Simulating Turbulence Using the Astrophysical Discontinuous Galerkin Code TENET

In astrophysics, the two main methods traditionally in use for solving the Euler equations of ideal fluid dynamics are smoothed particle hydrodynamics and finite volume discretization on a stationary mesh. However, the goal to efficiently make use of future exascale machines with their ever higher degree of parallel concurrency motivates the search for more efficient and more accurate techniques for computing hydrodynamics. Discontinuous Galerkin (DG) methods represent a promising class of methods in this regard, as they can be straightforwardly extended to arbitrarily high order while requiring only small stencils. Especially for applications involving comparatively smooth problems, higher-order approaches promise significant gains in computational speed for reaching a desired target accuracy. Here, we introduce our new astrophysical DG code TENET designed for applications in cosmology, and discuss our first results for 3D simulations of subsonic turbulence. We show that our new DG implementation provides accurate results for subsonic turbulence, at considerably reduced computational cost compared with traditional finite volume methods. In particular, we find that DG needs about 1.8 times fewer degrees of freedom to achieve the same accuracy and at the same time is more than 1.5 times faster, confirming its substantial promise for astrophysical applications.Comment: 21 pages, 7 figures, to appear in Proceedings of the SPPEXA symposium, Lecture Notes in Computational Science and Engineering (LNCSE), Springe

Historical roots of Agile methods: where did “Agile thinking” come from?

The appearance of Agile methods has been the most noticeable change to software process thinking in the last fifteen years [16], but in fact many of the “Agile ideas” have been around since 70’s or even before. Many studies and reviews have been conducted about Agile methods which ascribe their emergence as a reaction against traditional methods. In this paper, we argue that although Agile methods are new as a whole, they have strong roots in the history of software engineering. In addition to the iterative and incremental approaches that have been in use since 1957 [21], people who criticised the traditional methods suggested alternative approaches which were actually Agile ideas such as the response to change, customer involvement, and working software over documentation. The authors of this paper believe that education about the history of Agile thinking will help to develop better understanding as well as promoting the use of Agile methods. We therefore present and discuss the reasons behind the development and introduction of Agile methods, as a reaction to traditional methods, as a result of people's experience, and in particular focusing on reusing ideas from histor

Ab initio methods for finite temperature two-dimensional Bose gases

The stochastic Gross-Pitaevskii equation and modified Popov theory are shown to provide an ab initio description of finite temperature, weakly-interacting two-dimensional Bose gas experiments. Using modified Popov theory, a systematic approach is developed in which the momentum cut-off inherent to classical field methods is removed as a free parameter. This is shown to yield excellent agreement with the recent experiment of Hung et al. [Nature, 470, 236 (2011)], verifying that the stochastic Gross-Pitaevskii equation captures the observed universality and scale-invariance.Comment: 5 pages, 4 figure

Hyperbolic monopoles, JNR data and spectral curves

A large class of explicit hyperbolic monopole solutions can be obtained from JNR instanton data, if the curvature of hyperbolic space is suitably tuned. Here we provide explicit formulae for both the monopole spectral curve and its rational map in terms of JNR data. Examples with platonic symmetry are presented, together with some one-parameter families with cyclic and dihedral symmetries. These families include hyperbolic analogues of geodesics that describe symmetric monopole scatterings in Euclidean space and we illustrate the results with energy density isosurfaces. There is a metric on the moduli space of hyperbolic monopoles, defined using the Abelian connection on the boundary of hyperbolic space, and we provide a simple integral formula for this metric on the space of JNR data

Phase coherence in quasicondensate experiments: an ab initio analysis via the stochastic Gross-Pitaevskii equation

We perform an ab initio analysis of the temperature dependence of the phase coherence length of finite temperature, quasi-one-dimensional Bose gases measured in the experiments of Richard et al. (Phys. Rev. Lett. 91, 010405 (2003)) and Hugbart et al. (Eur. Phys. J. D 35, 155-163 (2005)), finding very good agreement across the entire observed temperature range ($0.8<T/T_{\phi}<28$). Our analysis is based on the one-dimensional stochastic Gross-Pitaevskii equation, modified to self-consistently account for transverse, quasi-one-dimensional effects, thus making it a valid model in the regime $\mu ~ few \hbar \omega_\perp$. We also numerically implement an alternative identification of $T_{\phi}$, based on direct analysis of the distribution of phases in a stochastic treatment.Comment: Amended manuscript with improved agreement to experiment, following some additional clarifications by Mathilde Hugbart and Fabrice Gerbier and useful comments by the reviewer; accepted for publication in Physical Review

Gender, war and militarism: making and questioning the links

The gender dynamics of militarism have traditionally been seen as straightforward, given the cultural mythologies of warfare and the disciplining of ‘masculinity’ that occurs in the training and use of men's capacity for violence in the armed services. However, women's relation to both war and peace has been varied and complex. It is women who have often been most prominent in working for peace, although there are no necessary links between women and opposition to militarism. In addition, more women than ever are serving in many of today's armies, with feminists rather uncertain on how to relate to this phenomenon. In this article, I explore some of the complexities of applying gender analyses to militarism and peace work in sites of conflict today, looking most closely at the Israeli feminist group, New Profile, and their insistence upon the costs of the militarized nature of Israeli society. They expose the very permeable boundaries between the military and civil society, as violence seeps into the fears and practices of everyday life in Israel. I place their work in the context of broader feminist analysis offered by researchers such as Cynthia Enloe and Cynthia Cockburn, who have for decades been writing about the ‘masculinist’ postures and practices of warfare, as well as the situation of women caught up in them. Finally, I suggest that rethinking the gendered nature of warfare must also encompass the costs of war to men, whose fundamental vulnerability to psychological abuse and physical injury is often downplayed, whether in mainstream accounts of warfare or in more specific gender analysis. Feminists need to pay careful attention to masculinity and its fragmentations in addressing the topic of gender, war and militarism

Tutorial on Hybridizable Discontinous Galerkin (HDG) for second-order elliptic problems

The HDG is a new class of discontinuous Galerkin (DG) methods that shares favorable properties with classical mixed methods such as the well known Raviart-Thomas methods. In particular, HDG provides optimal convergence of both the primal and the dual variables of the mixed formulation. This property enables the construction of superconvergent solutions, contrary to other popular DG methods. In addition, its reduced computational cost, compared to other DG methods, has made HDG an attractive alternative for solving problems governed by partial differential equations. A tutorial on HDG for the numerical solution of second-order elliptic problems is presented. Particular emphasis is placed on providing all the necessary details for the implementation of HDG methods.Peer ReviewedPreprin

Quantitative study of quasi-one-dimensional Bose gas experiments via the stochastic Gross-Pitaevskii equation

The stochastic Gross-Pitaevskii equation is shown to be an excellent model for quasi-one-dimensional Bose gas experiments, accurately reproducing the in situ density profiles recently obtained in the experiments of Trebbia et al. [Phys. Rev. Lett. 97, 250403 (2006)] and van Amerongen et al. [Phys. Rev. Lett. 100, 090402 (2008)], and the density fluctuation data reported by Armijo et al. [Phys. Rev. Lett. 105, 230402 (2010)]. To facilitate such agreement, we propose and implement a quasi-one-dimensional stochastic equation for the low-energy, axial modes, while atoms in excited transverse modes are treated as independent ideal Bose gases.Comment: 10 pages, 5 figures; updated figures with experimental dat