EXISTENCE RESULTS FOR ABSTRACT NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS

In this paper we discuss the existence of solutions for a class of abstract partial neutral functional differential equations.

Physical and dynamical characterization of (5201) Ferraz-Mello, a possible extinct Jupiter family comet

Context. The subject of asteroids in cometary orbits (ACOs) has been of growing interest lately. These objects have the orbital characteristics typical of comets, but are asteroidal in appearance, i.e., show no signs of a coma at any part of their orbits. At least a fraction of these objects are thought to be comets that have either exhausted all their volatile content or developed a refractory crust that prevents sublimation. In particular, the asteroid ( 5201) Ferraz-Mello has, since its discovery, been suspected to be an extinct Jupiter family comet due to the peculiar nature of its orbit. Aims. The aim of this work is to put constraints on the possible origin of ( 5201) Ferraz-Mello by means of spectroscopic characterization and a study of the dynamics of this asteroid. Methods. We used the SOAR Optical Imager (SOI) to obtain observations of ( 5201) Ferraz-Mello using four SDSS filters. These observations were compared to asteroids listed in the Sloan Moving objects catalog and also to photometry of cometary nuclei, Centaurs, and TNOs. The orbital evolution of ( 5201) Ferraz-Mello and of a sample of asteroids and comets that are close to that object in the a - e plane were simulated using a pure N-body code for 4 000 years forward and 4 000 years backward in time. Results. The reflectance spectrum obtained from its colors in the SDSS system is unusual, with a steep spectral gradient that is comparable to TNOs and Centaurs, but with an increase in the reflectance in the g band that is not common in those populations. A similar behavior is seen in cometary nuclei that were observed in the presence of a faint dust coma. The dynamical results confirm the very chaotic evolution found previously and its dynamical similarity to the chaotic evolution of some comets. The asteroid is situated in the very stochastic layer at the border of the 2/1 resonance, and it has a very short Lyapunov time ( 30 - 40) years. Together, the spectral characteristcs and the dynamical evolution suggest that ( 5201) Ferraz-Mello is a dormant or extinct comet.

Transiting exoplanets from the CoRoT space mission XVI. CoRoT-14b: an unusually dense very hot Jupiter

In this paper, the CoRoT Exoplanet Science Team announces its 14th discovery. Herein, we discuss the observations and analyses that allowed us to derive the parameters of this system: a hot Jupiter with a mass of 7.6 +/- 0.6 Jupiter masses orbiting a solar-type star (F9V) with a period of only 1.5 d, less than 5 stellar radii from its parent star. It is unusual for such a massive planet to have such a small orbit: only one other known higher mass exoplanet orbits with a shorter period.

Transiting exoplanets from the CoRoT space mission XVIII. CoRoT-18b: a massive hot Jupiter on a prograde, nearly aligned orbit

We report the detection of CoRoT-18b, a massive hot Jupiter transiting in front of its host star with a period of 1.9000693 +/- 0.0000028 days. This planet was discovered thanks to photometric data secured with the CoRoT satellite combined with spectroscopic and photometric ground-based follow-up observations. The planet has a mass M(p) = 3.47 +/- 0.38 M(Jup), a radius R(p) = 1.31 +/- 0.18 R(Jup), and a density rho(p) = 2.2 +/- 0.8 g cm(-3). It orbits a G9V star with a mass M(*) = 0.95 +/- 0.15 M(circle dot), a radius R(*) = 1.00 +/- 0.13 R(circle dot), and a rotation period P(rot) = 5.4 +/- 0.4 days. The age of the system remains uncertain, with stellar evolution models pointing either to a few tens Ma or several Ga, while gyrochronology and lithium abundance point towards ages of a few hundred Ma. This mismatch potentially points to a problem in our understanding of the evolution of young stars, with possibly significant implications for stellar physics and the interpretation of inferred sizes of exoplanets around young stars. We detected the RossiterMcLaughlin anomaly in the CoRoT-18 system thanks to the spectroscopic observation of a transit. We measured the obliquity psi = 20 degrees +/- 20 degrees +/- (sky-projected value lambda = -10 degrees +/- 20 degrees), indicating that the planet orbits in the same way as the star is rotating and that this prograde orbit is nearly aligned with the stellar equator.

