6,149 research outputs found
Axisymmetric general relativistic hydrodynamics: Long-term evolution of neutron stars and stellar collapse to neutron stars and black holes
We report a new implementation for axisymmetric simulation in full general
relativity. In this implementation, the Einstein equations are solved using the
Nakamura-Shibata formulation with the so-called cartoon method to impose an
axisymmetric boundary condition, and the general relativistic hydrodynamic
equations are solved using a high-resolution shock-capturing scheme based on an
approximate Riemann solver. As tests, we performed the following simulations:
(i) long-term evolution of non-rotating and rapidly rotating neutron stars,
(ii) long-term evolution of neutron stars of a high-amplitude damping
oscillation accompanied with shock formation, (iii) collapse of unstable
neutron stars to black holes, and (iv) stellar collapses to neutron stars. The
tests (i)--(iii) were carried out with the -law equation of state, and
the test (iv) with a more realistic parametric equation of state for
high-density matter. We found that this new implementation works very well: It
is possible to perform the simulations for stable neutron stars for more than
10 dynamical time scales, to capture strong shocks formed at stellar core
collapses, and to accurately compute the mass of black holes formed after the
collapse and subsequent accretion. In conclusion, this implementation is robust
enough to apply to astrophysical problems such as stellar core collapse of
massive stars to a neutron star and black hole, phase transition of a neutron
star to a high-density star, and accretion-induced collapse of a neutron star
to a black hole. The result for the first simulation of stellar core collapse
to a neutron star started from a realistic initial condition is also presented.Comment: 28 pages, to appear in PRD 67, 0440XX (2003
Phase transition in the one-dimensional Kondo lattice model with attractive electron-electron interaction
The one-dimensional Kondo lattice model with attractive interaction among the
conduction electrons is analyzed in the case of half-filling. It is shown that
there are three distinct phases depending on the coupling constants of the
model. Two phases have a spin and charge gap. While one shows a clear
separation of the spin and charge excitation spectrum the other phase may be
characterized as a band insulator type where both excitations are due to
two-particle states. The third phase is gapless in both channels and has quasi
long-range order in the spin and charge density wave correlation. In this phase
the spin and charge excitations have again a clearly separated spectrum. For
the analysis we discuss first two limiting cases. Then a density matrix
renormalization group calculation on finite systems is applied to determine the
phase diagram and the correlation functions in the gapped and gapless phase for
general couplding constants.Comment: 9 pages, 7 Postscript figures, REVTe
Domain Formation in v=2/3 Fractional Quantum Hall Systems
We study the domain formation in the v=2/3 fractional quantum Hall systems
basing on the density matrix renormalization group (DMRG) analysis. The
ground-state energy and the pair correlation functions are calculated for
various spin polarizations. The results confirm the domain formation in
partially spin polarized states, but the presence of the domain wall increases
the energy of partially spin polarized states and the ground state is either
spin unpolarized state or fully spin polarized state depending on the Zeeman
energy. We expect coupling with external degrees of freedom such as nuclear
spins is important to reduce the energy of partially spin polarized state.Comment: 7 pages, submitted to J. Phys. Soc. Jp
A Contemporary View of Coronal Heating
Determining the heating mechanism (or mechanisms) that causes the outer
atmosphere of the Sun, and many other stars, to reach temperatures orders of
magnitude higher than their surface temperatures has long been a key problem.
For decades the problem has been known as the coronal heating problem, but it
is now clear that `coronal heating' cannot be treated or explained in isolation
and that the heating of the whole solar atmosphere must be studied as a highly
coupled system. The magnetic field of the star is known to play a key role,
but, despite significant advancements in solar telescopes, computing power and
much greater understanding of theoretical mechanisms, the question of which
mechanism or mechanisms are the dominant supplier of energy to the chromosphere
and corona is still open. Following substantial recent progress, we consider
the most likely contenders and discuss the key factors that have made, and
still make, determining the actual (coronal) heating mechanism (or mechanisms)
so difficult
Dynamics of thermoelastic thin plates: A comparison of four theories
Four distinct theories describing the flexural motion of thermoelastic thin
plates are compared. The theories are due to Chadwick, Lagnese and Lions,
Simmonds, and Norris. Chadwick's theory requires a 3D spatial equation for the
temperature but is considered the most accurate as the others are derivable
from it by different approximations. Attention is given to the damping of
flexural waves. Analytical and quantitative comparisons indicate that the
Lagnese and Lions model with a 2D temperature equation captures the essential
features of the thermoelastic damping, but contains systematic inaccuracies.
