An Intuitive Approach to Geometric Continuity for Parametric Curves and Surfaces (Extended Abstract)

The notion of geometric continuity is extended to an arbitrary order for curves and surfaces, and an intuitive development of constraints equations is presented that are necessary for it. The constraints result from a direct application of the univariate chain rule for curves, and the bivariate chain rule for surfaces. The constraints provide for the introduction of quantities known as shape parameters. The approach taken is important for several reasons: First, it generalizes geometric continuity to arbitrary order for both curves and surfaces. Second, it shows the fundamental connection between geometric continuity of curves and geometric continuity of surfaces. Third, due to the chain rule derivation, constraints of any order can be determined more easily than derivations based exclusively on geometric measures

Lasing from a circular Bragg nanocavity with an ultra-small modal volume

We demonstrate single-mode lasing at telecommunication wavelengths from a circular nanocavity employing a radial Bragg reflector. Ultra-small modal volume and Sub milliwatt pump threshold level are observed for lasers with InGaAsP quantum well active membrane. The electromagnetic field is shown to be tightly confined within the 300nm central pillar of the cavity. The quality factors of the resonator modal fields are estimated to be on the order of a few thousands.Comment: 3 pages, 4 figures Submitted to AP

L-systems in Geometric Modeling

We show that parametric context-sensitive L-systems with affine geometry interpretation provide a succinct description of some of the most fundamental algorithms of geometric modeling of curves. Examples include the Lane-Riesenfeld algorithm for generating B-splines, the de Casteljau algorithm for generating Bezier curves, and their extensions to rational curves. Our results generalize the previously reported geometric-modeling applications of L-systems, which were limited to subdivision curves.Comment: In Proceedings DCFS 2010, arXiv:1008.127

Spitzer observations of Bow Shocks and Outflows in RCW 38

We report Spitzer observations of five newly identified bow shocks in the massive star-forming region RCW 38. Four are visible at IRAC wavelengths, the fifth is visible only at 24 microns. Chandra X-ray emission indicates that winds from the central O5.5 binary, IRS~2, have caused an outflow to the NE and SW of the central subcluster. The southern lobe of hot ionised gas is detected in X-rays; shocked gas and heated dust from the shock-front are detected with Spitzer at 4.5 and 24 microns. The northern outflow may have initiated the present generation of star formation, based on the filamentary distribution of the protostars in the central subcluster. Further, the bow-shock driving star, YSO 129, is photo-evaporating a pillar of gas and dust. No point sources are identified within this pillar at near- to mid-IR wavelengths. We also report on IRAC 3.6 & 5.8 micron observations of the cluster DBS2003-124, NE of RCW 38, where 33 candidate YSOs are identified. One star associated with the cluster drives a parsec-scale jet. Two candidate HH objects associated with the jet are visible at IRAC and MIPS wavelengths. The jet extends over a distance of ~3 pc. Assuming a velocity of 100 km/s for the jet material gives an age of about 30,000 years, indicating that the star (and cluster) are likely to be very young, with a similar or possibly younger age than RCW 38, and that star formation is ongoing in the extended RCW 38 region.Comment: 27 pages, 6 figures, accepted to Ap

Counterfactual reasoning and knowledge of possibilities

Williamson has argued against scepticism concerning our metaphysically modal knowledge, by arguing that standard patterns of suppositional reasoning to counterfactual conclusions provide reliable sources of correct ascriptions of possibility and necessity. The paper argues that, while Williamson’s claims relating to necessity may well be right, he has not provided adequate reasons for thinking that the familiar modes of counterfactual reasoning to which he points generalise to provide a decent route to ascriptions of possibility. The paper also explores another path to ascriptions of possibility that may be extracted from Williamson’s ideas, before briefly considering the general status of counterfactual reasoning in relation to our knowledge of possibilities

The Death Detectives

The death detectives is a series of blogs about death, photography and seeing the crime written in partnership with The Photographers' Gallery and Surviving Work

A millennium-length reconstruction of Bear River stream flow, Utah

The Bear River contributes more water to the eastern Great Basin than any other river system. It is also the most significant source of water for the burgeoning Wasatch Front metropolitan area in northern Utah. Despite its importance for water resources for the region’s agricultural, urban, and wildlife needs, our understanding of the variability of Bear River’s stream flow derives entirely from the short instrumental record (1943–2010). Here we present a 1200-year calibrated and verified tree-ring reconstruction of stream flow for the Bear River that explains 67% of the variance of the instrumental record over the period from 1943 to 2010. Furthermore, we developed this reconstruction from a species that is not typically used for dendroclimatology, Utah juniper (Juniperus osteosperma). We identify highly significant periodicity in our reconstruction at quasi-decadal (7–8 year), multi-decadal (30 year), and centennial (>50 years) scales. The latter half of the 20th century was found to be the 2nd wettest (∼40-year) period of the past 1200 years, while the first half of the 20th century marked the 4th driest period. The most severe period of reduced stream flow occurred during the Medieval Warm Period (ca. mid-1200s CE) and persisted for ∼70 years. Upper-level circulation anomalies suggest that atmospheric teleconnections originating in the western tropical Pacific are responsible for the delivery of precipitation to the Bear River watershed during the October–December (OND) season of the previous year. The Bear River flow was compared to recent reconstructions of the other tributaries to the Great Salt Lake (GSL) and the GSL level. Implications for water management could be drawn from the observation that the latter half of the 20th century was the 2nd wettest in 1200 years, and that management for future water supply should take into account the stream flow variability over the past millennium