221 research outputs found
Models of Saturn's Interior Constructed with Accelerated Concentric Maclaurin Spheroid Method
The Cassini spacecraft's Grand Finale orbits provided a unique opportunity to
probe Saturn's gravity field and interior structure. Doppler measurements
yielded unexpectedly large values for the gravity harmonics J_6, J_8, and J_10
that cannot be matched with planetary interior models that assume uniform
rotation. Instead we present a suite of models that assume the planet's
interior rotates on cylinders, which allows us to match all the observed even
gravity harmonics. For every interior model, the gravity field is calculated
self-consistently with high precision using the Concentric Maclaurin Spheroid
(CMS) method. We present an acceleration technique for this method, which
drastically reduces the computational cost, allows us to efficiently optimize
model parameters, map out allowed parameter regions with Monte Carlo sampling,
and increases the precision of the calculated J_2n gravity harmonics to match
the error bars of the observations, which would be difficult without
acceleration. Based on our models, Saturn is predicted to have a dense central
core of 15-18 Earth masses and an additional 1.5-5 Earth masses of heavy
elements in the envelope. Finally, we vary the rotation period in the planet's
deep interior and determine the resulting oblateness, which we compare with the
value from radio occultation measurements by the Voyager spacecraft. We predict
a rotation period of 10:33:34 h +- 55s, which is in agreement with recent
estimates derived from ring seismology.Comment: 12 color figures, 5 tables, Astrophysical Journal, in press (2019
New Phases of Water Ice Predicted at Megabar Pressures
Based on density functional calculations we predict water ice to attain two
new crystal structures with Pbca and Cmcm symmetry at 7.6 and 15.5 Mbar,
respectively. The known high pressure ice phases VII, VIII, X, and Pbcm as well
as the Pbca phase are all insulating and composed of two interpenetrating
hydrogen bonded networks, but the Cmcm structure is metallic and consists of
corrugated sheets of H and O atoms. The H atoms are squeezed into octahedral
positions between next-nearest O atoms while they occupy tetrahedral positions
between nearest O atoms in the ice X, Pbcm, and Pbca phases.Comment: submitted to Physical Review Letters on Jan 25, 201
Path Integral Monte Carlo Simulation of the Low-Density Hydrogen Plasma
Restricted path integral Monte Carlo simulations are used to calculate the
equilibrium properties of hydrogen in the density and temperature range of
and . We test the accuracy of the pair density matrix and
analyze the dependence on the system size, on the time step of the path
integral and on the type of nodal surface. We calculate the equation of state
and compare with other models for hydrogen valid in this regime. Further, we
characterize the state of hydrogen and describe the changes from a plasma to an
atomic and molecular liquid by analyzing the pair correlation functions and
estimating the number of atoms and molecules present.Comment: 12 pages, 21 figures, submitted for Phys. Rev.
An Adaptive, Kink-Based Approach to Path Integral Calculations
A kink-based expression for the canonical partition function is developed
using Feynman's path integral formulation of quantum mechanics and a discrete
basis set. The approach is exact for a complete set of states. The method is
tested on the 3x3 Hubbard model and overcomes the sign problem seen in
traditional path integral studies of fermion systems. Kinks correspond to
transitions between different N-electron states, much in the same manner as
occurs in configuration interaction calculations in standard ab initio methods.
The different N-electron states are updated, based on which states occur
frequently during a Monte Carlo simulation, giving better estimates of the true
eigenstates of the Hamiltonian.Comment: 24 pages, to be published in J. Chem. Phy
Variational Density Matrix Method for Warm Condensed Matter and Application to Dense Hydrogen
A new variational principle for optimizing thermal density matrices is
introduced. As a first application, the variational many body density matrix is
written as a determinant of one body density matrices, which are approximated
by Gaussians with the mean, width and amplitude as variational parameters. The
method is illustrated for the particle in an external field problem, the
hydrogen molecule and dense hydrogen where the molecular, the dissociated and
the plasma regime are described. Structural and thermodynamic properties
(energy, equation of state and shock Hugoniot) are presented.Comment: 26 pages, 13 figures. submitted to Phys. Rev. E, October 199
All-Electron Path Integral Monte Carlo Simulations of Warm Dense Matter: Application to Water and Carbon Plasmas
We develop an all-electron path integral Monte Carlo (PIMC) method with
free-particle nodes for warm dense matter and apply it to water and carbon
plasmas. We thereby extend PIMC studies beyond hydrogen and helium to elements
with core electrons. PIMC pressures, internal energies, and pair-correlation
functions compare well with density functional theory molecular dynamics
(DFT-MD) at temperatures of (2.5-7.5) K and both methods together
form a coherent equation of state (EOS) over a density-temperature range of
3--12 g/cm and 10--10 K
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