Consistent random vertex-orderings of graphs

Given a hereditary graph property $\mathcal{P}$, consider distributions of random orderings of vertices of graphs $G\in\mathcal{P}$ that are preserved under isomorphisms and under taking induced subgraphs. We show that for many properties $\mathcal{P}$ the only such random orderings are uniform, and give some examples of non-uniform orderings when they exist

Using single buffers and data reorganization to implement a multi-megasample fast Fourier transform

Data ordering in large fast Fourier transforms (FFT's) is both conceptually and implementationally difficult. Discribed here is a method of visualizing data orderings as vectors of address bits, which enables the engineer to use more efficient data orderings and reduce double-buffer memory designs. Also detailed are the difficulties and algorithmic solutions involved in FFT lengths up to 4 megasamples (Msamples) and sample rates up to 80 MHz

The electronic structure and band gap of LiFePO4 and LiMnPO4

Materials with the olivine LixMPO4 structure form an important new class of materials for rechargeable Li batteries. There is significant interest in their electronic properties because of the importance of electronic conductivity in batteries for high rate applications. The density of states of LixMPO4 (x = 0, 1 and M = Fe, Mn) has been determined with the ab initio GGA+U method, appropriate for these correlated electron systems. Computed results are compared with the optical gap of LiFePO4, as measured using UV-Vis-NIR diffuse reflectance spectroscopy. The results obtained from experiment (3.8-4.0 eV) and GGA+U computations (3.7 eV) are in very good agreement. However, standard GGA, without the same level of treatment of electron correlation, is shown to make large errors in predicting the electronic structure. It is argued that olivines are likely to be polaronic conductors with extrinsically determined carrier levels and that their electronic conductivity is therefore not simply related to the band gap.Comment: 17 pages, 2 figure

Chalcogen-height dependent magnetic interactions and magnetic order switching in FeSex_xTe1−x_{1-x}

Magnetic properties of iron chalcogenide superconducting materials are investigated using density functional calculations. We find the stability of magnetic phases is very sensitive to the height of chalcogen species from the Fe plane: while FeTe with optimized Te height has the double-stripe-type $(\pi,0)$ magnetic ordering, the single-stripe-type $(\pi,\pi)$ ordering becomes the ground state phase when Te height is lowered below a critical value by, e.g., Se doping. This behavior is understood by opposite Te-height dependences of the superexchange interaction and a longer-range magnetic interaction mediated by itinerant electrons. We also demonstrate a linear temperature dependence of the macroscopic magnetic susceptibility in the single-stripe phase in contrast to a constant behavior in the double-stripe phase. Our findings provide a comprehensive and unified view to understand the magnetism in FeSe$_x$Te$_{1-x}$ and iron pnictide superconductors.Comment: 4 pages, 4 figure