Transiting exoplanets from the CoRoT space mission XIII. CoRoT-13b: a dense hot Jupiter in transit around a star with solar metallicity and super-solar lithium content

We announce the discovery of the transiting planet CoRoT-13b. Ground-based follow-up in CFHT and IAC80 confirmed CoRoT's observations. The mass of the planet was measured with the HARPS spectrograph and the properties of the host star were obtained analyzing HIRES spectra from the Keck telescope. It is a hot Jupiter-like planet with an orbital period of 4.04 days, 1.3 Jupiter masses, 0.9 Jupiter radii, and a density of 2.34 g cm(-3). It orbits a G0V star with T(eff) = 5 945 K, M(*) = 1.09 M(circle dot), R(*) = 1.01 R(circle dot), solar metallicity, a lithium content of +1.45 dex, and an estimated age of between 0.12 and 3.15 Gyr. The lithium abundance of the star is consistent with its effective temperature, activity level, and age range derived from the stellar analysis. The density of the planet is extreme for its mass, implies that heavy elements are present with a mass of between about 140 and 300 M(circle plus).

Transiting exoplanets from the CoRoT space mission XI. CoRoT-8b: a hot and dense sub-Saturn around a K1 dwarf

Aims. We report the discovery of CoRoT-8b, a dense small Saturn-class exoplanet that orbits a K1 dwarf in 6.2 days, and we derive its orbital parameters, mass, and radius. Methods. We analyzed two complementary data sets: the photometric transit curve of CoRoT-8b as measured by CoRoT and the radial velocity curve of CoRoT-8 as measured by the HARPS spectrometer**. Results. We find that CoRoT-8b is on a circular orbit with a semi-major axis of 0.063 +/- 0.001 AU. It has a radius of 0.57 +/- 0.02 R(J), a mass of 0.22 +/- 0.03 M(J), and therefore a mean density of 1.6 +/- 0.1 g cm(-3). Conclusions. With 67% of the size of Saturn and 72% of its mass, CoRoT-8b has a density comparable to that of Neptune (1.76 g cm(-3)). We estimate its content in heavy elements to be 47-63 M(circle plus), and the mass of its hydrogen-helium envelope to be 7-23 M(circle plus). At 0.063 AU, the thermal loss of hydrogen of CoRoT-8b should be no more than similar to 0.1% over an assumed integrated lifetime of 3 Ga.

The CoRoT-7 planetary system: two orbiting super-Earths

We report on an intensive observational campaign carried out with HARPS at the 3.6 m telescope at La Silla on the star CoRoT-7. Additional simultaneous photometric measurements carried out with the Euler Swiss telescope have demonstrated that the observed radial velocity variations are dominated by rotational modulation from cool spots on the stellar surface. Several approaches were used to extract the radial velocity signal of the planet(s) from the stellar activity signal. First, a simple pre-whitening procedure was employed to find and subsequently remove periodic signals from the complex frequency structure of the radial velocity data. The dominant frequency in the power spectrum was found at 23 days, which corresponds to the rotation period of CoRoT-7. The 0.8535 day period of CoRoT-7b planetary candidate was detected with an amplitude of 3.3 m s(-1). Most other frequencies, some with amplitudes larger than the CoRoT-7b signal, are most likely associated with activity. A second approach used harmonic decomposition of the rotational period and up to the first three harmonics to filter out the activity signal from radial velocity variations caused by orbiting planets. After correcting the radial velocity data for activity, two periodic signals are detected: the CoRoT-7b transit period and a second one with a period of 3.69 days and an amplitude of 4 m s(-1). This second signal was also found in the pre-whitening analysis. We attribute the second signal to a second, more remote planet CoRoT-7c. The orbital solution of both planets is compatible with circular orbits. The mass of CoRoT-7b is 4.8 +/- 0.8 (M(circle plus)) and that of CoRoT-7c is 8.4 +/- 0.9 (M(circle plus)), assuming both planets are on coplanar orbits. We also investigated the false positive scenario of a blend by a faint stellar binary, and this may be rejected by the stability of the bisector on a nightly scale. According to their masses both planets belong to the super-Earth planet category. The average density of CoRoT-7b is rho = 5.6 +/- 1.3 g cm(-3), similar to the Earth. The CoRoT-7 planetary system provides us with the first insight into the physical nature of short period super-Earth planets recently detected by radial velocity surveys. These planets may be denser than Neptune and therefore likely made of rocks like the Earth, or a mix of water ice and rocks.

