2,415 research outputs found
Tidal Stabilization of Rigidly Rotating, Fully Relativistic Neutron Stars
It is shown analytically that an external tidal gravitational field increases
the secular stability of a fully general relativistic, rigidly rotating neutron
star that is near marginal stability, protecting it against gravitational
collapse. This stabilization is shown to result from the simple fact that the
energy required to raise a tide on such a star, divided by the
square of the tide's quadrupole moment , is a decreasing function of the
star's radius , (where, as changes, the
star's structure is changed in accord with the star's fundamental mode of
radial oscillation). If were positive, the tidal
coupling would destabilize the star. As an application, a rigidly rotating,
marginally secularly stable neutron star in an inspiraling binary system will
be protected against secular collapse, and against dynamical collapse, by tidal
interaction with its companion. The ``local-asymptotic-rest-frame'' tools used
in the analysis are somewhat unusual and may be powerful in other studies of
neutron stars and black holes interacting with an external environment. As a
byproduct of the analysis, in an appendix the influence of tidal interactions
on mass-energy conservation is elucidated.Comment: Revtex, 10 pages, 2 figures; accepted for publication in Physical
Review D. Revisions: Appendix rewritten to clarify how, in Newtonian
gravitation theory, ambiguity in localization of energy makes interaction
energy ambiguous but leaves work done on star by tidal gravity unambiguous.
New footnote 1 and Refs. [11] and [19
Turbulent Cells in Stars: I. Fluctuations in Kinetic Energy and Luminosity
Three-dimensional (3D) hydrodynamic simulations of shell oxygen burning
(Meakin and Arnett, 2007b) exhibit bursty, recurrent fluctuations in turbulent
kinetic energy. These are shown to be due to a general instability of the
convective cell, requiring only a localized source of heating or cooling. Such
fluctuations are shown to be suppressed in simulations of stellar evolution
which use mixing-length theory (MLT).
Quantitatively similar behavior occurs in the model of a convective roll
(cell) of Lorenz (1963), which is known to have a strange attractor that gives
rise to chaotic fluctuations in time of velocity and, as we show, luminosity.
Study of simulations suggests that the behavior of a Lorenz convective roll may
resemble that of a cell in convective flow. We examine some implications of
this simplest approximation, and suggest paths for improvement.
Using the Lorenz model as representative of a convective cell, a
multiple-cell model of a convective layer gives total luminosity fluctuations
which are suggestive of irregular variables (red giants and supergiants
(Schwarzschild 1975)), and of the long secondary period feature in semi-regular
AGB variables (Stothers 2010, Wood, Olivier and Kawaler 2004). This
"tau-mechanism" is a new source for stellar variability, which is inherently
non-linear (unseen in linear stability analysis), and one closely related to
intermittency in turbulence. It was already implicit in the 3D global
simulations of Woodward, Porter and Jacobs (2003). This fluctuating behavior is
seen in extended 2D simulations of CNeOSi burning shells (Arnett and Meakin
2011b), and may cause instability which leads to eruptions in progenitors of
core collapse supernovae PRIOR to collapse.Comment: 30 pages, 13 figure
A class of symplectic integrators with adaptive timestep for separable Hamiltonian systems
Symplectic integration algorithms are well-suited for long-term integrations
of Hamiltonian systems because they preserve the geometric structure of the
Hamiltonian flow. However, this desirable property is generally lost when
adaptive timestep control is added to a symplectic integrator. We describe an
adaptive-timestep symplectic integrator that can be used if the Hamiltonian is
the sum of kinetic and potential energy components and the required timestep
depends only on the potential energy (e.g. test-particle integrations in fixed
potentials). In particular, we describe an explicit, reversible, symplectic,
leapfrog integrator for a test particle in a near-Keplerian potential; this
integrator has timestep proportional to distance from the attracting mass and
has the remarkable property of integrating orbits in an inverse-square force
field with only "along-track" errors; i.e. the phase-space shape of a Keplerian
orbit is reproduced exactly, but the orbital period is in error by O(1/N^2),
where N is the number of steps per period.Comment: 24 pages, 3 figures, submitted to Astronomical Journal; minor errors
in equations and one figure correcte
A Self-Consistent Reduced Model for Dusty Magnetorotationally Unstable Discs
The interaction between settling of dust grains and magnetorotational
instability (MRI) turbulence in protoplanetary disks is analyzed. We use a
reduced system of coupled ordinary differential equations to represent the
interaction between the diffusion of grains and the inhibition of the MRI. The
coupled equations are styled on a Landau equation for the turbulence and a
Fokker-Planck equation for the diffusion. The turbulence-grain interaction is
probably most relevant near the outer edge of the disk's quiescent, or "dead"
zone. Settling is most pronounced near the midplane, where a high dust
concentration can self-consistently suppress the MRI. Under certain conditions,
however, grains can reach high altitudes, a result of some observational
interest. Finally, we show that the equilibrium solutions are linearly stable.Comment: 8 pages, 3 figures, accepted to MNRA
On the cosmological singularity
The long story of the oscillatory approach to the initial cosmological
singularity and its more recent incarnation in multidimensional universe models
is told.Comment: The invited paper for Proceedings of the XIII Marcel Grossmann
Meeting (Stockholm, 2012) by reason of the Marcel Grossmann Award to V.A.
Belinski and I.M. Khalatniko
A Gauss-Seidel projection method with the minimal number of updates for stray field in micromagnetic simulations
Magnetization dynamics in magnetic materials is often modeled by the
Landau-Lifshitz equation, which is solved numerically in general. In
micromagnetic simulations, the computational cost relies heavily on the
time-marching scheme and the evaluation of stray field. Explicit marching
schemes are efficient but suffer from severe stability constraints, while
nonlinear systems of equations have to be solved in implicit schemes though
they are unconditionally stable. A better compromise between stability and
efficiency is the semi-implicit scheme, such as the Gauss-Seidel projection
method (GSPM) and the second-order backward differentiation formula scheme
(BDF2). At each marching step, GSPM solves several linear systems of equations
with constant coefficients and updates the stray field several times, while
BDF2 updates the stray field only once but solves a larger linear system of
equations with variable coefficients and a nonsymmetric structure. In this
work, we propose a new method, dubbed as GSPM-BDF2, by combing the advantages
of both GSPM and BDF2. Like GSPM, this method is first-order accurate in time
and second-order accurate in space, and is unconditionally stable with respect
to the damping parameter. However, GSPM-BDF2 updates the stray field only once
per time step, leading to an efficiency improvement of about than the
state-of-the-art GSPM for micromagnetic simulations. For Standard Problem \#4
and \#5 from National Institute of Standards and Technology, GSPM-BDF2 reduces
the computational time over the popular software OOMMF by and ,
respectively. Thus, the proposed method provides a more efficient choice for
micromagnetic simulations
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