25,554 research outputs found
Fast and accurate evaluation of Wigner 3j, 6j, and 9j symbols using prime factorisation and multi-word integer arithmetic
We present an efficient implementation for the evaluation of Wigner 3j, 6j,
and 9j symbols. These represent numerical transformation coefficients that are
used in the quantum theory of angular momentum. They can be expressed as sums
and square roots of ratios of integers. The integers can be very large due to
factorials. We avoid numerical precision loss due to cancellation through the
use of multi-word integer arithmetic for exact accumulation of all sums. A
fixed relative accuracy is maintained as the limited number of floating-point
operations in the final step only incur rounding errors in the least
significant bits. Time spent to evaluate large multi-word integers is in turn
reduced by using explicit prime factorisation of the ingoing factorials,
thereby improving execution speed. Comparison with existing routines shows the
efficiency of our approach and we therefore provide a computer code based on
this work.Comment: 7 pages, 2 figures. Accepted for publication in SIAM Journal on
Scientific Computing (SISC
Accurate laboratory ultraviolet wavelengths for quasar absorption-line constraints on varying fundamental constants
The most precise method of investigating possible space-time variations of
the fine-structure constant, using high-redshift quasar absorption lines, is
the many-multiplet (MM) method. For reliable results this method requires very
accurate relative laboratory wavelengths for a number of UV resonance
transitions from several different ionic species. For this purpose laboratory
wavelengths and wavenumbers of 23 UV lines from MgI, MgII, TiII, CrII, MnII,
FeII and ZnII have been measured using high-resolution Fourier Transform (FT)
spectrometry. The spectra of the different ions (except for one FeII line, one
MgI line and the TiII lines) are all measured simultaneously in the same FT
spectrometry recording by using a composite hollow cathode as a light source.
This decreases the relative uncertainties of all the wavelengths. In addition
to any measurement uncertainty, the wavelength uncertainty is determined by
that of the ArII calibration lines, by possible pressure shifts and by
illumination effects. The absolute wavenumbers have uncertainties of typically
0.001 to 0.002 cm^(-1) (0.06 to 0.1 mAA at 2500 AA), while the relative
wavenumbers for strong, symmetric lines in the same spectral recording have
uncertainties of 0.0005 cm^(-1) (0.03 mAA at 2500 AA) or better, depending
mostly on uncertainties in the line fitting procedure. This high relative
precision greatly reduces the potential for systematic effects in the MM
method, while the new TiII measurements now allow these transitions to be used
in MM analyses.Comment: Accepted for publication in MNRAS, 10 pages, 9 figure
The Inflection Point of the Speed-Density Relation and the Social Force Model
It has been argued that the speed-density digram of pedestrian movement has
an inflection point. This inflection point was found empirically in
investigations of closed-loop single-file pedestrian movement. The reduced
complexity of single-file movement does not only allow a higher precision for
the evaluation of empirical data, but it occasionally also allows analytical
considerations for micosimulation models. In this way it will be shown that
certain (common) variants of the Social Force Model (SFM) do not produce an
inflection point in the speed-density diagram if infinitely many pedestrians
contribute to the force computed for one pedestrian. We propose a modified
Social Force Model that produces the inflection point.Comment: accepted for presentation at conference Traffic and Granular Flow
201
The Method of Fundamental Solutions for Direct Cavity Problems in EIT
The Method of Fundamental Solutions (MFS) is an effective technique for solving linear elliptic partial differential equations, such as the Laplace and Helmholtz equation. It is a form of indirect boundary integral equation method and a technique that uses boundary collocation or boundary fitting. In this paper the MFS is implemented to solve A numerically an inverse problem which consists of finding an unknown cavity within a region of interest based on given boundary Cauchy data. A range of examples are used to demonstrate that the technique is very effective at locating cavities in two-dimensional geometries for exact input data. The technique is then developed to include a regularisation parameter that enables cavities to be located accurately and stably even for noisy input data
Large time asymptotics of growth models on space-like paths II: PNG and parallel TASEP
We consider the polynuclear growth (PNG) model in 1+1 dimension with flat
initial condition and no extra constraints. The joint distributions of surface
height at finitely many points at a fixed time moment are given as marginals of
a signed determinantal point process. The long time scaling limit of the
surface height is shown to coincide with the Airy_1 process. This result holds
more generally for the observation points located along any space-like path in
the space-time plane. We also obtain the corresponding results for the discrete
time TASEP (totally asymmetric simple exclusion process) with parallel update.Comment: 39 pages,6 figure
Constrained simulations of the Antennae Galaxies: Comparison with Herschel-PACS observations
We present a set of hydro-dynamical numerical simulations of the Antennae
galaxies in order to understand the origin of the central overlap starburst.
