Adaptive Mesh Refinement for Characteristic Grids

I consider techniques for Berger-Oliger adaptive mesh refinement (AMR) when numerically solving partial differential equations with wave-like solutions, using characteristic (double-null) grids. Such AMR algorithms are naturally recursive, and the best-known past Berger-Oliger characteristic AMR algorithm, that of Pretorius & Lehner (J. Comp. Phys. 198 (2004), 10), recurses on individual "diamond" characteristic grid cells. This leads to the use of fine-grained memory management, with individual grid cells kept in 2-dimensional linked lists at each refinement level. This complicates the implementation and adds overhead in both space and time. Here I describe a Berger-Oliger characteristic AMR algorithm which instead recurses on null \emph{slices}. This algorithm is very similar to the usual Cauchy Berger-Oliger algorithm, and uses relatively coarse-grained memory management, allowing entire null slices to be stored in contiguous arrays in memory. The algorithm is very efficient in both space and time. I describe discretizations yielding both 2nd and 4th order global accuracy. My code implementing the algorithm described here is included in the electronic supplementary materials accompanying this paper, and is freely available to other researchers under the terms of the GNU general public license.Comment: 37 pages, 15 figures (40 eps figure files, 8 of them color; all are viewable ok in black-and-white), 1 mpeg movie, uses Springer-Verlag svjour3 document class, includes C++ source code. Changes from v1: revised in response to referee comments: many references added, new figure added to better explain the algorithm, other small changes, C++ code updated to latest versio

Numerical relativity simulations in the era of the Einstein Telescope

Numerical-relativity (NR) simulations of compact binaries are expected to be an invaluable tool in gravitational-wave (GW) astronomy. The sensitivity of future detectors such as the Einstein Telescope (ET) will place much higher demands on NR simulations than first- and second-generation ground-based detectors. We discuss the issues facing compact-object simulations over the next decade, with an emphasis on estimating where the accuracy and parameter space coverage will be sufficient for ET and where significant work is needed. <br/

Pure word deafness associated with extrapontine myelinolysis*

Extrapontine myelinolysis and pure word deafness are very uncommon disorders. Here, we report a case of a 19-year-old woman who suffered from osmotic demyelination syndrome with coincidence of typical pure word deafness. As a consequence of rapid correction of hyponatremia, the patient demonstrated an initial onset of cortical deafness, and then progressed to generalized auditory agnosia, which eventually developed into confined verbal auditory agnosia (pure word deafness). Bilateral extrapontine myelinolysis was confirmed using brain magnetic resonance imaging. This case suggests that verbal and nonverbal stimuli may involve separate thalamocortical pathways

High level expression of a chimeric anti-ganglioside GD2 antibody: Genomic kappa sequences improve expression in COS and CHO cells

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