438 research outputs found
Efficient adaptive integration of functions with sharp gradients and cusps in n-dimensional parallelepipeds
In this paper, we study the efficient numerical integration of functions with
sharp gradients and cusps. An adaptive integration algorithm is presented that
systematically improves the accuracy of the integration of a set of functions.
The algorithm is based on a divide and conquer strategy and is independent of
the location of the sharp gradient or cusp. The error analysis reveals that for
a function (derivative-discontinuity at a point), a rate of convergence
of is obtained in . Two applications of the adaptive integration
scheme are studied. First, we use the adaptive quadratures for the integration
of the regularized Heaviside function---a strongly localized function that is
used for modeling sharp gradients. Then, the adaptive quadratures are employed
in the enriched finite element solution of the all-electron Coulomb problem in
crystalline diamond. The source term and enrichment functions of this problem
have sharp gradients and cusps at the nuclei. We show that the optimal rate of
convergence is obtained with only a marginal increase in the number of
integration points with respect to the pure finite element solution with the
same number of elements. The adaptive integration scheme is simple, robust, and
directly applicable to any generalized finite element method employing
enrichments with sharp local variations or cusps in -dimensional
parallelepiped elements.Comment: 22 page
Half metallic digital ferromagnetic heterostructure composed of a -doped layer of Mn in Si
We propose and investigate the properties of a digital ferromagnetic
heterostructure (DFH) consisting of a -doped layer of Mn in Si, using
\textit{ab initio} electronic-structure methods. We find that (i) ferromagnetic
order of the Mn layer is energetically favorable relative to antiferromagnetic,
and (ii) the heterostructure is a two-dimensional half metallic system. The
metallic behavior is contributed by three majority-spin bands originating from
hybridized Mn- and nearest-neighbor Si- states, and the corresponding
carriers are responsible for the ferromagnetic order in the Mn layer. The
minority-spin channel has a calculated semiconducting gap of 0.25 eV. Analysis
of the total and partial densities of states, band structure, Fermi surfaces
and associated charge density reveals the marked two-dimensional nature of the
half metallicity. The band lineup is found to be favorable for retaining the
half metal character to near the Curie temperature (). Being Si based
and possibly having a high as suggested by an experiment on dilutely
doped Mn in Si, the heterostructure may be of special interest for integration
into mature Si technologies for spintronic applications.Comment: 4 pages, 4 figures, Revised version, to appear in Phys. Rev. Let
Soft and transferable pseudopotentials from multi-objective optimization
Ab initio pseudopotentials are a linchpin of modern molecular and condensed
matter electronic structure calculations. In this work, we employ
multi-objective optimization to maximize pseudopotential softness while
maintaining high accuracy and transferability. To accomplish this, we develop a
formulation in which softness and accuracy are simultaneously maximized, with
accuracy determined by the ability to reproduce all-electron energy differences
between Bravais lattice structures, whereupon the resulting Pareto frontier is
scanned for the softest pseudopotential that provides the desired accuracy in
established transferability tests. We employ an evolutionary algorithm to solve
the multi-objective optimization problem and apply it to generate a
comprehensive table of optimized norm-conserving Vanderbilt (ONCV)
pseudopotentials (https://github.com/SPARC-X/SPMS-psps). We show that the
resulting table is softer than existing tables of comparable accuracy, while
more accurate than tables of comparable softness. The potentials thus afford
the possibility to speed up calculations in a broad range of applications areas
while maintaining high accuracy.Comment: 13 pages, 4 figure
Kohn-Sham accuracy from orbital-free density functional theory via -machine learning
We present a -machine learning model for obtaining Kohn-Sham accuracy
from orbital-free density functional theory (DFT) calculations. In particular,
we employ a machine learned force field (MLFF) scheme based on the kernel
method to capture the difference between Kohn-Sham and orbital-free DFT
energies/forces. We implement this model in the context of on-the-fly molecular
dynamics simulations, and study its accuracy, performance, and sensitivity to
parameters for representative systems. We find that the formalism not only
improves the accuracy of Thomas-Fermi-von Weizs{\"a}cker (TFW) orbital-free
energies and forces by more than two orders of magnitude, but is also more
accurate than MLFFs based solely on Kohn-Sham DFT, while being more efficient
and less sensitive to model parameters. We apply the framework to study the
structure of molten AlSi, the results suggesting no
aggregation of Si atoms, in agreement with a previous Kohn-Sham study performed
at an order of magnitude smaller length and time scales.Comment: 10 pages, 7 figures, 2 table
Chebyshev polynomial filtered subspace iteration in the Discontinuous Galerkin method for large-scale electronic structure calculations
