2,350 research outputs found
The fast sampling algorithm for Lie-Trotter products
A fast algorithm for path sampling in path integral Monte Carlo simulations
is proposed. The algorithm utilizes the Levy-Ciesielski implementation of
Lie-Trotter products to achieve a mathematically proven computational cost of
n*log_2(n) with the number of time slices n, despite the fact that each path
variable is updated separately, for reasons of optimality. In this respect, we
demonstrate that updating a group of random variables simultaneously results in
loss of efficiency.Comment: 4 pages, 1 figure; fast rejection from Phys. Rev. Letts; transfered
to PRE as a Rapid Communication. Eq. 6 to 10 contained some inconsistencies
that have been repaired in the present version; A sample code implementing
the algorithm for LJ clusters is available from the author upon reques
Critical sets of nonlinear Sturm-Liouville operators of Ambrosetti-Prodi type
The critical set C of the operator F:H^2_D([0,pi]) -> L^2([0,pi]) defined by
F(u)=-u''+f(u) is studied. Here X:=H^2_D([0,pi]) stands for the set of
functions that satisfy the Dirichlet boundary conditions and whose derivatives
are in L^2([0,pi]). For generic nonlinearities f, C=\cup C_k decomposes into
manifolds of codimension 1 in X. If f''0, the set C_j is shown to be
non-empty if, and only if, -j^2 (the j-th eigenvalue of u -> u'') is in the
range of f'. The critical components C_k are (topological) hyperplanes.Comment: 6 pages, no figure
A flux-ratio anomaly in the CO spectral line emission from gravitationally-lensed quasar MG J0414+0534
We present an analysis of archival observations with the Atacama Large
(sub-)Millimetre Array (ALMA) of the gravitationally lensed quasar MG
J0414+0534, which show four compact images of the quasar and an Einstein ring
from the dust associated with the quasar host galaxy. We confirm that the
flux-ratio anomalies observed in the mid-infrared and radio persists into the
sub-mm for the continuum images of the quasar. We report the detection of CO
(11-10) spectral line emission, which traces a region of compact gas around the
quasar nucleus. This line emission also shows evidence of a flux-ratio anomaly
between the merging lensed images that is consistent with those observed at
other wavelengths, suggesting high-excitation CO can also provide a useful
probe of substructures that is unaffected by microlensing or dust extinction.
However, we do not detect the candidate dusty dwarf galaxy that was previously
reported with this dataset, which we conclude is due to a noise artefact. Thus,
the cause of the flux-ratio anomaly between the merging lensed images is still
unknown. The composite compact and diffuse emission in this system suggest
lensed quasar-starbursts will make excellent targets for detecting dark
sub-haloes and testing models for dark matter.Comment: Accepted as MNRAS Lette
The final candidate from the JVAS/CLASS search for 6 arcsec to 15 arcsec image separation lensing
A search for 6 arcsec to 15 arcsec image separation lensing in the Jodrell
Bank-Very Large Array Astrometric Survey (JVAS) and the Cosmic Lens All-Sky
Survey (CLASS) by Phillips et al. found thirteen group and cluster
gravitational lens candidates. Through radio and optical imaging and
spectroscopy, Phillips et al. ruled out the lensing hypothesis for twelve of
the candidates. In this paper, new optical imaging and spectroscopy of
J0122+427, the final lens candidate from the JVAS/CLASS 6 arcsec to 15 arcsec
image separation lens search, are presented. This system is found not to be a
gravitational lens, but is just two radio-loud active galactic nuclei that are
separated by ~10 arcsec on the sky and are at different redshifts. Therefore,
it is concluded that there are no gravitational lenses in the JVAS and CLASS
surveys with image separations between 6 arcsec to 15 arcsec. This result is
consistent with the expectation that group- and cluster-scale dark matter
haloes are inefficient lenses due to their relatively flat inner density
profiles.Comment: 5 pages, 3 figures, 2 tables, accepted for publication in MNRA
Volatility and dividend risk in perpetual American options
American options are financial instruments that can be exercised at any time
before expiration. In this paper we study the problem of pricing this kind of
derivatives within a framework in which some of the properties --volatility and
dividend policy-- of the underlaying stock can change at a random instant of
time, but in such a way that we can forecast their final values. Under this
assumption we can model actual market conditions because some of the most
relevant facts that may potentially affect a firm will entail sharp predictable
effects. We will analyse the consequences of this potential risk on perpetual
American derivatives, a topic connected with a wide class of recurrent problems
in physics: holders of American options must look for the fair price and the
optimal exercise strategy at once, a typical question of free absorbing
boundaries. We present explicit solutions to the most common contract
specifications and derive analytical expressions concerning the mean and higher
moments of the exercise time.Comment: 21 pages, 5 figures, iopart, submitted for publication; deep
revision, two new appendice
ALMA imaging of SDP.81 - I. A pixelated reconstruction of the far-infrared continuum emission
We present a sub-50 pc-scale analysis of the gravitational lens system SDP.81
at redshift 3.042 using Atacama Large Millimetre/submillimetre Array (ALMA)
science verification data. We model both the mass distribution of the
gravitational lensing galaxy and the pixelated surface brightness distribution
of the background source using a novel Bayesian technique that fits the data
