49,750 research outputs found
Hydrodynamic Simulations of the Bardeen-Petterson Effect
We present SPH simulations of accretion discs in orbit about rotating compact
objects such as black holes and neutron stars, and study the structure of
warped discs produced by the Bardeen-Petterson effect. We calculate the
transition radius out to which the disc specific angular momentum vector is
aligned with that of the black hole. We focus on the parameter regime where the
warp dynamics are controlled by bending wave propagation, but also consider
models in which warps are subject to diffusion rather than wave transport, and
are able to consider the fully nonlinear regime. Because of hydrodynamic or
pressure effects, for the parameter range investigated, the transition radius
is always found to be much smaller than that obtained by Bardeen & Petterson
(1975). For discs with midplane Mach numbers of about 10, the transition occurs
between 10 - 16 gravitational radii, whereas for a Mach number of about 30 it
occurs at around 30 gravitational radii. A thicker disc with a Mach number of 5
is found to produce no discernible warped structure. The rate of black hole -
disc alignment is found to be consistent with the ideas of Ress (1978), with
the alignment torque behaving as if it arises from the accreted material
transferring its misaligned component of angular momentum at the larger
transition radius of Bardeen & Petterson (1975). The inclusion of Einstein
precession in the calculations modified both the warped disc structure and,
consistent with linear analysis, produced an increased alignment rate by up to
a factor of 4 because of the effect that a non Keplerian potential has on the
propagation of warps.Comment: 18 pages, 14 figures. Accepted for publication in M.N.R.A.S. A
version with posctcript figures included can be obtained from
http://www.maths.qmw.ac.uk/~rp
Interface Ferromagnetism in a SrMnO3/LaMnO3 Superlattice
Resonant soft x-ray absorption measurements at the O K edge on a
SrMnO3/LaMnO3 superlattice show a shoulder at the energy of doped holes, which
corresponds to the main peak of resonant scattering from the modulation in the
doped hole density. Scattering line shape at the Mn L3,2 edges has a strong
variation below the ferromagnetic transition temperature. This variation has a
period equal to half the superlattice superperiod and follows the development
of the ferromagnetic moment, pointing to a ferromagnetic phase developing at
the interfaces. It occurs at the resonant energies for Mn3+ and Mn4+ valences.
A model for these observations is presented, which includes a double-exchange
two-site orbital and the variation with temperature of the hopping frequency
tij between the two sites.Comment: 8.1 pages, 6 figure
Effects of CP Violation from Neutral Heavy Fermions on Neutrino Oscillations, and the LSND/MiniBooNE Anomalies
Neutrinos may mix with ultralight fermions, which gives flavor oscillations,
and with heavier fermions, which yields short distance flavor change. I
consider the case where both effects are present. I show that in the limit
where a single oscillation length is experimentally accessible, the effects of
heavier fermions on neutrino oscillations can generically be accounted for by a
simple formula containing four parameters, including observable CP violation. I
consider the anomalous LSND and MiniBooNE results, and show that these can be
fit in a model with CP violation and two additional sterile neutrinos, one in
the mass range between 0.1 and 20 eV, and the other with mass between 33 eV and
40 GeV. I also show that this model can avoid conflict with constraints from
existing null short baseline experimental results.Comment: 12 pages, 3 figure
Optimal approximate matrix product in terms of stable rank
We prove, using the subspace embedding guarantee in a black box way, that one
can achieve the spectral norm guarantee for approximate matrix multiplication
with a dimensionality-reducing map having
rows. Here is the maximum stable rank, i.e. squared ratio of
Frobenius and operator norms, of the two matrices being multiplied. This is a
quantitative improvement over previous work of [MZ11, KVZ14], and is also
optimal for any oblivious dimensionality-reducing map. Furthermore, due to the
black box reliance on the subspace embedding property in our proofs, our
theorem can be applied to a much more general class of sketching matrices than
what was known before, in addition to achieving better bounds. For example, one
can apply our theorem to efficient subspace embeddings such as the Subsampled
Randomized Hadamard Transform or sparse subspace embeddings, or even with
subspace embedding constructions that may be developed in the future.