These are attributable to the approximation for the first moment of the
temperature used in deriving the Lagnese and Lions equation. Simmonds' model
with an explicit formula for temperature in terms of plate deflection is the
simplest of all but is accurate only at low frequency, where the damping is
linearly proportional to the frequency. It is shown that the Norris model,
which is almost as simple as Simmond's, is as accurate as the more precise but
involved theory of Chadwick.Comment: 2 figures, 1 tabl
Various features of quasiequilibrium sequences of binary neutron stars in general relativity
Quasiequilibrium sequences of binary neutron stars are numerically calculated
in the framework of the Isenberg-Wilson-Mathews (IWM) approximation of general
relativity. The results are presented for both rotation states of synchronized
spins and irrotational motion, the latter being considered as the realistic one
for binary neutron stars just prior to the merger. We assume a polytropic
equation of state and compute several evolutionary sequences of binary systems
composed of different-mass stars as well as identical-mass stars with adiabatic
indices gamma=2.5, 2.25, 2, and 1.8. From our results, we propose as a
conjecture that if the turning point of binding energy (and total angular
momentum) locating the innermost stable circular orbit (ISCO) is found in
Newtonian gravity for some value of the adiabatic index gamma_0, that of the
ADM mass (and total angular momentum) should exist in the IWM approximation of
general relativity for the same value of the adiabatic index.Comment: Text improved, some figures changed or deleted, new table, 38 pages,
31 figures, accepted for publication in Phys. Rev.
Stability of the Excitonic Phase in Bilayer Quantum Hall Systems at Total Filling One -- Effects of Finite Well Width and Pseudopotentials --
The ground state of a bilayer quantum Hall system at with
model pseudopotential is investigated by the DMRG method. Firstly,
pseudopotential parameters appropriate for the system with finite layer
thickness are derived, and it is found that the finite thickness makes the
excitonic phase more stable. Secondly, a model, where only a few
pseudopotentials with small relative angular momentum have finite values, is
studied, and it is clarified how the excitonic phase is destroyed as
intra-layer pseudopotential becomes larger. The importance of the intra-layer
repulsive interaction at distance twice of the magnetic length for the
destruction of the excitonic phase is found.Comment: 7 pages, 7 figure
Glueball mass from quantized knot solitons and gauge-invariant gluon mass
We propose an approach which enables one to obtain simultaneously the
glueball mass and the gluon mass in the gauge-invariant way to shed new light
on the mass gap problem in Yang-Mills theory. First, we point out that the
Faddeev (Skyrme--Faddeev-Niemi) model can be induced through the
gauge-invariant vacuum condensate of mass dimension two from SU(2) Yang-Mills
theory. Second, we obtain the glueball mass spectrum by performing the
collective coordinate quantization of the topological knot soliton in the
Faddeev model. Third, we demonstrate that a relationship between the glueball
mass and the gluon mass is obtained, since the gauge-invariant gluon mass is
also induced from the relevant vacuum condensate. Finally, we determine
physical values of two parameters in the Faddeev model and give an estimate of
the relevant vacuum condensation in Yang-Mills theory. Our results indicate
that the Faddeev model can play the role of a low-energy effective theory of
the quantum SU(2) Yang-Mills theory.Comment: 17 pages, 2 figures, 3 tables; a version accepted for publication in
J. Phys. A: Math. Gen.; Sect. 2 and sect. 5 (old sect. 4) are modified. Sect.
4, Tables 1 and Table 3 are adde
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