directly in visibility space. We find the 1 and 1.3 mm dust emission to be
magnified by a factor of u_tot = 17.6+/-0.4, giving an intrinsic total
star-formation rate of 315+/-60 M_sol/yr and a dust mass of 6.4+/-1.5*10^8
M_sol. The reconstructed dust emission is found to be non-uniform, but composed
of multiple regions that are heated by both diffuse and strongly clumped
star-formation. The highest surface brightness region is a ~1.9*0.7 kpc
disk-like structure, whose small extent is consistent with a potential
size-bias in gravitationally lensed starbursts. Although surrounded by extended
star formation, with a density of 20-30+/-10 M_sol/yr/kpc^2, the disk contains
three compact regions with densities that peak between 120-190+/-20
M_sol/yr/kpc^2. Such star-formation rate densities are below what is expected
for Eddington-limited star-formation by a radiation pressure supported
starburst. There is also a tentative variation in the spectral slope of the
different star-forming regions, which is likely due to a change in the dust
temperature and/or opacity across the source.Comment: MNRAS accepted 2015 April 1
Resolving on 100 pc scales the UV-continuum in Lyman- emitters between redshift 2 to 3 with gravitational lensing
We present a study of seventeen LAEs at redshift 23 gravitationally
lensed by massive early-type galaxies (ETGs) at a mean redshift of
approximately 0.5. Using a fully Bayesian grid-based technique, we model the
gravitational lens mass distributions with elliptical power-law profiles and
reconstruct the UV-continuum surface brightness distributions of the background
sources using pixellated source models. We find that the deflectors are close
to, but not consistent with isothermal models in almost all cases, at the
-level. We take advantage of the lensing magnification (typically
20) to characterise the physical and morphological properties of
these LAE galaxies. From reconstructing the ultra-violet continuum emission, we
find that the star-formation rates range from 0.3 to 8.5 M yr
and that the galaxies are typically composed of several compact and diffuse
components, separated by 0.4 to 4 kpc. Moreover, they have peak star-formation
rate intensities that range from 2.1 to 54.1 M yr kpc.
These galaxies tend to be extended with major axis ranging from 0.2 to 1.8 kpc
(median 561 pc), and with a median ellipticity of 0.49. This morphology is
consistent with disk-like structures of star-formation for more than half of
the sample. However, for at least two sources, we also find off-axis components
that may be associated with mergers. Resolved kinematical information will be
needed to confirm the disk-like nature and possible merger scenario for the
LAEs in the sample.Comment: 19 pages, 7 figures, accepted for publication on MNRA
A novel search for gravitationally lensed radio sources in wide-field VLBI imaging from the mJIVE-20 survey
We present a novel pilot search for gravitational lenses in the mJIVE-20
survey, which observed radio sources selected from FIRST with the
VLBA at an angular resolution of 5 mas. We have taken the visibility data for
an initial sources that were detected by the mJIVE-20 observations and
re-mapped them to make wide-field images, selecting fourteen sources that had
multiple components separated by mas, with a flux-ratio of
: and a surface brightness consistent with gravitational lensing.
Two of these candidates are re-discoveries of gravitational lenses found as
part of CLASS. The remaining twelve candidates were then re-observed at 1.4 GHz
and then simultaneously at 4.1 and 7.1 GHz with the VLBA to measure the
spectral index and surface brightness of the individual components as a
function of frequency. Ten were rejected as core-jet or core-hotspot(s)
systems, with surface brightness distributions and/or spectral indices
inconsistent with gravitational lensing, and one was rejected after lens
modelling demonstrated that the candidate lensed images failed the parity test.
The final lens candidate has an image configuration that is consistent with a
simple lens mass model, although further observations are required to confirm
the lensing nature. Given the two confirmed gravitational lenses in the
mJIVE-20 sample, we find a robust lensing-rate of :() for a
statistical sample of 635 radio sources detected on mas-scales, which is
consistent with that found for CLASS.Comment: 31 pages, 22 figures; accepted for publication in MNRA
ALMA imaging of SDP.81 - II. A pixelated reconstruction of the CO emission lines
We present a sub-100 pc-scale analysis of the CO molecular gas emission and
kinematics of the gravitational lens system SDP.81 at redshift 3.042 using
Atacama Large Millimetre/submillimetre Array (ALMA) science verification data
and a visibility-plane lens reconstruction technique. We find clear evidence
for an excitation dependent structure in the unlensed molecular gas
distribution, with emission in CO (5-4) being significantly more diffuse and
structured than in CO (8-7). The intrinsic line luminosity ratio is r_8-7/5-4 =
0.30 +/- 0.04, which is consistent with other low-excitation starbursts at z ~
3. An analysis of the velocity fields shows evidence for a star-forming disk
with multiple velocity components that is consistent with a
merger/post-coalescence merger scenario, and a dynamical mass of M(< 1.56 kpc)
= 1.6 +/- 0.6 x 10^10 M_sol . Source reconstructions from ALMA and the Hubble
Space Telescope show that the stellar component is offset from the molecular
gas and dust components. Together with Karl G. Jansky Very Large Array CO (1-0)
data, they provide corroborative evidence for a complex ~2 kpc-scale starburst
that is embedded within a larger ~15 kpc structure.Comment: MNRAS accepted, 6th July 201
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