An algebraic multigrid method for Q2−Q1Q_2-Q_1 mixed discretizations of the Navier-Stokes equations

Algebraic multigrid (AMG) preconditioners are considered for discretized systems of partial differential equations (PDEs) where unknowns associated with different physical quantities are not necessarily co-located at mesh points. Specifically, we investigate a $Q_2-Q_1$ mixed finite element discretization of the incompressible Navier-Stokes equations where the number of velocity nodes is much greater than the number of pressure nodes. Consequently, some velocity degrees-of-freedom (dofs) are defined at spatial locations where there are no corresponding pressure dofs. Thus, AMG approaches leveraging this co-located structure are not applicable. This paper instead proposes an automatic AMG coarsening that mimics certain pressure/velocity dof relationships of the $Q_2-Q_1$ discretization. The main idea is to first automatically define coarse pressures in a somewhat standard AMG fashion and then to carefully (but automatically) choose coarse velocity unknowns so that the spatial location relationship between pressure and velocity dofs resembles that on the finest grid. To define coefficients within the inter-grid transfers, an energy minimization AMG (EMIN-AMG) is utilized. EMIN-AMG is not tied to specific coarsening schemes and grid transfer sparsity patterns, and so it is applicable to the proposed coarsening. Numerical results highlighting solver performance are given on Stokes and incompressible Navier-Stokes problems.Comment: Submitted to a journa

Low energy spin fluctuations in the heavy fermion compound Ce0.925_{0.925}La0.075_{0.075}Ru2_{2}Si2_{2}

We report inelastic neutron scattering measurements performed on a single crystal of the heavy fermion compound Ce$_{0.925}$La$_{0.075}$Ru$_{2}$Si$_{2}$, which is at the borderline between an antiferromagnetically ordered and a paramagnetic ground state. Intensity maps as a function of wavevector and energy ($0.1<E<1.2$ meV) were obtained at temperatures $T=0.1$ and 2 K, using the time-of-flight spectrometer IRIS. An unexpected saturation of the relaxation rate and static susceptibility of the spin fluctuations is found at low temperatures.Comment: 2 pages, 2 figures, SCES'04 Proceeding

Amending the Wagner Act: The Problem From the Manufacturer’s Viewpoint

Till följd av den globala finanskrisen år 2008 ställdes det europeiska samarbetet på prov. I och med detta presenterade EU ett förslag till ett direktiv angående en finansiell transaktionsskatt för samtliga länder inom EU. Elva av EU:s 28 medlemsländer har valt att ställa sig bakom förslaget om en finansiell transaktionsskatt, vilket innebär att dessa länder avser införa en finansiell transaktionsskatt. Tidigare empiriska erfarenheter har dock visat att en finansiell transaktionsskatt är mindre effektiv än vad förespråkarna gör gällande, varken påverkan på skatteintäkter eller marknadens volatilitet har i dessa fall levt upp till de önskvärda effekterna. Denna uppsats syfte är att analysera vad som ligger till grund för ländernas ställningstagande och uppsatsens hypotes ger vid handen att det föreligger ett positivt samband mellan finanskrisens påverkan på respektive EU land, inhemsk opinion och ett positivt ställningstagande till en finansiell transaktionsskatt inom EU. För att testa hypotesen används en induktiv metod vilken är uppbyggd på vetenskapliga artiklar och ekonomisk litteratur. Vidare genomförs flera regressionsanalyser i syfte att påvisa de positiva samband som hypotesen antar föreligger. I de uppvisade resultaten framgår att det går att stödja uppsatsens hypotes. Uppsatsen kommer därför fram till att det föreligger ett positivt samband mellan finanskrisens påverkan på respektive EU-land, inhemsk opinion och ett positivt ställningstagande till en finansiell transaktionsskatt.In the aftermath of the 2008 financial crisis the European Union was put to the test. As a result, the EU submitted a proposal for a directive regarding a financial transactions tax levied throughout every nation in the European Union. Eleven of the 28 EU member states decided to support the proposal for a financial transactions tax. The eleven member states adopted the stance to support the proposal in spite of the historical empirical evidence indicating a financial transactions tax to not be as effective as the advocators claim. This paper aims to analyse the basis of the EU member states adopted stance towards a financial transactions tax. The thesis statement suggest that there is a positive correlation between the impact of the financial crisis on each respective EU country, domestic public opinion and a positive stance towards a financial transactions tax in the EU. To test the thesis statement an inductive method, based on academic articles and economic literature, is applied. Furthermore a regression analysis is used to prove the appearance of the expected positive relationships in the thesis statement. The results of the paper indicate the thesis statement to be probable. Therefore, this paper concludes that there is a positive relationship between the impact of the financial crisis in the EU states, domestic opinion and a positive stance to a financial transactions tax

Exact results in a slave boson saddle point approach for a strongly correlated electron model

We revisit the Kotliar-Ruckenstein (KR) slave boson saddle point evaluation for a two-site correlated electron model. As the model can be solved analytically, it is possible to compare the KR saddle point results to the exact many particle levels. The considered two site cluster mimics an infinite-$U$ single-impurity Anderson model with a nearest neighbor Coulomb interaction: one site is strongly correlated with an infinite local Coulomb repulsion which hybridizes with the second site, on which the local Coulomb repulsion vanishes. Making use of the flexibility of the representation we introduce appropriate weight factors in the KR saddle point scheme. Ground state and all excitation levels agree with the exact diagonalization results. Thermodynamics and correlation functions may be recovered in a suitably renormalized saddle point evaluation.Comment: 4 page