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The problem of astrophysical sources of detectable gravitational radiation is considered from the stellar-evolution viewpoint. Calculations are presented which indicate that the final stages of evolution may well be dominated by rapidly rotating, collapsing cores which develop nonaxisymmetric configurations. Such events emit large amounts of gravitational radiation which should be detectable in the near future.
The evolution of initially spherical, uniform-density, and uniform-velocity-dispersion stellar systems is investigated by means of a three-dimensional N-body computer model. Some 100,000 simulation stars are used to follow the collapse and relaxation of the system for various amounts of angular momentum in solid-body rotation. For initially low values of the angular momentum satisfying the Ostriker-Pebbles stability criterion the systems quickly relax to an axisymmetric shape and resemble elliptical galaxies in appearance. The maximum flattening for these systems is equivalent only to an E2 system. For larger values of the initial angular momentum bars develop, and the systems undergo a much more drastic evolution. The apparent rotational and random velocities of the barred systems are very sensitive to the viewing direction. An additional complication is the frequent misalignment of the apparent major axis with the direction that reflects the maximum rotation.
A general procedure is developed for describing non-Keplerian accretion in the region between the event horizon of a black hole or a Rosen collapsed object and a distance greater than or equal to the marginally stable circular orbit. The relevant equations and boundary conditions are described, ways to obtain solutions are discussed, and some flow solutions are examined. The consistency and advantages of the proposed method are examined.
A horn antenna that is readily collapsible while not in use is described. A number of different sized annular metal rings are arranged in a sequence such that each ring is larger than the one that precedes it in the sequence. A number of thin flexible electrically conductive members attach successive metal rings together physically and connect them together electrically. Each flexible conductive member is attached to make electrical contact between the outside surface of a metal ring and the inside surface of an adjacent metal ring in the sequence.
The paper shows how trains of nonlinear, dispersive waves can be produced by allowing a region of mixed fluid, with a potential energy greater than its surroundings, to collapse towards its equilibrium state. The number of waves and their amplitude depend on the properties of the mixed region and of the ambient stratification. Three different geometrical configurations have been chosen and while each gives qualitatively the same results the form taken by the generated waves and the final equilibrium shape of the mixed region depend critically on these geometrical factors. The internal waves produced by this mechanism are related to waves produced in natural systems and it is shown that the observations support at least one possible explanation for those found in the oceans and planetary atmospheres.
The results of a preliminary investigation of several processes that are of interest both for the formation of stars and for the evolution of planetary systems are presented. It is shown that turbulent viscosity is capable of playing an important role in conveying angular momentum over time scales that are short enough to be significant. Meridional circulation can also act in this fashion during some phases of the evolution. This transport may reduce the probability of formation of the rings that have been found by most earlier investigators. Transport and mixing on a faster than cooling time scale should also inhibit usual modes of fragmentation and the present work casts some doubt on the multiple successive fragmentation scenarios that lead from a massive molecular cloud to a collection of roughly solar mass protostars. The conditions that are probable in the disks that would exist at varying phases of collapse are examined and it is concluded that turbulent viscosity would be very important in a pre-solar nebula.
The evolution of a Population I star of 15 solar masses is described from the carbon shell burning stage to the formation and collapse of an iron core. An unusual aspect of the evolution is that neon ignition occurs off-center and neon burning propagates inward by a series of shell flashes. The extent of the core burning is generally smaller than the Chandrasekhar mass, so that most of the nuclear energy generation occurs in shell sources. Because of degeneracy and the influence of rapid convective mixing, these shell sources are unstable and the core goes through large excursions in temperature and density. The small core also causes the shell sources to converge into a narrow mass region slightly above the Chandrasekhar mass. Thus, the final nucleosynthesis yields are generally small, with silicon being most strongly enhanced with respect to solar system abundances.
The isothermal collapse of a rotating protostar with pressure and self-gravity is calculated by a hydrodynamic computer code that treats three space dimensions. A number of initial conditions are tested to determine the conditions under which a cloud is unstable to fragmentation. It is shown that fragmentation does not proceed to a significant extent during the first free-fall time, but that in most cases fragmentation has occurred by 1.5 to 2 times the initial free-fall time. The extent to which the density in the fragments is enhanced over that in their surroundings on this time scale depends on the initial ratio of thermal to gravitational energy, but is only weakly dependent on the type and amplitude of the perturbation and on the initial rotational energy.
Properties of self-consistent numerical hydrodynamic models are compared with observed properties of several dark clouds. The results are consistent with the view that these clouds are undergoing gravitational collapse. The clouds appear to have evolved from similar initial states and to have ages comparable to their free-fall times. Derived cloud masses range between 10 and 1000 solar masses, correlating with cloud size. The models reproduce observed cloud-to-cloud variations in the (C-13)O abundance, and they offer additional evidence that the (C-13)O abundance varies within individual clouds.
