420 research outputs found
Methods for Computing the Greatest Common Divisor and Applications in Mathematical Programming.
Several methods are presented for determining the greatest
common divisor of a set of positive integers by solving the
n
integer program: find the integers x. that minimize Z = E a.x.
i = l
subject to Z 2: 1. The methods are programmed for use on a computer
and compared with the Euclidean algorithm. Computational results
and applications are given.http://www.archive.org/details/methodsforcomput00macgCaptain, United States ArmyMajor, United States Arm
Elastically Induced Coexistence of Surface Reconstructions
Scanning tunneling microscopy of Sb-capped GaAs shows the coexistence of different surface reconstructions. The majority of the surface consists of an α2(2×4) reconstruction typically observed for GaAs(001) surfaces. At step edges, an α(4×3) reconstruction, common for GaSb(001), is observed. We argue that strain couples the surface reconstruction to the film morphology. Density functional theory calculations show that the (2×4) reconstruction is stabilized in GaSb films when the lattice parameter is constrained to that of GaAs, as happens in the middle of a terrace, while the (4×3) reconstruction is stabilized when the lattice parameter is allowed to relax toward that of GaSb at step edges. This result confirms the importance of elastic relaxation in the coexistence of surface reconstructions
Machine learning the electronic structure of matter across temperatures
We introduce machine learning (ML) models that predict the electronic
structure of materials across a wide temperature range. Our models employ
neural networks and are trained on density functional theory (DFT) data. Unlike
other ML models that use DFT data, our models directly predict the local
density of states (LDOS) of the electronic structure. This provides several
advantages, including access to multiple observables such as the electronic
density and electronic total free energy. Moreover, our models account for both
the electronic and ionic temperatures independently, making them ideal for
applications like laser-heating of matter. We validate the efficacy of our
LDOS-based models on a metallic test system. They accurately capture energetic
effects induced by variations in ionic and electronic temperatures over a broad
temperature range, even when trained on a subset of these temperatures. These
findings open up exciting opportunities for investigating the electronic
structure of materials under both ambient and extreme conditions
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Atomic Size Mismatch Strain Induced Surface Reconstructions
The effects of lattice mismatch strain and atomic size mismatch strain on surface reconstructions are analyzed using density functional theory. These calculations demonstrate the importance of an explicit treatment of alloying when calculating the energies of alloyed surface reconstructions. Lattice mismatch strain has little impact on surface dimer ordering for the α2(2×4) reconstruction of GaAs alloyed with In. However, atomic size mismatch strain induces the surface In atoms to preferentially alternate position, which, in turn, induces an alternating configuration of the surface anion dimers. These results agree well with experimental data for α2(2×4) domains in InGaAs∕GaAs surfaces
Variational finite-difference representation of the kinetic energy operator
A potential disadvantage of real-space-grid electronic structure methods is
the lack of a variational principle and the concomitant increase of total
energy with grid refinement. We show that the origin of this feature is the
systematic underestimation of the kinetic energy by the finite difference
representation of the Laplacian operator. We present an alternative
representation that provides a rigorous upper bound estimate of the true
kinetic energy and we illustrate its properties with a harmonic oscillator
potential. For a more realistic application, we study the convergence of the
total energy of bulk silicon using a real-space-grid density-functional code
and employing both the conventional and the alternative representations of the
kinetic energy operator.Comment: 3 pages, 3 figures, 1 table. To appear in Phys. Rev. B. Contribution
for the 10th anniversary of the eprint serve
Real-space grid representation of momentum and kinetic energy operators for electronic structure calculations
We show that the central finite difference formula for the first and the
second derivative of a function can be derived, in the context of quantum
mechanics, as matrix elements of the momentum and kinetic energy operators
using, as a basis set, the discrete coordinate eigenkets
defined on the uniform grid . Simple closed form expressions of the
matrix elements are obtained starting from integrals involving the canonical
commutation rule. A detailed analysis of the convergence toward the continuum
limit with respect to both the grid spacing and the approximation order is
presented. It is shown that the convergence from below of the eigenvalues in
electronic structure calculations is an intrinsic feature of the finite
difference method
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