984 resultados para Orbital velocities


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Hamiltonian systems in stellar and planetary dynamics are typically near integrable. For example, Solar System planets are almost in two-body orbits, and in simulations of the Galaxy, the orbits of stars seem regular. For such systems, sophisticated numerical methods can be developed through integrable approximations. Following this theme, we discuss three distinct problems. We start by considering numerical integration techniques for planetary systems. Perturbation methods (that utilize the integrability of the two-body motion) are preferred over conventional "blind" integration schemes. We introduce perturbation methods formulated with Cartesian variables. In our numerical comparisons, these are superior to their conventional counterparts, but, by definition, lack the energy-preserving properties of symplectic integrators. However, they are exceptionally well suited for relatively short-term integrations in which moderately high positional accuracy is required. The next exercise falls into the category of stability questions in solar systems. Traditionally, the interest has been on the orbital stability of planets, which have been quantified, e.g., by Liapunov exponents. We offer a complementary aspect by considering the protective effect that massive gas giants, like Jupiter, can offer to Earth-like planets inside the habitable zone of a planetary system. Our method produces a single quantity, called the escape rate, which characterizes the system of giant planets. We obtain some interesting results by computing escape rates for the Solar System. Galaxy modelling is our third and final topic. Because of the sheer number of stars (about 10^11 in Milky Way) galaxies are often modelled as smooth potentials hosting distributions of stars. Unfortunately, only a handful of suitable potentials are integrable (harmonic oscillator, isochrone and Stäckel potential). This severely limits the possibilities of finding an integrable approximation for an observed galaxy. A solution to this problem is torus construction; a method for numerically creating a foliation of invariant phase-space tori corresponding to a given target Hamiltonian. Canonically, the invariant tori are constructed by deforming the tori of some existing integrable toy Hamiltonian. Our contribution is to demonstrate how this can be accomplished by using a Stäckel toy Hamiltonian in ellipsoidal coordinates.

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The X-ray LIII absorption-edge structure of rhenium in Cs2[ReCl6] has been measured with a bent-crystal X-ray spectrograph. An analysis in terms of molecular-orbital (m.o.) theory has been attempted. The energies of the m.o. levels, crystal-field splitting parameter, effective magnetic moment, magnetic susceptibility, and Landég parameter have been determined from this analysis. An estimate of the Re–Cl bond length has also been made.

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The free-base octabromotetraphenylporphyrin (H2OBP) has been prepared by a novel bromination reaction of (meso-tetraphenylporphyrinato)copper(II). The metal [V(IV)O, Co(II), Ni(II), Cu(II), Zn(II), Pd(II), Ag(II), Pt(II)] derivatives exhibit interesting electronic spectral features and electrochemical redox properties. The electron-withdrawing bromine substituents at the pyrrole carbons in H2OBP and M(OBP) derivatives produce remarkable red shifts in the Soret (50 nm) and visible bands (100 nm) of the porphyrin. The low magnitude of protonation constants (pK3 = 2.6 and pK4 = 1.75) and the large red-shifted Soret and visible absorption bands make the octabromoporphyrin unique. The effect of electronegative bromine substituents at the peripheral positions of the porphyrin has been quantitatively analyzed by using the four-orbital approach of Gouterman. A comparison of MO parameters of MOBP derivatives with those of the meso-substituted tetraphenylporphyrin (M(TPP)) and unsubstituted porphine (M(P)) derivatives provides an explanation for the unusual spectral features. The configuration interaction matrix element of the M(OBP) derivatives is found to be the lowest among the known substituted porphyrins, indicating delocalization of ring charge caused by the increase in conjugation of p orbitals of the bromine onto the ring orbitals. The electron-transfer reactivities of the porphyrins have been dramatically altered by the peripheral bromine substituents, producing large anodic shifts in the ring and metal-centered redox potentials. The increase in anodic shift in the reduction potential of M(OBP)s relative to M(TPP)s is found to be large (550 mV) compared to the shift in the oxidation potential (300 mV). These shifts are interpreted in terms of the resonance and inductive interactions of the bromine substituents.

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The Norrish type II process is examined in three ketones containing primary, secondary and tertiary C---H bonds in the γ position relative to the carbonyl groups; the MINDO/3 semiempirical self-consistent field (SCF) molecular orbital (MO) method was used with complete geometry optimization in the unrestricted Hartree—Fock frame for the open-shell species. Results show that barriers to conformational change in ketones play an important role in the triplet reaction.

