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.

Control and chaos for vibro-impact and non-ideal oscillators

In the paper, we discuss dynamics of two kinds of mechanical systems. Initially, we consider vibro-impact systems which have many implementations in applied mechanics, ranging from drilling machinery and metal cutting processes to gear boxes. Moreover, from the point of view of dynamical systems, vibro-impact systems exhibit a rich variety of phenomena, particularly chaotic motion. In this paper, we review recent works on the dynamics of vibro-impact systems, focusing on chaotic motion and its control. The considered systems are a gear-rattling model and a smart damper to suppress chaotic motion. Furthermore, we investigate systems with non-ideal energy source, represented by a limited power supply. As an example of a non-ideal system, we analyse chaotic dynamics of the damped Duffing oscillator coupled to a rotor. Then, we show how to use a tuned liquid damper to control the attractors of this non-ideal oscillator.

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.

The effects of anticalcification treatments and hydration on the molecular dynamics of bovine pericardium collagen as revealed by (13)C solid-state NMR

This article describes a solid-state NMR (SSNMR) investigation of the influence of hydration and chemical cross-linking on the molecular dynamics of the constituents of the bovine pericardium (BP) tissues and its relation to the mechanical properties of the tissue. Samples of natural phenetylamine-diepoxide (DE)- and glutaraldehyde (GL)-fixed BP were investigated by (13)C cross-polarization SSNMR to probe the dynamics of the collagen, and the results were correlated to the mechanical properties of the tissues, probed by dynamical mechanical analysis. For samples of natural BP, the NMR results show that the higher the hydration level the more pronounced the molecular dynamics of the collagen backbone and sidechains, decreasing the tissue`s elastic modulus. In contrast, in DE- and GL-treated samples, the collagen molecules are more rigid, and the hydration seems to be less effective in increasing the collagen molecular dynamics and reducing the mechanical strength of the samples. This is mostly attributed to the presence of cross-links between the collagen plates, which renders the collagen mobility less dependent on the water absorption in chemically treated samples. Copyright (C) 2010 John Wiley & Sons, Ltd.

The Mobility of Chondroitin Sulfate in Articular and Artificial Cartilage Characterized by (13)C Magic-Angle Spinning NMR Spectroscopy

We have studied the molecular dynamics of one of the major macromolecules in articular cartilage, chondroitin sulfate. Applying (13)C high-resolution magic-angle spinning NMR techniques, the NMR signals of all rigid macromolecules in cartilage can be suppressed, allowing the exclusive detection of the highly mobile chondroitin sulfate. The technique is also used to detect the chondroitin sulfate in artificial tissue-engineered cartilage. The tissue-engineered material that is based on matrix producing chondrocytes cultured in a collagen gel should provide properties as close as possible to those of the natural cartilage. Nuclear relaxation times of the chondroitin sulfate were determined for both tissues. Although T(1) relaxation times are rather similar, the T(2) relaxation in tissue-engineered cartilage is significantly shorter. This suggests that the motions of chondroitin sulfate in data:rat and artificial cartilage different. The nuclear relaxation times of chondroitin sulfate in natural and tissue-engineered cartilage were modeled using a broad distribution function for the motional correlation times. Although the description of the microscopic molecular dynamics of the chondroitin sulfate in natural and artificial cartilage required the identical broad distribution functions for the correlation times of motion, significant differences in the correlation times of motion that are extracted from the model indicate that the artificial tissue does not fully meet the standards of the natural ideal. This could also be confirmed by macroscopic biomechanical elasticity measurements. Nevertheless, these results suggest that NMR is a useful tool for the investigation of the quality of artificially engineered tissue. (C) 2010 Wiley Periodicals, Inc. Biopolymers 93: 520-532, 2010.

