The topological ordering algorithm sorts nodes of a directed graph such that the order of the tail of each arc is lower than the order of its head. In this paper, we introduce the notion of covering between nodes of a directed graph. Then, we apply the topological orderingalgorithm on graphs containing the covering nodes. We show that there exists a cut set withforward arcs in these...

Results are presented of single crystal structural, thermodynamic, and reflectivity measurements of the double-perovskite Ba2NaOsO6. These characterize the material as a 5d1 ferromagnetic Mott insulator with an ordered moment of approximately 0.2microB per formula unit and TC=6.8(3) K. The magnetic entropy associated with this phase transition is close to Rln2, indicating that the quartet groun...

Charge-lattice fluctuations are observed in the layered perovskite manganite LaSr2Mn2O7 by Raman spectroscopy at temperatures as high as 340 K, and with decreasing temperature they become static, forming a charge-ordered ~CO! phase below TCO5210 K. In the static regime, superlattice reflections are observed by neutron and x-ray diffraction with a propagation vector ~1/4, 21/4, 0!. Crystallograp...

Charge, spin, and lattice degrees of orderings are of great interest in the layered quantum material RFe2O4 (R = Y, Er, Yb, Tm, and Lu) system. Recently many unique properties have been found using various experimental methods. However so far the nature of the two-dimensional (2D) charge ordering (CO) state is not clear and no observation of its fine structure in energy has been reported. Here ...

Garnet-type Li7La3Zr2O12 (LLZO) is a solid electrolyte material with a low-conductivity tetragonal and a high-conductivity cubic phase. Using density-functional theory and variable cell shape molecular dynamics simulations, we show that the tetragonal phase stability is dependent on a simultaneous ordering of the Li ions on the Li sublattice and a volume-preserving tetragonal distortion that re...

Using liquid crystalline self-assembly of cellulose nanocrystals, we achieve long-range alignment of anisotropic metal nanoparticles in colloidal nanocrystal dispersions that are then used to deposit thin structured films with ordering features highly dependent on the deposition method. These hybrid films are comprised of gold nanorods unidirectionally aligned in a matrix that can be made of or...

The concept of generalized order statistics (GOSs) was introduced as a unified approach to a variety of models of ordered random variables. The purpose of this paper is to investigate condi- tions on the underlying distribution functions and the parameters on which GOSs are based, to establish Shaked-Shanthikumar multivari- ate dispersive ordering of GOSs from one sample and Khaledi-Kochar mu...

Neutron small angle scattering on a colossal magnetoresistance material shows clear signatures of a rise in characteristic length of paramagnetic fluctuations as the maximum of dc susceptibility is approached from high temperatures. The phenomenon is accompanied by a rise in intensity of a broad peak that appears at wave vectors of Q<0.025 Å−1, and this is interpreted as a fingerprint of the on...