Evolution of magnetic Dirac bosons in a honeycomb lattice

We examine the presence and evolution of magnetic Dirac nodes in the Heisenberg honeycomb lattice. Using linear spin theory, we evaluate the collinear phase diagram as well as the change in the spin dynamics with various exchange interactions. We show that the ferromagnetic structure produces bosonic Dirac and Weyl points due to the competition between superexchange interactions. Furthermore, it is shown that the criteria for magnetic Dirac nodes are coupled to the magnetic structure and not the overall crystal symmetry, where the breaking of inversion symmetry greatly affects the antiferromagnetic configurations. The tunability of the nodal points through variation of the exchange parameters leads to the possibility of controlling Dirac symmetries through an external manipulation of the orbital interactions.Comment: 9 pages, 7 figures, Submitted for publicatio

Invariants of Triangular Lie Algebras

Triangular Lie algebras are the Lie algebras which can be faithfully represented by triangular matrices of any finite size over the real/complex number field. In the paper invariants ('generalized Casimir operators') are found for three classes of Lie algebras, namely those which are either strictly or non-strictly triangular, and for so-called special upper triangular Lie algebras. Algebraic algorithm of [J. Phys. A: Math. Gen., 2006, V.39, 5749; math-ph/0602046], developed further in [J. Phys. A: Math. Theor., 2007, V.40, 113; math-ph/0606045], is used to determine the invariants. A conjecture of [J. Phys. A: Math. Gen., 2001, V.34, 9085], concerning the number of independent invariants and their form, is corroborated.Comment: LaTeX2e, 16 pages; misprints are corrected, some proofs are extende

Computation of Invariants of Lie Algebras by Means of Moving Frames

A new purely algebraic algorithm is presented for computation of invariants (generalized Casimir operators) of Lie algebras. It uses the Cartan's method of moving frames and the knowledge of the group of inner automorphisms of each Lie algebra. The algorithm is applied, in particular, to computation of invariants of real low-dimensional Lie algebras. A number of examples are calculated to illustrate its effectiveness and to make a comparison with the same cases in the literature. Bases of invariants of the real solvable Lie algebras up to dimension five, the real six-dimensional nilpotent Lie algebras and the real six-dimensional solvable Lie algebras with four-dimensional nilradicals are newly calculated and listed in tables.Comment: 17 pages, extended versio

A note about convected time derivatives for flows of complex fluids

We present a direct derivation of the typical time derivatives used in a continuum description of complex fluid flows, harnessing the principles of the kinematics of line elements. The evolution of the microstructural conformation tensor in a flow and the physical interpretation of different derivatives then follow naturally.Comment: 1 figur

Evaluation of Rock Fall Hazards using LiDAR Technology

Lidar (light detection and ranging) is a relatively new technology that is being used in many aspects of geology and engineering, including researching the potential for rock falls on highway rock cuts. At Missouri University of Science and Technology, we are developing methods for measuring joint orientations remotely and quantifying the raveling process. Measuring joint orientations remotely along highways is safer, more accurate and can result in larger and more accurate data sets, including measurements from otherwise inaccessible areas. Measuring the nature of rock raveling will provide the data needed to begin the process of modeling the rock raveling process. In both cases, terrestrial lidar scanning is used to generate large point clouds of coordinate triplets representing the surface of the rock cut. Automated algorithms have been developed to organize the lidar data, register successive images without survey control, and removal of vegetation and non-rock artifacts. In the first case, we look for planar elements, identify the plane and calculate the orientations. In the second case, we take a series of scans over time and use sophisticated change detection algorithms to calculate the numbers and volumes of rock that has fallen off the rock face

Higher-order Abel equations: Lagrangian formalism, first integrals and Darboux polynomials

A geometric approach is used to study a family of higher-order nonlinear Abel equations. The inverse problem of the Lagrangian dynamics is studied in the particular case of the second-order Abel equation and the existence of two alternative Lagrangian formulations is proved, both Lagrangians being of a non-natural class (neither potential nor kinetic term). These higher-order Abel equations are studied by means of their Darboux polynomials and Jacobi multipliers. In all the cases a family of constants of the motion is explicitly obtained. The general n-dimensional case is also studied

Genetic recombination is targeted towards gene promoter regions in dogs

The identification of the H3K4 trimethylase, PRDM9, as the gene responsible for recombination hotspot localization has provided considerable insight into the mechanisms by which recombination is initiated in mammals. However, uniquely amongst mammals, canids appear to lack a functional version of PRDM9 and may therefore provide a model for understanding recombination that occurs in the absence of PRDM9, and thus how PRDM9 functions to shape the recombination landscape. We have constructed a fine-scale genetic map from patterns of linkage disequilibrium assessed using high-throughput sequence data from 51 free-ranging dogs, Canis lupus familiaris. While broad-scale properties of recombination appear similar to other mammalian species, our fine-scale estimates indicate that canine highly elevated recombination rates are observed in the vicinity of CpG rich regions including gene promoter regions, but show little association with H3K4 trimethylation marks identified in spermatocytes. By comparison to genomic data from the Andean fox, Lycalopex culpaeus, we show that biased gene conversion is a plausible mechanism by which the high CpG content of the dog genome could have occurred.Comment: Updated version, with significant revision