Conformational Properties of Angiotensin II and Its Active and Inactive TOAC-Labeled Analogs in the Presence of Micelles. Electron Paramagnetic Resonance, Fluorescence, and Circular Dichroism Studies

The interaction between angiotensin II (AII, DRVYIHPF) and its analogs carrying 2,2,6,6-tetramethylpiperidine-1-oxyl-4-amino-4-carboxylic acid (TOAC) and detergents-negatively charged sodium dodecyl sulfate (SDS) and zwitterionic N-hexadecyl-N,N-dimethyl-3-ammonio-1-propanesulfonate (HPS)-was examined by means of EPR, CD, and fluorescence. EPR spectra of partially active TOAC(1)-AII and inactive TOAC(3)-AII in aqueous solution indicated fast tumbling, the freedom of motion being greater at the N-terminus. Line broadening occurred upon interaction with micelles. Below SDS critical micelle concentration, broader lines indicated complex formation with tighter molecular packing than in micelles. Small changes in hyperfine splittings evinced TOAC location at the micelle-water interface. The interaction with anionic micelles was more effective than with zwitterionic micelles. Peptide-micelle interaction caused fluorescence increase. The TOAC-promoted intramolecular fluorescence quenching was more, pronounced for TOAC(3)-AII because of the proximity between the nitroxide and Tyr(4). CD spectra showed that although both AII and TOAC(1)-AII presented flexible conformations in water, TOAC(3)-AII displayed conformational restriction because of the TOAC-imposed bend (Schreier et al., Biopolymers 2004, 74, 389). In HPS, conformational changes were observed for the labeled peptides at neutral and basic pH. In SDS, all peptides underwent pH-dependent conformational changes. Although the spectra suggested similar folds for All and TOAC(1)-AII, different conformations were acquired by TOAC(3)-AII. The membrane environment has been hypothesized to shift conformational equilibria so as to stabilize the receptor-bound conformation of ligands. The fact that TOAC(3)-AII is unable to acquire conformations similar to those of native AII and partially active TOAC(1)-AII is probably the explanation for its lack of biological activity. (C) 2009 Wiley Periodicals, Inc. Biopolymers (Pept Sci) 92: 525-537, 2009.

Excited-state dynamics of polyfluorene derivatives in solution

The excited-state dynamics of two polyfluorene copolymers, one fully conjugated containing phenylene vinylene units alternated with 9,9`-dihexylfluorenyl groups and the other segmented by -(CH2)(8)- spacer, were studied in dilute solution of different solvents using a picosecond single-photon timing technique. The excited-state dynamics of the segmented copolymer follows the Forster resonant energy-transfer model which describes intrachain energy-transfer kinetics among random oriented chromophores. Energy transfer is confirmed by analysis of fluorescence anisotropy relaxation with the measurement of a short decay component of about 60 ps. The fluorescence decay surface of the fully conjugated copolymer is biexponential with decay times of about 470 and 900 ps, ascribed to deactivation of chain moieties containing trans and cis isomers already in a photostationary condition. Thus, energy transfer is very fast due to the conjugated nature and rigid-rod-like structure of this copolymer chain.

Intrachain Energy Migration to Weak Charge-Transfer State in Polyfluorene End-Capped with Naphthalimide Derivative

Polyfluorene end-capped with N-(2-benzothiazole)-1 8-naphthalimide (PF-BNI) is a highly fluorescent material with fluorescence emission modulated by solvent polarity Its low energy excited state is assigned as a mixed configuration state between the singlet S(1) of the fluorene backbone (F) with the charge transfer (CI) of the end group BNI The triexponential fluorescence decays of PF-BNI were associated with fast energy migration to form an intrachain charge-transfer (ICCT) state polyfluorene backbone decay and ICCT deactivation Time-resolved fluorescence anisotropy exhibited biexponential relaxation with a fast component of 12-16 ps in addition to a slow one in the range 0 8-1 4 ns depending on the solvent showing that depolarization occurs from two different processes energy migration to form the ICCT state and slow rotational diffusion motion of end segments at a longer time Results from femtosecond transient absorption measurements agreed with anisotropy decay and showed a decay component of about 16 ps at 605 nm in PF BNI ascribed to the conversion of S(1) to the ICCT excited state From the ratio of asymptotic and initial amplitudes of the transient absorption measurement the efficiency of intrachain ICCT formation is estimated in 0 5 which means that on average, half of the excited state formed in a BNI-(F)(n)-BNI chain with n = 32 is converted to its low energy intrachain charge-transfer (ICCT) state