30,138 research outputs found
Testing a Simplified Version of Einstein's Equations for Numerical Relativity
Solving dynamical problems in general relativity requires the full machinery
of numerical relativity. Wilson has proposed a simpler but approximate scheme
for systems near equilibrium, like binary neutron stars. We test the scheme on
isolated, rapidly rotating, relativistic stars. Since these objects are in
equilibrium, it is crucial that the approximation work well if we are to
believe its predictions for more complicated systems like binaries. Our results
are very encouraging.Comment: 9 pages (RevTeX 3.0 with 6 uuencoded figures), CRSR-107
Quasi-circular Orbits for Spinning Binary Black Holes
Using an effective potential method we examine binary black holes where the
individual holes carry spin. We trace out sequences of quasi-circular orbits
and locate the innermost stable circular orbit as a function of spin. At large
separations, the sequences of quasi-circular orbits match well with
post-Newtonian expansions, although a clear signature of the simplifying
assumption of conformal flatness is seen. The position of the ISCO is found to
be strongly dependent on the magnitude of the spin on each black hole. At close
separations of the holes, the effective potential method breaks down. In all
cases where an ISCO could be determined, we found that an apparent horizon
encompassing both holes forms for separations well inside the ISCO.
Nevertheless, we argue that the formation of a common horizon is still
associated with the breakdown of the effective potential method.Comment: 13 pages, 10 figures, submitted to PR
Device measures conductivity and velocity of ionized gas streams
Coaxial arrangement of primary coil and two sensing secondary coils contained inside slender quartz tube inserted into ionized stream permits simultaneous determination of conductivity and linear velocity. System results agree favorably with theory
Perturbative evolution of conformally flat initial data for a single boosted black hole
The conformally flat families of initial data typically used in numerical
relativity to represent boosted black holes are not those of a boosted slice of
the Schwarzschild spacetime. If such data are used for each black hole in a
collision, the emitted radiation will be partially due to the ``relaxation'' of
the individual holes to ``boosted Schwarzschild'' form. We attempt to compute
this radiation by treating the geometry for a single boosted conformally flat
hole as a perturbation of a Schwarzschild black hole, which requires the use of
second order perturbation theory. In this we attempt to mimic a previous
calculation we did for the conformally flat initial data for spinning holes. We
find that the boosted black hole case presents additional subtleties, and
although one can evolve perturbatively and compute radiated energies, it is
much less clear than in the spinning case how useful for the study of
collisions are the radiation estimates for the ``spurious energy'' in each
hole. In addition to this we draw some lessons on which frame of reference
appears as more favorable for computing black hole collisions in the close
limit approximation.Comment: 11 pages, RevTex, 4 figures included with psfig, to appear in PR
Tropical–North Pacific Climate Linkages over the Past Four Centuries
Analyses of instrumental data demonstrate robust linkages between decadal-scale North Pacific and tropical Indo-Pacific climatic variability. These linkages encompass common regime shifts, including the noteworthy 1976 transition in Pacific climate. However, information on Pacific decadal variability and the tropical high-latitude climate connection is limited prior to the twentieth century. Herein tree-ring analysis is employed to extend the understanding of North Pacific climatic variability and related tropical linkages over the past four centuries. To this end, a tree-ring reconstruction of the December-May North Pacific index (NPI)-an index of the atmospheric circulation related to the Aleutian low pressure cell-is presented (1600-1983). The NPI reconstruction shows evidence for the three regime shifts seen in the instrumental NPI data, and for seven events in prior centuries. It correlates significantly with both instrumental tropical climate indices and a coral-based reconstruction of an optimal tropical Indo-Pacific climate index, supporting evidence for a tropical-North Pacific link extending as far west as the western Indian Ocean. The coral-based reconstruction (1781-1993) shows the twentieth-century regime shifts evident in the instrumental NPI and instrumental tropical Indo-Pacific climate index, and three previous shifts. Changes in the strength of correlation between the reconstructions over time, and the different identified shifts in both series prior to the twentieth century, suggest a varying tropical influence on North Pacific climate, with greater influence in the twentieth century. One likely mechanism is the low-frequency variability of the El Nino-Southern Oscillation (ENSO) and its varying impact on Indo-Pacific climate.</p
The collision of boosted black holes: second order close limit calculations
We study the head-on collision of black holes starting from unsymmetrized,
Brill--Lindquist type data for black holes with non-vanishing initial linear
momentum. Evolution of the initial data is carried out with the ``close limit
approximation,'' in which small initial separation and momentum are assumed,
and second-order perturbation theory is used. We find agreement that is
remarkably good, and that in some ways improves with increasing momentum. This
work extends a previous study in which second order perturbation calculations
were used for momentarily stationary initial data, and another study in which
linearized perturbation theory was used for initially moving holes. In addition
to supplying answers about the collisions, the present work has revealed
several subtle points about the use of higher order perturbation theory, points
that did not arise in the previous studies. These points include issues of
normalization, and of comparison with numerical simulations, and will be
important to subsequent applications of approximation methods for collisions.Comment: 20 pages, RevTeX, 6 figures included with psfi
Random billiards with wall temperature and associated Markov chains
By a random billiard we mean a billiard system in which the standard specular
reflection rule is replaced with a Markov transition probabilities operator P
that, at each collision of the billiard particle with the boundary of the
billiard domain, gives the probability distribution of the post-collision
velocity for a given pre-collision velocity. A random billiard with
microstructure (RBM) is a random billiard for which P is derived from a choice
of geometric/mechanical structure on the boundary of the billiard domain. RBMs
provide simple and explicit mechanical models of particle-surface interaction
that can incorporate thermal effects and permit a detailed study of
thermostatic action from the perspective of the standard theory of Markov
chains on general state spaces.
