The Probability Distribution Function of Column Density in Molecular Clouds

(Abridged) We discuss the probability distribution function (PDF) of column density resulting from density fields with lognormal PDFs, applicable to isothermal gas (e.g., probably molecular clouds). We suggest that a ``decorrelation length'' can be defined as the distance over which the density auto-correlation function has decayed to, for example, 10% of its zero-lag value, so that the density ``events'' along a line of sight can be assumed to be independent over distances larger than this, and the Central Limit Theorem should be applicable. However, using random realizations of lognormal fields, we show that the convergence to a Gaussian is extremely slow in the high- density tail. Thus, the column density PDF is not expected to exhibit a unique functional shape, but to transit instead from a lognormal to a Gaussian form as the ratio $\eta$ of the column length to the decorrelation length increases. Simultaneously, the PDF's variance decreases. For intermediate values of $\eta$, the column density PDF assumes a nearly exponential decay. We then discuss the density power spectrum and the expected value of $\eta$ in actual molecular clouds. Observationally, our results suggest that $\eta$ may be inferred from the shape and width of the column density PDF in optically-thin-line or extinction studies. Our results should also hold for gas with finite-extent power-law underlying density PDFs, which should be characteristic of the diffuse, non-isothermal neutral medium (temperatures ranging from a few hundred to a few thousand degrees). Finally, we note that for $\eta \gtrsim 100$, the dynamic range in column density is small ($\lesssim$ a factor of 10), but this is only an averaging effect, with no implication on the dynamic range of the underlying density distribution.Comment: 13 pages, 7 figures (10 postscript files). Accepted in ApJ. Eliminated implication that ratio of column length to correlation length necessarily increases with resolution, and thus that 3D simulations are unresolved. Added discussion of dependence of autocorrelation function with parameters of the turbulenc

The secondary infall model of galactic halo formation and the spectrum of cold dark matter particles on Earth

The spectrum of cold dark matter particles on Earth is expected to have peaks in velocity space associated with particles which are falling onto the Galaxy for the first time and with particles which have fallen in and out of the Galaxy only a small number of times in the past. We obtain estimates for the velocity magnitudes and the local densities of the particles in these peaks. To this end we use the secondary infall model of galactic halo formation which we have generalized to take account of the angular momentum of the dark matter particles. The new model is still spherically symmetric and it admits self-similar solutions. In the absence of angular momentum, the model produces flat rotation curves for a large range of values of a parameter $\epsilon$ which is related to the spectrum of primordial density perturbations. We find that the presence of angular momentum produces an effective core radius, i.e. it makes the contribution of the halo to the rotation curve go to zero at zero radius. The model provides a detailed description of the large scale properties of galactic halos including their density profiles, their extent and total mass. We obtain predictions for the kinetic energies of the particles in the velocity peaks and estimates for their local densities as functions of the amount of angular momentum, the age of the universe and $\epsilon$.Comment: LaTeX, 39 pages including 18 figure

The fundamental cycle of concept construction underlying various theoretical frameworks

In this paper, the development of mathematical concepts over time is considered. Particular reference is given to the shifting of attention from step-by-step procedures that are performed in time, to symbolism that can be manipulated as mental entities on paper and in the mind. The development is analysed using different theoretical perspectives, including the SOLO model and various theories of concept construction to reveal a fundamental cycle underlying the building of concepts that features widely in different ways of thinking that occurs throughout mathematical learning

6-thioguanine treatment in inflammatory bowel disease: A critical appraisal by a European 6-TG working party

Recently, the suggestion to use 6-thioguanine (6-TG) as an alternative thiopurine in patients with inflammatory bowel disease (IBD) has been discarded due to reports about possible (hepato) toxicity. During meetings arranged in Vienna and Prague in 2004, European experts applying 6-TG further on in IBD patients presented data on safety and efficacy of 6-TG. After thorough evaluation of its risk-benefit ratio, the group consented that 6-TG may still be considered as a rescue drug in stringently defined indications in IBD, albeit restricted to a clinical research setting. As a potential indication for administering 6-TG, we delineated the requirement for maintenance therapy as well as intolerance and/or resistance to aminosalicylates, azathioprine, 6-mercaptopurine, methotrexate and infliximab. Furthermore, indications are preferred in which surgery is thought to be inappropriate. The standard 6-TG dosage should not exceed 25 mg daily. Routine laboratory controls are mandatory in short intervals. Liver biopsies should be performed after 6-12 months, three years and then three-yearly accompanied by gastroduodenoscopy, to monitor for potential hepatotoxicity, including nodular regenerative hyperplasia (NRH) and veno-occlusive disease (VOD). Treatment with 6-TG must be discontinued in case of overt or histologically proven hepatotoxicity. Copyright (c) 2006 S. Karger AG, Basel

Gains and losses of coral skeletal porosity changes with ocean acidification acclimation

