An Improved Numerical Fit to the Peak Harmonic Gravitational Wave Frequency Emitted by an Eccentric Binary

I present a numerical fit to the peak harmonic gravitational wave frequency emitted by an eccentric binary system in the post-Newtonian approximation. This fit significantly improves upon a previous commonly-used fit in population synthesis studies, in particular for eccentricities ≲0.8.

CCD astrometric observations of faint satellites and update of their orbits

This paper reports on our observing campaign of faint satellites performed at the National Time Service Center and Sheshan station of SHAO from 1994 up to today. In the past few years due to benefit from using a large size CCD and the publication of the modern catalogues (UCAC2), a series of observations of faint satellites were obtained by us. Moreover the work of improving the orbit of Phoebe via numerical fit to the observations over a century is also presented.

Autofrettage of Open-End Tubes—Pressures, Stresses, Strains, and Code Comparisons

Autofrettage is used to introduce advantageous residual stresses into pressure vessels. The Bauschinger effect can produce less compressive residual hoop stresses near the bore than are predicted by “ideal” autofrettage solutions. A recently developed numerical analysis procedure is adopted and extended. The ratio of calculated autofrettage pressure (numerical)/ideal autofrettage pressure (Tresca criterion and plane stress) is calculated and verified against available solutions. The case of open-end conditions based upon von Mises and engineering plane strain (constant axial strain with zero net axial force) is examined in detail. The ratio in this case varies between unity and 2/3, but exhibits very significant variations from the plane stress case when the diameter ratio of the tube exceeds 1.8. Results are within 0.5 percent of available analytical, numerical, and experimental results. A simple numerical fit allows all autofrettage pressures to be replicated to within 0.5 percent. The true plane strain pressure ratio is examined and shown to be inappropriate in modeling engineering plane strain. A number of residual hoop and axial stress profiles is presented for radius ratio 2.0. Calculated pressures are used to determine residual hoop stress values for tube diameter ratios from 1.1 to 3.0 for the full range of percentage overstrain levels. These comparisons indicate that Bauschinger effect is evident when the ratio autofrettage radius/bore radius exceeds 1.2, irrespective of diameter ratio. To assist designers the important values of residual hoop stress at the bore are summarized in a composite plot and a numerical fit is provided. The accuracy of the current ASME code using pressure criteria is assessed. The code is shown to be generally and modestly conservative. A design procedure is proposed which appears capable of extending code validity beyond 40 percent overstrain (the limit of the current code) and of eliminating the small nonconservatism at very low overstrain. Hoop strain values are calculated at both the bore and outside diameter of a tube of radius ratio 2 at the peak of the autofrettage cycle using von Mises criterion with open-end, closed-end, and plane strain conditions. These are compared with available solutions; general agreement is demonstrated, with agreement within 2 percent with an accepted simple formula in the case of open ends. ASME code predictions of percentage overstrain based upon strains at the peak of the autofrettage cycle are generally within 6 percent of numerical predictions. This is in turn produces an agreement within approximately 3 percent in residual bore hoop stress calculation. This discrepancy is generally conservative, becoming non-conservative only at overstrain levels exceeding 80 percent. Strain during removal of autofrettage pressure, in the presence of Bauschinger effect, is also calculated. This shows that the difference in strain during the unloading phase is up to 8 percent (ID) and 6.3 percent (OD) compared with the predictions of elastic unloading. These latter results show similar agreement with the ASME code as in the peak-strain analysis and permit correction of estimates of percentage overstrain based upon permanent bore enlargement.

High S/N Na I D Line Profiles in Late-Type MS Stars and their Importance for Stellar Modelling

Progress in observational techniques (i.e. high S/N spectroscopy) and modelling (e.g. RE models including convection, nonLTE codes, accurate atomic data) make significant to carry to extremes the numerical fit of a portion of the stellar spectrum and try to interpret the residual differences between calculations and observations in terms of stellar characteristics new respect to the employed model.We have started to apply this synthesis method to a set of high resolution, high S/N spectra of late-type dwarfs in the region of the Na I D lines, obtained at ESO with the 1.4m CAT on May 1989 (Franchini et al. 1992). The dwarf stars are modelled in radiative equilibrium (RE), and the Na I D line synthesis accounts for nonLTE and blend effects.