7,860 research outputs found
Phase Field Modeling of Fracture and Stress Induced Phase Transitions
We present a continuum theory to describe elastically induced phase
transitions between coherent solid phases. In the limit of vanishing elastic
constants in one of the phases, the model can be used to describe fracture on
the basis of the late stage of the Asaro-Tiller-Grinfeld instability. Starting
from a sharp interface formulation we derive the elastic equations and the
dissipative interface kinetics. We develop a phase field model to simulate
these processes numerically; in the sharp interface limit, it reproduces the
desired equations of motion and boundary conditions. We perform large scale
simulations of fracture processes to eliminate finite-size effects and compare
the results to a recently developed sharp interface method. Details of the
numerical simulations are explained, and the generalization to multiphase
simulations is presented
XO-2b: a hot Jupiter with a variable host star that potentially affects its measured transit depth
The transiting hot Jupiter XO-2b is an ideal target for multi-object
photometry and spectroscopy as it has a relatively bright (-mag = 11.25) K0V
host star (XO-2N) and a large planet-to-star contrast ratio
(R/R). It also has a nearby (31.21") binary stellar
companion (XO-2S) of nearly the same brightness (-mag = 11.20) and spectral
type (G9V), allowing for the characterization and removal of shared systematic
errors (e.g., airmass brightness variations). We have therefore conducted a
multiyear (2012--2015) study of XO-2b with the University of Arizona's 61"
(1.55~m) Kuiper Telescope and Mont4k CCD in the Bessel U and Harris B
photometric passbands to measure its Rayleigh scattering slope to place upper
limits on the pressure-dependent radius at, e.g., 10~bar. Such measurements are
needed to constrain its derived molecular abundances from primary transit
observations. We have also been monitoring XO-2N since the 2013--2014 winter
season with Tennessee State University's Celestron-14 (0.36~m) automated
imaging telescope to investigate stellar variability, which could affect
XO-2b's transit depth. Our observations indicate that XO-2N is variable,
potentially due to {cool star} spots, {with a peak-to-peak amplitude of ~R-mag and a period of ~days for the 2013--2014
observing season and a peak-to-peak amplitude of ~R-mag and
~day period for the 2014--2015 observing season. Because of}
the likely influence of XO-2N's variability on the derivation of XO-2b's
transit depth, we cannot bin multiple nights of data to decrease our
uncertainties, preventing us from constraining its gas abundances. This study
demonstrates that long-term monitoring programs of exoplanet host stars are
crucial for understanding host star variability.Comment: published in ApJ, 9 pages, 11 figures, 3 tables; updated figures with
more ground-based monitoring, added more citations to previous work
Breaking a one-dimensional chain: fracture in 1 + 1 dimensions
The breaking rate of an atomic chain stretched at zero temperature by a
constant force can be calculated in a quasiclassical approximation by finding
the localized solutions ("bounces") of the equations of classical dynamics in
imaginary time. We show that this theory is related to the critical cracks of
stressed solids, because the world lines of the atoms in the chain form a
two-dimensional crystal, and the bounce is a crack configuration in (unstable)
mechanical equilibrium. Thus the tunneling time, Action, and breaking rate in
the limit of small forces are determined by the classical results of Griffith.
For the limit of large forces we give an exact bounce solution that describes
the quantum fracture and classical crack close to the limit of mechanical
stability. This limit can be viewed as a critical phenomenon for which we
establish a Levanyuk-Ginzburg criterion of weakness of fluctuations, and
propose a scaling argument for the critical regime. The post-tunneling dynamics
is understood by the analytic continuation of the bounce solutions to real
time.Comment: 15 pages, 5 figure
Symmetry adapted finite-cluster solver for quantum Heisenberg model in two-dimensions: a real-space renormalization approach
We present a quantum cluster solver for spin- Heisenberg model on a
two-dimensional lattice. The formalism is based on the real-space
renormalization procedure and uses the lattice point group-theoretical analysis
and nonabelian SU(2) spin symmetry technique. The exact diagonalization
procedure is used twice at each renormalization group step. The method is
applied to the spin-half antiferromagnet on a square lattice and a calculation
of local observables is demonstrated. A symmetry based truncation procedure is
suggested and verified numerically.Comment: willm appear in J. Phys.
Orbital liquid in ferromagnetic manganites: The orbital Hubbard model for electrons
We have analyzed the symmetry properties and the ground state of an orbital
Hubbard model with two orbital flavors, describing a partly filled
spin-polarized band on a cubic lattice, as in ferromagnetic manganites.
We demonstrate that the off-diagonal hopping responsible for transitions
between and orbitals, and the absence of SU(2) invariance
in orbital space, have important implications. One finds that superexchange
contributes in all orbital ordered states, the Nagaoka theorem does not apply,
and the kinetic energy is much enhanced as compared with the spin case.
Therefore, orbital ordered states are harder to stabilize in the Hartree-Fock
approximation (HFA), and the onset of a uniform ferro-orbital polarization and
antiferro-orbital instability are similar to each other, unlike in spin case.
