30,968 research outputs found
Thermal effects on lattice strain in hcp Fe under pressure
We compute the c/a lattice strain versus temperature for nonmagnetic hcp iron
at high pressures using both first-principles linear response quasiharmonic
calculations based on the full potential linear-muffin-tin-orbital (LMTO)
method and the particle-in-cell (PIC) model for the vibrational partition
function using a tight-binding total-energy method. The tight-binding model
shows excellent agreement with the all-electron LMTO method. When hcp structure
is stable, the calculated geometric mean frequency and Helmholtz free energy of
hcp Fe from PIC and linear response lattice dynamics agree very well, as does
the axial ratio as a function of temperature and pressure. On-site
anharmonicity proves to be small up to the melting temperature, and PIC gives a
good estimate of its sign and magnitude. At low pressures, hcp Fe becomes
dynamically unstable at large c/a ratios, and the PIC model might fail where
the structure approaches lattice instability. The PIC approximation describes
well the vibrational behavior away from the instability, and thus is a
reasonable approach to compute high temperature properties of materials. Our
results show significant differences from earlier PIC studies, which gave much
larger axial ratio increases with increasing temperature, or reported large
differences between PIC and lattice dynamics results.Comment: 9 figure
First-principles thermal equation of state and thermoelasticity of hcp Fe at high pressures
We investigate the equation of state and elastic properties of hcp iron at
high pressures and high temperatures using first principles linear response
linear-muffin-tin-orbital method in the generalized-gradient approximation. We
calculate the Helmholtz free energy as a function of volume, temperature, and
volume-conserving strains, including the electronic excitation contributions
from band structures and lattice vibrational contributions from quasi-harmonic
lattice dynamics. We perform detailed investigations on the behavior of elastic
moduli and equation of state properties as functions of temperature and
pressure, including the pressure-volume equation of state, bulk modulus, the
thermal expansion coefficient, the Gruneisen ratio, and the shock Hugoniot.
Detailed comparison has been made with available experimental measurements and
theoretical predictions.Comment: 33 pages, 12 figure
First-principles thermoelasticity of bcc iron under pressure
We investigate the elastic and isotropic aggregate properties of
ferromagnetic bcc iron as a function of temperature and pressure by computing
the Helmholtz free energies for the volume-conserving strained structures using
the first-principles linear response linear-muffin-tin-orbital method and the
generalized-gradient approximation. We include the electronic excitation
contributions to the free energy from the band structures, and phonon
contributions from quasi-harmonic lattice dynamics. We make detailed
comparisons between our calculated elastic moduli and their temperature and
pressure dependences with available experimental and theoretical data.Comment: 5 figures, 2 table
Pseudorandom Generators for Width-3 Branching Programs
We construct pseudorandom generators of seed length that -fool ordered read-once branching programs
(ROBPs) of width and length . For unordered ROBPs, we construct
pseudorandom generators with seed length . This is the first improvement for pseudorandom
generators fooling width ROBPs since the work of Nisan [Combinatorica,
1992].
Our constructions are based on the `iterated milder restrictions' approach of
Gopalan et al. [FOCS, 2012] (which further extends the Ajtai-Wigderson
framework [FOCS, 1985]), combined with the INW-generator [STOC, 1994] at the
last step (as analyzed by Braverman et al. [SICOMP, 2014]). For the unordered
case, we combine iterated milder restrictions with the generator of
Chattopadhyay et al. [CCC, 2018].
Two conceptual ideas that play an important role in our analysis are: (1) A
relabeling technique allowing us to analyze a relabeled version of the given
branching program, which turns out to be much easier. (2) Treating the number
of colliding layers in a branching program as a progress measure and showing
that it reduces significantly under pseudorandom restrictions.
In addition, we achieve nearly optimal seed-length
for the classes of: (1) read-once polynomials on
variables, (2) locally-monotone ROBPs of length and width
(generalizing read-once CNFs and DNFs), and (3) constant-width ROBPs of length
having a layer of width in every consecutive
layers.Comment: 51 page
Comparing the Weighted Density Approximation with the LDA and GGA for Ground State Properties of Ferroelectric Perovskites
First-principles calculations within the weighted density approximation (WDA)
were performed for ground state properties of ferroelectric perovskites
PbTiO, BaTiO, SrTiO, KNbO and KTaO. We used the plane-wave
pseudopotential method, a pair distribution function based on the uniform
electron gas, and shell partitioning. Comparing with the local density
approximation (LDA) and the general gradient approximation (GGA), we found that
the WDA significantly improves the equilibrium volume of these materials in
cubic symmetry over both the LDA and GGA; Ferroelectric instabilities
calculated by the WDA agree with the LDA and GGA very well; At the experimental
ferroelectric lattice, optimized atom positions by the WDA are in good
agreement with measured data; However the WDA overestimates the strain of
tetragonal PbTiO at experimental volume; The WDA overestimates the volume
of fully relaxed structures, but the GGA results are even worse. Some
calculations were also done with other models for . It is found that a
with longer range behavior yields improved relaxed structures. Possible avenues
for improving the WDA are discussed.Comment: 19 pages, 3 figures, submitted to PR
Jet-like tunneling from a trapped vortex
We analyze the tunneling of vortex states from elliptically shaped traps.
Using the hydrodynamic representation of the Gross-Pitaevskii (Nonlinear
Schr\"odinger) equation, we derive analytically and demonstrate numerically a
novel type of quantum fluid flow: a jet-like singularity formed by the
interaction between the vortex and the nonhomogenous field. For strongly
elongated traps, the ellipticity overwhelms the circular rotation, resulting in
the ejection of field in narrow, well-defined directions. These jets can also
be understood as a formation of caustics since they correspond to a convergence
of trajectories starting from the top of the potential barrier and meeting at a
certain point on the exit line. They will appear in any coherent wave system
with angular momentum and non-circular symmetry, such as superfluids,
Bose-Einstein condensates, and light.Comment: 4 pages, 4 figure
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