We focus on the operator P itself and how it relates to the
mechanical/geometric features of the microstructure, such as mass ratios,
curvatures, and potentials. The main results are as follows: (1) we
characterize the stationary probabilities (equilibrium states) of P and show
how standard equilibrium distributions studied in classical statistical
mechanics, such as the Maxwell-Boltzmann distribution and the Knudsen cosine
law, arise naturally as generalized invariant billiard measures; (2) we obtain
some basic functional theoretic properties of P. Under very general conditions,
we show that P is a self-adjoint operator of norm 1 on an appropriate Hilbert
space. In a simple but illustrative example, we show that P is a compact
(Hilbert-Schmidt) operator. This leads to the issue of relating the spectrum of
eigenvalues of P to the features of the microstructure;(3) we explore the
latter issue both analytically and numerically in a few representative
examples;(4) we present a general algorithm for simulating these Markov chains
based on a geometric description of the invariant volumes of classical
statistical mechanics
Power spectra of TASEPs with a localized slow site
The totally asymmetric simple exclusion process (TASEP) with a localized
defect is revisited in this article with attention paid to the power spectra of
the particle occupancy N(t). Intrigued by the oscillatory behaviors in the
power spectra of an ordinary TASEP in high/low density phase(HD/LD) observed by
Adams et al. (2007 Phys. Rev. Lett. 99 020601), we introduce a single slow site
with hopping rate q<1 to the system. As the power spectrum contains
time-correlation information of the particle occupancy of the system, we are
particularly interested in how the defect affects fluctuation in particle
number of the left and right subsystems as well as that of the entire system.
Exploiting Monte Carlo simulations, we observe the disappearance of
oscillations when the defect is located at the center of the system. When the
defect is off center, oscillations are restored. To explore the origin of such
phenomenon, we use a linearized Langevin equation to calculate the power
spectrum for the sublattices and the whole lattice. We provide insights into
the interactions between the sublattices coupled through the defect site for
both simulation and analytical results.Comment: 16 pages, 6 figures; v2: Minor revision
Innermost stable circular orbits around relativistic rotating stars
We investigate the innermost stable circular orbit (ISCO) of a test particle
moving on the equatorial plane around rotating relativistic stars such as
neutron stars. First, we derive approximate analytic formulas for the angular
velocity and circumferential radius at the ISCO making use of an approximate
relativistic solution which is characterized by arbitrary mass, spin, mass
quadrupole, current octapole and mass -pole moments. Then, we show that
the analytic formulas are accurate enough by comparing them with numerical
results, which are obtained by analyzing the vacuum exterior around numerically
computed geometries for rotating stars of polytropic equation of state. We
demonstrate that contribution of mass quadrupole moment for determining the
angular velocity and, in particular, the circumferential radius at the ISCO
around a rapidly rotating star is as important as that of spin.Comment: 12 pages, 2 figures, accepted for publication in Phys. Rev.
The Innermost Stable Circular Orbit of Binary Black Holes
We introduce a new method to construct solutions to the constraint equations
of general relativity describing binary black holes in quasicircular orbit.
Black hole pairs with arbitrary momenta can be constructed with a simple method
recently suggested by Brandt and Bruegmann, and quasicircular orbits can then
be found by locating a minimum in the binding energy along sequences of
constant horizon area. This approach produces binary black holes in a
"three-sheeted" manifold structure, as opposed to the "two-sheeted" structure
in the conformal-imaging approach adopted earlier by Cook. We focus on locating
the innermost stable circular orbit and compare with earlier calculations. Our
results confirm those of Cook and imply that the underlying manifold structure
has a very small effect on the location of the innermost stable circular orbit.Comment: 8 pages, 3 figures, RevTex, submitted to PR
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