20,542 research outputs found
AFLOW-SYM: Platform for the complete, automatic and self-consistent symmetry analysis of crystals
Determination of the symmetry profile of structures is a persistent challenge
in materials science. Results often vary amongst standard packages, hindering
autonomous materials development by requiring continuous user attention and
educated guesses. Here, we present a robust procedure for evaluating the
complete suite of symmetry properties, featuring various representations for
the point-, factor-, space groups, site symmetries, and Wyckoff positions. The
protocol determines a system-specific mapping tolerance that yields symmetry
operations entirely commensurate with fundamental crystallographic principles.
The self consistent tolerance characterizes the effective spatial resolution of
the reported atomic positions. The approach is compared with the most used
programs and is successfully validated against the space group information
provided for over 54,000 entries in the Inorganic Crystal Structure Database.
Subsequently, a complete symmetry analysis is applied to all 1.7 million
entries of the AFLOW data repository. The AFLOW-SYM package has been
implemented in, and made available for, public use through the automated,
framework AFLOW.Comment: 24 pages, 6 figure
A simple, efficient, and general treatment of the singularities in Hartree-Fock and exact-exchange Kohn-Sham methods for solids
We present a general scheme for treating the integrable singular terms within
exact exchange (EXX) Kohn-Sham or Hartree-Fock (HF) methods for periodic
solids. We show that the singularity corrections for treating these
divergencies depend only on the total number and the positions of k-points and
on the lattice vectors, in particular the unit cell volume, but not on the
particular positions of atoms within the unit cell. The method proposed here to
treat the singularities constitutes a stable, simple to implement, and general
scheme that can be applied to systems with arbitrary lattice parameters within
either the EXX Kohn-Sham or the HF formalism. We apply the singularity
correction to a typical symmetric structure, diamond, and to a more general
structure, trans-polyacetylene. We consider the effect of the singularity
corrections on volume optimisations and k-point convergence. While the
singularity corrections clearly depends on the total number of k-points, it
exhibits a remarkably small dependence upon the choice of the specific
arrangement of the k-points.Comment: 24 pages, 5 Figures, re-submitted to Phys. Rev. B after revision
Grid generation for the solution of partial differential equations
A general survey of grid generators is presented with a concern for understanding why grids are necessary, how they are applied, and how they are generated. After an examination of the need for meshes, the overall applications setting is established with a categorization of the various connectivity patterns. This is split between structured grids and unstructured meshes. Altogether, the categorization establishes the foundation upon which grid generation techniques are developed. The two primary categories are algebraic techniques and partial differential equation techniques. These are each split into basic parts, and accordingly are individually examined in some detail. In the process, the interrelations between the various parts are accented. From the established background in the primary techniques, consideration is shifted to the topic of interactive grid generation and then to adaptive meshes. The setting for adaptivity is established with a suitable means to monitor severe solution behavior. Adaptive grids are considered first and are followed by adaptive triangular meshes. Then the consideration shifts to the temporal coupling between grid generators and PDE-solvers. To conclude, a reflection upon the discussion, herein, is given
On the Evolution of Thermonuclear Flames on Large Scales
The thermonuclear explosion of a massive white dwarf in a Type Ia supernova
explosion is characterized by vastly disparate spatial and temporal scales. The
extreme dynamic range inherent to the problem prevents the use of direct
numerical simulation and forces modelers to resort to subgrid models to
describe physical processes taking place on unresolved scales.
We consider the evolution of a model thermonuclear flame in a constant
gravitational field on a periodic domain. The gravitational acceleration is
aligned with the overall direction of the flame propagation, making the flame
surface subject to the Rayleigh-Taylor instability. The flame evolution is
followed through an extended initial transient phase well into the steady-state
regime. The properties of the evolution of flame surface are examined. We
confirm the form of the governing equation of the evolution suggested by
Khokhlov (1995). The mechanism of vorticity production and the interaction
between vortices and the flame surface are discussed. The results of our
investigation provide the bases for revising and extending previous
subgrid-scale model.Comment: 15 pages, 22 postscript figures. Accepted for publication by the
Astrophysical Journal. High resolution figures can be found at
http://flash.uchicago.edu/~zhang/research_paper.htm
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