Shedding Light on the Matter of Abell 781

The galaxy cluster Abell 781 West has been viewed as a challenge to weak gravitational lensing mass calibration, as Cook and dell'Antonio (2012) found that the weak lensing signal-to-noise in three independent sets of observations was consistently lower than expected from mass models based on X-ray and dynamical measurements. We correct some errors in statistical inference in Cook and dell'Antonio (2012) and show that their own results agree well with the dynamical mass and exhibit at most 2.2--2.9$\sigma$ low compared to the X-ray mass, similar to the tension between the dynamical and X-ray masses. Replacing their simple magnitude cut with weights based on source photometric redshifts eliminates the tension between lensing and X-ray masses; in this case the weak lensing mass estimate is actually higher than, but still in agreement with, the dynamical estimate. A comparison of lensing analyses with and without photometric redshifts shows that a 1--2$\sigma$ chance alignment of low-redshift sources lowers the signal-to-noise observed by all previous studies which used magnitude cuts rather than photometric redshifts. The fluctuation is unexceptional, but appeared to be highly significant in Cook and dell'Antonio (2012) due to the errors in statistical interpretation.Comment: 7 pages, submitted to MNRA

Graphite ionization vacuum gauge

Triode gauge with electron source, electron collector, and positive ion collector made from either graphite or carbon material extends low-pressure ranges of existing gauges by changing only materials used in construction. Advantages of graphite gauge stem from physical properties of graphite (or carbon)

Study of Umbrella-Type Erectable Paraboloidal Solar Concentrators for Generation of Spacecraft Auxiliary Power

An investigation was made of some aspects of erectable umbrella-type paraboloidal solar-energy concentrators for use in spacecraft auxiliary power systems. An analysis is presented for the design of concentrators employing radial ribs and membrane-type coverings. The rib stiffness necessary to give a desired parabolic curvature upon erection is determined. Rib contour measurements were made in an upright and inverted position on an experimental 10-foot-diameter concentrator giving a focal length of 30.78 inches and 30.6 inches, respectively, as compared with a design focal length of 30 inches. Calorimetric tests employing spherical heat receivers showed a maximum geometrical concentrator efficiency of 75.3 percent with a concentration ratio of 92.2 at a focal length of approximately 30.5 inches. Within the scope of this investigation, it was found that, as the concentrator size increases, the weight per unit projected area increases, time to damp to one-half amplitude increases, and the natural frequency decreases. Umbrella-type solar concentrators appear to be feasible for power conversion systems using low concentration ratios; however, for large concentrators the time required to damp out disturbances may be a problem

Stratifying derived categories of cochains on certain spaces

In recent years, Benson, Iyengar and Krause have developed a theory of stratification for compactly generated triangulated categories with an action of a graded commutative Noetherian ring. Stratification implies a classification of localizing and thick subcategories in terms of subsets of the prime ideal spectrum of the given ring. In this paper two stratification results are presented: one for the derived category of a commutative ring-spectrum with polynomial homotopy and another for the derived category of cochains on certain spaces. We also give the stratification of cochains on a space a topological content.Comment: 27 page

Pattern formation in reaction diffusion models with spatially inhomogeneous diffusion coefficients

Reaction-diffusion models for biological pattern formation have been studied extensively in a variety of embryonic and ecological contexts. However, despite experimental evidence pointing to the existence of spatial inhomogeneities in various biological systems, most models have only been considered in a spatially homogeneous environment. The authors consider a two-chemical reaction-diffusion mechanism in one space dimension in which one of the diffusion coefficients depends explicitly on the spatial variable. The model is analysed in the case of a step function diffusion coefficient and the insight gained for this special case is used to discuss pattern generation for smoothly varying diffusion coefficients. The results show that spatial inhomogeneity may be an important biological pattern regulator, and possible applications of the model to chondrogenesis in the vertebrate limb are suggested