Angular Elements Research Articles

An Extra-Solar Planet in a Double Stellar System: The Modelling of Insufficient Orbital Elements

AbstractThe modelling of the insufficient orbital elements of extra-solar planets (EPs) revolving around one component in a binary star system is investigated in the present paper. This problem is considered in the frame of the three-body problem using the analytical theory of Orlov & Solovaya (1998). In the general case, the motion is defined by the masses of the components and by the six pairs of the initial values of the Keplerian elements. For EPs, it is not possible to obtain the complete set of elements for the orbit, in particular, the ascending node and the angle of the inclination. So, it is possible the two different variants of orbital evolution of EPs depend on the initial conditions. In one case, the orbit is unstable. Using the stability conditions of Solovaya & Pittich (2004), which are presented by the angle of the mutual inclination of the orbits between the EP and distant star, we varied unknown angular elements and defined the regions with possible values of the elements for which the motion of EP stays stable. We applied these calculations to the particular specific EPs: HD19994b, HD196885Ab and HD222404b.

Variations of angular elements of the geomagnetic field in Europe during the last 24 centuries

The analysis of variations in angular elements of the geomagnetic field during the period since 350 B.C. to the present day according to the findings from the study of thermal magnetization of baked archaeological samples from England, France, and East Europe showed that the key feature in the behavior of the geomagnetic inclination in all three regions is a millennial variation. The trend in the behavior of the inclination of the geomagnetic field can be regarded as a manifestation of a variation with a characteristic time scale of several thousand years. Despite the general likeness of variations in inclination and declination of the ancient geomagnetic field, they also exhibit a noticeable dissimilarity. The paths of the virtual geomagnetic pole reconstructed from the variations of angular elements of the geomagnetic field in East Europe indicate that the geomagnetic polar motion is quasi-cyclic. The duration of the first cycle was about 1000 years, while the second cycle has not been completed due to the change of the motion to the opposite direction in the middle of the XVII century.

Composition and Characterization of Femtosecond Optical Lattices Using Double Axicon Holographic Pattern

We demonstrate a method for tailoring the light structure of a femtosecond field using a double-axicon holographic pattern without compensating for additional angular dispersion elements. Tailored light structured on the femtosecond field can be obtained by creating a pair of femtoseond Bessel beams and synthesize them. The spatial property of tailored light structure on femtosecond field investigated and compared to the CW case. We also showed the temporal characteristics of the tailored femtosecond light structure can be expressed by the interference of Bessel beams with different time shift.

Sympathetic cooling of the Ba+ion by collisions with ultracold Rb atoms: Theoretical prospects

State-of-the-art {\em ab initio} techniques have been applied to compute the potential energy curves of the (BaRb)$^+$ molecular ion in the Born-Oppenheimer approximation. The long-range coefficients describing the electrostatic, induction, and dispersion interactions at large interatomic distances are also reported. The electric transition dipole moments governing the X$^1\Sigma \to ^1\Sigma, ^1\Pi$ have been obtained as the first residue of the polarization propagator computed with the linear response coupled-cluster method restricted to single and double excitations. Nonadiabatic radial and angular coupling matrix elements, as well as the spin-orbit coupling matrix elements have been evaluated using the multireference configuration interaction method restricted to single and double excitations with a large active space. With these couplings, the spin-orbit coupled (relativistic) potential energy curves for the 0$^+$ and 1 states relevant for the running experiments have been obtained. Finally, relativistic transition moments and nonadiabatic coupling matrix elements were obtained from the nonrelativistic results and spin-orbit eigenvectors. The electronic structure input has been employed in the single channel scattering calculations of the collisional cross sections between the Ba$^+$ ion and Rb atom. Both nonrelativistic and relativistic potentials were used in these calculations. Our results show that the inelastic cross section corresponding to the charge transfer from the Rb atom to the Ba$^+$ ion is much smaller than the elastic one over a wide range of energies up to 1 mK. This suggests that sympathetic cooling of the Ba$^+$ ion by collisions with ultracold Rb atoms should be possible.

New efficient algorithm for the calculation of energy levels of AB3 type molecules

This paper illustrates a method for the construction of a symmetry-adapted contracted angular basis set for AB3 molecules. Simple formulas that use this basis set for calculations of the angular matrix elements of the kinetic energy (KE) operator and angular matrix elements of potential energy surface (PES) are reported. The efficient recursive algorithm based on the tensorial formalism is used for the calculation of vibrational matrix elements. The symmetric form of vibration KE operators without the sin(q)−2 type singularity is applied. A good basis set convergence for the calculations of vibrational levels of the PH3 molecule is demonstrated.

