Vibrational-rotational analysis of the Hulthen potential using hydrogenic eigenfunction bases

Hulthen's potential admits analytical solutions for its energy eigenvalues and eigenfunctions corresponding to zero orbital angular momentum stales, but its non zero angular momentum states are not equally known. This work presents a vibrational-rotational analy sis of Hulthen's potential using hydrogenic eigenfunction bases, which may be of interest and useful to students of quantum mechanics at different stages.

Vibrational-rotational analysis of supersingular plus quadratic A/r(4)+r(2) potential

Most work on supersingular potentials has focused on the study of the ground state. In this paper, a global analysis of the ground and excited states for the successive values of the orbital angular momentum of the supersingular plus quadratic potential is carried out, making use of centrifugal plus quadratic potential eigenfunction bases. First, the radially nodeless states are variationally analyzed for each value of the orbital angular momentum using the corresponding functions of the bases; the output includes the centrifugal and frequency parameters of the auxiliary potentials and their eigenfunction bases. In the second stage, these bases are used to construct the matrix representation of the Hamiltonian of the system, and from its diagonalization the energy eigenvalues and eigenvectors of the successive states are obtained. The systematics of the accuracy and convergence of the overall results are discussed with emphasis on the dependence on the intensity of the supersingular part of the potential and on the orbital angular momentum.

Vibrational and rotational spectroscopy of (CD3OD)-C-13

We have used Fourier Transform spectral data on the C-O stretching mode of (CD3OD)-C-13 in order to perform a vibro-rotational analysis for this molecule. We have estimated a few molecular parameters of the ground and C-O stretching vibrational modes. Based on these parameters, and by using the Kwan-Dennison model, we propose assignments for a number of far-infrared laser transitions of (CD3OD)-C-13.

Analytical and semi-analytical analysis of an artificial satellite's rotational motion

The rotational motion of an artificial satellite is studied by considering torques produced by gravity gradient and direct solar radiation pressure. A satellite of circular cylinder shape is considered here, and Andoyers variables are used to describe the rotational motion. Expressions for direct solar radiation torque are derived. When the earth's shadow is not considered, an analytical solution is obtained using Lagrange's method of variation of parameters. A semi-analytical procedure is proposed to predict the satellite's attitude under the influence of the earth's shadow. The analytical solution shows that angular variables are linear and periodic functions of time while their conjugates suffer only periodic variations. When compared, numerical and analytical solutions have a good agreement during the time range considered.

Study of Stability of Rotational Motion of Spacecraft with Canonical Variables

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Quantitative Analysis of Placental Vasculature by Three-Dimensional Power Doppler Ultrasonography in Normal Pregnancies From 12 to 40 Weeks of Gestation

Evaluate the distribution and variation of placental vascular indices according to gestational age and placental volume. From March to November 2007, three-dimensional (3D)-power Doppler ultrasound was performed in 295 normal pregnancies from 12 to 40 weeks of gestation. Using the same preestablished settings for all patients, power Doppler was applied to the placenta and placental Volume was obtained by the rotational technique (VOCAL(TM)). The 3D-power histogram was used to determine the placental vascular indices: vascularization index (VI), flow index (FI) and vascularization-flow index (VFI). The placental vascular indices were then plotted against gestational age and placental volume. All placental vascular indices showed constant distribution throughout gestation. A tendency for a reduction in placental vascular indices with increased placental volume was observed, but was only statistically significant when placental FI was considered (p < 0.05). All placental vascular indices estimated by 3D-power Doppler ultrasonography presented constant distribution throughout gestation, despite the increase in placental volume according to gestational age. (C) 2008 Elsevier Ltd. All rights reserved.

Dielectric thermal analysis as a tool for quantitative-evaluation of the viscosity and the kinetics of epoxy resin cure

Dielectric thermal analysis has been proved as a valuable tool for monitoring the epoxy curing process and the related rheological properties in the fabrication of polymer-matrix composite materials. This technique also has the potential to be applied in the monitoring of magnet impregnation processes as well as in quality control. In this work we present the quantitative evaluation of the viscosity changing and the curing kinetics for a commercial Stycast epoxy resin system at different temperatures through the impedance analysis. The results showed correlation between the real component of the complex impedance and the isothermal reaction extent. Comparing the dielectric analysis result with the viscosity measured by rotational rheometer we observed a similar behavior reported for dynamic mechanic analysis. The results comparison have shown that the kinetics parameters obtained from DSC and DETA analysis showed different sensitivities related to the characteristics of curing stages. We concluded that the dielectric thermal analysis should be applied in quantitative evaluation of cure kinetics.

Stability analysis of the attitude of artificial satellites subject to gravity gradient torque

Using a canonical formulation, the stability of the rotational motion of artificial satellites is analyzed considering perturbations due to the gravity gradient torque. Here Andoyer's variables are used to describe the rotational motion. One of the approaches that allow the analysis of the stability of Hamiltonian systems needs the reduction of the Hamiltonian to a normal form. Firstly equilibrium points are found. Using generalized coordinates, the Hamiltonian is expanded in the neighborhood of the linearly stable equilibrium points. In a next step a canonical linear transformation is used to diagonalize the matrix associated to the linear part of the system. The quadratic part of the Hamiltonian is normalized. Based in a Lie-Hori algorithm a semi-analytic process for normalization is applied and the Hamiltonian is normalized up to the fourth order. Once the Hamiltonian is normalized up to order four, the analysis of stability of the equilibrium point is performed using the theorem of Kovalev and Savichenko. This semi-analytical approach was applied considering some data sets of hypothetical satellites. For the considered satellites it was observed few cases of stable motion. This work contributes for space missions where the maintenance of spacecraft attitude stability is required.

Assessment of first molars sagittal and rotational position in Class II, division 1 malocclusion

OBJECTIVE: This study assessed the anterior-posterior positioning of the upper and lower first molars, and the degree of rotation of the upper first molars in individuals with Class II, division 1, malocclusion. METHODS: Asymmetry I, an accurate device, was used to assess sixty sets of dental casts from 27 females and 33 males, aged between 12 and 21 years old, with bilateral Class II, division 1. The sagittal position of the molars was determined by positioning the casts onto the device, considering the midpalatal suture as a symmetry reference, and then measuring the distance between the mesial marginal ridge of the most distal molar and the mesial marginal ridge of its counterpart. With regard to the degree of rotation of the upper molar, the distance between landmarks on the mesial marginal ridge was measured. Chi-square test with a 5% significance level was used to verify the variation in molars position. Student's t test at 5% significance was used for statistical analysis. RESULTS: A great number of lower molars mesially positioned was registered, and the comparison between the right and left sides also demonstrated a higher number of mesially positioned molars on the right side of both arches. The average rotation of the molars was found to be 0.76 mm and 0.93 mm for the right and left sides, respectively. CONCLUSION: No statistically significant difference was detected between the mean values of molars mesialization regardless of the side and arch. Molars rotation, measured in millimeters, represented ¼ of Class II.

Semi-analytical study of the rotational motion stability of artificial satellites using quaternions

This study at aims performing the stability analysis of the rotational motion to artificial satellites using quaternions to describe the satellite attitude (orientation on the space). In the system of rotational motion equations, which is composed by four kinematic equations of the quaternions and by the three Euler equations in terms of the rotational spin components. The influence of the gravity gradient and the direct solar radiation pressure torques have been considered. Equilibrium points were obtained through numerical simulations using the softwares Matlab and Octave, which are then analyzed by the Routh-Hurwitz Stability Criterion.