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

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

Spherical Harmonic Decomposition of Gravitational Waves Across Mesh Refinement Boundaries

We evolve a linearized (Teukolsky) solution of the Einstein equations with a non-linear Einstein solver. Using this testbed, we are able to show that such gravitational waves, defined by the Weyl scalars in the Newman-Penrose formalism, propagate faithfully across mesh refinement boundaries, and use, for the first time to our knowledge, a novel algorithm due to Misner to compute spherical harmonic components of our waveforms. We show that the algorithm performs extremely well, even when the extraction sphere intersects refinement boundaries

Evolving a puncture black hole with fixed mesh refinement

We present an algorithm for treating mesh refinement interfaces in numerical relativity. We detail the behavior of the solution near such interfaces located in the strong field regions of dynamical black hole spacetimes, with particular attention to the convergence properties of the simulations. In our applications of this technique to the evolution of puncture initial data with vanishing shift, we demonstrate that it is possible to simultaneously maintain second order convergence near the puncture and extend the outer boundary beyond 100M, thereby approaching the asymptotically flat region in which boundary condition problems are less difficult and wave extraction is meaningful.Comment: 18 pages, 12 figures. Minor changes, final PRD versio

Moving black holes via singularity excision

We present a singularity excision algorithm appropriate for numerical simulations of black holes moving throughout the computational domain. The method is an extension of the excision procedure previously used to obtain stable simulations of single, non-moving black holes. The excision procedure also shares elements used in recent work to study the dynamics of a scalarfield in the background of a single, boosted black hole. The robustness of our excision method is tested with single black-hole evolutions using a coordinate system in which the coordinate location of the black hole, and thus the excision boundary, moves throughout the computational domain.Comment: 9 pages and 11 figure

Growth and mass wasting of volcanic centers in the northern South Sandwich arc, South Atlantic, revealed by new multibeam mapping

New multibeam (swath) bathymetric sonar data acquired using an EM120 system on the RRS James Clark Ross, supplemented by sub-bottom profiling, reveals the underwater morphology of a not, vert, similar 12,000 km2 area in the northern part of the mainly submarine South Sandwich volcanic arc. The new data extend between 55° 45′S and 57° 20′S and include Protector Shoal and the areas around Zavodovski, Visokoi and the Candlemas islands groups. Each of these areas is a discrete volcanic center. The entirely submarine Protector Shoal area, close to the northern limit of the arc, forms a 55 km long east–west-trending seamount chain that is at least partly of silicic composition. The seamounts are comparable to small subaerial stratovolcanoes in size, with volumes up to 83 km3, indicating that they are the product of multiple eruptions over extended periods. Zavodovski, Visokoi and the Candlemas island group are the summits of three 3–3.5 km high volcanic edifices. The bathymetric data show evidence for relationships between constructional volcanic features, including migrating volcanic centers, structurally controlled constructional ridges, satellite lava flows and domes, and mass wasting of the edifices. Mass wasting takes place mainly by strong erosion at sea level, and dispersal of this material along chutes, probably as turbidity currents and other mass flows that deposit in extensive sediment wave fields. Large scale mass wasting structures include movement of unconsolidated debris in slides, slumps and debris avalanches. Volcanism is migrating westward relative to the underlying plate and major volcanoes are asymmetrical, being steep with abundant recent volcanism on their western flanks, and gently sloping with extinct, eroded volcanic sequences to their east. This is consistent with the calculated rate of subduction erosion of the fore-arc

The bashful and the boastful : prestigious leaders and social change in Mesolithic Societies

The creation and maintenance of influential leaders and authorities is one of the key themes of archaeological and historical enquiry. However the social dynamics of authorities and leaders in the Mesolithic remains a largely unexplored area of study. The role and influence of authorities can be remarkably different in different situations yet they exist in all societies and in almost all social contexts from playgrounds to parliaments. Here we explore the literature on the dynamics of authority creation, maintenance and contestation in egalitarian societies, and discuss the implications for our interpretation and understanding of the formation of authorities and leaders and changing social relationships within the Mesolithic

Fortune Favours the Bold: An Agent-Based Model Reveals Adaptive Advantages of Overconfidence in War

Overconfidence has long been considered a cause of war. Like other decision-making biases, overconfidence seems detrimental because it increases the frequency and costs of fighting. However, evolutionary biologists have proposed that overconfidence may also confer adaptive advantages: increasing ambition, resolve, persistence, bluffing opponents, and winning net payoffs from risky opportunities despite occasional failures. We report the results of an agent-based model of inter-state conflict, which allows us to evaluate the performance of different strategies in competition with each other. Counter-intuitively, we find that overconfident states predominate in the population at the expense of unbiased or underconfident states. Overconfident states win because: (1) they are more likely to accumulate resources from frequent attempts at conquest; (2) they are more likely to gang up on weak states, forcing victims to split their defences; and (3) when the decision threshold for attacking requires an overwhelming asymmetry of power, unbiased and underconfident states shirk many conflicts they are actually likely to win. These “adaptive advantages” of overconfidence may, via selection effects, learning, or evolved psychology, have spread and become entrenched among modern states, organizations and decision-makers. This would help to explain the frequent association of overconfidence and war, even if it no longer brings benefits today