Second Class Of Solutions Research Articles

CAUSAL BULK VISCOUS DISSIPATIVE ISOTROPIC COSMOLOGIES WITH VARIABLE GRAVITATIONAL AND COSMOLOGICAL CONSTANTS

We consider the evolution of a flat Friedmann–Robertson–Walker Universe, filled with a causal bulk viscous cosmological fluid, in the presence of variable gravitational and cosmological constants. The basic equation for the Hubble parameter, generalizing the evolution equation in the case of constant gravitational coupling and cosmological term is derived, under the supplementary assumption that the total energy of the Universe is conserved. By assuming that the cosmological constant is proportional to the square of the Hubble parameter and a power law dependence of the bulk viscosity coefficient, temperature and relaxation time on the energy density of the cosmological fluid, two classes of exact solutions of the field equations are obtained. In the first class of solutions the Universe ends in an inflationary era, while in the second class of solutions the expan-sion of the Universe is noninflationary for all times. In both models the cosmological "constant" is a decreasing function of time, while the gravitational "constant" increases in the early period of evolution of the Universe and tends in the large time limit to a constant value.

General Gauss–Bonnet brane cosmology

We consider five-dimensional spacetimes of constant three-dimensional spatial curvature in the presence of a bulk cosmological constant. We find the general solution of such a configuration in the presence of a Gauss–Bonnet term. Two classes of non-trivial bulk solutions are found. The first class is valid only under a fine-tuning relation between the Gauss–Bonnet coupling constant and the cosmological constant of the bulk spacetime. The second class of solutions are static and are the extensions of the AdS–Schwarzchild black holes. Hence in the absence of a cosmological constant or if the fine-tuning relation is not true, the generalized Birkhoff's staticity theorem holds even in the presence of Gauss–Bonnet curvature terms. We examine the consequences in braneworld cosmology obtaining the generalized Friedmann equations for a perfect fluid 3-brane and discuss how this modifies the usual scenario.

N-body simulations of interactions and mergings in small galaxy groups

AbstractIn this paper I focus on three topics related to the dynamical evolution of small galaxy groups, for which the input of N-body simulations has been decisive. These are the merging rates in compact groups, the properties of remnants of multiple mergers, and the evolution of disc galaxies surrounded by one or more satellites. The short dynamical times of compact groups make it difficult to understand why such groups are observed at all. N-body simulations have pointed out two possible classes of solutions to this problem. The first one proposes that there is ongoing formation of compact groups, or that the longevity of the group is due to secondary infall. For the second class of solutions the longevity of compact groups is due either to their specific initial conditions, or to a massive common halo, encompassing the whole group. I discuss here these alternatives, together with their respective advantages and disadvantages. I then turn to the structure of remnants of multiple mergers and compare the results of N-body simulations with the properties of observed elliptical galaxies. Finally I discuss the dynamical evolution of a disc galaxy surrounded by one or more spherical satellites.

The Evolution of Dust Opacity in Galaxies

We investigate the evolution of the opacity of galaxies as a function of redshift, using simple assumptions about the metal and dust enrichment of the gas and the distribution of dust in galaxies. The method presented in this paper uses an iterative procedure to reconstruct the intrinsic star formation rate (SFR) density of galaxies as a function of redshift, by correcting the observed UV emission for the obscuring effects of the dust produced by the star formation itself. Where necessary, gas inflows/outflows are included to dilute/remove the excess of metals produced by the stars for fixed yield. The iterative procedure converges to multiple solutions for the intrinsic SFR density, divided into two basic classes. The first class of solutions predicts a relatively large amount of UV attenuation at high redshift, with A1500 ? = 1.9 mag at z ~ 3, and smaller attenuations at low redshift (z < 1), with A2800 ? = 1.25 mag. The SFR density of this set of solutions is constant for z 1.2 and declines for z < 1.2; it resembles in shape the monolithic collapse scenario for star formation. The second class of solutions predicts relatively low-UV attenuations at high redshift, with A1500 ? = 0.75 mag at z ~ 3, and larger attenuations at low redshift, with A2800 ? = 1.50 mag at z < 1. The SFR density in this case has a peak at z 1.2. The advantages and shortcomings of both classes are analyzed in the light of available observational constraints, including the opacity of galaxies at 0 ? z ? 1 and the intensity and spectral energy distribution of the cosmic infrared background from the COBE DIRBE and FIRAS data. We conclude that both classes of models are acceptable within the current uncertainties, but the monolithic collapse class matches the available observations better than the other one. We also investigate the dependence of our solutions on the different model assumptions.

