The Fractal Dimension of Projected Clouds

The interstellar medium seems to have an underlying fractal structure which can be characterized through its fractal dimension. However, interstellar clouds are observed as projected two-dimensional images, and the projection of a tri-dimensional fractal distorts its measured properties. Here we use simulated fractal clouds to study the relationship between the tri-dimensional fractal dimension (D_f) of modeled clouds and the dimension resulting from their projected images. We analyze different fractal dimension estimators: the correlation and mass dimensions of the clouds, and the perimeter-based dimension of their boundaries (D_per). We find the functional forms relating D_f with the projected fractal dimensions, as well as the dependence on the image resolution, which allow to estimatethe "real" D_f value of a cloud from its projection. The application of these results to Orion A indicates in a self-consistent way that 2.5 < D_f < 2.7 for this molecular cloud, a value higher than the result D_per+1 = 2.3 some times assumed in literature for interstellar clouds.Comment: 27 pages, 13 figures, 1 table. Accepted for publication in ApJ. Minor change

Can Reflection from Grains Diagnose the Albedo?

By radiation transfer models with a realistic power spectra of the projected density distributions, we show that the optical properties of grains are poorly constrained by observations of reflection nebulae. The ISM is known to be hierarchically clumped from a variety of observations (molecules, H I, far-infrared). Our models assume the albedo and phase parameter of the dust, the radial optical depth of the sphere averaged over all directions, and random distributions of the dust within the sphere. The outputs are the stellar extinction, optical depth, and flux of scattered light as seen from various viewing angles. Observations provide the extinction and scattered flux from a particular direction. Hierarchical geometry has a large effect on the flux of scattered light emerging from a nebula for a particular extinction of the exciting star. There is a very large spread in both scattered fluxes and extinctions for any distribution of dust. Consequently, an observed stellar extinction and scattered flux can be fitted by a wide range of albedos. With hierarchical geometry it is not completely safe to determine even relative optical constants from multiwavelength observations of the same reflection nebula. The geometry effectively changes with wavelength as the opacity of the clumps varies. Limits on the implications of observing the same object in various wavelengths are discussed briefly. Henry (2002) uses a recipe to determine the scattered flux from a star with a given extinction. It is claimed to be independent of the geometry. It provides considerably more scattering than our models, probably leading to an underestimate of the grain albedos from the UV Diffuse Galactic Light.Comment: 27 pages, including 7 figures. Accepted by Ap

Constraining ^(26)Al+p resonances using ^(26)Al(^3He,d)^(27)Si

The ^(26)Al(^3He,d)^(27)Si reaction was measured from 0°≤θ_(c.m.)≤35° at E(^3He)=20 MeV using a quadrupole-dipole-dipole-dipole magnetic spectrometer. States in ^(27)Si were observed above the background at 7652 and 7741 keV and upper limits were set for the state at 7592 keV. Implications for the ^(26)Al(p,γ)^(27)Si stellar reaction rate are discussed

On the use of fractional Brownian motion simulations to determine the 3D statistical properties of interstellar gas

Based on fractional Brownian motion (fBm) simulations of 3D gas density and velocity fields, we present a study of the statistical properties of spectro-imagery observations (channel maps, integrated emission, and line centroid velocity) in the case of an optically thin medium at various temperatures. The power spectral index gamma_W of the integrated emission is identified with that of the 3D density field (gamma_n) provided the medium's depth is at least of the order of the largest transverse scale in the image, and the power spectrum of the centroid velocity map is found to have the same index gamma_C as that of the velocity field (gamma_v). Further tests with non-fBm density and velocity fields show that this last result holds, and is not modified either by the effects of density-velocity correlations. A comparison is made with the theoretical predictions of Lazarian & Pogosyan (2000).Comment: 28 pages, 14 figures, accepted for publication in ApJ. For preprint with higher-resolution figures, see http://www.cita.utoronto.ca/~mamd/miville_fbm2003.pd

