Asymptotic solutions of a Hamiltonian system in intervals with several turning points
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A parallel algorithm for the efficient solution of a time dependent reaction convection diffusion equation with small parameter on the diffusion term is presented. The method is based on a domain decomposition that is dictated by singular perturbation analysis. The analysis is used to determine regions where certain reduced equations may be solved in place of the full equation. Parallelism is evident at two levels. Domain decomposition provides parallelism at the highest level, and within each domain there is ample opportunity to exploit parallelism. Run time results demonstrate the viability of the method.
The magnetohydrodynamic wave emission from several localized, periodic, kinematically specified fluid velocity fields are calculated using Lighthill's method for finding the far-field wave forms. The waves propagate through an isothermal and uniform plasma with a constant B field. General properties of the energy flux are illustrated with models of pulsating flux tubes and convective rolls. Interference theory from geometrical optics is used to find the direction of minimum fast-wave emission from multipole sources and slow-wave emission from discontinuous sources. The distribution of total flux in fast and slow waves varies with the ratios of the source dimensions l to the acoustic and Alfven wavelengths.
Using available infrared catalogs, an inventory is taken of the AGB star losing large amounts of mass within about 1 kpc of the sun. A surface density of these stars is estimated of about 25/sq kpc projected onto the plane of the Galaxy. Of these stars, about one-half are oxygen-rich while the other half are carbon-rich. The total mass-loss rate from AGB stars into the interstellar medium is probably between 3 and 6 x 10 to the -4th solar mass/sq kpc/yr. Within the uncertainties, this is in reasonable agreement with an estimated net loss rate of about 8 x 10 to the -4th solar mass/sq kpc/yr for main-sequence stars with initial masses between 1 and 5 solar masses as they evolve to white dwarfs. However, it is possible that there are important sources of mass loss which have not yet been identified. In the solar neighborhood, about one-half of all about 1.2 solar mass main-sequence stars spend greater than 30,000 yr in a carbon-star phase where they lose 1-2 x 10 to the -5th solar mass/yr and then become white dwarfs with about 0.7 solar mass.
A new scheme to integrate a system of stiff differential equations for both the elasto-plastic creep and the unified viscoplastic theories is presented. The method has high stability, allows large time increments, and is implicit and iterative. It is suitable for use with continuum damage theories. The scheme was incorporated into MARC, a commercial finite element code through a user subroutine called HYPELA. Results from numerical problems under complex loading histories are presented for both small and large scale analysis. To demonstrate the scheme's accuracy and efficiency, comparisons to a self-adaptive forward Euler method are made.
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The circumstellar grains of two hot evolved postasymptotic giant branch stars, HD 89353 and HD 213985, are examined, deriving the extinction around 2175 A. An unsuccessful attempt to detect 6614 A diffuse band absorption arising from the grains implies that the carrier of this diffuse band is not the carrier of the unidentified IR features reported by other investigators nor of the 2175 A bump. It is found that the linear UV extinction of the carbon-rich star HD 89353 continues across the 2175 A region with no sign of the bump; for HD 213985 the reverse is found: a strong, wide bump in the mid-UV. A wavelength of 2300 A is derived for the HD 213985 bump, which lies longward of its unusual position in the interstellar medium. Since HD 89353 is metal-poor yet rich in hydrogen and carbon, the linear extinction arises from hydrocarbon grains of radius less than 300 A.
The transition from oxygen-rich (M) stars to S stars and then to C stars is examined using data on the chemical properties of the stars. The photospheric and circumstellar spectral characteristics of M and C stars are summarized. Consideration is given to the color distributions of carbon stars, visual carbon stars as transition objects, and radio observations of visual carbon stars. The chemical characteristics of S stars, the evolution of oxygen-rich stars on the AGB, and the transition between AGB stars and planetary nebulae are discussed. IRAS data are used to construct an evolutionary scenario for AGB stars, in which some mass-losing M stars remain oxygen rich, while others become carbon rich.
Brackett series lines with very broad inverted P Cygni and shell-like profiles have been detected toward the post-AGB star HD 56126. These profiles suggest that an active phase of mass loss has begun recently in this star. The star has had at least one previous episode of intense mass loss, attested to by its strong far-infrared emission. HD 56126 is also known for having a broad emission feature at 21 microns. The unidentified emission bands at 3.3 and 3.4 microns are also present in the spectrum of HD 56126, but the near-infrared spectrum provides little help in establishing the carrier of the 21 microns band.