The Discontinuous Galerkin (DG) electronic structure method employs an
adaptive local basis (ALB) set to solve the Kohn-Sham equations of density
functional theory (DFT) in a discontinuous Galerkin framework. The adaptive
local basis is generated on-the-fly to capture the local material physics, and
can systematically attain chemical accuracy with only a few tens of degrees of
freedom per atom. A central issue for large-scale calculations, however, is the
computation of the electron density (and subsequently, ground state properties)
from the discretized Hamiltonian in an efficient and scalable manner. We show
in this work how Chebyshev polynomial filtered subspace iteration (CheFSI) can
be used to address this issue and push the envelope in large-scale materials
simulations in a discontinuous Galerkin framework. We describe how the subspace
filtering steps can be performed in an efficient and scalable manner using a
two-dimensional parallelization scheme, thanks to the orthogonality of the DG
basis set and block-sparse structure of the DG Hamiltonian matrix. The
on-the-fly nature of the ALBs requires additional care in carrying out the
subspace iterations. We demonstrate the parallel scalability of the DG-CheFSI
approach in calculations of large-scale two-dimensional graphene sheets and
bulk three-dimensional lithium-ion electrolyte systems. Employing 55,296
computational cores, the time per self-consistent field iteration for a sample
of the bulk 3D electrolyte containing 8,586 atoms is 90 seconds, and the time
for a graphene sheet containing 11,520 atoms is 75 seconds.Comment: Submitted to The Journal of Chemical Physic
First observation of two hyperfine transitions in antiprotonic He-3
We report on the first experimental results for microwave spectroscopy of the
hyperfine structure of antiprotonic He-3. Due to the helium nuclear spin,
antiprotonic He-3 has a more complex hyperfine structure than antiprotonic He-4
which has already been studied before. Thus a comparison between theoretical
calculations and the experimental results will provide a more stringent test of
the three-body quantum electrodynamics (QED) theory. Two out of four
super-super-hyperfine (SSHF) transition lines of the (n,L)=(36,34) state were
observed. The measured frequencies of the individual transitions are
11.12559(14) GHz and 11.15839(18) GHz, less than 1 MHz higher than the current
theoretical values, but still within their estimated errors. Although the
experimental uncertainty for the difference of these frequencies is still very
large as compared to that of theory, its measured value agrees with theoretical
calculations. This difference is crucial to be determined because it is
proportional to the magnetic moment of the antiproton.Comment: 8 pages, 6 figures, just published (online so far) in Physics Letters
Twisted k-graph algebras associated to Bratteli diagrams
Given a system of coverings of k-graphs, we show that the cohomology of the
resulting (k+1)-graph is isomorphic to that of any one of the k-graphs in the
system. We then consider Bratteli diagrams of 2-graphs whose twisted
C*-algebras are matrix algebras over noncommutative tori. For such systems we
calculate the ordered K-theory and the gauge-invariant semifinite traces of the
resulting 3-graph C*-algebras. We deduce that every simple C*-algebra of this
form is Morita equivalent to the C*-algebra of a rank-2 Bratteli diagram in the
sense of Pask-Raeburn-R{\o}rdam-Sims.Comment: 28 pages, pictures prepared using tik
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Calculation of positron observables using a finite-element-based approach
We report the development of a new method for calculating positron observables using a finite-element approach for the solution of the Schrodinger equation. This method combines the advantages of both basis-set and real-space-grid approaches. The strict locality in real space of the finite element basis functions results in a method that is well suited for calculating large systems of a thousand or more atoms, as required for calculations of extended defects such as dislocations. In addition, the method is variational in nature and its convergence can be controlled systematically. The calculation of positron observables is straightforward due to the real-space nature of this method. We illustrate the power of this method with positron lifetime calculations on defects and defect-free materials, using overlapping atomic charge densities
Preliminary Results from Recent Measurements of the Antiprotonic Helium Hyperfine Structure
We report on preliminary results from a systematic study of the hyperfine
(HF) structure of antiprotonic helium. This precise measurement which was
commenced in 2006, has now been completed. Our initial analysis shows no
apparent density or power dependence and therefore the results can be averaged.
The statistical error of the observable M1 transitions is a factor of 60
smaller than that of three body quantum electrodynamic (QED) calculations,
while their difference has been resolved to a precision comparable to theory (a
factor of 10 better than our first measurement). This difference is sensitive
to the antiproton magnetic moment and agreement between theory and experiment
would lead to an increased precision of this parameter, thus providing a test
of CPT invariance.Comment: 6 pages, 4 figure
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