6,846 research outputs found
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
Invariants of Lie Algebras with Fixed Structure of Nilradicals
An algebraic algorithm is developed for computation of invariants
('generalized Casimir operators') of general Lie algebras over the real or
complex number field. Its main tools are the Cartan's method of moving frames
and the knowledge of the group of inner automorphisms of each Lie algebra.
Unlike the first application of the algorithm in [J. Phys. A: Math. Gen., 2006,
V.39, 5749; math-ph/0602046], which deals with low-dimensional Lie algebras,
here the effectiveness of the algorithm is demonstrated by its application to
computation of invariants of solvable Lie algebras of general dimension
restricted only by a required structure of the nilradical.
Specifically, invariants are calculated here for families of real/complex
solvable Lie algebras. These families contain, with only a few exceptions, all
the solvable Lie algebras of specific dimensions, for whom the invariants are
found in the literature.Comment: LaTeX2e, 19 page
The Confinement Property in SU(3) Gauge Theory
We study confinement property of pure SU(3) gauge theory, combining in this
effort the non-perturbative gluon and ghost propagators obtained as solutions
of Dyson--Schwinger equations with solutions of an integral ladder diagram
summation type equation for the Wilson loop. We obtain the string potential and
effective UV coupling.Comment: 7 pages, 7 figures, v2: references added, discussion reorganize
All solvable extensions of a class of nilpotent Lie algebras of dimension n and degree of nilpotency n-1
We construct all solvable Lie algebras with a specific n-dimensional
nilradical n_(n,2) (of degree of nilpotency (n-1) and with an (n-2)-dimensional
maximal Abelian ideal). We find that for given n such a solvable algebra is
unique up to isomorphisms. Using the method of moving frames we construct a
basis for the Casimir invariants of the nilradical n_(n,2). We also construct a
basis for the generalized Casimir invariants of its solvable extension s_(n+1)
consisting entirely of rational functions of the chosen invariants of the
nilradical.Comment: 19 pages; added references, changes mainly in introduction and
conclusions, typos corrected; submitted to J. Phys. A, version to be
publishe
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
The atomic structure of large-angle grain boundaries and in and their transport properties
We present the results of a computer simulation of the atomic structures of
large-angle symmetrical tilt grain boundaries (GBs) (misorientation
angles \q{36.87}{^{\circ}} and \q{53.13}{^{\circ}}),
(misorientation angles \q{22.62}{^{\circ}} and \q{67.38}{^{\circ}}). The
critical strain level criterion (phenomenological criterion)
of Chisholm and Pennycook is applied to the computer simulation data to
estimate the thickness of the nonsuperconducting layer enveloping
the grain boundaries. The is estimated also by a bond-valence-sum
analysis. We propose that the phenomenological criterion is caused by the
change of the bond lengths and valence of atoms in the GB structure on the
atomic level. The macro- and micro- approaches become consistent if the
is greater than in earlier papers. It is predicted that the
symmetrical tilt GB \theta = \q{53.13}{^{\circ}} should demonstrate
a largest critical current across the boundary.Comment: 10 pages, 2 figure
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
- …