Our main theorem, via connections with spectral error matrix multiplication
shown in prior work, implies quantitative improvements for approximate least
squares regression and low rank approximation. Our main result has also already
been applied to improve dimensionality reduction guarantees for -means
clustering [CEMMP14], and implies new results for nonparametric regression
[YPW15].
We also separately point out that the proof of the "BSS" deterministic
row-sampling result of [BSS12] can be modified to show that for any matrices
of stable rank at most , one can achieve the spectral norm
guarantee for approximate matrix multiplication of by deterministically
sampling rows that can be found in polynomial
time. The original result of [BSS12] was for rank instead of stable rank. Our
observation leads to a stronger version of a main theorem of [KMST10].Comment: v3: minor edits; v2: fixed one step in proof of Theorem 9 which was
wrong by a constant factor (see the new Lemma 5 and its use; final theorem
unaffected
Radiation counting technique allows density measurement of metals in high-pressure/ high-temperature environment
Radioactive tracers induced by neutron irradiation provide a gamma ray flux proportional to the density of a metal, allowing density measurement of these metals in extreme high-temperature and high-pressure environments. This concept is applicable to most metals, as well as other substances
Quasars in the 2MASS Second Incremental Data Release
Using the 2MASS Second Incremental Data Release, we have searched for near
infrared counterparts to 13214 quasars from the Veron-Cetty & Veron(2000)
catalog. We have detected counterparts within 4 arcsec for 2277 of the
approximately 6320 quasars within the area covered by the 2MASS Second
Incremental Data Release. Only 1.6% of these are expected to be chance
coincidences. Though this sample is heterogeneous, we find that known
radio-loud quasars are more likely to have large near-infrared-to-optical
luminosity ratios than radio-quiet quasars are, at a statistically significant
level. This is consistent with dust-reddened quasars being more common in
radio-selected samples than in optically-selected samples, due to stronger
selection effects against dust-reddened quasars in the latter. We also find a
statistically significant dearth of optically luminous quasars with large
near-infrared-to-optical luminosity ratios. This can be explained in a dust
obscuration model but not in a model where synchrotron emission extends from
the radio into the near-infrared and creates such large ratios. We also find
that selection of quasar candidates from the B-J/J-K color-color diagram,
modelled on the V-J/J-K selection method of Warren, Hewett & Foltz (2000), is
likely to be more sensitive to dust-obscured quasars than selection using only
infrared-infrared colors.Comment: To be published in May issue of Astronomical Journal (26 pages, 8
figures, 2 tables) Replaced Figure 6 and
What is the Brillouin Zone of an Anisotropic Photonic Crystal?
The concept of the Brillouin zone (BZ) in relation to a photonic crystal
fabricated in an optically anisotropic material is explored both experimentally
and theoretically. In experiment, we used femtosecond laser pulses to excite
THz polaritons and image their propagation in lithium niobate and lithium
tantalate photonic crystal (PhC) slabs. We directly measured the dispersion
relation inside PhCs and observed that the lowest bandgap expected to form at
the BZ boundary forms inside the BZ in the anisotropic lithium niobate PhC. Our
analysis shows that in an anisotropic material the BZ - defined as the
Wigner-Seitz cell in the reciprocal lattice - is no longer bounded by Bragg
planes and thus does not conform to the original definition of the BZ by
Brillouin. We construct an alternative Brillouin zone defined by Bragg planes
and show its utility in identifying features of the dispersion bands. We show
that for an anisotropic 2D PhC without dispersion, the Bragg plane BZ can be
constructed by applying the Wigner-Seitz method to a stretched or compressed
reciprocal lattice. We also show that in the presence of the dispersion in the
underlying material or in a slab waveguide, the Bragg planes are generally
represented by curved surfaces rather than planes. The concept of constructing
a BZ with Bragg planes should prove useful in understanding the formation of
dispersion bands in anisotropic PhCs and in selectively tailoring their optical
properties.Comment: 9 pages, 6 figure
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