2,223 research outputs found
Planets in Mean-Motion Resonances and the System Around HD45364
In some planetary systems, the orbital periods of two of its members present
a commensurability, usually known by mean-motion resonance. These resonances
greatly enhance the mutual gravitational influence of the planets. As a
consequence, these systems present uncommon behaviors, and their motions need
to be studied with specific methods. Some features are unique and allow us a
better understanding and characterization of these systems. Moreover,
mean-motion resonances are a result of an early migration of the orbits in an
accretion disk, so it is possible to derive constraints on their formation.
Here we review the dynamics of a pair of resonant planets and explain how their
orbits evolve in time. We apply our results to the HD 45365 planetary system.Comment: invited review, 17 pages, 6 figure
Imaging the symmetry breaking of molecular orbitals in carbon nanotubes
Carbon nanotubes have attracted considerable interest for their unique
electronic properties. They are fascinating candidates for fundamental studies
of one dimensional materials as well as for future molecular electronics
applications. The molecular orbitals of nanotubes are of particular importance
as they govern the transport properties and the chemical reactivity of the
system. Here we show for the first time a complete experimental investigation
of molecular orbitals of single wall carbon nanotubes using atomically resolved
scanning tunneling spectroscopy. Local conductance measurements show
spectacular carbon-carbon bond asymmetry at the Van Hove singularities for both
semiconducting and metallic tubes, demonstrating the symmetry breaking of
molecular orbitals in nanotubes. Whatever the tube, only two types of
complementary orbitals are alternatively observed. An analytical tight-binding
model describing the interference patterns of ? orbitals confirmed by ab initio
calculations, perfectly reproduces the experimental results
Evolutionary Dynamics While Trapped in Resonance: A Keplerian Binary System Perturbed by Gravitational Radiation
The method of averaging is used to investigate the phenomenon of capture into
resonance for a model that describes a Keplerian binary system influenced by
radiation damping and external normally incident periodic gravitational
radiation. The dynamical evolution of the binary orbit while trapped in
resonance is elucidated using the second order partially averaged system. This
method provides a theoretical framework that can be used to explain the main
evolutionary dynamics of a physical system that has been trapped in resonance.Comment: REVTEX Style, Submitte
Dissipation in planar resonant planetary systems
Close-in planetary systems detected by the Kepler mission present an excess
of periods ratio that are just slightly larger than some low order resonant
values. This feature occurs naturally when resonant couples undergo dissipation
that damps the eccentricities. However, the resonant angles appear to librate
at the end of the migration process, which is often believed to be an evidence
that the systems remain in resonance.
Here we provide an analytical model for the dissipation in resonant planetary
systems valid for low eccentricities. We confirm that dissipation accounts for
an excess of pairs that lie just aside from the nominal periods ratios, as
observed by the Kepler mission. In addition, by a global analysis of the phase
space of the problem, we demonstrate that these final pairs are non-resonant.
Indeed, the separatrices that exist in the resonant systems disappear with the
dissipation, and remains only a circulation of the orbits around a single
elliptical fixed point. Furthermore, the apparent libration of the resonant
angles can be explained using the classical secular averaging method. We show
that this artifact is only due to the severe damping of the amplitudes of the
eigenmodes in the secular motion.Comment: 18 pages, 20 figures, accepted to A&
Stable manifolds and homoclinic points near resonances in the restricted three-body problem
The restricted three-body problem describes the motion of a massless particle
under the influence of two primaries of masses and that circle
each other with period equal to . For small , a resonant periodic
motion of the massless particle in the rotating frame can be described by
relatively prime integers and , if its period around the heavier primary
is approximately , and by its approximate eccentricity . We give a
method for the formal development of the stable and unstable manifolds
associated with these resonant motions. We prove the validity of this formal
development and the existence of homoclinic points in the resonant region.
In the study of the Kirkwood gaps in the asteroid belt, the separatrices of
the averaged equations of the restricted three-body problem are commonly used
to derive analytical approximations to the boundaries of the resonances. We use
the unaveraged equations to find values of asteroid eccentricity below which
these approximations will not hold for the Kirkwood gaps with equal to
2/1, 7/3, 5/2, 3/1, and 4/1.