Results are presented of an analytical investigation on the dynamic collapse of an elastic periodically supported column. The column has an attached mass at one end and impacts a rigid surface with prescribed velocity and angle of incidence at the other end. A first-order approximate nonlinear analysis is developed in which it is assumed that only first-order nonlinear terms need be retained. Differential equations are derived and solved numerically by explicit time integration in order to determine specific ranges of the basic nondimensional parameters for which the response characteristics are markedly different. To assess modeling sophistication relative to prediction accuracy, a comparison is made of the results from this approximate analysis with those of a finite element computer code based on a convected coordinate formulation.
Many investigations have considered structural collapse from strictly the transient point of view. While such an approach is ideally correct, certain difficulties have to be overcome in its implementation. The present investigation is concerned with the development of self-adaptive algorithms which make it possible to conduct the analysis of both static elastic and elastic-plastic postbuckling, as well as static loading to the onset of buckling followed by subsequent dynamic postbuckling. The approach employed to solve the static portion of loading is to extend the constrained Incremental Newton-Raphson (INR) algorithm by incorporating elastic-plastic constitutive characterizations. Large deformation moderate strain theory is adopted to establish the overall strategy. Attention is given to governing field equations, aspects of algorithmic development, and numerical experiments conducted to illustrate the efficiency and stability of the developed schemes.
Cable-controlled mechanisms allow large structures stored in small spaces. Combination of telescoping struts and pivot points allows very large structure collapsed into very small one. Concept used not only for straight but for tapered or curved ones as well. Structure adaptable to terrestrial uses as portable towers, scaffolds, and bridge beams folded compactly for transportation or storage.
Solutions that describe the collapse of a molecular cloud core that is initially in unstable equilibrium, embedded within an envelope of uniform density, and rotating at the same rate as the envelope are given. Hydrodynamic equations, including self gravity, are deduced to a set of ordinary differential equations, which are solved by the method of matched asymptotic expansions. Results of these calculations are: (1) the range of stellar masses derived seems to correspond to realistic ranges of observed stellar masses and interstellar cloud parameters, (2) the proper measure of dissipation rate is the ratio of accretion time to viscous diffusion time, and (3) the pressure distribution on the surface of an accreting protostar is nonuniform in a way that favors the channeling of a stellar wind into a bipolar flow directed along the rotation axis.
Stellar collapse is accompanied by emission of E sub neutrino approximately 10 MeV neutrinos and antineutrinos with the energy output W sub neutrino approximately 10 to the 53rd power to 10 to the 54th power erg. Annihilation of these particles in the vicinity of collapsar is considered. The physical consequences are discussed.
Preliminary results of a surface photometry survey of globular cluster cores are reported. Two new cores with post-collapse morphology have been found, and two possible candidates. The estimated fraction of clusters with this core morphology in the Galaxy is only a few percent. Most clusters do not show a morphology similar to the predictions of the central black hole models.
The extinction of marine phyto-and zoo-plankton across the K-T boundary has been well documented. Such an event may have resulted in decreased photosynthetic fixation of carbon in surface waters and a collapse of the food chain in the marine biosphere. Because the vertical and horizontal distribution of the carbon isotopic composition of total dissolved carton (TDC) in the modern ocean is controlled by the transfer of organic carbon from the surface to deep reservoirs, it follows that a major disruption of the marine biosphere would have had a major effect on the distribution of carbon isotopes in the ocean. Negative carbon isotope excursions have been identified at many marine K-T boundary sequences worldwide and are interpreted as a signal of decreased oceanic primary productivity. However, the magnitude, duration and consequences of this productivity crisis have been poorly constrained. On the basis of planktonic and benthic calcareous microfossil carbon isotope and other geochemical data from DSDP Site 577 located on the Shatsky Rise in the north-central Pacific, as well as other sites, researchers have been able to provide a reasonable estimate of the duration and magnitude of this event.
Simple models of the Martian crust are summarized that predict extensional deformation style on the basis of depth, material friction and strength, and hydraulic conditions appropriate to the planet. These models indicate that tension fractures may be common features on Mars, given adequate differential stress conditions. Examples of tension fractures on Mars inferred from morphological criteria are examined based on the probable geologic conditions in which they formed and on model constraints. It is proposed that the grabens and collapse features of Valles Marineris are controlled by tension fractures in intact basement rocks that lie below impact ejecta.
The prediction of the ultimate load carrying capability for compressively loaded shell structures is a challenging nonlinear analysis problem. Selected areas of finite element technology research and nonlinear solution technology are assessed. Herein, a finite element analysis procedure is applied to four shell collapse problems which have been used by computational structural mechanics researchers in the past. This assessment will focus on a number of different shell element formulations and on different approaches used to account for geometric nonlinearities. The results presented confirm that these aspects of nonlinear shell analysis can have a significant effect on the predicted nonlinear structural response. All analyses were performed using the CSM Testbed software system which allowed a convenient assessment of different element formulations with a consistent approach to solving the discretized nonlinear equations.