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X-Ray structural data, as well as semiempirical and ab initio molecular orbital calculations, reveal no systematic and substantial difference between the C–C bond lengths of cis and trans 1,2-diketones. Additional results on various conformations of 1,2-diimines and 1,2-dithiones follow the same pattern. Therefore, lone-pair repulsions cannot be implicated in the observed lengthening of C–C bonds in isatin and several related molecules. Conjugation in these systems occurs peripherally avoiding the participation of the central C–C bond. Negative hyperconjugative interaction between the oxygen lone pairs and the adjacent C–C σ* orbital is suggested to be the principal reason for the relatively long C–C bond in diketones. This effect is found in both the cis and trans conformations.

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The present article deals with the development of a finite element modelling approach for the prediction of residual velocities of hard core ogival-nose projectiles following normal impact on mild steel target plates causing perforation. The impact velocities for the cases analysed are in the range 818–866.3 m/s. Assessment of finite element modelling and analysis includes a comprehensive mesh convergence study using shell elements for representing target plates and solid elements for jacketed projectiles with a copper sheath and a rigid core. Dynamic analyses were carried out with the explicit contact-impact LS-DYNA 970 solver. It has been shown that proper choice of element size and strain rate-based material modelling of target plate are crucial for obtaining test-based residual velocity.The present modelling procedure also leads to realistic representation of target plate failure and projectile sheath erosion during perforation, and confirms earlier observations that thermal effects are not significant for impact problems within the ordnance range. To the best of our knowledge, any aspect of projectile failure or degradation obtained in simulation has not been reported earlier in the literature. The validated simulation approach was applied to compute the ballistic limits and to study the effects of plate thickness and projectile diameter on residual velocity, and trends consistent with experimental data for similar situations were obtained.

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Chemical shifts, ΔE, of the X-ray K-absorption edge in several compounds, complexes of copper including its superconducting oxides possessing formal oxidation states +1 and +2 have been measured. It has been shown that the chemical shift is primarily governed by the effective ionic charge on the absorbing ion and the nature of the atoms in the first coordination shell around the absorbing ion. The relation between the chemical shift, ΔE , and the effective charge q on the absorbing ion is found to be ΔE=Aq+Bq2+Cq3+Dq4 (A, B, C and D are constants). The effects of electronegativity, atomic number, oxidation state, crystal structure, the valence d-orbital electrons, etc. on the X-ray absorption chemical shift have been discussed. ©1990 The Physical Society of Japan

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Details of an efficient optimal closed-loop guidance algorithm for a three-dimensional launch are presented with simulation results. Two types of orbital injections, with either true anomaly or argument of perigee being free at injection, are considered. The resulting steering-angle profile under the assumption of uniform gravity lies in a canted plane which transforms a three-dimensional problem into an equivalent two-dimensional one. Effects of thrust are estimated using a series in a recursive way. Encke's method is used to predict the trajectory during powered flight and then to compute the changes due to actual gravity using two gravity-related vectors. Guidance parameters are evaluated using the linear differential correction method. Optimality of the algorithm is tested against a standard ground-based trajectory optimization package. The performance of the algorithm is tested for accuracy, robustness, and efficiency for a sun-synchronous mission involving guidance for a multistage vehicle that requires large pitch and yaw maneuver. To demonstrate applicability of the algorithm to a range of missions, injection into a geostationary transfer orbit is also considered. The performance of the present algorithm is found to be much better than others.

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The excitation gaps in the singlet and triplet manifolds for finite Hubbard models in one, two and three dimensions have been obtained using different approximate configuration interaction (CI) schemes, as a function of the correlation strength, by using valence bond (VB) functions constructed over the molecular orbital (MO) basis. These are compared with numerically exact results and it is found that the scheme in which all particle hole excitations below a given threshold are included is the method of choice. The excitation energies are well reproduced, in trend as well as magnitude, particularly when the threshold equals the bandwidth of the corresponding noninteracting system.

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A general model of a foam bed reactor has been developed which rigorously accounts for the extent of gas absorption with chemical reaction occurring in both the storage and foam sections. Its applicability extends to a wide spectrum of reaction velocities. The possibilities of the predominance of the bulk-liquid reaction in the storage section or the absorption with reaction in the foam section can be handled as merely special cases of the general analysis. The importance of foam for carrying out a particular gas-liquid reaction is characterised by a criterion in terms of the fractional rate of reaction in the foam section. Trends of variations in the concentrations of dissolved free A, solute B, and gas-phase A with time of operation of the reactor are presented. The nature of the variation in the fractional rate of reaction in the foam section with time, at different reaction velocities, and the effect of the liquid flow rate (across the storage section) on the transience are also illustrated. Finally, the predictions of the general model have been validated using the available experimental data on the oxidation of sodium sulphide in a foam bed reactor. The agreement between the experimental and the present theoretical information is fairly good, apart from being more insightful than all the previous models of this reactor.

