Magnetic order in GdBiPt studied by x-ray resonant magnetic scattering

Rare earth (R) half-Heusler compounds, RBiPt, exhibit a wide spectrum of novel ground states. Recently, GdBiPt has been proposed as a potential antiferromagnetic topological insulator (AFTI). We have employed x-ray resonant magnetic scattering to elucidate the microscopic details of the magnetic structure in GdBiPt below T_N = 8.5 K. Experiments at the Gd L_2 absorption edge show that the Gd moments order in an antiferromagnetic stacking along the cubic diagonal [1 1 1] direction satisfying the requirement for an AFTI, where both time-reversal symmetry and lattice translational symmetry are broken, but their product is conserved.Comment: 4 pages, 4 figure

Multidimensional Conservation Laws: Overview, Problems, and Perspective

Some of recent important developments are overviewed, several longstanding open problems are discussed, and a perspective is presented for the mathematical theory of multidimensional conservation laws. Some basic features and phenomena of multidimensional hyperbolic conservation laws are revealed, and some samples of multidimensional systems/models and related important problems are presented and analyzed with emphasis on the prototypes that have been solved or may be expected to be solved rigorously at least for some cases. In particular, multidimensional steady supersonic problems and transonic problems, shock reflection-diffraction problems, and related effective nonlinear approaches are analyzed. A theory of divergence-measure vector fields and related analytical frameworks for the analysis of entropy solutions are discussed.Comment: 43 pages, 3 figure

Magnetic order in GdBiPt studied by x-ray resonant magnetic scattering

Rare-earth (R) half-Heusler compounds RBiPt exhibit a wide spectrum of interesting ground states. We have employed x-ray resonant magnetic scattering to elucidate the microscopic details of the magnetic structure in GdBiPt below TN=8.5 K. Experiments at the Gd L2 absorption edge show that the Gd moments order in an antiferromagnetic stacking along the cubic diagonal [111] direction, satisfying one of the requirements for an antiferromagnetic topological insulator as proposed previously, where both time-reversal symmetry and lattice translational symmetry are broken, but their product is conserved.This article is published as Kreyssig, A., M. G. Kim, J. W. Kim, D. K. Pratt, S. M. Sauerbrei, S. D. March, G. R. Tesdall et al. "Magnetic order in GdBiPt studied by x-ray resonant magnetic scattering." Physical Review B 84, no. 22 (2011): 220408. DOI: 10.1103/PhysRevB.84.220408. Posted with permission.</p

Fine structures for the solutions of the two-dimensional Riemann problems by high-order WENO schemes

The two-dimensional Riemann problem with polytropic gas is considered. By a restriction on the constant states of each quadrant of the computational domain such that there is only one planar centered wave connecting two adjacent quadrants, there are nineteen genuinely different initial configurations of the problem. The configurations are numerically simulated on a fine grid and compared by the 5th-order WENO-Z5, 6th-order WENO-6, and 7th-order WENO-Z7 schemes. The solutions are very well approximated with high resolution of waves interactions phenomena and different types of Mach shock reflections. Kelvin-Helmholtz instability-like secondary-scaled vortices along contact continuities are well resolved and visualized. Numerical solutions show that WENO-6 outperforms the comparing WENO-Z5 and WENO-Z7 in terms of shock capturing and small-scaled vortices resolution. A catalog of the numerical solutions of all nineteen configurations obtained from the WENO-6 scheme is listed. Thanks to their excellent resolution and sharp shock capturing, the numerical solutions presented in this work can be served as reference solutions for both future numerical and theoretical analyses of the 2D Riemann problem