4,265 research outputs found
Better Answers to Real Questions
We consider existential problems over the reals. Extended quantifier
elimination generalizes the concept of regular quantifier elimination by
providing in addition answers, which are descriptions of possible assignments
for the quantified variables. Implementations of extended quantifier
elimination via virtual substitution have been successfully applied to various
problems in science and engineering. So far, the answers produced by these
implementations included infinitesimal and infinite numbers, which are hard to
interpret in practice. We introduce here a post-processing procedure to
convert, for fixed parameters, all answers into standard real numbers. The
relevance of our procedure is demonstrated by application of our implementation
to various examples from the literature, where it significantly improves the
quality of the results
Neutrino-driven supernova of a low-mass iron-core progenitor boosted by three-dimensional turbulent convection
We present the first successful simulation of a neutrino-driven supernova
explosion in three dimensions (3D), using the Prometheus-Vertex code with an
axis-free Yin-Yang grid and a sophisticated treatment of three-flavor,
energy-dependent neutrino transport. The progenitor is a nonrotating,
zero-metallicity 9.6 Msun star with an iron core. While in spherical symmetry
outward shock acceleration sets in later than 300 ms after bounce, a successful
explosion starts at ~130 ms postbounce in two dimensions (2D). The 3D model
explodes at about the same time but with faster shock expansion than in 2D and
a more quickly increasing and roughly 10 percent higher explosion energy of
>10^50 erg. The more favorable explosion conditions in 3D are explained by
lower temperatures and thus reduced neutrino emission in the cooling layer
below the gain radius. This moves the gain radius inward and leads to a bigger
mass in the gain layer, whose larger recombination energy boosts the explosion
energy in 3D. These differences are caused by less coherent, less massive, and
less rapid convective downdrafts associated with postshock convection in 3D.
The less violent impact of these accretion downflows in the cooling layer
produces less shock heating and therefore diminishes energy losses by neutrino
emission. We thus have, for the first time, identified a reduced mass accretion
rate, lower infall velocities, and a smaller surface filling factor of
convective downdrafts as consequences of 3D postshock turbulence that
facilitate neutrino-driven explosions and strengthen them compared to the 2D
case.Comment: 7 pages, 5 figures; revised version with more discussion of
resolution dependence and differences to other 3D results; accepted by ApJ
Concurrence of mixed multi-partite quantum states
We propose generalizations of concurrence for multi-partite quantum systems
that can distinguish qualitatively distinct quantum correlations. All
introduced quantities can be evaluated efficiently for arbitrary mixed sates
Measures and dynamics of entangled states
We develop an original approach for the quantitative characterisation of the
entanglement properties of, possibly mixed, bi- and multipartite quantum states
of arbitrary finite dimension. Particular emphasis is given to the derivation
of reliable estimates which allow for an efficient evaluation of a specific
entanglement measure, concurrence, for further implementation in the monitoring
of the time evolution of multipartite entanglement under incoherent environment
coupling. The flexibility of the technical machinery established here is
illustrated by its implementation for different, realistic experimental
scenarios.Comment: Physics Reports, in pres
Fast time variations of supernova neutrino fluxes and their detectability
In the delayed explosion scenario of core-collapse supernovae (SNe), the
accretion phase shows pronounced convective overturns and a low-multipole
hydrodynamic instability, the standing accretion shock instability (SASI).
These effects imprint detectable fast time variations on the emerging neutrino
flux. Among existing detectors, IceCube is best suited to this task, providing
an event rate of ~1000 events per ms during the accretion phase for a fiducial
SN distance of 10 kpc, comparable to what could be achieved with a megaton
water Cherenkov detector. If the SASI activity lasts for several hundred ms, a
Fourier component with an amplitude of 1% of the average signal clearly sticks
out from the shot noise. We analyze in detail the output of axially symmetric
hydrodynamical simulations that predict much larger amplitudes up to
frequencies of a few hundred Hz. If these models are roughly representative for
realistic SNe, fast time variations of the neutrino signal are easily
detectable in IceCube or future megaton-class instruments. We also discuss the
information that could be deduced from such a measurement about the physics in
the SN core and the explosion mechanism of the SN.Comment: 14 pages, 11 figures. Final version accepted in PRD. Section on
astrophysical relevance and several references adde
Erratum: Progenitor-explosion connection and remnant birth masses for neutrino-driven supernovae of iron-core progenitors (2012, ApJ, 757, 69)
An erroneous interpretation of the hydrodynamical results led to an incorrect
determination of the fallback masses in Ugliano et al. (2012), which also (on a
smaller level) affects the neutron star masses provided in that paper. This
problem was already addressed and corrected in the follow-up works by Ertl et
al. (2015) and Sukhbold et al. (2015). Therefore, the reader is advised to use
the new data of the latter two publications. In the remaining text of this
Erratum we present the differences of the old and new fallback results in
detail and explain the origin of the mistake in the original analysis by
Ugliano et al. (2012).Comment: 3 pages, 2 figures; submitted to The Astrophysical Journa
Magneto-optical probing of weak disorder in a two-dimensional hole gas
In two-beam magneto-photoluminescence spectra of a two-dimensional valence
hole gas we identify the three-level energy spectrum of a free positive trion
with a field-induced singlet-triplet transition. The recombination spectrum of
acceptor-bound trions is also detected, including a cyclotron replica
corresponding to the hole shake-up process. The emergence of a shake-up peak at
low temperature is shown to be a sensitive probe of the presence of a small
number of impurities inside the high-mobility quantum well, and its relative
position is directly related to the hole cyclotron mass.Comment: 4 pages, 5 figure
Core-Collapse Supernovae: Reflections and Directions
Core-collapse supernovae are among the most fascinating phenomena in
astrophysics and provide a formidable challenge for theoretical investigation.
They mark the spectacular end of the lives of massive stars and, in an
explosive eruption, release as much energy as the sun produces during its whole
life. A better understanding of the astrophysical role of supernovae as birth
sites of neutron stars, black holes, and heavy chemical elements, and more
reliable predictions of the observable signals from stellar death events are
tightly linked to the solution of the long-standing puzzle how collapsing stars
achieve to explode. In this article our current knowledge of the processes that
contribute to the success of the explosion mechanism are concisely reviewed.
After a short overview of the sequence of stages of stellar core-collapse
events, the general properties of the progenitor-dependent neutrino emission
will be briefly described. Applying sophisticated neutrino transport in
axisymmetric (2D) simulations with general relativity as well as in simulations
with an approximate treatment of relativistic effects, we could find successful
neutrino-driven explosions for a growing set of progenitor stars. First results
of three-dimensional (3D) models have been obtained, and magnetohydrodynamic
simulations demonstrate that strong initial magnetic fields in the pre-collapse
core can foster the onset of neutrino-powered supernova explosions even in
nonrotating stars. These results are discussed in the context of the present
controversy about the value of 2D simulations for exploring the supernova
mechanism in realistic 3D environments, and they are interpreted against the
background of the current disagreement on the question whether the standing
accretion shock instability (SASI) or neutrino-driven convection is the crucial
agency that supports the onset of the explosion.Comment: 36 pages, 20 figures (43 eps files); submitted to Progress of
Theoretical and Experimental Physics (PTEP
- …