Ocean acidification is predicted to impact ecosystems reliant on calcifying organisms, potentially reducing the socioeconomic benefits these habitats provide. Here we investigate the acclimation potential of stony corals living along a pH gradient caused by a Mediterranean CO(2) vent that serves as a natural long-term experimental setting. We show that in response to reduced skeletal mineralization at lower pH, corals increase their skeletal macroporosity (features >10 μm) in order to maintain constant linear extension rate, an important criterion for reproductive output. At the nanoscale, the coral skeleton's structural features are not altered. However, higher skeletal porosity, and reduced bulk density and stiffness may contribute to reduce population density and increase damage susceptibility under low pH conditions. Based on these observations, the almost universally employed measure of coral biomineralization, the rate of linear extension, might not be a reliable metric for assessing coral health and resilience in a warming and acidifying ocean

Performance Evaluation of Pseudospectral Ultrasound Simulations on a Cluster of Xeon Phi Accelerators

The rapid development of novel procedures in medical ultrasonics, including treatment planning in therapeutic ultrasound and image reconstruction in photoacoustic tomography, leads to increasing demand for large-scale ultrasound simulations. However, routine execution of such simulations using traditional methods, e.g., finite difference time domain, is expensive and often considered intractable due to the computational and memory requirements. The k-space corrected pseudospectral time domain method used by the k-Wave toolbox allows for significant reductions in spatial and temporal grid resolution. These improvements are achieved at the cost of all-to-all communication, which are inherent to the multi-dimensional fast Fourier transforms. To improve data locality, reduce communication and allow efficient use of accelerators, we recently implemented a domain decomposition technique based on a local Fourier basis. In this paper, we investigate whether it is feasible to run the distributed k-Wave implementation on the Salomon cluster equipped with 864 Intel Xeon Phi (Knight’s Corner) accelerators. The results show the immaturity of the KNC platform with issues ranging from limited support of Infiniband and LustreFS in Intel MPI on this platform to poor performance of 3D FFTs achieved by Intel MKL on the KNC architecture. Yet, we show that it is possible to achieve strong and weak scaling comparable to CPU-only platforms albeit with the runtime 1.8× to 4.3× longer. However, the accounting policy for Salomon’s accelerators is far more favorable and thus their employment reduces the computational cost significantly

Business ethics : practical proposals

While most people agree that the inculcation of ethical awareness is desirable, the means of stimulating this awareness vary among companies, industries and cultures. The fundamental question surrounding the difference between social responsibility and ethics is addressed. Guidelines for establishing ethical priorities from both the individual, group and organisational perspectives are provided. <br /

Vector meson dominance pion electromagnetic form factor with the sigma-model loop corrections

A model is developed for electromagnetic form factor of the pion. One-loop corrections are included in the linear sigma-model. The rho-meson contribution is added in an extended VMD model. The form factor, calculated without fitting parameters, is in a good agreement with experiment for space-like and time-like photon momenta. Loop corrections to the two-pion hadronic contribution a^{(had, \pi)}_\mu to the muon anomalous magnetic moment are calculated. The optimal value of the sigma-meson mass appears to be close to the rho-meson mass.Comment: 12 pages, 3 figures, to be published in JET

The Discrepancy Between tau and e+e- Spectral Functions Revisited and the Consequences for the Muon Magnetic Anomaly

We revisit the procedure for comparing the pi pi spectral function measured in tau decays to that obtained in e+e- annihilation. We re-examine the isospin-breaking corrections using new experimental and theoretical input, and find improved agreement between the tau- --> pi- pi0 nu_tau branching fraction measurement and its prediction using the isospin-breaking-corrected e+e- --> pi+pi- spectral function, though not resolving all discrepancies. We recompute the lowest order hadronic contributions to the muon g-2 using e+e- and tau data with the new corrections, and find a reduced difference between the two evaluations. The new tau-based estimate of the muon magnetic anomaly is found to be 1.9 standard deviations lower than the direct measurement.Comment: 10 pages, 6 figures, submitted to Eur. Phys. J. C; (v2): Revised version with improved and uniform treatment of tau and e+e- data with HVPTools and a few minor bug fixes; (v3): Final version accepted for publicatio

Conceptualizing Communication Capital for a Changing Environment

With rapidly evolving technologies, boundaries between traditional modes of communication have blurred, creating an environment that scholars still describe from viewpoints as researchers in interpersonal, organizational or mass communication. This manuscript looks at the social capital literature and argues for conceptualizing “communication capital” to help understand the impact of communication phenomena in a changing environment. The literature has treated interpersonal communication variables as components of social capital and mass communication variables as factors affecting social capital, but scholars long ago recognized their reinforcing nature, leading us to develop a concept of communication capital merging symbolic activity across domains in its potential for impacting civic engagement, defined as persistent communication patterns that facilitate social problem solving in the community. Analysis of survey data shows that 4 dimensions of communication capital explain variance in civic engagement beyond that accounted for by traditional measures of social capital, media use, neighborhood communication, and efficacy