Low-Background gamma counting at the Kimballton Underground Research Facility

The next generation of low-background physics experiments will require the use of materials with unprecedented radio-purity. A gamma-counting facility at the Kimballton Underground Research Facility (KURF) has been commissioned to perform initial screening of materials for radioactivity primarily from nuclides in the 238U and 232Th decay chains, 40K and cosmic-ray induced isotopes. The facility consists of two commercial low-background high purity germanium (HPGe) detectors. A continuum background reduction better than a factor of 10 was achieved by going underground. This paper describes the facility, detector systems, analysis techniques and selected assay results.Comment: 7 pages, 7 figures. Submitted to NIM

A Fractal Analysis of the HI Emission from the Large Magellanic Cloud

A composite map of HI in the LMC using the ATCA interferometer and the Parkes multibeam telescope was analyzed in several ways in an attempt to characterize the structure of the neutral gas and to find an origin for it. Fourier transform power spectra in 1D, 2D, and in the azimuthal direction were found to be approximate power laws over 2 decades in length. Delta-variance methods also showed the same power-law structure. Detailed models of these data were made using line-of-sight integrals over fractals that are analogous to those generated by simulations of turbulence with and without phase transitions. The results suggested a way to measure directly for the first time the line-of-sight thickness of the cool component of the HI disk of a nearly face-on galaxy. The signature of this thickness was found to be present in all of the measured power spectra. The character of the HI structure in the LMC was also viewed by comparing positive and negative images of the integrated emission. The geometric structure of the high-emission regions was found to be filamentary, whereas the geometric structure of the low-emission (intercloud) regions was found to be patchy and round. This result suggests that compressive events formed the high-emission regions, and expansion events, whether from explosions or turbulence, formed the low-emission regions. The character of the structure was also investigated as a function of scale using unsharp masks. All of these results suggest that most of the ISM in the LMC is fractal, presumably the result of pervasive turbulence, self-gravity, and self-similar stirring.Comment: 30 pages, 21 figures, scheduled for ApJ Vol 548n1, Feb 10, 200

Evidence-based sizing of non-inferiority trials using decision models

Abstract Background There are significant challenges to the successful conduct of non-inferiority trials because they require large numbers to demonstrate that an alternative intervention is “not too much worse” than the standard. In this paper, we present a novel strategy for designing non-inferiority trials using an approach for determining the appropriate non-inferiority margin (δ), which explicitly balances the benefits of interventions in the two arms of the study (e.g. lower recurrence rate or better survival) with the burden of interventions (e.g. toxicity, pain), and early and late-term morbidity. Methods We use a decision analytic approach to simulate a trial using a fixed value for the trial outcome of interest (e.g. cancer incidence or recurrence) under the standard intervention (pS) and systematically varying the incidence of the outcome in the alternative intervention (pA). The non-inferiority margin, pA – pS = δ, is reached when the lower event rate of the standard therapy counterbalances the higher event rate but improved morbidity burden of the alternative. We consider the appropriate non-inferiority margin as the tipping point at which the quality-adjusted life-years saved in the two arms are equal. Results Using the European Polyp Surveillance non-inferiority trial as an example, our decision analytic approach suggests an appropriate non-inferiority margin, defined here as the difference between the two study arms in the 10-year risk of being diagnosed with colorectal cancer, of 0.42% rather than the 0.50% used to design the trial. The size of the non-inferiority margin was smaller for higher assumed burden of colonoscopies. Conclusions The example demonstrates that applying our proposed method appears feasible in real-world settings and offers the benefits of more explicit and rigorous quantification of the various considerations relevant for determining a non-inferiority margin and associated trial sample size.https://deepblue.lib.umich.edu/bitstream/2027.42/146777/1/12874_2018_Article_643.pd

