Numerical stability of the AA evolution system compared to the ADM and BSSN systems

We explore the numerical stability properties of an evolution system suggested by Alekseenko and Arnold. We examine its behavior on a set of standardized testbeds, and we evolve a single black hole with different gauges. Based on a comparison with two other evolution systems with well-known properties, we discuss some of the strengths and limitations of such simple tests in predicting numerical stability in general.Comment: 16 pages, 12 figure

Computational science and re-discovery: open-source implementations of ellipsoidal harmonics for problems in potential theory

We present two open-source (BSD) implementations of ellipsoidal harmonic expansions for solving problems of potential theory using separation of variables. Ellipsoidal harmonics are used surprisingly infrequently, considering their substantial value for problems ranging in scale from molecules to the entire solar system. In this article, we suggest two possible reasons for the paucity relative to spherical harmonics. The first is essentially historical---ellipsoidal harmonics developed during the late 19th century and early 20th, when it was found that only the lowest-order harmonics are expressible in closed form. Each higher-order term requires the solution of an eigenvalue problem, and tedious manual computation seems to have discouraged applications and theoretical studies. The second explanation is practical: even with modern computers and accurate eigenvalue algorithms, expansions in ellipsoidal harmonics are significantly more challenging to compute than those in Cartesian or spherical coordinates. The present implementations reduce the "barrier to entry" by providing an easy and free way for the community to begin using ellipsoidal harmonics in actual research. We demonstrate our implementation using the specific and physiologically crucial problem of how charged proteins interact with their environment, and ask: what other analytical tools await re-discovery in an era of inexpensive computation?Comment: 25 pages, 3 figure

Making the Grade:Do International Branch Campuses and Their Home Campuses Differ in International Student Satisfaction With the Academic Experience?

This study investigates differences in academic satisfaction among undergraduate international students studying at international branch campuses (IBCs) and their home campuses, considering student stage of study, gender, and institution. It draws on data from 2,145 undergraduate international students enrolled at four home campuses and their six affiliated IBCs that responded to the 2018 International Student Barometer (ISB). Results indicate that international students studying at IBCs were significantly less satisfied with their academic experience-including constructs of academic and teaching quality, academic environment, and academic engagement-than international students studying at the associated home campuses. Results have important implications for how institutions carry out internationalization amid uncertain times; in particular, ensuring that the unique experiences of students are understood and considered in the planning and provision of transnational education

Adaptive mesh refinement approach to construction of initial data for black hole collisions

The initial data for black hole collisions is constructed using a conformal-imaging approach and a new adaptive mesh refinement technique, a fully threaded tree (FTT). We developed a second-order accurate approach to the solution of the constraint equations on a non-uniformly refined high resolution Cartesian mesh including second-order accurate treatment of boundary conditions at the black hole throats. Results of test computations show convergence of the solution as the numerical resolution is increased. FTT-based mesh refinement reduces the required memory and computer time by several orders of magnitude compared to a uniform grid. This opens up the possibility of using Cartesian meshes for very high resolution simulations of black hole collisions.Comment: 13 pages, 11 figure

5-Approximation for ?-Treewidth Essentially as Fast as ?-Deletion Parameterized by Solution Size

The notion of ?-treewidth, where ? is a hereditary graph class, was recently introduced as a generalization of the treewidth of an undirected graph. Roughly speaking, a graph of ?-treewidth at most k can be decomposed into (arbitrarily large) ?-subgraphs which interact only through vertex sets of size ?(k) which can be organized in a tree-like fashion. ?-treewidth can be used as a hybrid parameterization to develop fixed-parameter tractable algorithms for ?-deletion problems, which ask to find a minimum vertex set whose removal from a given graph G turns it into a member of ?. The bottleneck in the current parameterized algorithms lies in the computation of suitable tree ?-decompositions. We present FPT-approximation algorithms to compute tree ?-decompositions for hereditary and union-closed graph classes ?. Given a graph of ?-treewidth k, we can compute a 5-approximate tree ?-decomposition in time f(?(k)) ? n^?(1) whenever ?-deletion parameterized by solution size can be solved in time f(k) ? n^?(1) for some function f(k) ? 2^k. The current-best algorithms either achieve an approximation factor of k^?(1) or construct optimal decompositions while suffering from non-uniformity with unknown parameter dependence. Using these decompositions, we obtain algorithms solving Odd Cycle Transversal in time 2^?(k) ? n^?(1) parameterized by bipartite-treewidth and Vertex Planarization in time 2^?(k log k) ? n^?(1) parameterized by planar-treewidth, showing that these can be as fast as the solution-size parameterizations and giving the first ETH-tight algorithms for parameterizations by hybrid width measures

Simultaneous Spectrophotometric Calibration of Wavelength and Absorbance in an Interlaboratory Survey Using Holmium Oxide (HO2O3) in Perchloric Acid as Reference, Compared with p-Nitrophenol and Cobaltous Sulphate Solutions (1978-1984)

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