Constraining primordial black hole fraction at the galactic centre using radio observational data

ABSTRACT Recent gamma-ray and cosmic-ray observations have put strong constraints on the amount of primordial black holes (PBHs) in our universe. In this paper, we use the archival radio data of the inner Galactic Centre to constrain the PBH to dark matter ratio for three different PBH mass distributions including monochromatic, lognormal, and power law. We show that the amount of PBHs only constitutes a very minor component of dark matter at the Galactic Centre for a large parameter space.

Interrelationships of Pressure-Dependent Hole Fraction and Elongational Viscosity in Polymer Melts

The elongational flow behavior of polyethylene, polypropylene, polystyrene, poly(methyl methacrylate), and polycarbonate, temperatures from 70 to 290 °C and pressures up to 70 MPa, is examined with the Yahsi-Dinc-Tav (YDT) model and its particular case known as the Cross model. The viscosity data employed in the range of 3-405 s-1 elongational rates were acquired from the literature at ambient and elevated pressures. The predictions and the fitting results of the proposed YDT model with the same measurement data are compared with the Cross model. The average absolute deviations of the viscosities predicted by the YDT model range from 0.54% to 9.44% at ambient and 1.95% to 6.28% at high pressures. Additionally, the linear formulations derived from the YDT model are employed to relate the viscosity with temperature and hole fraction (“thermooccupancy” function) at zero level of elongational rate and constant elongational rate along with constant elongational stress. The effects of the four viscosity parameters (such as transmission and activation energy coefficients in these equations) on the elongational viscosity are analyzed in detail and some conclusions on the structural differences for the polymers are discussed.

Microstructure and Mechanical Properties of Air Core Polymer Photonic Crystal Fibers

Polymer based photonic crystal fibers with low cost manufacturability, and the mechanical and chemical flexibility offer key advantages over traditional silica based photonic crystal fibers. PMMA photonic crystal fiber was fabricated by stacking an array of PMMA capillaries to form a preform, and followed by fusing and drawing into fiber with a draw tower. The air hole diameter and fraction of photonic crystal fiber can be manipulated by the thickness of PMMA capillaries and drawing temperature. The measurement of mechanical properties was performed by universal testing machine. The air core guiding phenomena was observed in air-core PMMA photonic crystal fiber. The ultimate tensile strength of PMMA photonic crystal fiber increases with the increase of the air-hole fraction. The mechanical strengths of all the microstructured optical fibers are higher than those of traditional PMMA fibers. This can be attributed to the introduction of more cellular interfaces which hinder the crack propagation and hence improve the mechanical strength. The plastic extension of PMMA microstructured optical fiber decreases with the increase of the air-hole fraction. Overall, the mechanical flexibility of PMMA microstructured optical fiber is superior than that of traditional PMMA optical fibers.

On the Estimation of Confidence Intervals for Binomial Population Proportions in Astronomy: The Simplicity and Superiority of the Bayesian Approach

I present a critical review of techniques for estimating confidence intervals on binomial population proportions inferred from success counts in small to intermediate samples. Population proportions arise frequently as quantities of interest in astronomical research; for instance, in studies aiming to constrain the bar fraction, active galactic nucleus fraction, supermassive black hole fraction, merger fraction, or red sequence fraction from counts of galaxies exhibiting distinct morphological features or stellar populations. However, two of the most widely-used techniques for estimating binomial confidence intervals — the ‘normal approximation’ and the Clopper & Pearson approach — are liable to misrepresent the degree of statistical uncertainty present under sampling conditions routinely encountered in astronomical surveys, leading to an ineffective use of the experimental data (and, worse, an inefficient use of the resources expended in obtaining that data). Hence, I provide here an overview of the fundamentals of binomial statistics with two principal aims: (I) to reveal the ease with which (Bayesian) binomial confidence intervals with more satisfactory behaviour may be estimated from the quantiles of the beta distribution using modern mathematical software packages (e.g.r, matlab, mathematica, idl, python); and (ii) to demonstrate convincingly the major flaws of both the ‘normal approximation’ and the Clopper & Pearson approach for error estimation.