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A new scheme to integrate a system of stiff differential equations for both the elasto-plastic creep and the unified viscoplastic theories is presented. The method has high stability, allows large time increments, and is implicit and iterative. It is suitable for use with continuum damage theories. The scheme was incorporated into MARC, a commercial finite element code through a user subroutine called HYPELA. Results from numerical problems under complex loading histories are presented for both small and large scale analysis. To demonstrate the scheme's accuracy and efficiency, comparisons to a self-adaptive forward Euler method are made.
Stability analyses are performed for nonradial g(+)-mode pulsations of postasymptotic AGB stellar models to determine the location of their pulsational instability strips in the Hertzsprung-Russell diagram. Stellar models are analyzed that are assumed to have undergone a major mass loss event either near the tip of the AGB or shortly thereafter and, therefore, consist of a 50-percent carbon 50-percent oxygen core. Their mass is 0.6 solar mass, which is in good agreement with the peak of the observed distribution of white dwarf masses. The results are compared both to the observed planetary nebula nuclei variables and the hot pulsating DO variables. An analysis is also presented of the stability of DB white dwarfs, which have much deeper and stronger convection zones, and an instability strip is found between about 18,000 and 26,000 K approximately as observed for the known variable stars.
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The possibility is studied that during its transition from the AGB to the central star of a PN, a rotating star blows a collimated wind along the symmetry axis. The wind results from the deformation of the stellar surface due to fast rotation. Evolutionary calculations using a spherical stellar model are used to argue that an essential ingredient in the proposed scenario is that the evolving star is in a common envelope with a lower mass companion which spins up the envelope.
Ground-based 7.4-24-micron spectra of two post-AGB objects, HD 161796 and HD 179821, are reported, and they are compared to those of other preplanetary nebulae. HD 161796 and HD 17982 show emission features at 10-12 microns and at 10 microns, and they exhibit a very rapid increase in flux between 13 and 15.5 microns. In view of the O-rich photosphere of HD 161796 and the presence of OH maser emission around all three objects, these features are ascribed to various oxides. The observed spectral features are quite different from the canonical silicate features observed in most O-rich giants. It is argued that HD 161796 and the bipolar nebulae Roberts 22 and NGC 6302 have all undergone the third dredge-up, with most of the dredged-up carbon having been converted to nitrogen by envelope-burning. It is concluded that carbon-rich grain material, produced during the interval between the end of the third dredge-up and the moment when envelope burning finally reduced the C/O ratio below unity again, could be responsible for the UIR bands now being excited in Roberts 22 and NGC 6302.
The question of whether isotopically anomalous SiC particles found in meteorites originate in AGB stars is addressed. It is shown that if the peak helium shell flash temperatures of massive (6-9 solar masses) stars are about 10 percent larger than they are normally assumed to be, alpha particle reactions with the magnesium will become significant. Then the (Mg-29)(alpha, n)Si-29 reaction produces a large excess of Si-29. With a light element nuclear reaction network, the evolution of the silicon isotopic composition during AGB evolution is calculated. It is found that the experimentally determined correlation between excess Si-29 and excess Si-30 in SiC particles from carbonaceous chondrites can indeed be naturally produced in this way. It is suggested that if the large isotopically anomalous SiC particles carrying nearly pure-process krypton and xenon do indeed originate in AGB stars, those stars were massive and had peak shell flash temperatures near 450 KM.
A theory for predicting the noise field of supersonic propellers with realistic blade geometries is presented. The theory, which utilizes a large-blade-count approximation, provides an efficient formula for predicting the radiation of sound from all three sources of propeller noise. Comparisons with a full numerical integration indicate that the levels predicted by this formula are quite accurate. Calculations also show that, for high speed propellers, the noise radiated by the Lighthill quadrupole source is rather substantial when compared with the noise radiated by the blade thickness and loading sources. Results from a preliminary application of the theory indicate that the peak noise level generated by a supersonic propeller initially increases with increasing tip helical Mach number, but is eventually reaches a plateau and does not increase further. The predicted trend shows qualitative agreement with the experimental observations.