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Electron energy loss spectra (EELS) of Cr, Mo and W hexacarbonyls in the vapour phase are reported. Most of the bands observed are similar to those in optical spectra, but the two high energy transitions in the 9·8–11·2 eV region are reported here for the first time. Based on the orbital energies from the ultraviolet photoelectron spectra and the electronic transition energies from EELS and earlier optical studies, the molecular energy level schemes of these molecules are constructed.

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Working under the hypothesis that magnetic flux in the sun is generated at the bottom of the convection zone, Choudhuri and Gilman (1987; Astrophys. J. 316, 788) found that a magnetic flux tube symmetric around the rotation axis, when released at the bottom of the convection zone, gets deflected by the Coriolis force and tends to move parallel to the rotation axis as it rises in the convection zone. As a result, all the flux emerges at rather high latitudes and the flux observed at the typical sunspot latitudes remains unexplained. Choudhuri (1989; Solar Physics, in press) finds that non-axisymmetric perturbations too cannot subdue the Coriolis force. In this paper, we no longer treat the convection zone to be passive as in the previous papers, but we consider the role of turbulence in the convection zone in inhibiting the Coriolis force. The interaction of the flux tubes with the turbulence is treated in a phenomenological way as follows: (1) Large scale turbulence on the scale of giant cells can physically drag the tubes outwards, thus pulling the flux towards lower latitudes by dominating over the Coriolis force. (2) Small scale turbulence of the size of the tubes can exchange angular momentum with the tube, thus suppressing the growth of the Coriolis force and making the tubes emerge at lower latitudes. Numerical simulations show that the giant cells can drag the tubes and make them emerge at lower latitufes only if the velocities within the giant cells are unrealistically large of if the radii of the flux tubes are as small as 10 km. However, small scale turbulence can successfully suppress the growth of the Coriolis force if the tubes have radii smaller than about 300 km which may not be unreasonable. Such flux tubes can then emerge at low latitudes where sunspots are seen.

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The restricted three-body method is used to model the effect of the mean tidal field of a cluster of galaxies on the internal dynamics of a disk galaxy falling into the cluster for the first time. In the model adopted the galaxy experiences a tidal field that is compressive within the core of the cluster. The planar random velocities of all components in the disk increase after the galaxy passes through the core of the cluster. The low-velocity dispersion gas clouds experience a relatively larger increase in random velocity than the hotter stellar components. The increase in planar velocities results in a strong anisotropy between the planar and vertical velocity dispersions. It is argued that this will make the disk unstable to the 'fire-hose instability' which leads to bending modes in the disk and which will thicken the disk slightly. The mean tidal fields in rich clusters were probably stronger during the epoch of cluster formation and relaxation than they are in present-day relaxed clusters.

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During their main sequence evolution, massive stars can develop convective regions very close to their surface. These regions are caused by an opacity peak associated with iron ionization. Cantiello et al. (2009) found a possible connection between the presence of sub-photospheric convective motions and small scale stochastic velocities in the photosphere of early-type stars. This supports a physical mechanism where microturbulence is caused by waves that are triggered by subsurface convection zones. They further suggest that clumping in the inner parts of the winds of OB stars could be related to subsurface convection, and that the convective layers may also be responsible for stochastic excitation of non-radial pulsations. Furthermore, magnetic fields produced in the iron convection zone could appear at the surface of such massive stars. Therefore subsurface convection could be responsible for the occurrence of observable phenomena such as line profile variability and discrete absorption components. These phenomena have been observed for decades, but still evade a clear theoretical explanation. Here we present preliminary results from 3D MHD simulations of such subsurface convection.

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Some recent observations at Pic-du-Midi (Mulleret al., 1992a) suggest that the photospheric footpoints of coronal magnetic field lines occasionally move rapidly with typical velocities of the order 3 km s–1 for about 3 or 4 min. We argue that such occasional rapid footpoint motions could have a profound impact on the heating of the quiet corona. Qualitative estimates indicate that these occasional rapid motions can account for the entire energy flux needed to heat the quiet corona. We therefore carry out a mathematical analysis to study in detail the response of a vertical thin flux tube to photospheric footpoint motions in terms of a superposition of linear kink modes for an isothermal atmosphere. We find the resulting total energy that is asymptotically injected into an isothermal atmosphere (i.e., an atmosphere without any back reflection). By using typical parameter values for fast and slow footpoint motions, we show that, even if the footpoints spend only 2.5% of the time undergoing rapid motions, still these rapid motions could be more efficient in transporting energy to the corona than the slow motions that take place most of the time.