Analytical solution of a satellite orbit disturbed by atmospheric drag

In this paper, we derive the analytical solution of a satellite orbit disturbed by atmospheric drag. The disturbance force vector is first transformed and rotated to the orbital frame so that it can be used in the simplified Gaussian equations of satellite motion. Then, the force vector is expanded to triangular functions of the Keplerian angular elements and the disturbances are separated into three parts: short-periodic terms with triangular functions of M, long-periodic terms with triangular functions of (ω, i) and secular terms [non-periodic functions of (a, e)] with a program using mathematical symbolic operation software. The integrations are then carried out with respect to M, (ω, i) and t, respectively, to obtain the analytical solutions of satellite orbits disturbed by atmospheric drag. Some interesting conclusions are obtained theoretically. The atmospheric disturbance force is not a function of Ω. The semimajor axis a of the orbital ellipse is reduced in a constant and strong manner by the air disturbance; the shape of the ellipse (eccentricity e) changes towards a more circular orbit in a linear and weak manner. The right ascension of the ascending node Ω and the mean anomaly M are influenced by the disturbance only short periodically.

Transformation method of exterior orientation angular elements obtained via position and orientation system under Gauss-Kruger projection coordinate system

Data obtained via airborne position and orientation system (POS) is in WGS 84 global geocentric reference frame, while the national coordinate reference system for topographic mapping in China is generally Gauss-Kruger projection coordinate system. Therefore, data obtained via a POS must be transformed to national coordinate system. Owing to the effects of earth curvature and meridian deviation, there are some errors in the process of angle transformation from roll, pitch, and heading (Φ,Θ,Ψ) obtained directly via a POS to the attitude angles of images (φ,ω,κ) needed in photogrammetry. On the basis of effect theories of earth curvature and meridian deviation on exterior orientation angular elements of images, a method using a compensation matrix to correct the transformation errors from attitude angles obtained via the POS to exterior orientation angular elements of images is proposed in this paper. Moreover, the rigorous formula of the compensation matrix is deduced. Two sets of actual data obtained via a POS AV 510, which are different in scale and terrain, are selected and used to perform experiments. The empirical results not only indicate that the compensation matrix proposed in this paper is correct and practical but also show that transformation accuracy of exterior orientation angular elements obtained via the POS based on compensation matrix is relevant to the selection of vertical axis (a projection of central meridian) of Gauss-Kruger projection coordinate system; the proper vertical axis should be the Gauss-Kruger projection of the central meridian of projection zone in which the survey area locates. However, the transformation accuracy of exterior orientation angular elements is irrelevant to the choice of origin of coordinate system; it is appropriate that the origin of coordinate system locates at the center point of the survey area. Moreover, transformation accuracy of exterior orientation angular elements achieved based on the compensation matrix deduced in this paper is higher than that obtained via the existing POS processing software.

DIRAC: A new version of computer algebra tools for studying the properties and behavior of hydrogen-like ions

During recent years, the Dirac package has proved to be an efficient tool for studying the structural properties and dynamic behavior of hydrogen-like ions. Originally designed as a set of Maple procedures, this package provides interactive access to the wave and Green's functions in the non-relativistic and relativistic frameworks and supports analytical evaluation of a large number of radial integrals that are required for the construction of transition amplitudes and interaction cross sections. We provide here a new version of the Dirac program which is developed within the framework of Mathematica (version 6.0). This new version aims to cater to a wider community of researchers that use the Mathematica platform and to take advantage of the generally faster processing times therein. Moreover, the addition of new procedures, a more convenient and detailed help system, as well as source code revisions to overcome identified shortcomings should ensure expanded use of the new Dirac program over its predecessor.

Enhanced dispersion compensation capability of angular elements based on beam expansion

We demonstrate that beam size manipulation plays an important role in dispersion compensation. With expanded beam, the maximal negative group delay dispersion (GDD) provided by angular elements increases by an order of magnitude compared with original beam. Both calculation and experimental results show that a modest 2 x and 4 x expanded beams can improve dispersion compensation capability of prisms or acousto-optical deflectors: the restored minimal pulse width decreases by 50% and the corresponding distance between angular elements is shortened more than 70 cm. These findings will be helpful for designing dispersion compensation schemes for femtosecond pulse laser application systems such as multiphoton microscopy or laser micromachining.

