Error and symmetry analysis of Misner's algorithm for spherical harmonic decomposition on a cubic grid

Computing spherical harmonic decompositions is a ubiquitous technique that arises in a wide variety of disciplines and a large number of scientific codes. Because spherical harmonics are defined by integrals over spheres, however, one must perform some sort of interpolation in order to compute them when data is stored on a cubic lattice. Misner (2004, Class. Quant. Grav., 21, S243) presented a novel algorithm for computing the spherical harmonic components of data represented on a cubic grid, which has been found in real applications to be both efficient and robust to the presence of mesh refinement boundaries. At the same time, however, practical applications of the algorithm require knowledge of how the truncation errors of the algorithm depend on the various parameters in the algorithm. Based on analytic arguments and experience using the algorithm in real numerical simulations, I explore these dependencies and provide a rule of thumb for choosing the parameters based on the truncation errors of the underlying data. I also demonstrate that symmetries in the spherical harmonics themselves allow for an even more efficient implementation of the algorithm than was suggested by Misner in his original paper.Comment: 10 pages, 3 tables, 1 figure. Version 2 has a broader introduction, and includes additional information on choosing parameter

Toward Making the Constraint Hypersurface an Attractor in Free Evolution

There is an abundance of empirical evidence in the numerical relativity literature that the form in which the Einstein evolution equations are written plays a significant role in the lifetime of numerical simulations. This paper attempts to present a consistent framework for modifying any system of evolution equations by adding terms that push the evolution toward the constraint hypersurface. The method is, in principle, applicable to any system of partial differential equations which can be divided into evolution equations and constraints, although it is only demonstrated here through an application to the Maxwell equations.Comment: 6 pages, 3 figures, 1 table. Uses REVTeX

Graphite formation in cast iron, phase 2

Several types of cast irons are directionally solidified aboard the KC-135 aircraft. Also, control samples are run on Earth for comparison. Some of these samples are unusable because of various mechanical problems; the analysis and the interpretation of results on the samples that are run successfully is discussed

Excising das All: Evolving Maxwell waves beyond scri

We study the numerical propagation of waves through future null infinity in a conformally compactified spacetime. We introduce an artificial cosmological constant, which allows us some control over the causal structure near null infinity. We exploit this freedom to ensure that all light cones are tilted outward in a region near null infinity, which allows us to impose excision-style boundary conditions in our finite difference code. In this preliminary study we consider electromagnetic waves propagating in a static, conformally compactified spacetime.Comment: 13 pages; incorporated material from gr-qc/051216

Waist Circumference as a Vital Sign

Conversion of research protocol into QI project at Norwalk Community Health Center. Goal is to implement waist circumference as a vital sign.https://scholarworks.uvm.edu/fmclerk/1782/thumbnail.jp

Breccia dikes from the Beaverhead Impact structure, southwest Montana

While shatter cones are generally accepted as indicators of meteorite impact, older petrologic features are not widely recognized in the geologic community. Breccia dikes are one such feature. They are found in many large impact structures occurring over an area at least as extensively as shatter cones. Breccia dikes will survive moderate degrees of metamorphism and tectonism, unlike many other microscopic features (shocked quartz grains, high-pressure polymorphs, etc.) and even large-scale features such as annular or bowl-shaped topographic features. Thus, they are important diagnostic criteria, especially for large, poorly preserved impact structures. The Beaverhead Impact structure is a recently discovered, deeply eroded impact structure in southwestern Montana. The remains of the structure are delineated by the occurrence of shatter cones, found in an area greater than 200 sq km, occurring within the Cabin thrust plate, part of the Cretaceous Sevier fold and thrust system. The distribution of shatter cones is further truncated by Tertiary normal faults. The present remains represent an allochthonous fragment of a larger structure

Making Justice Work for Women. Uganda Country Report.

The Uganda Country Report sits in a series of three reports of the findings of 'Making Transitional Justice Work for Women: Rights, Resilience and Responses to Violence Against Women in Democratic Republic of Congo, Northern Uganda and Kenya', funded by Australia's Department of Foreign Affairs and Trade (2013-2016). It outlines Ugandan women's thoughts about justice, the background and context to violence against women in Uganda, identifies women's justice needs and priorities and analyses justice responses in Uganda