Our dynamical model provides a good match to the observed nuclear and overlap
star formation, especially when using a range of rather inefficient stellar
feedback efficiencies (0.01 < q_EoS < 0.1). In this case a simple conversion of
local star formation to molecular hydrogen surface density motivated by
observations accounts well for the observed distribution of CO. Using radiative
transfer post-processing we model synthetic far-infrared spectral energy
distributions (SEDs) and two-dimensional emission maps for direct comparison
with Herschel-PACS observations. For a gas-to-dust ratio of 62:1 and the best
matching range of stellar feedback efficiencies the synthetic far-infrared SEDs
of the central star forming region peak at values of ~65 - 81 Jy at 99 - 116
um, similar to a three-component modified black body fit to infrared
observations. Also the spatial distribution of the far-infrared emission at 70
um, 100 um, and 160 um compares well with the observations: >50% (> 35%) of the
emission in each band is concentrated in the overlap region while only < 30% (<
15%) is distributed to the combined emission from the two galactic nuclei in
the simulations (observations). As a proof of principle we show that parameter
variations in the feedback model result in unambiguous changes both in the
global and in the spatially resolved observable far-infrared properties of
Antennae galaxy models. Our results strengthen the importance of direct,
spatially resolved comparative studies of matched galaxy merger simulations as
a valuable tool to constrain the fundamental star formation and feedback
physics.Comment: 17 pages, 8 figures, 4 tables, submitted to MNRAS, including
revisions after first referee report, comments welcom
Revisited abundance diagnostics in quasars: Fe II/Mg II ratios
Both the Fe II UV emission in the 2000- 3000 A region [Fe II (UV)] and
resonance emission line complex of Mg II at 2800 A are prominent features in
quasar spectra. The observed Fe II UV/ Mg II emission ratios have been proposed
as means to measure the buildup of the Fe abundance relative to that of the
alpha-elements C, N, O, Ne and Mg as a function of redshift. The current
observed ratios show large scatter and no obvious dependence on redshift. Thus,
it remains unresolved whether a dependence on redshift exists and whether the
observed Fe II UV/ Mg II ratios represent a real nucleosynthesis diagnostic. We
have used our new 830-level model atom for Fe+ in photoionization calculations,
reproducing the physical conditions in the broad line regions of quasars. This
modeling reveals that interpretations of high values of Fe II UV/ Mg II are
sensitive not only to Fe and Mg abundance, but also to other factors such as
microturbulence, density, and properties of the radiation field. We find that
the Fe II UV/ Mg II ratio combined with Fe II (UV)/ Fe II (Optical) emission
ratio, where Fe II (Optical) denotes Fe II emission in 4000 - 6000 A can be
used as a reliable nucleosynthesis diagnostic for the Fe/Mg abundance ratios
for the physical conditions relevant to the broad-line regions (BLRs) of
quasars. This has extreme importance for quasar observations with the Hubble
Space Telescope and also with the future James Webb Space Telescope.Comment: kverner.gzip, 9 pages, f1-5.eps; aastex.cls; aastexug.sty, ApJL in
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