Another application is to the existence of asymmetric librations in the
exterior resonances. We give values of asteroid eccentricity below which
asymmetric librations will not exist for the 1/7, 1/6, 1/5, 1/4, 1/3, and 1/2
resonances for any however small. But if the eccentricity exceeds these
thresholds, asymmetric librations will exist for small enough in the
unaveraged restricted three-body problem
Low frequency Raman studies of multi-wall carbon nanotubes: experiments and theory
In this paper, we investigate the low frequency Raman spectra of multi-wall
carbon nanotubes (MWNT) prepared by the electric arc method. Low frequency
Raman modes are unambiguously identified on purified samples thanks to the
small internal diameter of the MWNT. We propose a model to describe these
modes. They originate from the radial breathing vibrations of the individual
walls coupled through the Van der Waals interaction between adjacent concentric
walls. The intensity of the modes is described in the framework of bond
polarization theory. Using this model and the structural characteristics of the
nanotubes obtained from transmission electron microscopy allows to simulate the
experimental low frequency Raman spectra with an excellent agreement. It
suggests that Raman spectroscopy can be as useful regarding the
characterization of MWNT as it is in the case of single-wall nanotubes.Comment: 4 pages, 2 eps fig., 2 jpeg fig., RevTex, submitted to Phys. Rev.
Multiple plasmon resonances in naturally-occurring multiwall nanotubes: infrared spectra of chrysotile asbestos
Chrysotile asbestos is formed by densely packed bundles of multiwall hollow
nanotubes. Each wall in the nanotubes is a cylindrically wrapped layer of . We show by experiment and theory that the infrared spectrum
of chrysotile presents multiple plasmon resonances in the Si-O stretching
bands. These collective charge excitations are universal features of the
nanotubes that are obtained by cylindrically wrapping an anisotropic material.
The multiple plasmons can be observed if the width of the resonances is
sufficiently small as in chrysotile.Comment: 4 pages, 5 figures. Revtex4 compuscript. Misprint in Eq.(6) correcte
ORIGIN OF THE CHAOTIC MOTION OF THE SATURNIAN SATELLITE ATLAS
âThe final publication is available at http://iopscience.iop.org/article/10.3847/0004-6256/151/5/122/meta
van der Waals interaction in nanotube bundles : consequences on vibrational modes
We have developed a pair-potential approach for the evaluation of van der
Waals interaction between carbon nanotubes in bundles.
Starting from a continuum model, we show that the intertube modes range from
to . Using a non-orthogonal tight-binding approximation
for describing the covalent intra-tube bonding in addition, we confirme a
slight chiral dependance of the breathing mode frequency and we found that this
breathing mode frequency increase by 10 % if the nanotube lie inside a
bundle as compared to the isolated tube.Comment: 5 pages, 2 figure
Secular dynamics of planetesimals in tight binary systems: Application to Gamma-Cephei
The secular dynamics of small planetesimals in tight binary systems play a
fundamental role in establishing the possibility of accretional collisions in
such extreme cases. The most important secular parameters are the forced
eccentricity and secular frequency, which depend on the initial conditions of
the particles, as well as on the mass and orbital parameters of the secondary
star. We construct a second-order theory (with respect to the masses) for the
planar secular motion of small planetasimals and deduce new expressions for the
forced eccentricity and secular frequency. We also reanalyze the radial
velocity data available for Gamma-Cephei and present a series of orbital
solutions leading to residuals compatible with the best fits. Finally, we
discuss how different orbital configurations for Gamma-Cephei may affect the
dynamics of small bodies in circunmstellar motion. For Gamma-Cephei, we find
that the classical first-order expressions for the secular frequency and forced
eccentricity lead to large inaccuracies around 50 % for semimajor axes larger
than one tenth the orbital separation between the stellar components. Low
eccentricities and/or masses reduce the importance of the second-order terms.
The dynamics of small planetesimals only show a weak dependence with the
orbital fits of the stellar components, and the same result is found including
the effects of a nonlinear gas drag. Thus, the possibility of planetary
formation in this binary system largely appears insensitive to the orbital fits
adopted for the stellar components, and any future alterations in the system
parameters (due to new observations) should not change this picture. Finally,
we show that planetesimals migrating because of gas drag may be trapped in
mean-motion resonances with the binary, even though the migration is divergent.Comment: 11 pages, 9 figure
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