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

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

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

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 pres