These results hold over a smooth
manifold endowed with a flat projective structure.
As an application, we classify the Vect(M)-equivariant maps from to
over any manifold M, recovering and improving earlier results by N.
Poncin. This provides the complete answer to a question raised by P. Lecomte
about the extension of a certain intrinsic homotopy operator.Comment: 14 page
Impact of the frequency dependence of tidal Q on the evolution of planetary systems
Context. Tidal dissipation in planets and in stars is one of the key physical
mechanisms that drive the evolution of planetary systems.
Aims. Tidal dissipation properties are intrisically linked to the internal
structure and the rheology of studied celestial bodies. The resulting
dependence of the dissipation upon the tidal frequency is strongly different in
the cases of solids and fluids.
Methods. We compute the tidal evolution of a two-body coplanar system, using
the tidal quality factor's frequency-dependencies appropriate to rocks and to
convective fluids.
Results. The ensuing orbital dynamics comes out smooth or strongly erratic,
dependent on how the tidal dissipation depends upon frequency.
Conclusions. We demonstrate the strong impact of the internal structure and
of the rheology of the central body on the orbital evolution of the tidal
perturber. A smooth frequency-dependence of the tidal dissipation renders a
smooth orbital evolution while a peaked dissipation can furnish erratic orbital
behaviour.Comment: Accepted for publication as a letter in Astronomy And Astrophysic
Time and frequency transfer with a microwave link in the ACES/PHARAO mission
The Atomic Clocks Ensemble in Space (ACES/PHARAO mission), which will be
installed on board the International Space Station (ISS), uses a dedicated
two-way Micro-Wave Link (MWL) in order to compare the timescale generated on
board with those provided by many ground stations disseminated on the Earth.
Phase accuracy and stability of this long range link will have a key role in
the success of the ACES/PHARAO experiment. SYRTE laboratory is heavily involved
in the design and development of the data processing software : from
theoretical modelling and numerical simulations to the development of a
software prototype. Our team is working on a wide range of problems that need
to be solved in order to achieve high accuracy in (almost) real time. In this
article we present some key aspects of the measurement, as well as current
status of the software's development.Comment: Proceedings of the European Frequency and Time Forum (EFTF) 2012 held
in Gothenburg, Sweden, April 201
Scaling laws to understand tidal dissipation in fluid planetary regions and stars I - Rotation, stratification and thermal diffusivity
Tidal dissipation in planets and stars is one of the key physical mechanisms
driving the evolution of star-planet and planet-moon systems. Several
signatures of its action are observed in planetary systems thanks to their
orbital architecture and the rotational state of their components. Tidal
dissipation inside the fluid layers of celestial bodies are intrinsically
linked to the dynamics and the physical properties of the latter. This complex
dependence must be characterized. We compute the tidal kinetic energy
dissipated by viscous friction and thermal diffusion in a rotating local fluid
Cartesian section of a star/planet/moon submitted to a periodic tidal forcing.
The properties of tidal gravito-inertial waves excited by the perturbation are
derived analytically as explicit functions of the tidal frequency and local
fluid parameters (i.e. the rotation, the buoyancy frequency characterizing the
entropy stratification, viscous and thermal diffusivities) for periodic normal
modes. The sensitivity of the resulting possibly highly resonant dissipation
frequency-spectra to a control parameter of the system is either important or
negligible depending on the position in the regime diagram relevant for
planetary and stellar interiors. For corresponding asymptotic behaviors of
tidal gravito-inertial waves dissipated by viscous friction and thermal
diffusion, scaling laws for the frequencies, number, width, height and contrast
with the non-resonant background of resonances are derived to quantify these
variations. We characterize the strong impact of the internal physics and
dynamics of fluid planetary layers and stars on the dissipation of tidal
kinetic energy in their bulk. We point out the key control parameters that
really play a role and demonstrate how it is now necessary to develop ab-initio
modeling for tidal dissipation in celestial bodies.Comment: 24 pages, 14 figures, accepted for publication in Astronomy &
Astrophysic
How to test SME with space missions ?
In this communication, we focus on possibilities to constrain SME
coefficients using Cassini and Messenger data. We present simulations of
radioscience observables within the framework of the SME, identify the linear
combinations of SME coefficients the observations depend on and determine the
sensitivity of these measurements to the SME coefficients. We show that these
datasets are very powerful for constraining SME coefficients.Comment: Presented at the Sixth Meeting on CPT and Lorentz Symmetry,
Bloomington, Indiana, June 17-21, 2013. 4 pages, 1 figur
Scaling laws to understand tidal dissipation in fluid planetary layers and stars
Tidal dissipation is known as one of the main drivers of the secular
evolution of planetary systems. It directly results from dissipative mechanisms
that occur in planets and stars' interiors and strongly depends on the
structure and dynamics of the bodies. This work focuses on the mechanism of
viscous friction in stars and planetary layers. A local model is used to study
tidal dissipation. It provides general scaling laws that give a qualitative
overview of the different possible behaviors of fluid tidal waves. Furthermore,
it highlights the sensitivity of dissipation to the tidal frequency and the
roles played by the internal parameters of the fluid such as rotation,
stratification, viscosity and thermal diffusivity that will impact the
spins/orbital architecture in planetary systems.Comment: 4 pages, 3 figures, IAU 310 symposium proceedings, Complex planetary
system
Tidal interactions in rotating multiple stars and their impact on their evolution
Tidal dissipation in stars is one of the key physical mechanisms that drive
the evolution of binary and multiple stars. As in the Earth oceans, it
corresponds to the resonant excitation of their eigenmodes of oscillation and
their damping. Therefore, it strongly depends on the internal structure,
rotation, and dissipative mechanisms in each component. In this work, we
present a local analytical modeling of tidal gravito-inertial waves excited in
stellar convective and radiative regions respectively. This model allows us to
understand in details the properties of the resonant tidal dissipation as a
function of the excitation frequencies, the rotation, the stratification, and
the viscous and thermal properties of the studied fluid regions. Then, the
frequencies, height, width at half-height, and number of resonances as well as
the non-resonant equilibrium tide are derived analytically in asymptotic
regimes that are relevant in stellar interiors. Finally, we demonstrate how
viscous dissipation of tidal waves leads to a strongly erratic orbital
evolution in the case of a coplanar binary system. We characterize such a
non-regular dynamics as a function of the height and width of resonances, which
have been previously characterized thanks to our local fluid model.Comment: 2 pages, 1 figure, IAU 307 symposium proceedings, New windows on
massive stars: asteroseismology, interferometry, and spectropolarimetry, Eds.
G. Meynet, C. Georgy, J. H. Groh, and P. Ste
Testing Gravitation in the Solar System with Radio Science experiments
The laws of gravitation have been tested for a long time with steadily
improving precision, leading at some moment of time to paradigmatic evolutions.
Pursuing this continual effort is of great importance for science. In this
communication, we focus on Solar System tests of gravity and more precisely on
possible tests that can be performed with radio science observations (Range and
Doppler). After briefly reviewing the current tests of gravitation at Solar
System scales, we give motivations to continue such experiments. In order to
obtain signature and estimate the amplitude of anomalous signals that could
show up in radio science observables because of modified gravitational laws, we
developed a new software that simulates Range/Doppler signals. We present this
new tool that simulates radio science observables directly from the space-time
metric. We apply this tool to the Cassini mission during its cruise from
Jupiter to Saturn and derive constraints on the parameters entering alternative
theories of gravity beyond the standard Parametrized Post Newtonian theory.Comment: proceedings of SF2A 2011 - minor changes (typos corrected -
references updated
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