Effect of partial mixing of matter on the hydrodynamic angular momentum transport processes in massive main-sequence stars

We consider the evolution of a rotating star with a mass of 16M ⊙ and an angular momentum of 3.25 × 1052 g cm2 s−1, along with the hydrodynamic transport of angular momentum and chemical elements in its interiors. When the partial mixing of matter of the turbulent radiative envelope and the convective core is taken into account, the efficiency of the angular momentum transport by meridional circulation in the stellar interiors and the duration of the hydrogen burning phase increase. Depending on the Schmidt number in the turbulent radiative stellar envelope, the ratio of the equatorial rotational velocity to the circular one increases with time in the process of stellar evolution and can become typical of early-type Be stars during an additional evolution time of the star on the main sequence. Partial mixing of matter is a necessary condition under which the hydrodynamic transport processes can increase the angular momentum of the outer stellar layer to an extent that the equatorial rotational velocity begins to increase during the second half of the evolutionary phase of the star on the main sequence, as shown by observations of the brightest stars in open star clusters with ages of 10–25 Myr. When the turbulent Schmidt number is 0.4, the equatorial rotational velocity of the star increases during the second half of the hydrogen burning phase in the convective core from 330 to 450 km s−1.

A mixture of grass and clover combines the positive effects of both plant species on selected soil biota

The introduction of N 2-fixing white clover ( Trifolium repens) in grassland is a management measure that may contribute to sustainable grassland systems by making them less dependent on inorganic fertilizers. However, little is known about the impact of this measure on soil biota and ecosystem services. We investigated earthworms, nematodes, bacteria and fungi in an experiment in which white clover-only and a mixture of grass and white clover without fertilization were compared with grass-only with and without fertilization. In comparison with grass-only, white clover-only had a lower total root biomass and a lower C/N-ratio in the above- and below-ground plant biomass. These plant characteristics resulted in a lower bacterial biomass, a lower fungal biomass, a higher proportion of bacterivorous nematode dauerlarvae, a lesser proportion of herbivorous nematodes and a greater abundance of earthworms in clover-only. The quantity and quality (C/N-ratio) of the above- and below-ground plant biomass in the mixture of grass and white clover (20–30% clover in the DM) was comparable with grass fertilized with 150 kg N ha −1 of inorganic fertilizer. Differences between these treatments might show specific clover effects in the grass–clover mixture on soil biota other than quantity and C/N-ratio of the litter. However, the only differences were a higher proportion of bacterivorous nematode dauerlarvae and a different nematode community composition in grass–clover. The soil structure in white clover-only showed a higher proportion of angular blocky elements, a lower penetration resistance, a higher number of earthworm burrows, a higher potential N-mineralization and respiration than the soil in grass-only. This suggests that clover stimulates the ecosystem services of water infiltration and supply of nutrients, but is less conducive to soil structure maintenance. The grass–clover mixture differed from grass-only in a higher respiration and from clover-only in a higher percentage of soil crumbs. We suggest that when clover is introduced in grassland to reduce the reliance on inorganic fertilizer, the mixture of grass and clover maintains the positive impact of grass roots on soil structure and increases the supply of nutrients via the soil food web. Thus, a grass–clover mixture combines the agronomic benefits of the two plant types.

Quasi-relativistic treatment of the low-lying KCs states

The potential energy curves, permanent and transition dipole moments as well as spin-orbit and angular coupling matrix elements between the KCs electronic states converging to the lowest three dissociation limits were evaluated in the basis of the spin-averaged wavefunctions corresponding to pure Hund’s coupling case ( a). The quasi-relativistic matrix elements have been obtained for a wide range of internuclear distance by using of small (9-electrons) effective core pseudopotentials of both atoms. The core-valence correlation has been accounted for a large scale multi-reference configuration interaction method combined with semi-empirical core polarization potentials. The static dipole polarizabilities of the ground X 1 Σ + and a 3 Σ + states were extracted from the closed-shell coupled-cluster energies by the finite-field method. Among the singlet and triplet Σ + states manifold the pronounced avoided crossing effect between repulsive walls of the (2,3) 3 Σ + states has been discovered and analyzed by finite-difference calculation of radial coupling matrix elements. The resulting transition dipole moments and potentials were used to predict radiative lifetimes and emission branching ratios of excited vibronic states while the calculated angular coupling matrix elements were transformed to Λ -doubling constants of the (1,2) 1 Π states and magnetic g -factor of the ground state. The accuracies of the present results are discussed by comparing with experimental data and preceding calculations.