Next we formulate a cubic (gauge) invariant slave boson approach using the
orbitals with complex coefficients. In the mean-field approximation it leads to
the renormalization of the kinetic energy, and provides a reliable estimate for
the ground state energy of the disordered state. Using this approach one finds
that the HFA fails qualitatively in the regime of large Coulomb repulsion
-- the orbital order is unstable, and instead a strongly
correlated orbital liquid with disordered orbitals is realized at any electron
filling.Comment: 25 pages, 9 figure
One-dimensional orbital fluctuations and the exotic magnetic properties of YVO
Starting from the Mott insulator picture for cubic vanadates, we derive and
investigate the model of superexchange interactions between V ions, with
nearly degenerate orbitals occupied by two electrons each. The
superexchange interactions are strongly frustrated and demonstrate a strong
interrelation between possible types of magnetic and orbital order. We
elucidate the prominent role played by fluctuations of and orbitals
which generate ferromagnetic superexchange interactions even in the absence of
Hund's exchange. In this limit we find orbital valence bond state which is
replaced either by -type antiferromagnetic order with weak -type orbital
order at increasing Hund's exchange, or instead by -type antiferromagnetic
order when the lattice distortions stabilize -type orbital order. Both
phases are observed in YVO and we argue that a dimerized -type
antiferromagnetic phase with stronger and weaker FM bonds alternating along the
c axis may be stabilized by large spin-orbital entropy at finite temperature.
This suggests a scenario which explains the origin of the exotic -AF order
observed in YVO in the regime of intermediate temperatures and allows one
to specify the necessary ingredients of a more complete future theory.Comment: 23 pages, 15 figure
Immersed boundary-finite element model of fluid-structure interaction in the aortic root
It has long been recognized that aortic root elasticity helps to ensure
efficient aortic valve closure, but our understanding of the functional
importance of the elasticity and geometry of the aortic root continues to
evolve as increasingly detailed in vivo imaging data become available. Herein,
we describe fluid-structure interaction models of the aortic root, including
the aortic valve leaflets, the sinuses of Valsalva, the aortic annulus, and the
sinotubular junction, that employ a version of Peskin's immersed boundary (IB)
method with a finite element (FE) description of the structural elasticity. We
develop both an idealized model of the root with three-fold symmetry of the
aortic sinuses and valve leaflets, and a more realistic model that accounts for
the differences in the sizes of the left, right, and noncoronary sinuses and
corresponding valve cusps. As in earlier work, we use fiber-based models of the
valve leaflets, but this study extends earlier IB models of the aortic root by
employing incompressible hyperelastic models of the mechanics of the sinuses
and ascending aorta using a constitutive law fit to experimental data from
human aortic root tissue. In vivo pressure loading is accounted for by a
backwards displacement method that determines the unloaded configurations of
the root models. Our models yield realistic cardiac output at physiological
pressures, with low transvalvular pressure differences during forward flow,
minimal regurgitation during valve closure, and realistic pressure loads when
the valve is closed during diastole. Further, results from high-resolution
computations demonstrate that IB models of the aortic valve are able to produce
essentially grid-converged dynamics at practical grid spacings for the
high-Reynolds number flows of the aortic root
Theory of NMR chemical shift in an electronic state with arbitrary degeneracy
We present a theory of nuclear magnetic resonance (NMR) shielding tensors for
electronic states with arbitrary degeneracy. The shieldings are here expressed
in terms of generalized Zeeman () and hyperfine () tensors,
of all ranks allowed by the size of degeneracy. Contrary to recent
proposals [T. O. Pennanen and J. Vaara, Phys. Rev. Lett. 100, 133002 (2008)],
our theory is valid in the strong spin-orbit coupling limit. Ab initio
calculations for the 4-fold degenerate ground state of
lanthanide-doped fluorite crystals CaF:Ln (Ln = Pr, Nd,
Sm, and Dy) show that previously neglected contributions can
account for more than 50% of the paramagnetic shift.Comment: Supporting information included; 5 pages; new figure adde
Optical response of ferromagnetic YTiO_3 studied by spectral ellipsometry
We have studied the temperature dependence of spectroscopic ellipsometry
spectra of an electrically insulating, nearly stoichiometric YTiO_3 single
crystal with ferromagnetic Curie temperature T_C = 30 K. The optical response
exhibits a weak but noticeable anisotropy. Using a classical dispersion
analysis, we identify three low-energy optical bands at 2.0, 2.9, and 3.7 eV.
Although the optical conductivity spectra are only weakly temperature dependent
below 300 K, we are able to distinguish high- and low-temperature regimes with
a distinct crossover point around 100 K. The low-temperature regime in the
optical response coincides with the temperature range in which significant
deviations from Curie-Weiss mean field behavior are observed in the
magnetization. Using an analysis based on a simple superexchange model, the
spectral weight rearrangement can be attributed to intersite d_i^1d_j^1
\longrightarrow d_i^2d_j^0 optical transitions. In particular, Kramers-Kronig
consistent changes in optical spectra around 2.9 eV can be associated with the
high-spin-state (^3T_1) optical transition. This indicates that other
mechanisms, such as weakly dipole-allowed p-d transitions and/or
exciton-polaron excitations, can contribute significantly to the optical band
at 2 eV. The recorded optical spectral weight gain of 2.9 eV optical band is
significantly suppressed and anisotropic, which we associate with complex
spin-orbit-lattice phenomena near ferromagnetic ordering temperature in YTiO_3
Amplitude equations for systems with long-range interactions
We derive amplitude equations for interface dynamics in pattern forming
systems with long-range interactions. The basic condition for the applicability
of the method developed here is that the bulk equations are linear and solvable
by integral transforms. We arrive at the interface equation via long-wave
asymptotics. As an example, we treat the Grinfeld instability, and we also give
a result for the Saffman-Taylor instability. It turns out that the long-range
interaction survives the long-wave limit and shows up in the final equation as
a nonlocal and nonlinear term, a feature that to our knowledge is not shared by
any other known long-wave equation. The form of this particular equation will
then allow us to draw conclusions regarding the universal dynamics of systems
in which nonlocal effects persist at the level of the amplitude description.Comment: LaTeX source, 12 pages, 4 figures, accepted for Physical Review
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