68,755 research outputs found
Edge reconstruction in armchair phosphorene nanoribbons revealed by discontinuous Galerkin density functional theory
With the help of our recently developed massively parallel DGDFT
(Discontinuous Galerkin Density Functional Theory) methodology, we perform
large-scale Kohn-Sham density functional theory calculations on phosphorene
nanoribbons with armchair edges (ACPNRs) containing a few thousands to ten
thousand atoms. The use of DGDFT allows us to systematically achieve
conventional plane wave basis set type of accuracy, but with a much smaller
number (about 15) of adaptive local basis (ALB) functions per atom for this
system. The relatively small number degrees of freedom required to represent
the Kohn-Sham Hamiltonian, together with the use of the pole expansion the
selected inversion (PEXSI) technique that circumvents the need to diagonalize
the Hamiltonian, result in a highly efficient and scalable computational scheme
for analyzing the electronic structures of ACPNRs as well as its dynamics. The
total wall clock time for calculating the electronic structures of large-scale
ACPNRs containing 1080-10800 atoms is only 10-25 s per self-consistent field
(SCF) iteration, with accuracy fully comparable to that obtained from
conventional planewave DFT calculations. For the ACPNR system, we observe that
the DGDFT methodology can scale to 5,000-50,000 processors. We use DGDFT based
ab-initio molecular dynamics (AIMD) calculations to study the thermodynamic
stability of ACPNRs. Our calculations reveal that a 2 * 1 edge reconstruction
appears in ACPNRs at room temperature.Comment: 9 pages, 5 figure
Projected Commutator DIIS Method for Accelerating Hybrid Functional Electronic Structure Calculations
The commutator direct inversion of the iterative subspace (commutator DIIS or
C-DIIS) method developed by Pulay is an efficient and the most widely used
scheme in quantum chemistry to accelerate the convergence of self consistent
field (SCF) iterations in Hartree-Fock theory and Kohn-Sham density functional
theory. The C-DIIS method requires the explicit storage of the density matrix,
the Fock matrix and the commutator matrix. Hence the method can only be used
for systems with a relatively small basis set, such as the Gaussian basis set.
We develop a new method that enables the C-DIIS method to be efficiently
employed in electronic structure calculations with a large basis set such as
planewaves for the first time. The key ingredient is the projection of both the
density matrix and the commutator matrix to an auxiliary matrix called the
gauge-fixing matrix. The resulting projected commutator-DIIS method (PC-DIIS)
only operates on matrices of the same dimension as the that consists of
Kohn-Sham orbitals. The cost of the method is comparable to that of standard
charge mixing schemes used in large basis set calculations. The PC-DIIS method
is gauge-invariant, which guarantees that its performance is invariant with
respect to any unitary transformation of the Kohn-Sham orbitals. We demonstrate
that the PC-DIIS method can be viewed as an extension of an iterative
eigensolver for nonlinear problems. We use the PC-DIIS method for accelerating
Kohn-Sham density functional theory calculations with hybrid
exchange-correlation functionals, and demonstrate its superior performance
compared to the commonly used nested two-level SCF iteration procedure
DGDFT: A Massively Parallel Method for Large Scale Density Functional Theory Calculations
We describe a massively parallel implementation of the recently developed
discontinuous Galerkin density functional theory (DGDFT) [J. Comput. Phys.
2012, 231, 2140] method, for efficient large-scale Kohn-Sham DFT based
electronic structure calculations. The DGDFT method uses adaptive local basis
(ALB) functions generated on-the-fly during the self-consistent field (SCF)
iteration to represent the solution to the Kohn-Sham equations. The use of the
ALB set provides a systematic way to improve the accuracy of the approximation.
It minimizes the number of degrees of freedom required to represent the
solution to the Kohn-Sham problem for a desired level of accuracy. In
particular, DGDFT can reach the planewave accuracy with far fewer numbers of
degrees of freedom. By using the pole expansion and selected inversion (PEXSI)
technique to compute electron density, energy and atomic forces, we can make
the computational complexity of DGDFT scale at most quadratically with respect
to the number of electrons for both insulating and metallic systems. We show
that DGDFT can achieve 80% parallel efficiency on 128,000 high performance
computing cores when it is used to study the electronic structure of
two-dimensional (2D) phosphorene systems with 3,500-14,000 atoms. This high
parallel efficiency results from a two-level parallelization scheme that we
will describe in detail.Comment: 13 pages, 8 figures in J. Chem. Phys. 2015. arXiv admin note: text
overlap with arXiv:1501.0503
Interpolative Separable Density Fitting through Centroidal Voronoi Tessellation With Applications to Hybrid Functional Electronic Structure Calculations
The recently developed interpolative separable density fitting (ISDF)
decomposition is a powerful way for compressing the redundant information in
the set of orbital pairs, and has been used to accelerate quantum chemistry
calculations in a number of contexts. The key ingredient of the ISDF
decomposition is to select a set of non-uniform grid points, so that the values
of the orbital pairs evaluated at such grid points can be used to accurately
interpolate those evaluated at all grid points. The set of non-uniform grid
points, called the interpolation points, can be automatically selected by a QR
factorization with column pivoting (QRCP) procedure. This is the
computationally most expensive step in the construction of the ISDF
decomposition. In this work, we propose a new approach to find the
interpolation points based on the centroidal Voronoi tessellation (CVT) method,
which offers a much less expensive alternative to the QRCP procedure when ISDF
is used in the context of hybrid functional electronic structure calculations.
