7,055 research outputs found
Time-dependent density-functional theory beyond the adiabatic approximation: insights from a two-electron model system
Most applications of time-dependent density-functional theory (TDDFT) use the
adiabatic local-density approximation (ALDA) for the dynamical
exchange-correlation potential Vxc(r,t). An exact (i.e., nonadiabatic)
extension of the ground-state LDA into the dynamical regime leads to a Vxc(r,t)
with a memory, which causes the electron dynamics to become dissipative. To
illustrate and explain this nonadiabatic behavior, this paper studies the
dynamics of two interacting electrons on a two-dimensional quantum strip of
finite size, comparing TDDFT within and beyond the ALDA with numerical
solutions of the two-electron time-dependent Schroedinger equation. It is shown
explicitly how dissipation arises through multiple particle-hole excitations,
and how the nonadiabatic extension of the ALDA fails for finite systems, but
becomes correct in the thermodynamic limit.Comment: 10 pages, 7 figure
Immortal homogeneous Ricci flows
We show that for an immortal homogeneous Ricci flow solution any sequence of
parabolic blow-downs subconverges to a homogeneous expanding Ricci soliton.
This is established by constructing a new Lyapunov function based on curvature
estimates which come from real geometric invariant theory.Comment: Final version, to appear in Invent. Mat
Bayesian weak lensing tomography: Reconstructing the 3D large-scale distribution of matter with a lognormal prior
We present a Bayesian reconstruction algorithm that infers the
three-dimensional large-scale matter distribution from the weak gravitational
lensing effects measured in the image shapes of galaxies. The algorithm is
designed to also work with non-Gaussian posterior distributions which arise,
for example, from a non-Gaussian prior distribution. In this work, we use a
lognormal prior and compare the reconstruction results to a Gaussian prior in a
suite of increasingly realistic tests on mock data. We find that in cases of
high noise levels (i.e. for low source galaxy densities and/or high shape
measurement uncertainties), both normal and lognormal priors lead to
reconstructions of comparable quality, but with the lognormal reconstruction
being prone to mass-sheet degeneracy. In the low-noise regime and on small
scales, the lognormal model produces better reconstructions than the normal
model: The lognormal model 1) enforces non-negative densities, while negative
densities are present when a normal prior is employed, 2) better traces the
extremal values and the skewness of the true underlying distribution, and 3)
yields a higher pixel-wise correlation between the reconstruction and the true
density.Comment: 23 pages, 12 figures; updated to match version accepted for
publication in PR
Low temperature alteration carbonates in the ocean crust and their importance for CO2 uptake and the global Ca cycle
Hysteresis of Backflow Imprinted in Collimated Jets
We report two different types of backflow from jets by performing 2D special
relativistic hydrodynamical simulations. One is anti-parallel and
quasi-straight to the main jet (quasi-straight backflow), and the other is bent
path of the backflow (bent backflow). We find that the former appears when the
head advance speed is comparable to or higher than the local sound speed at the
hotspot while the latter appears when the head advance speed is slower than the
sound speed bat the hotspot. Bent backflow collides with the unshocked jet and
laterally squeezes the jet. At the same time, a pair of new oblique shocks are
formed at the tip of the jet and new bent fast backflows are generated via
these oblique shocks. The hysteresis of backflow collisions is thus imprinted
in the jet as a node and anti-node structure. This process also promotes
broadening of the jet cross sectional area and it also causes a decrease in the
head advance velocity. This hydrodynamic process may be tested by observations
of compact young jets.Comment: 9 pages, 5 figures, accepted for publication in ApJ
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