A Test of the Standard Hypothesis for the Origin of the HI Holes in Holmberg II

The nearby irregular galaxy Holmberg II has been extensively mapped in HI using the Very Large Array (VLA), revealing intricate structure in its interstellar gas component (Puche et al. 1992). An analysis of these structures shows the neutral gas to contain a number of expanding HI holes. The formation of the HI holes has been attributed to multiple supernova events occurring within wind-blown shells around young, massive star clusters, with as many as 10-200 supernovae required to produce many of the holes. From the sizes and expansion velocities of the holes, Puche et al. assigned ages of ~10^7 to 10^8 years. If the supernova scenario for the formation of the HI holes is correct, it implies the existence of star clusters with a substantial population of late-B, A and F main sequence stars at the centers of the holes. Many of these clusters should be detectable in deep ground-based CCD images of the galaxy. In order to test the supernova hypothesis for the formation of the HI holes, we have obtained and analyzed deep broad-band BVR and narrow-band H-alpha images of Ho II. We compare the optical and HI data and search for evidence of the expected star clusters in and around the HI holes. We also use the HI data to constrain models of the expected remnant stellar population. We show that in several of the holes the observed upper limits for the remnant cluster brightness are strongly inconsistent with the SNe hypothesis described in Puche et al. Moreover, many of the HI holes are located in regions of very low optical surface brightness which show no indication of recent star formation. Here we present our findings and explore possible alternative explanations for the existence of the HI holes in Ho II, including the suggestion that some of the holes were produced by Gamma-ray burst events.Comment: 30 pages, including 6 tables and 3 images. To appear in Astron. Journal (June 1999

Theory and experiment of differential acoustic resonance spectroscopy

Abstract Recent advances in Differential Acoustic Resonance Spectroscopy (DARS) techniques have given rise to applications in the field of poromechanics. We report on the experimental demonstration of bulk modulus measurements on poroelastic samples at sonic frequencies (1 kHz) with DARS. Normal mode perturbation is due to scattering of a foreign object (i.e., a rock sample) within an otherwise fluid-filled resonator. The perturbation theory on an elastic object determines its bulk modulus (inverse compressibility). The experimental bulk modulus of medium-to high-permeability (&gt;10 mD) poroelastic samples is in agreement with predictions from quasi-static loading of a porous sphere using the Biot theory. This result demonstrates that pore fluid flow governs the dominant relaxation process of the rock during compression. For low-permeability samples (&lt;10 mD), pressure equilibration via slow wave diffusion is limited, and only qualitative agreement is found between the upper bound (Gassmann undrained modulus) and the lower bound (volume-weighted compressibilities of the two constituents). DARS experiments, in conjunction with the poroelastic theory presented here, allow one to infer such rock physical properties as the effective bulk modulus at sonic frequencies

Multifractal Scaling, Geometrical Diversity, and Hierarchical Structure in the Cool Interstellar Medium

Multifractal scaling (MFS) refers to structures that can be described as a collection of interwoven fractal subsets which exhibit power-law spatial scaling behavior with a range of scaling exponents (concentration, or singularity, strengths) and dimensions. The existence of MFS implies an underlying multiplicative (or hierarchical, or cascade) process. Panoramic column density images of several nearby star- forming cloud complexes, constructed from IRAS data and justified in an appendix, are shown to exhibit such multifractal scaling, which we interpret as indirect but quantitative evidence for nested hierarchical structure. The relation between the dimensions of the subsets and their concentration strengths (the "multifractal spectrum'') appears to satisfactorily order the observed regions in terms of the mixture of geometries present: strong point-like concentrations, line- like filaments or fronts, and space-filling diffuse structures. This multifractal spectrum is a global property of the regions studied, and does not rely on any operational definition of "clouds.'' The range of forms of the multifractal spectrum among the regions studied implies that the column density structures do not form a universality class, in contrast to indications for velocity and passive scalar fields in incompressible turbulence, providing another indication that the physics of highly compressible interstellar gas dynamics differs fundamentally from incompressible turbulence. (Abstract truncated)Comment: 27 pages, (LaTeX), 13 figures, 1 table, submitted to Astrophysical Journa