Transport properties in nontwist area-preserving maps

Nontwist systems, common in the dynamical descriptions of fluids and plasmas, possess a shearless curve with a concomitant transport barrier that eliminates or reduces chaotic transport, even after its breakdown. In order to investigate the transport properties of nontwist systems, we analyze the barrier escape time and barrier transmissivity for the standard nontwist map, a paradigm of such systems. We interpret the sensitive dependence of these quantities upon map parameters by investigating chaotic orbit stickiness and the associated role played by the dominant crossing of stable and unstable manifolds. (C) 2009 American Institute of Physics. [doi: 10.1063/1.3247349]

Dynamical estimates of chaotic systems from Poincare recurrences

We show a function that fits well the probability density of return times between two consecutive visits of a chaotic trajectory to finite size regions in phase space. It deviates from the exponential statistics by a small power-law term, a term that represents the deterministic manifestation of the dynamics. We also show how one can quickly and easily estimate the Kolmogorov-Sinai entropy and the short-term correlation function by realizing observations of high probable returns. Our analyses are performed numerically in the Henon map and experimentally in a Chua's circuit. Finally, we discuss how our approach can be used to treat the data coming from experimental complex systems and for technological applications. (C) 2009 American Institute of Physics. [doi: 10.1063/1.3263943]

Interlayer interference in double wells in a tilted magnetic field

Magnetotransport measurements on bilayer electron systems reveal repeated reentrance of the resistance minima at filling factors nu=4N+1 and nu=4N+3, where N is the Landau index number, in the tilted magnetic field. At high filling factors, the Shubnikov-de Haas oscillations exhibit beating effects at certain tilt angles. We attribute such behavior to oscillations of the tunneling gap due to Aharonov-Bohm interference effect between cyclotron orbits in different layers. The interplay between quantum and quasiclassical regimes is established.

Transition to chaotic scattering: Signatures in the differential cross section

We show that bifurcations in chaotic scattering manifest themselves through the appearance of an infinitely fine-scale structure of singularities in the cross section. These ""rainbow singularities"" are created in a cascade, which is closely related to the bifurcation cascade undergone by the set of trapped orbits (the chaotic saddle). This cascade provides a signature in the differential cross section of the complex pattern of bifurcations of orbits underlying the transition to chaotic scattering. We show that there is a power law with a universal coefficient governing the sequence of births of rainbow singularities and we verify this prediction by numerical simulations.

SYNCHRONIZATION OF A CLASS OF SECOND-ORDER NONLINEAR SYSTEMS

The asymptotic behavior of a class of coupled second-order nonlinear dynamical systems is studied in this paper. Using very mild assumptions on the vector-field, conditions on the coupling parameters that guarantee synchronization are provided. The proposed result does not require solutions to be ultimately bounded in order to prove synchronization, therefore it can be used to study coupled systems that do not globally synchronize, including synchronization of unbounded solutions. In this case, estimates of the synchronization region are obtained. Synchronization of two-coupled nonlinear pendulums and two-coupled Duffing systems are studied to illustrate the application of the proposed theory.

A simple way to introduce fibers into FEM models

This communication proposes a simple way to introduce fibers into finite element modelling. This is a promising formulation to deal with fiber-reinforced composites by the finite element method (FEM), as it allows the consideration of short or long fibers placed arbitrarily inside a continuum domain (matrix). The most important feature of the formulation is that no additional degree of freedom is introduced into the pre-existent finite element numerical system to consider any distribution of fiber inclusions. In other words, the size of the system of equations used to solve a non-reinforced medium is the same as the one used to solve the reinforced counterpart. Another important characteristic is the reduced work required by the user to introduce fibers, avoiding `rebar` elements, node-by-node geometrical definitions or even complex mesh generation. An additional characteristic of the technique is the possibility of representing unbounded stresses at the end of fibers using a finite number of degrees of freedom. Further studies are required for non-linear applications in which localization may occur. Along the text the linear formulation is presented and the bounded connection between fibers and continuum is considered. Four examples are presented, including non-linear analysis, to validate and show the capabilities of the formulation. Copyright (c) 2007 John Wiley & Sons, Ltd.

Hamiltonian mappings and circle packing phase spaces.

We introduce three area preserving maps with phase space structures which resemble circle packings. Each mapping is derived from a kicked Hamiltonian system with one of the three different phase space geometries (planar, hyperbolic or spherical) and exhibits an infinite number of coexisting stable periodic orbits which appear to ‘pack’ the phase space with circular resonances.

Experimental control of single-mode laser chaos by using continuous, time-delayed feedback

Control of chaos in the single-mode optically pumped far-infrared (NH3)-N-15 laser is experimentally demonstrated using continuous time-delay control. Both the Lorenz spiral chaos and the detuned period-doubling chaos exhibited by the laser have been controlled. While the laser is in the Lorenz spiral chaos regime the chaos has been controlled both such that the laser output is cw, with corrections of only a fraction of a percent necessary to keep it there, and to period one. The laser has also been controlled while in the period-doubling chaos regime, to both the period-one and -two states.