The incorporation of matter into characteristic numerical relativity

A code that implements Einstein equations in the characteristic formulation in 3D has been developed and thoroughly tested for the vacuum case. Here, we describe how to incorporate matter, in the form of a perfect fluid, into the code. The extended code has been written and validated in a number of cases. It is stable and capable of contributing towards an understanding of a number of problems in black hole astrophysics.Comment: 15 pages + 4 (eps) figure

A Large Nonmetastatic Anaplastic Thyroid Cancer with Complete Thyroidal Confinement

Anaplastic thyroid cancer (ATC) is rare but extremely aggressive, which accounts for about 2% of all thyroid cancers yet nearly 50% of thyroid-cancer-associated deaths in the United States. The median survival time from diagnosis is 5 months, with a 1-year survival rate of only 20%. We report here a case of ATC in a 56-year-old man who survived a large ATC. Preoperative fine-needle aspiration biopsy study to a large right thyroid mass suggested ATC. Total thyroidectomy with radical lateral neck and central neck dissection removed a well-circumscribed 9.5 cm tumor without extrathyroidal extension or lymphovascular invasion. All 73 lymph nodes removed were negative for metastasis. The tumor consisted of highly pleomorphic, undifferentiated cells with large zones of necrosis and loss of thyroid transcription factor-1 and thyroglobulin expression. A focal well-differentiated component and PAX8 expression confirmed its thyroid follicular cell origin. Nine months after postsurgical adjuvant concurrent radiation therapy and chemotherapy, the patient remained well without clinical, biochemical, and radiographical evidence for cancer recurrence. This is an unusual case of ATC in that it is one of the largest ATC tumors reported to display mild pathologic behavior and relatively long-term patient survival

Theoretical Evaluation of Anisotropic Reflectance Correction Approaches for Addressing Multi-Scale Topographic Effects on the Radiation-Transfer Cascade in Mountain Environments

Research involving anisotropic-reflectance correction (ARC) of multispectral imagery to account for topographic effects has been ongoing for approximately 40 years. A large body of research has focused on evaluating empirical ARC methods, resulting in inconsistent results. Consequently, our research objective was to evaluate commonly used ARC methods using first-order radiation-transfer modeling to simulate ASTER multispectral imagery over Nanga Parbat, Himalaya. Specifically, we accounted for orbital dynamics, atmospheric absorption and scattering, direct- and diffuse-skylight irradiance, land cover structure, and surface biophysical variations to evaluate their effectiveness in reducing multi-scale topographic effects. Our results clearly reveal that the empirical methods we evaluated could not reasonably account for multi-scale topographic effects at Nanga Parbat. The magnitude of reflectance and the correlation structure of biophysical properties were not preserved in the topographically-corrected multispectral imagery. The CCOR and SCS+C methods were able to remove topographic effects, given the Lambertian assumption, although atmospheric correction was required, and we did not account for other primary and secondary topographic effects that are thought to significantly influence spectral variation in imagery acquired over mountains. Evaluation of structural-similarity index images revealed spatially variable results that are wavelength dependent. Collectively, our simulation and evaluation procedures strongly suggest that empirical ARC methods have significant limitations for addressing anisotropic reflectance caused by multi-scale topographic effects. Results indicate that atmospheric correction is essential, and most methods failed to adequately produce the appropriate magnitude and spatial variation of surface reflectance in corrected imagery. Results were also wavelength dependent, as topographic effects influence radiation-transfer components differently in different regions of the electromagnetic spectrum. Our results explain inconsistencies described in the literature, and indicate that numerical modeling efforts are required to better account for multi-scale topographic effects in various radiation-transfer components.Open access journalThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

A value proposition for early physical therapist management of neck pain: a retrospective cohort analysis

BACKGROUND: Neck pain is one of the most common reasons for entry into the healthcare system. Recent increases in healthcare utilization and medical costs have not correlated with improvements in health. Therefore there is a need to identify management strategies for neck pain that are effective for the patient, cost efficient for the payer and provided at the optimal time during an episode of neck pain. METHODS: One thousand five hundred thirty-one patients who underwent physical therapist management with a primary complaint of non-specific neck pain from January 1, 2008 to December 31, 2012 were identified from the Rehabilitation Outcomes Management System (ROMS) database at Intermountain Healthcare. Patients reporting duration of symptoms less than 4 weeks were designated as undergoing "early" management and patients with duration of symptoms greater than 4 weeks were designated as receiving "delayed" management. These groups were compared using binary logistic regression to examine odds of achieving Minimal Clinically Important Difference (MCID) on the Neck Disability Index (NDI) and Numerical Pain Rating Scale (NPRS). Separate generalized linear modeling examined the effect of timing of physical therapist management on the metrics of value and efficiency. RESULTS: Patients who received early physical therapist management had increased odds of achieving MCID on the NDI (aOR = 2.01, 95 % CI 1.57, 2.56) and MCID on the NPRS (aOR = 1.82, 95 % CI 1.42, 2.38), when compared to patients receiving delayed management. Patients who received early management demonstrated the greatest value in decreasing disability with a 2.27 percentage point change in NDI score per 100 dollars, best value in decreasing pain with a 0.38 point change on the NPRS per 100 dollars. Finally, patients receiving early management were managed more efficiently with a 3.44 percentage point change in NDI score per visit and 0.57 point change in NPRS score per visit. CONCLUSIONS: These findings suggest that healthcare systems that provide pathways for patients to receive early physical therapist management of neck pain may realize improved patient outcomes, greater value and higher efficiency in decreasing disability and pain compared to delayed management. Further research is needed to confirm this assertion