Determination of the ancient geomagnetic field elements from thermal remanent magnetization corrected for magnetic anisotropy

A method is proposed for correcting the magnetic anisotropy of baked magnetic material from archaeological objects and rocks intended for the study of its magnetization and for gaining data on the angular elements of the ancient geomagnetic field. The application of this correction decreases the spread of individual determinations obtained in studying the sample magnetization from an object and increases the determination accuracy of the average value of the ancient geomagnetic field elements. This, in turn, makes it possible to increase the accuracy of its dating.

Numerical studies of chaotic Hilda-type orbits

Earlier work indicates a comparatively rapid chaotic evolution of the orbits of some Hilda asteroids that move at the border of the domain occupied by the characteristic parameters of the objects at the 3/2 mean motion resonance. A simple Jupiter–Saturn model of the forces leads to numerical results on some of these cases and allows a search for additional resonances that can contribute to the chaotic evolution. In this context the importance of the secondary resonances that depend on the period of revolution of the argument of perihelion is pointed out. Among the studied additional resonances there are three-body resonances with arguments that depend on the mean longitudes of Jupiter, Saturn, and asteroid, but on slowly circulating angular elements of the asteroid as well, and the frequency of these arguments is close to a rational ratio with respect to the frequency of the libration due to the basic resonance.

The problem of optimal control of the orientation of an orbit of a spacecraft as a deformable figure

The problem of optimal control of the orbit orientation of a spacecraft regarded as a deformable figure is studied. The problem of optimal re-orientation of an orbit is formulated as a problem of optimal control of the motion of the center of mass of a spacecraft with a movable right end of the trajectory and is solved based on the Pontryagin maximum principle. To describe the orientation of an instantaneous orbit, a new quaternion osculating element that replaces three classical angular elements of the orbit is applied. Necessary optimality conditions are obtained; several first integrals of the system of equations of the boundary-value problem of the maximum principle are found; transformations that reduce the dimension of the system of differential equations of the boundary-value problem (without their complication) are proposed; the proposed approach is analyzed, and an example of numerical solution of the problem is presented

An evaluation of the uncertainty associated with the measurement of the geomagnetic field with a D/I fluxgate theodolite

An analysis of the sources of uncertainty in measuring the angular elements of the geomagnetic field with the D/I fluxgate theodolite on the basis of the Guide to the Expression of Uncertainty in Measurement published by the International Organization for Standardization is presented. Along with the uncertainty associated with random effects, the habitual measurement procedure evidences the existence of systematic effects that are often ignored in the daily observatory practice. Special emphasis has been put on the development of a plausible theoretical scheme to explain the origin of such effects, and a series of procedures are proposed to find their actual sources as well as several recommendations with the final aim to improve the accuracy of the observations. Other effects, which strictly do not seem to suit the traditional classification into either systematic or random, are also analysed. Some of the results obtained have been applied to the absolute instruments in use at the Livingston Island Geomagnetic Observatory and at certain European observatories. Systematic contributions to uncertainty are difficult to outline in a general case, since they depend on each particular instrument. On the other hand, an accurate estimation of the uncertainty associated with random effects has been obtained, concluding that their magnitude does not generally exceed 0.1 arcmin for an experienced observer, for either declination or inclination.

The problem of rendezvous of a controlled space vehicle with an uncontrolled space vehicle moving along an elliptical Keplerian orbit in the central Newtonian gravitational field

The problem of rendezvous of a controlled space vehicle with an uncontrolled space vehicle moving along an elliptical Keplerian orbit in the central Newtonian gravitational field is considered. The problem is formulated as the problem of optimal control motion of the center of mass of the controlled space vehicle with a flexible right end of the trajectory and is solved on the basis of the Pontryagin maximum principle. A new quaternion osculating orbital element, instead of three classical angular elements, is used for description of the orientation of the instantaneous orbit of the space vehicle. Necessary optimal conditions are obtained; first integrals of the system of equations of the boundary value problem of the maximum principle are found; transformations reducing the dimensionality of the system of differential equations of the boundary value problem (without their complication) are proposed; analysis of the proposed solution is given; and examples of numerical solution of the problem are presented.

