Dynamics of two planets in co-orbital motion

We study the stability regions and families of periodic orbits of two planets locked in a co-orbital configuration. We consider different ratios of planetary masses and orbital eccentricities; we also assume that both planets share the same orbital plane. Initially, we perform numerical simulations over a grid of osculating initial conditions to map the regions of stable/chaotic motion and identify equilibrium solutions. These results are later analysed in more detail using a semi-analytical model. Apart from the well-known quasi-satellite orbits and the classical equilibrium Lagrangian points L(4) and L(5), we also find a new regime of asymmetric periodic solutions. For low eccentricities these are located at (delta lambda, delta pi) = (+/- 60 degrees, -/+ 120 degrees), where delta lambda is the difference in mean longitudes and delta pi is the difference in longitudes of pericentre. The position of these anti-Lagrangian solutions changes with the mass ratio and the orbital eccentricities and are found for eccentricities as high as similar to 0.7. Finally, we also applied a slow mass variation to one of the planets and analysed its effect on an initially asymmetric periodic orbit. We found that the resonant solution is preserved as long as the mass variation is adiabatic, with practically no change in the equilibrium values of the angles.

Dynamic portrait of the planetary 2/1 mean-motion resonance - II. Systems with a more massive inner planet

This paper presents the second part in our study of the global structure of the planar phase space of the planetary three-body problem, when both planets lie in the vicinity of a 2/1 mean-motion resonance. While Paper I was devoted to cases where the outer planet is the more massive body, the present work is devoted to the cases where the more massive body is the inner planet. As before, outside the well-known Apsidal Corotation Resonances (ACR), the phase space shows a complex picture marked by the presence of several distinct regimes of resonant and non-resonant motion, crossed by families of periodic orbits and separated by chaotic zones. When the chosen values of the integrals of motion lead to symmetric ACR, the global dynamics are generally similar to the structure presented in Paper I. However, for asymmetric ACR the resonant phase space is strikingly different and shows a galore of distinct dynamical states. This structure is shown with the help of dynamical maps constructed on two different representative planes, one centred on the unstable symmetric ACR and the other on the stable asymmetric equilibrium solution. Although the study described in the work may be applied to any mass ratio, we present a detailed analysis for mass values similar to the Jupiter-Saturn case. Results give a global view of the different dynamical states available to resonant planets with these characteristics. Some of these dynamical paths could have marked the evolution of the giant planets of our Solar system, assuming they suffered a temporary capture in the 2/1 resonance during the latest stages of the formation of our Solar system.

DNA alters the bilayer structure of cationic lipid diC14-amidine: A spin label study

Cationic lipids-DNA complexes (lipoplexes) have been used for delivery of nucleic acids into cells in vitro and in vivo. Despite the fact that, over the last decade, significant progress in the understanding of the cellular pathways and mechanisms involved in lipoplexes-mediated gene transfection have been achieved, a convincing relationship between the structure of lipoplexes and their in vivo and in vitro transfection activity is still missing. How does DNA affect the lipid packing and what are the consequences for transfection efficiency is the point we want to address here. We investigated the bilayer organization in cationic liposomes by electron spin resonance (ESR). Phospholipids spin labeled at the 5th and 16th carbon atoms were incorporated into the DNA/diC14-amidine complex. Our data demonstrate that electrostatic interactions involved in the formation of DNA-cationic lipid complex modify the packing of the cationic lipid membrane. DNA rigidifies the amidine fluid bilayer and fluidizes the amidine rigid bilayer just below the gel-fluid transition temperature. These effects were not observed with single nucleotides and are clearly related to the repetitive charged motif present in the DNA chain and not to a charge-charge interaction. These modifications of the initial lipid packing of the cationic lipid may reorient its cellular pathway towards different routes. A better knowledge of the cationic lipid packing before and after interaction with DNA may therefore contribute to the design of lipoplexes capable to reach specific cellular targets. (c) 2009 Elsevier B.V. All rights reserved.