The CVT method only uses information from the electron density, and can be
efficiently implemented using a K-Means algorithm. We find that this new method
achieves comparable accuracy to the ISDF-QRCP method, at a cost that is
negligible in the overall hybrid functional calculations. For instance, for a
system containing silicon atoms simulated using the HSE06 hybrid
functional on computational cores, the cost of QRCP-based method for
finding the interpolation points costs seconds, while the CVT procedure
only takes seconds. We also find that the ISDF-CVT method also enhances
the smoothness of the potential energy surface in the context of \emph{ab
initio} molecular dynamics (AIMD) simulations with hybrid functionals
Phase Dynamics in Intrinsic Josephson Junctions and its Electrodynamics
We present a theoretical description of the phase dynamics and its
corresponding electrodynamics in a stack of inductively coupled intrinsic
Josephson junctions of layered high- superconductors in the absence of an
external magnetic field. Depending on the spatial structure of the gauge
invariant phase difference, the dynamic state is classified into: state with
kink, state without kink, and state with solitons. It is revealed that in the
state with phase kink, the plasma is coupled to the cavity and the plasma
oscillation is enhanced. In contrast, in the state without kink, the plasma
oscillation is weak. It points a way to enhance the radiation of
electromagnetic from high- superconductors. We also perform numerical
simulations to check the theory and a good agreement is achieved. The radiation
pattern of the state with and without kink is calculated, which may serve as a
fingerprint of the dynamic state realized by the system. At last, the power
radiation of the state with solitons is calculated by simulations. The possible
state realized in the recent experiments is discussed in the viewpoint of the
theoretical description. The state with kink is important for applications
including terahertz generators and amplifiers.Comment: 14 pages, 13 figure
Distance between unitary orbits of normal elements in simple C*-algebras of real rank zero
Let be two normal elements in a unital simple C*-algebra We
introduce a function and show that in a unital simple AF-algebra
there is a constant such that where and are
the closures of the unitary orbits of and of respectively. We also
generalize this to unital simple C*-algebras with real rank zero, stable rank
one and weakly unperforated -group. More complicated estimates are given
in the presence of non-trivial -information.Comment: 64 pages, JFA to appea
On the Cauchy problem for two dimensional incompressible viscoelastic flows
We study the large-data Cauchy problem for two dimensional Oldroyd model of
incompressible viscoelastic fluids. We prove the global-in-time existence of
the Leray-Hopf type weak solutions in the physical energy space. Our method
relies on a new estimate on the space-time norm in
L^{\f32}_{loc} of the Cauchy-Green strain tensor \tau=\F\F^\top, or
equivalently the norm of the Jacobian of the flow map \F. It
allows us to rule out possible concentrations of the energy due to deformations
associated with the flow maps. Following the general compactness arguments due
to DiPerna and Lions (\cite{DL}, \cite{FNP}, \cite{PL}), and using the
so-called \textit{effective viscous flux}, , which was introduced
in our previous work \cite{HL}, we are able to control the possible
oscillations of deformation gradients as well
In-plane dissipation as a possible synchronization mechanism for terahertz radiation from intrinsic Josephson junctions of layered superconductors
Strong terahertz radiation from mesa structure of
single crystal has been observed recently,
where the mesa intrinsically forms a cavity. For a thick mesa of large number
of junctions, there are many cavity modes with different wave vectors along the
c-axis corresponding to almost degenerate bias voltages. The mechanism
responsible for exciting the uniform mode which radiates coherent terahertz
waves in experiments is unknown. In this work, we show that the in-plane
dissipation selects the uniform mode. For perturbations with non-zero wave
numbers along the c-axis, the in-plane dissipations are significantly enhanced,
which prevent the excitation of corresponding cavity modes. Our analytical
results are confirmed by numerical simulations.Comment: 7 pages, 5 figure
The Convergence Rate and Necessary-and-Sufficient Condition for the Consistency of Isogeometric Collocation Method
Although the isogeometric collocation (IGA-C) method has been successfully
utilized in practical applications due to its simplicity and efficiency, only a
little theoretical results have been established on the numerical analysis of
the IGA-C method. In this paper, we deduce the convergence rate of the
consistency of the IGA-C method. Moreover, based on the formula of the
convergence rate, the necessary and sufficient condition for the consistency of
the IGA-C method is developed. These results advance the numerical analysis of
the IGA-C method.Comment: 19 pages, 3 figure
The natural measure of a symbolic dynamical system
This study investigates the natural or intrinsic measure of a symbolic
dynamical system . The measure of a
pattern in is an asymptotic ratio of
, which arises in all patterns of length within
very long patterns, such that in a typical long pattern, the pattern
appears with frequency
. When is a shift of finite
type and is an irreducible non-negative matrix, the measure
is the Parry measure. is ergodic with maximum entropy. The result
holds for sofic shift , which is irreducible. The
result can be extended to , where is a countably infinite matrix
that is irreducible, aperiodic and positive recurrent. By using the Krieger
cover, the natural measure of a general shift space is studied in the way of a
countably infinite state of sofic shift, including context free shift. The
Perron-Frobenius Theorem for non-negative matrices plays an essential role in
this study
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