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

Invalid Votes, Deliberate Abstentions, and the Brazilian Crisis of Representation

August 31, 2016 registered the historical impeachment of Brazilian president, Dilma Rousseff, indicted for contravening the budget law and misstating the public deficit that propelled the country into deep economic recession. Many disagreements on this matter have permeated the country’s conflict atmosphere, supported by arguments that the collective will of more than 54 million voters was disrespected. Based on 3,010 interviews conducted in 204 Brazilian cities, we construct a pairwise comparison to present arguments that Rousseff had no legitimate representation in the 2014 national elections. We demonstrate how the suboptimal support of invalid votes and deliberate abstentions might have misrepresented the results of Brazilian presidential election by choosing a pseudo-Condorcet loser candidate. The results in the Brazilian case study presented here point to the weakness in the social process of aggregating preferences by relative or absolute majority, and sets out recommendations