Strichartz estimates for the Schr\"odinger equation on polygonal domains

We prove Strichartz estimates with a loss of derivatives for the Schr\"odinger equation on polygonal domains with either Dirichlet or Neumann homogeneous boundary conditions. Using a standard doubling procedure, estimates the on polygon follow from those on Euclidean surfaces with conical singularities. We develop a Littlewood-Paley squarefunction estimate with respect to the spectrum of the Laplacian on these spaces. This allows us to reduce matters to proving estimates at each frequency scale. The problem can be localized in space provided the time intervals are sufficiently small. Strichartz estimates then follow from a result of the second author regarding the Schr\"odinger equation on the Euclidean cone.Comment: 12 page

A Comparison of DEM-based methods for fluvial terrace mapping and sediment volume calculation: Application to the Sheepscot River Watershed, Maine

Thesis advisor: Noah P. SnyderThesis advisor: Gail KinekeFluvial terraces form in both erosional and depositional landscapes and are important recorders of land-use, climate, and tectonic history. Terrace morphology consists of a flat surface bounded by valley walls and a steep-sloping scarp adjacent to the river channel. Combining these defining characteristics with high-resolution digital elevation models (DEMs) derived from airborne light detection and ranging (lidar) surveys, several methods have been developed to identify and map terraces. This research introduces a newly developed objective terrace mapping method and compares it with three existing DEM-based techniques to determine which is most applicable over entire watersheds. This work also tests multiple methods that use lidar DEMs to quantify the thickness and volume of fill terrace deposits identified upstream of dam sites. The preliminary application is to the Sheepscot River watershed, Maine, where strath and fill terraces are present and record Pleistocene deglaciation, Holocene eustatic forcing, and Anthropocene land-use change. Terraces were mapped at four former dam sites along the river using four separate methodologies and compared to manually delineated area. The methods tested were: (1) edge detection using MATLAB, (2) feature classification algorithms developed by Wood (1996), (3) spatial relationships between interpreted terraces and surrounding natural topography (Walter et al., 2007), and (4) the TerEx terrace mapping toolbox developed by Stout and Belmont (2013). Thickness and volume estimates of fill sediment were calculated at two of the study sites using three DEM-based models and compared to in situ data collected from soil pits, cut bank exposures, and ground penetrating radar surveys. The results from these comparisons served as the basis for selecting methods to map terraces throughout the watershed and quantify fill sediment upstream of current and historic dam sites. Along the main stem and West Branch of the Sheepscot River, terraces were identified along the longitudinal profile of the river using an algorithm developed by Finnegan and Balco (2013), which computes the elevation frequency distribution at regularly spaced cross-sections normal to the channel, and then mapped using the feature classification (Wood, 1996) method. For terraces upstream of current or historic dam sites, thickness and volume estimates were calculated using the two best performing datum surfaces. If all analyzed terraces are composed of impounded sediment, these DEM-based results suggest that terraces along the main stem and West Branch of the Sheepscot River potentially contain up to 1.5 x 106 m3 of fill. These findings suggest powerful new ways to quickly analyze landscape history over large regions using high-resolution, LiDAR DEMs while relying less heavily on the need for detailed and costly field data collection.Thesis (MS) — Boston College, 2014.Submitted to: Boston College. Graduate School of Arts and Sciences.Discipline: Geology and Geophysics

Exploring 2+2\boldsymbol{2+2} Answers to 3+1\boldsymbol{3+1} Questions

We explore potential uses of physics formulated in Kleinian (i.e., $2+2$) signature spacetimes as a tool for understanding properties of physics in Lorentzian (i.e., $3+1$) signature. Much as Euclidean (i.e., $4+0$) signature quantities can be used to formally construct the ground state wavefunction of a Lorentzian signature quantum field theory, a similar analytic continuation to Kleinian signature constructs a state of low particle flux in the direction of analytic continuation. There is also a natural supersymmetry algebra available in $2+2$ signature, which serves to constrain the structure of correlation functions. Spontaneous breaking of Lorentz symmetry can produce various $\mathcal{N} = 1/2$ supersymmetry algebras that in $3 + 1$ signature correspond to non-supersymmetric systems. We speculate on the possible role of these structures in addressing the cosmological constant problem.Comment: 22 pages, 1 figur

Tantalum Surgical Clip Presenting As an Intraorbital Foreign Body

This is a Photo Essay and does not have an abstract. Please download the PDF or view the article in HTML

The only known egg of the Night Parrot? A molecular and morphometric assessment of an alleged egg from the Tanami Desert

The Night Parrot Pezoporus occidentalis is a much sought-after, recently ‘rediscovered’, endangered nocturnal parrot, endemic to arid Central Australia. Very little is known of its ecology, and its eggs have never been formally described. The literature on the eggs of the Night Parrot is collated here, and the provenance of an alleged Night Parrot egg found in the Tanami Desert, Northern Territory, in 1983 was assessed using DNA analysis and physical characteristics. Anecdotal reports from the late 19th–early 20th Century indicate that the Night Parrot lays a clutch of two to six roundish, white eggs. We suggest that its eggs are probably similar to and slightly larger than those of its congener, the Ground Parrot P. wallicus. The alleged Night Parrot egg was definitively identified by mitochondrial DNA analysis to be from the Brown Quail Synoicus ypsilophorus. This represents the first evidence of breeding by this species in the Tanami Desert, and lays to rest a long-standing misconception regarding the parrot

Observation of a Free-Shercliff-Layer Instability in Cylindrical Geometry

We report on observations of a free-Shercliff-layer instability in a Taylor-Couette experiment using a liquid metal over a wide range of Reynolds numbers, $Re\sim 10^3-10^6$. The free Shercliff layer is formed by imposing a sufficiently strong axial magnetic field across a pair of differentially rotating axial endcap rings. This layer is destabilized by a hydrodynamic Kelvin-Helmholtz-type instability, characterized by velocity fluctuations in the $r-\theta$ plane. The instability appears with an Elsasser number above unity, and saturates with an azimuthal mode number $m$ which increases with the Elsasser number. Measurements of the structure agree well with 2D global linear mode analyses and 3D global nonlinear simulations. These observations have implications for a range of rotating MHD systems in which similar shear layers may be produced.Comment: 5 pages, 4 figure