13,498 research outputs found

### Quasi Periodic Oscillations in Low Mass X-Ray Binaries and Constraints on the Equation of State of Neutron Star Matter

Recently discovered quasi periodic oscillations in the X-ray brightness of
low mass X-ray binaries are used to derive constraints on the mass of the
neutron star component and the equation of state of neutron star matter. The
observations are compared with models of rapidly rotating neutron stars which
are calculated by means of an exact numerical method in full relativity. For
the equations of state we select a broad collection of models representing
different assumptions about the many-body structure and the complexity of the
composition of super dense matter. The mass constraints differ from their
values in the approximate treatment by \sim 10%. Under the assumption that the
maximum frequency of the quasi periodic oscillations originates from the
innermost stable orbit the mass of the neutron star is in the range: $M\sim
1.92-2.25 M_\odot$. Especially the quasi periodic oscillation in the
Atoll-source 4U 1820-30 is only consistent with equations of state which are
rather stiff at high densities which is explainable, so far, only with pure
nucleonic/leptonic composition. This interpretation contradicts the hypothesis
that the protoneutron star formed in SN 1987A collapsed to a black hole, since
this would demand a maximum neutron star mass below $1.6 M_\odot$. The recently
suggested identification of quasi periodic oscillations with frequencies around
10 Hz with the Lense-Thirring precession of the accretion disk is found to be
inconsistent with the models studied in this work, unless it is assumed that
the first overtone of the precession is observed.Comment: 12 pages including figures, to be published in MNRA

### Axisymmetric circumstellar interaction in supernovae

Multiwavelength observations of Type II supernovae have shown evidence for
the interaction of supernovae with the dense slow winds from the red supergiant
progenitor stars. Observations of planetary nebulae and the nebula around SN
1987A show that the slow winds from extended stars frequently have an axisymme-
tric structure with a high density in the equatorial plane. We have carried out
numerical calculations of the interaction of a supernova with such an axisymme-
tric density distribution. For small values of the angular density gradient at
the pole, the asymmetry in the interaction shell is greater than, but close to,
that expected from purely radial motion. If the angular density gradient is
above a moderate value, the flow qualitatively changes and a protrusion emerges
along the axis. For a power-law supernova density profile, the flow approaches
a self-similar state in which the protrusion length is $2-4$ times the radius
of the main shell. The critical density gradient is larger for steeper density
profiles of the ejecta. Most of our calculations are axisymmetric, but we have
carried out a 3-dimensional calculation to show that the protrusion is not a
numerical artifact along the symmetry axis. For typical supernova parameters,
the protrusions take $\gtrsim$ several years to develop. The appearance of the
shell with protrusions is similar to that observed in VLBI radio images of the
remnant 41.9 +58 in M82 and, possibly, of SN 1986J. We also considered the
possibility of asymmetric ejecta and found that it had a relatively small
effect on the asymmetry of the interaction region.Comment: 22 page postscript file (gzipped and uuencoded), 10 gzipped
postscript figures may be retrieved from
ftp://www.astro.su.se/pub/supernova/blc96_asym/ Submitted to Ap

### Tight Bounds for Consensus Systems Convergence

We analyze the asymptotic convergence of all infinite products of matrices
taken in a given finite set, by looking only at finite or periodic products. It
is known that when the matrices of the set have a common nonincreasing
polyhedral norm, all infinite products converge to zero if and only if all
infinite periodic products with period smaller than a certain value converge to
zero, and bounds exist on that value.
We provide a stronger bound holding for both polyhedral norms and polyhedral
seminorms. In the latter case, the matrix products do not necessarily converge
to 0, but all trajectories of the associated system converge to a common
invariant space. We prove our bound to be tight, in the sense that for any
polyhedral seminorm, there is a set of matrices such that not all infinite
products converge, but every periodic product with period smaller than our
bound does converge.
Our technique is based on an analysis of the combinatorial structure of the
face lattice of the unit ball of the nonincreasing seminorm. The bound we
obtain is equal to half the size of the largest antichain in this lattice.
Explicitly evaluating this quantity may be challenging in some cases. We
therefore link our problem with the Sperner property: the property that, for
some graded posets, -- in this case the face lattice of the unit ball -- the
size of the largest antichain is equal to the size of the largest rank level.
We show that some sets of matrices with invariant polyhedral seminorms lead
to posets that do not have that Sperner property. However, this property holds
for the polyhedron obtained when treating sets of stochastic matrices, and our
bound can then be easily evaluated in that case. In particular, we show that
for the dimension of the space $n \geq 8$, our bound is smaller than the
previously known bound by a multiplicative factor of $\frac{3}{2 \sqrt{\pi
n}}$

### Efficient Algorithms for the Consensus Decision Problem

We address the problem of determining if a discrete time switched consensus
system converges for any switching sequence and that of determining if it
converges for at least one switching sequence. For these two problems, we
provide necessary and sufficient conditions that can be checked in singly
exponential time. As a side result, we prove the existence of a polynomial time
algorithm for the first problem when the system switches between only two
subsystems whose corresponding graphs are undirected, a problem that had been
suggested to be NP-hard by Blondel and Olshevsky.Comment: Small modifications after comments from reviewer

### Reachability of Consensus and Synchronizing Automata

We consider the problem of determining the existence of a sequence of
matrices driving a discrete-time consensus system to consensus. We transform
this problem into one of the existence of a product of the transition
(stochastic) matrices that has a positive column. We then generalize some
results from automata theory to sets of stochastic matrices. We obtain as a
main result a polynomial-time algorithm to decide the existence of a sequence
of matrices achieving consensus.Comment: Update after revie

### Study of hot hardness characteristics of tool steels

Hardness measurements of tool steel materials in electric furnace at elevated temperatures and low oxygen environment are discussed. Development of equation to predict short term hardness as function of intial room temperature hardness of steel is reported. Types of steel involved in the process are identified

### X-ray Spectroscopy of Candidate Ultracompact X-ray Binaries

We present high-resolution spectroscopy of the neutron star/low-mass X-ray
binaries (LMXBs) 4U 1850-087 and 4U 0513-40 as part of our continuing study of
known and candidate ultracompact binaries. The LMXB 4U 1850-087 is one of four
systems in which we had previously inferred an unusual Ne/O ratio in the
absorption along the line of sight, most likely from material local to the
binaries. However, our recent Chandra X-ray Observatory LETGS spectrum of 4U
1850-087 finds a Ne/O ratio by number of 0.22+/-0.05, smaller than previously
measured and consistent with the expected interstellar value. We propose that
variations in the Ne/O ratio due to source variability, as previously observed
in these sources, can explain the difference between the low- and
high-resolution spectral results for 4U 1850-087. Our XMM-Newton RGS
observation of 4U 0513-40 also shows no unusual abundance ratios in the
absorption along the line of sight. We also present spectral results from a
third candidate ultracompact binary, 4U 1822-000, whose spectrum is well fit by
an absorbed power-law + blackbody model with absorption consistent with the
expected interstellar value. Finally, we present the non-detection of a fourth
candidate ultracompact binary, 4U 1905+000, with an upper limit on the source
luminosity of < 1 x 10^{32} erg s^{-1}. Using archival data, we show that the
source has entered an extended quiescent state.Comment: 8 pages, 3 figures, accepted for publication to the Astrophysical
Journa

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