Frictional properties of natural fault gouge from a low‐angle normal fault, Panamint Valley, California

We investigate the relationship between frictional strength and clay mineralogy of natural fault gouge from a low‐angle normal fault in Panamint Valley, California. Gouge samples were collected from the fault zone at five locations along a north–south transect of the range‐bounding fault system, spanning a variety of bedrock lithologies. Samples were powdered and sheared in the double‐direct shear configuration at room temperature and humidity. The coefficient of friction, μ, was measured at a range of normal stresses from 5 to 150 MPa for all samples. Our results reinforce the intuitive understanding that natural fault gouge zones are inherently heterogeneous. Samples from a single location exhibit dramatic differences in behavior, yet all three were collected within a meter of the fault core. For most of the samples, friction varies from μ = 0.6 to μ = 0.7, consistent with Byerlee's law. However, samples with greater than 50 wt % total clay content were much weaker (μ = 0.2–0.4). Expandable clay content of the samples ranged from 10 to 40 wt %. Frictional weakness did not correlate with expandable clays. Our results indicate that friction decreases with increasing total clay content, rather than with the abundance of expandable clays. The combination of field relations, analytical results, and friction measurements indicates a positive correlation between clay content, fabric intensity, and localization of strain in the fault core. A mechanism based upon foliations enveloping angular elements to reduce friction is suggested for weakening of fault gouge composed of mixed clay and granular material. We provide broad constraints of 1–5 km on the depth of gouge generation and the depth at which fault weakness initiates. We show that slip on the Panamint Valley fault and similar low‐angle normal faults is mechanically feasible in the mid‐upper crust if the strength of the fault is limited by weak, clay‐rich fault gouge.

Calculation of the mean orbit of a meteoroid stream

The traditional approach used for averaging the parameters of a meteoroid gives results that are biased by several conceptual defects: among others things, the mean orbital elements do not satisfy the laws of celestial mechanics. The Voloshchuk & Kashcheev method in the domain of geocentric parameters removes all of these defects except one: the epoch corresponding to the mean geocentric values, which is critical for the calculation of the mean heliocentric orbital elements from the mean geocentric radiant coordinates and velocity. We propose a new approach: our solution gives the mean orbital elements and the geocentric radiant parameters of the meteor stream, free from all conceptual faults. Instead of the Keplerian orbital elements, we average the heliocentric vectorial elements, and the solution is obtained by the leastsquares method completed by placing two constraints on the mean vectorial elements. One may calculate the corresponding geocentric parameters using the theoretical radiant approach. However, to obtain mutually numerically consistent helioparameters and geoparameters, all members of the stream should be pre-integrated into a common epoch of time. Our approach, due to simultaneous averaging of seven variables, is limited to the streams of seven or more members only. We give the results of the numerical example, which shows that the mean values obtained by our approach differ slightly from those obtained by the traditional averaging. However, for some streams and for some particular orbital elements, the differences can exceeds 2 au in the semimajor axes or 0. 5 in the angular orbital elements.

Experimental and theoretical studies of Λ doublings and permanent electric dipoles in the low-lying Π1 states of NaCs

We present experimental data on the electric permanent dipole moments d(v',J') and lambda splittings (q factors) in the quasidegenerate (3) 1pi(e/f) state of the NaCs molecule over a wide range of the vibrational (v') and rotational (J') quantum numbers by using the combination of dc Stark mixing and electric radio frequency-optical double resonance methods. Within the experimental (3) 1pi state v' ranged from v' = 0 to 34, q values exhibited a pronounced decrease from 7.91x10(-6) to 0.47x10(-6) cm(-1), while absolute value(d) values varied between 8.0 and 5.0 D. Experimental evaluation yielded small d values about 1 D for D2 1pi state v' < 3 levels. The experiment is supported by ab initio electronic structure calculations performed for the (1-3) 1pi states of NaCs by means of the many-body multipartitioning perturbation theory of potential energy curves, permanent dipole, and angular coupling matrix elements for the lowest singlet states. The predicted d values reproduce their experimental counterparts within the measurement errors while theoretical q factors reproduce the measured v' dependence being, however, systematically overestimated by ca. 1x10(-6) cm(-1). The present NaCs data are compared with those of the NaK and NaRb molecules.