A Polynomial Spectral Calculus for Analysis of DG Spectral Element Methods

We introduce a polynomial spectral calculus that follows from the summation by parts property of the Legendre-Gauss-Lobatto quadrature. We use the calculus to simplify the analysis of two multidimensional discontinuous Galerkin spectral element approximations

Entropy Stable Finite Volume Approximations for Ideal Magnetohydrodynamics

This article serves as a summary outlining the mathematical entropy analysis of the ideal magnetohydrodynamic (MHD) equations. We select the ideal MHD equations as they are particularly useful for mathematically modeling a wide variety of magnetized fluids. In order to be self-contained we first motivate the physical properties of a magnetic fluid and how it should behave under the laws of thermodynamics. Next, we introduce a mathematical model built from hyperbolic partial differential equations (PDEs) that translate physical laws into mathematical equations. After an overview of the continuous analysis, we thoroughly describe the derivation of a numerical approximation of the ideal MHD system that remains consistent to the continuous thermodynamic principles. The derivation of the method and the theorems contained within serve as the bulk of the review article. We demonstrate that the derived numerical approximation retains the correct entropic properties of the continuous model and show its applicability to a variety of standard numerical test cases for MHD schemes. We close with our conclusions and a brief discussion on future work in the area of entropy consistent numerical methods and the modeling of plasmas

Prompt K_short production in pp collisions at sqrt(s)=0.9 TeV

The production of K_short mesons in pp collisions at a centre-of-mass energy of 0.9 TeV is studied with the LHCb detector at the Large Hadron Collider. The luminosity of the analysed sample is determined using a novel technique, involving measurements of the beam currents, sizes and positions, and is found to be 6.8 +/- 1.0 microbarn^-1. The differential prompt K_short production cross-section is measured as a function of the K_short transverse momentum and rapidity in the region 0 < pT < 1.6 GeV/c and 2.5 < y < 4.0. The data are found to be in reasonable agreement with previous measurements and generator expectations.Comment: 6+18 pages, 6 figures, updated author lis

Polymorphic nodal elements and their application in discontinuous Galerkin methods

In this work, we discuss two different but related aspects of the development of efficient discontinuous Galerkin methods on hybrid element grids for the computational modeling of gas dynamics in complex geometries or with adapted grids. In the first part, a recursive construction of different nodal sets for hp finite elements is presented. They share the property that the nodes along the sides of the two-dimensional elements and along the edges of the three-dimensional elements are the Legendre–Gauss–Lobatto points. The different nodal elements are evaluated by computing the Lebesgue constants of the corresponding Vandermonde matrix. In the second part, these nodal elements are applied within the modal discontinuous Galerkin framework. We still use a modal based formulation, but introduce a nodal based integration technique to reduce computational cost in the spirit of pseudospectral methods. We illustrate the performance of the scheme on several large scale applications and discuss its use in a recently developed space-time expansion discontinuous Galerkin scheme

How hard is it to find extreme Nash equilibria in network congestion games?

We study the complexity of finding extreme pure Nash equilibria in symmetric (unweighted) network congestion games. In our context best and worst equilibria are those with minimum respectively maximum makespan. On series-parallel graphs a worst Nash equilibrium can be found by a Greedy approach while finding a best equilibrium is NP-hard. For a fixed number of users we give a pseudo-polynomial algorithm to find the best equilibrium in series-parallel networks. For general network topologies also finding a worst equilibrium is NP-hard

Measurement of sigma (pp -> bbX) at √s=7 TeV in the forward region

Decays of b hadrons into final states containing a D-0 meson and a muon are used to measure the bb; production cross-section in proton-proton collisions at a centre-of-mass energy of 7 TeV at the LHC. In the pseudorapidity interval 2 < eta < 6 and integrated over all transverse momenta we find that the average cross-section to produce b-flavoured or b-flavoured hadrons is (75.3 +/- 5.4 +/- 13.0) mu b

Time integration in the discontinuous galerkin code MIGALE -unsteady problems

This chapter presents recent developments of a high-order Discontinuous Galerkin (DG) method to deal with unsteady simulation of turbulent flows by using high-order implicit time integration schemes. The approaches considered during the IDIHOM project were the Implicit Large Eddy Simulation (ILES), where no explicit subgrid-scale (SGS) model is included and the DG discretization itself acts like a SGS model, and two hybrid approaches between Reynolds-averaged Navier- Stokes (RANS) and Large Eddy Simulation (LES) models, namely the Spalart-Allmaras Detached Eddy Simulation (SA-DES) and the eXtra- Large Eddy Simulation (X-LES). Accurate time integration is based on high-order linearly implicit Rosenbrock-type Runge-Kutta schemes, implemented in the DG code MIGALE up to sixth-order accuracy. Several high-order DG results of both incompressible and compressible 3D turbulent test cases proposed within the IDIHOM project demonstrate the capability of the method

Energetic particle instabilities in fusion plasmas

Remarkable progress has been made in diagnosing energetic particle instabilities on present-day machines and in establishing a theoretical framework for describing them. This overview describes the much improved diagnostics of Alfvén instabilities and modelling tools developed world-wide, and discusses progress in interpreting the observed phenomena. A multi-machine comparison is presented giving information on the performance of both diagnostics and modelling tools for different plasma conditions outlining expectations for ITER based on our present knowledge