Dynamics of Enceladus and Dione inside the 2:1 Mean-Motion Resonance under Tidal Dissipation

In a previous work (Callegari and Yokoyama 2007, Celest. Mech. Dyn. Astr. vol. 98), the main features of the motion of the pair Enceladus-Dione were analyzed in the frozen regime, i.e., without considering the tidal evolution. Here, the results of a great deal of numerical simulations of a pair of satellites similar to Enceladus and Dione crossing the 2:1 mean-motion resonance are shown. The resonance crossing is modeled with a linear tidal theory, considering a two-degrees-of-freedom model written in the framework of the general three-body planar problem. The main regimes of motion of the system during the passage through resonance are studied in detail. We discuss our results comparing them with classical scenarios of tidal evolution of the system. We show new scenarios of evolution of the Enceladus-Dione system through resonance not shown in previous approaches of the problem.Comment: 36 pages, 12 figures. Accepted in Celestial Mechanics and Dynamical Astronom

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

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 $1-\mu$ and $\mu$ that circle each other with period equal to $2\pi$. For small $\mu$, a resonant periodic motion of the massless particle in the rotating frame can be described by relatively prime integers $p$ and $q$, if its period around the heavier primary is approximately $2\pi p/q$, and by its approximate eccentricity $e$. 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 $q/p$ 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 $\mu$ however small. But if the eccentricity exceeds these thresholds, asymmetric librations will exist for $\mu$ 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.

Localized state and charge transfer in nitrogen-doped graphene

Nitrogen-doped epitaxial graphene grown on SiC(000?1) was prepared by exposing the surface to an atomic nitrogen flux. Using Scanning Tunneling Microscopy (STM) and Spectroscopy (STS), supported by Density Functional Theory (DFT) calculations, the simple substitution of carbon by nitrogen atoms has been identified as the most common doping configuration. High-resolution images reveal a reduction of local charge density on top of the nitrogen atoms, indicating a charge transfer to the neighboring carbon atoms. For the first time, local STS spectra clearly evidenced the energy levels associated with the chemical doping by nitrogen, localized in the conduction band. Various other nitrogen-related defects have been observed. The bias dependence of their topographic signatures demonstrates the presence of structural configurations more complex than substitution as well as hole-doping.Comment: 5 pages, accepted in PR

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 $Mg_3 Si_2 O_5 (OH)_4$. 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

Interesting dynamics at high mutual inclination in the framework of the Kozai problem with an eccentric perturber

We study the dynamics of the 3-D three-body problem of a small body moving under the attractions of a star and a giant planet which orbits the star on a much wider and elliptic orbit. In particular, we focus on the influence of an eccentric orbit of the outer perturber on the dynamics of a small highly inclined inner body. Our analytical study of the secular perturbations relies on the classical octupole hamiltonian expansion (third-order theory in the ratio of the semi-major axes), as third-order terms are needed to consider the secular variations of the outer perturber and potential secular resonances between the arguments of the pericenter and/or longitudes of the node of both bodies. Short-period averaging and node reduction (Laplace plane) reduce the problem to two degrees of freedom. The four-dimensional dynamics is analyzed through representative planes which identify the main equilibria of the problem. As in the circular problem (i.e. perturber on a circular orbit), the "Kozai-bifurcated" equilibria play a major role in the dynamics of an inner body on quasi-circular orbit: its eccentricity variations are very limited for mutual inclination between the orbital planes smaller than ~40^{\deg}, while they become large and chaotic for higher mutual inclination. Particular attention is also given to a region around 35^{\deg} of mutual inclination, detected numerically by Funk et al. (2011) and consisting of long-time stable and particularly low eccentric orbits of the small body. Using a 12th-order Hamiltonian expansion in eccentricities and inclinations, in particular its action-angle formulation obtained by Lie transforms in Libert & Henrard (2008), we show that this region presents an equality of two fundamental frequencies and can be regarded as a secular resonance. Our results also apply to binary star systems where a planet is revolving around one of the two stars.Comment: 12 pages, 9 figures, accepted for publication in MNRA

On the diffraction pattern of C60 peapods

We present detailed calculations of the diffraction pattern of a powder of bundles of C$_{60}$ peapods. The influence of all pertinent structural parameters of the bundles on the diffraction diagram is discussed, which should lead to a better interpretation of X-ray and neutron diffraction diagrams. We illustrate our formalism for X-ray scattering experiments performed on peapod samples synthesized from 2 different technics, which present different structural parameters. We propose and test different criteria to solve the difficult problem of the filling rate determination.Comment: Sumitted 19 May 200

Forming limit predictions for single-point incremental sheet metal forming

peer reviewedA characteristic of incremental sheet metal forming is that much higher deformations can be achieved than conventional forming limits. In this paper it is investigated to which extent the highly non-monotonic strain paths during such a process may be responsible for this high formability. A Marciniak-Kuczynski (MK) model is used to predict the onset of necking of a sheet subjected to the strain paths obtained by finite-element simulations. The predicted forming limits are considerably higher than for monotonic loading, but still lower than the experimental ones. This discrepancy is attributed to the strain gradient over the sheet thickness, which is not taken into account in the currently used MK model

Effect of FEM choices in the modelling of incremental forming of aluminium sheets

peer reviewedThis paper investigates the process of single point incremental forming of an aluminium cone with a 50-degree wall angle. Finite element (FE) models are established to simulate the process. Different FE packages have been used. Various aspects associated with the numerical choices as well as the material and process parameters have been studied. The final geometry and the reaction forces are presented as the results of the simulations. Comparison between the simulation results and the experimental data is also made