The Dirac–Maxwell equations with cylindrical symmetry

A reduction of the Dirac–Maxwell equations in the case of static cylindrical symmetry is performed. The behavior of the resulting system of o.d.e.s. is examined analytically and numerical solutions presented. There are two classes of solutions. The first type of solution is a Dirac field surrounding a charged “wire.’’ The Dirac field is highly localized, being concentrated in cylindrical shells about the wire. A comparison with the usual linearized theory demonstrates that this localization is entirely due to the nonlinearities in the equations which result from the inclusion of the “self-field.’’ The second class of solutions have the electrostatic potential finite along the axis of symmetry but unbounded at large distances from the axis.

HIGH-ORDER CONTRASTS FOR SELF-ADAPTIVE SOURCE SEPARATION

This paper is concerned with the problem of separating independent non-Gaussian sources. This is done by adaptively maximizing a contrast function based on fourth-order cumulants of the (mixed) obser$softhyphen;vations. The first cla ss of solutions involves a first stage where the signal vector is adaptively whitened. In order to implement in the second stage the proper separating task, new contrast functions are proposed, especially when all the source kurtosises have the same sign. These contrasts involve only self-cumulants of the outputs. The second class of solutions requires a single separating stage. However, the associated contrasts involve cross-cumulants in addition to self-cumulants. They essentially apply to correlated ve ctors with normalized powers (rather than to white vectors). The resulting adaptive one-stage and two-stage systems achieve satisfactory separation performance independently of the statistics of sources and of the kind of linear mixture.

Self-similar scalar field collapse: Naked singularities and critical behavior.

Homothetic scalar field collapse is considered in this article. By making a suitable choice of variables the equations are reduced to an autonomous system. Then using a combination of numerical and analytic techniques it is shown that there are two classes of solutions. The first consists of solutions with a non-singular origin in which the scalar field collapses and disperses again. There is a singularity at one point of these solutions, however it is not visible to observers at finite radius. The second class of solutions includes both black holes and naked singularities with a critical evolution (which is neither) interpolating between these two extremes. The properties of these solutions are discussed in detail. The paper also contains some speculation about the significance of self-similarity in recent numerical studies.

Kinetic structure of slow shocks: Effects of the electromagnetic ion/ion cyclotron instability