Cauchy boundaries in linearized gravitational theory

We investigate the numerical stability of Cauchy evolution of linearized gravitational theory in a 3-dimensional bounded domain. Criteria of robust stability are proposed, developed into a testbed and used to study various evolution-boundary algorithms. We construct a standard explicit finite difference code which solves the unconstrained linearized Einstein equations in the 3+1 formulation and measure its stability properties under Dirichlet, Neumann and Sommerfeld boundary conditions. We demonstrate the robust stability of a specific evolution-boundary algorithm under random constraint violating initial data and random boundary data.Comment: 23 pages including 3 figures and 2 tables, revte

GlacierNet2: A Hybrid Multi-Model Learning Architecture for Alpine Glacier Mapping

In recent decades, climate change has significantly affected glacier dynamics, resulting in mass loss and an increased risk of glacier-related hazards including supraglacial and proglacial lake development, as well as catastrophic outburst flooding. Rapidly changing conditions dictate the need for continuous and detailed observations and analysis of climate-glacier dynamics. Thematic and quantitative information regarding glacier geometry is fundamental for understanding climate forcing and the sensitivity of glaciers to climate change, however, accurately mapping debris-cover glaciers (DCGs) is notoriously difficult based upon the use of spectral information and conventional machine-learning techniques. The objective of this research is to improve upon an earlier proposed deep-learning-based approach, GlacierNet, which was developed to exploit a convolutional neural-network segmentation model to accurately outline regional DCG ablation zones. Specifically, we developed an enhanced GlacierNet2 architecture thatincorporates multiple models, automatic post-processing, and basin-level hydrological flow techniques to improve the mapping of DCGs such that it includes both the ablation and accumulation zones. Experimental evaluations demonstrate that GlacierNet2 improves the estimation of the ablation zone and allows a high level of intersection over union (IOU: 0.8839) score. The proposed architecture provides complete glacier (both accumulation and ablation zone) outlines at regional scales, with an overall IOU score of 0.8619. This is a crucial first step in automating complete glacier mapping that can be used for accurate glacier modeling or mass-balance analysis

Exact Solutions for the Intrinsic Geometry of Black Hole Coalescence

We describe the null geometry of a multiple black hole event horizon in terms of a conformal rescaling of a flat space null hypersurface. For the prolate spheroidal case, we show that the method reproduces the pair-of-pants shaped horizon found in the numerical simulation of the head-on-collision of black holes. For the oblate case, it reproduces the initially toroidal event horizon found in the numerical simulation of collapse of a rotating cluster. The analytic nature of the approach makes further conclusions possible, such as a bearing on the hoop conjecture. From a time reversed point of view, the approach yields a description of the past event horizon of a fissioning white hole, which can be used as null data for the characteristic evolution of the exterior space-time.Comment: 21 pages, 6 figures, revtex, to appear in Phys. Rev.

Grazing Collisions of Black Holes via the Excision of Singularities

We present the first simulations of non-headon (grazing) collisions of binary black holes in which the black hole singularities have been excised from the computational domain. Initially two equal mass black holes $m$ are separated a distance $\approx10m$ and with impact parameter $\approx2m$. Initial data are based on superposed, boosted (velocity $\approx0.5c$) solutions of single black holes in Kerr-Schild coordinates. Both rotating and non-rotating black holes are considered. The excised regions containing the singularities are specified by following the dynamics of apparent horizons. Evolutions of up to $t \approx 35m$ are obtained in which two initially separate apparent horizons are present for $t\approx3.8m$. At that time a single enveloping apparent horizon forms, indicating that the holes have merged. Apparent horizon area estimates suggest gravitational radiation of about 2.6% of the total mass. The evolutions end after a moderate amount of time because of instabilities.Comment: 2 References corrected, reference to figure update

Mode coupling in the nonlinear response of black holes

We study the properties of the outgoing gravitational wave produced when a non-spinning black hole is excited by an ingoing gravitational wave. Simulations using a numerical code for solving Einstein's equations allow the study to be extended from the linearized approximation, where the system is treated as a perturbed Schwarzschild black hole, to the fully nonlinear regime. Several nonlinear features are found which bear importance to the data analysis of gravitational waves. When compared to the results obtained in the linearized approximation, we observe large phase shifts, a stronger than linear generation of gravitational wave output and considerable generation of radiation in polarization states which are not found in the linearized approximation. In terms of a spherical harmonic decomposition, the nonlinear properties of the harmonic amplitudes have simple scaling properties which offer an economical way to catalog the details of the waves produced in such black hole processes.Comment: 17 pages, 20 figures, abstract and introduction re-writte

The Asymmetric Merger of Black Holes

We study event horizons of non-axisymmetric black holes and show how features found in axisymmetric studies of colliding black holes and of toroidal black holes are non-generic and how new features emerge. Most of the details of black hole formation and black hole merger are known only in the axisymmetric case, in which numerical evolution has successfully produced dynamical space-times. The work that is presented here uses a new approach to construct the geometry of the event horizon, not by locating it in a given spacetime, but by direct construction. In the axisymmetric case, our method produces the familiar pair-of-pants structure found in previous numerical simulations of black hole mergers, as well as event horizons that go through a toroidal epoch as discovered in the collapse of rotating matter. The main purpose of this paper is to show how new - substantially different - features emerge in the non-axisymmetric case. In particular, we show how black holes generically go through a toroidal phase before they become spherical, and how this fits together with the merger of black holes.Comment: 28 pages, 10 figures, uses REVTEX. Improved quality figures and additional color images are provided at http://www.phyast.pitt.edu/~shusa/EH