Study of sodium tellurite glass using the thermally stimulated depolarization current technique (TSDC)

In order to have a better understanding of the role of the structure and the defects involved in the polarization processes in an 85TeO(2)-15Na(2)O mol% glass, we used the thermally stimulated depolarization currents (TSDC technique). The TSDC of the non-irradiated sample presented a strong negative peak of current at the temperature of 340 K, preceded by a relatively weak positive peak at about 300 K. after different d.c. voltages of 1200, 1500 and 2000 V were applied. No response was obtained with 1000 V. but the peak intensity increased considerably for voltages above 1200 V. After gamma-irradiation of 25 and 50 KGy doses, a depolarization of the negative peak was observed in the sample submitted to 25 KGy, whereas for the sample irradiated with 50 KGy, six TSDC peaks appeared at regular intervals of 5 KGy, in the temperature range of 100 and 300 K. Crown Copyright (C) 2010 Published by Elsevier B.V. All rights reserved.

A Multitechnique Study of Structure and Dynamics of Polyfluorene Cast Films and the Influence on Their Photoluminescence

This article describes the microstructure and dynamics in the solid state of polyfluorene-based polymers, poly(9,)-dioctylfluorenyl-2,7-diyl) (PFO), a semicrystalline polymer, and poly [(9,9-dioctyl- 2,7-divinylene-fluorenylene)-alt-co-{2-methoxy-5-(2-ethyl-hexyloxy)- 1,4-phenylene vinylene}, a copolymer with mesomorphic phase properties. These Structures were determined by wide-angle X-ray scattering (WAXS) measurements, Assuming a packing model for the copolymer structure, where the planes of the phenyl rings are stacked and separated by an average distance of similar to 4.5 angstrom and laterally spaced by about similar to 16 angstrom, we followed the evolution of these distances as a function of temperature using WAXS and associated the changes observed to the polymer relaxation processes identified by dynamical mechanical thermal analysis. Specific molecular motions were studied by solid-state nuclear magnetic resonance. The onset of the side-chain motion at about 213 K (beta-relaxation) produced a small increase in the lateral spacing and in the stacking distance of the phenyl rings in them aggregated Structures, Besides, at about 383 K (alpha-relaxation) there occurs a significant increase in the amplitude of the torsion motion in the backbone, producing a greater increase in the stacking distance of the phenyl rings. Similar results were observed in the semicrystalline phase of PFO, but in this case the presence of the crystalline structure affects considerably the overall dynamics, which tends to be more hindered. Put together, Our data explain many features of the temperature dependence of the photoluminescence of these two polymers.

Nuclear Magnetic Resonance Study of Hydrated Bentonite

Impedance spectroscopy and nuclear magnetic resonance (NMR) were used to investigate the mobility of water molecules located in the interlayer space of H(+) - exchanged bentonite clay. The conductivity obtained by ac measurements was 1.25 x 10(-4) S/cm at 298 K. Proton ((1)H) lineshapes and spin-lattice relaxation times were measured as a function of temperature over the temperature range 130-320 K. The NMR experiments exhibit the qualitative features associated with the proton motion, namely the presence of a (1)H NMR line narrowing and a well-defined spin-lattice relaxation rate maximum. The temperature dependence of the proton spin-lattice relaxation rates was analyzed with the spectral density function appropriate for proton dynamics in a two-dimensional system. The self-diffusion coefficient estimated from our NMR data, D similar to 2 x 10(-7) cm(2)/s at 300 K, is consistent with those reported for exchanged montmorillonite clay hydrates studied by NMR and quasi-elastic neutron scattering (QNS).

On the motion under focal attraction in a rotating medium

New results are established here on the phase portraits and bifurcations of the kinematic model in system (1), first presented by H.K. Wilson in [3], and by him attributed to L. Markus (unpublished). A new, self-sufficient, study which extends that of [3] and allows an essential conclusion for the applicability of the model is reported here.