Using a one‐dimensional electromagnetic hybrid code (particle ions, fluid electrons), the structure of and ion heating at slow magnetosonic shocks are investigated in the low beta regime. In particular, the effects of the waves generated at or upstream of the shock by the electromagnetic ion/ion cyclotron (EMIIC) instability are studied. To understand the role of shock initialization and boundary conditions on the resulting solutions, three methods of shock formation are utilized. One is a relaxation method, where the shock is started as a structureless discontinuity and allowed to evolve to a possible steady state solution. It is shown that this method of shock formation can lead to spurious results and therefore is not reliable. The other two investigated methods are similar, in that the shock is formed via flow interactions in a dynamic fashion. One of these is the usual piston method, where the plasma is injected from one side of the simulation box and reflected from the other side. In a new, third method (flow‐flow) the plasma is injected from both boundaries, which results in the formation of a pair of slow shocks. Both of these shock formation methods result in reliable solutions. Using the piston or flow‐flow interactions, it is found that slow magnetosonic shocks have a number of different structures depending on the plasma parameters and the shock normal angle. One set of solutions corresponds to the classical structure where a coherent Alfvén wave train is formed downstream of the shock. However, Alfvén waves generated by the backstreaming ions via the electromagnetic ion/ion cyclotron instability are also observed upstream of the shock. The second class of solutions corresponds to structures with Alfvén turbulence upstream and downstream of the shock. These shocks are found to have a nonsteady behavior, due to transport of upstream waves generated by the EMIIC instability into the downstream region. The nonsteady behavior of the shock prevents the formation of a coherent trailing wave train. A third class of structure is associated with much weaker laminar shocks, where little or no wave activity is present both upstream and downstream of the shock. Using the full electromagnetic dispersion equation, it is shown that large linear damping of Alfvén or slow waves prevents the formation of a wave train downstream of such shocks. A fourth class of solutions is associated with no wave activity in the downstream but has Alfvén waves at and upstream of the shock. The excitation of these waves at the shock leads to a nonsteady behavior, even though their Poynting vector is toward the upstream. By using the average magnetic moment and deviations from its upstream value, the role of the EMIIC instability in ion dissipation has also been investigated. It is shown that ion orbits are adiabatic at weak laminar shocks, leading to anisotropic heating with T∥ &gt; T⊥. On the other hand, when upstream Alfvén waves are present, they lead to incident ion scattering; before the shock transition region. This scattering, however, does not always lead to complete thermalization immediately downstream of the shock. As such, the length scales associated with the magnetic structure and ion dissipation may vary considerably at slow shocks.

Does accretion cease when a star approaches breakup?

view Abstract Citations (161) References (14) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Does Accretion Cease When a Star Approaches Breakup? Popham, Robert ; Narayan, Ramesh Abstract A steady-state thin accretion disk is modeled around a uniformly rotating unmagnetized star in order to investigate whether disk accretion can continue as the accreted angular momentum spins the central star to near breakup. A mapping between the specific angular momentum (SAM) added to the star and the stellar rotation rate (SRR) is obtained. When SRR is somewhat less than the breakup rotation rate of the star, a class of solutions is found where the angular velocity of the disk attains a maximum close to the star and then decreases rapidly in a boundary layer to match SRR. If SRR is near breakup, a second class of solutions is found where the disk angular velocity has no maximum but increases monotonically all the way down to the stellar surface. SAM decreases very rapidly with increasing SRR and even takes on fairly large negative values. The spin-up of an accreting star slows down and eventually stops at a rotation rate near breakup. Beyond this point, the star can continue to accrete any amount of matter without actually breaking up. Publication: The Astrophysical Journal Pub Date: April 1991 DOI: 10.1086/169847 Bibcode: 1991ApJ...370..604P Keywords: Accretion Disks; Binary Stars; Stellar Mass Accretion; Stellar Rotation; White Dwarf Stars; Angular Momentum; Boundary Conditions; Hydrodynamics; Numerical Analysis; Radial Velocity; Star Formation; Subsonic Flow; Supersonic Flow; Astrophysics; ACCRETION; STARS: ACCRETION; STARS: BINARIES; STARS: FORMATION; STARS: ROTATION; STARS: WHITE DWARFS full text sources ADS |

Rotating string sources in three-dimensional gravity

The problem of finding the regular three-dimensional space-times, subject to the boundary condition g 00(∞) = 1, generated by a rotating string with tension is solved by a matrix method. According to the values of the string parameters, we obtain two classes of solutions. The solutions of the first class, which exist only if the string parameters are such that the string tension and centrifugal energy precisely balance, are topologically Euclidean. The second class of solutions, which exist only for negative or zero string mass densities, have an extra point at spatial infinity; in most instances, a satisfactory physical interpretation of these solutions is possible. We also briefly discuss stationary open string solutions.