23,153 research outputs found
Optimal 3D Angular Resolution for Low-Degree Graphs
We show that every graph of maximum degree three can be drawn in three
dimensions with at most two bends per edge, and with 120-degree angles between
any two edge segments meeting at a vertex or a bend. We show that every graph
of maximum degree four can be drawn in three dimensions with at most three
bends per edge, and with 109.5-degree angles, i.e., the angular resolution of
the diamond lattice, between any two edge segments meeting at a vertex or bend.Comment: 18 pages, 10 figures. Extended version of paper to appear in Proc.
18th Int. Symp. Graph Drawing, Konstanz, Germany, 201
Achieving Good Angular Resolution in 3D Arc Diagrams
We study a three-dimensional analogue to the well-known graph visualization
approach known as arc diagrams. We provide several algorithms that achieve good
angular resolution for 3D arc diagrams, even for cases when the arcs must
project to a given 2D straight-line drawing of the input graph. Our methods
make use of various graph coloring algorithms, including an algorithm for a new
coloring problem, which we call localized edge coloring.Comment: 12 pages, 5 figures; to appear at the 21st International Symposium on
Graph Drawing (GD 2013
A Coloring Algorithm for Disambiguating Graph and Map Drawings
Drawings of non-planar graphs always result in edge crossings. When there are
many edges crossing at small angles, it is often difficult to follow these
edges, because of the multiple visual paths resulted from the crossings that
slow down eye movements. In this paper we propose an algorithm that
disambiguates the edges with automatic selection of distinctive colors. Our
proposed algorithm computes a near optimal color assignment of a dual collision
graph, using a novel branch-and-bound procedure applied to a space
decomposition of the color gamut. We give examples demonstrating the
effectiveness of this approach in clarifying drawings of real world graphs and
maps
Measuring the Angular Momentum Distribution in Core-Collapse Supernova Progenitors with Gravitational Waves
The late collapse, core bounce, and the early postbounce phase of rotating
core collapse leads to a characteristic gravitational wave (GW) signal. The
precise shape of the signal is governed by the interplay of gravity, rotation,
nuclear equation of state (EOS), and electron capture during collapse. We
explore the dependence of the signal on total angular momentum and its
distribution in the progenitor core by means of a large set of axisymmetric
general-relativistic core collapse simulations in which we vary the initial
angular momentum distribution in the core. Our simulations include a
microphysical finite-temperature EOS, an approximate electron capture treatment
during collapse, and a neutrino leakage scheme for the postbounce evolution. We
find that the precise distribution of angular momentum is relevant only for
very rapidly rotating cores with T/|W|>~8% at bounce. We construct a numerical
template bank from our baseline set of simulations, and carry out additional
simulations to generate trial waveforms for injection into simulated advanced
LIGO noise at a fiducial galactic distance of 10 kpc. Using matched filtering,
we show that for an optimally-oriented source and Gaussian noise, advanced
Advanced LIGO could measure the total angular momentum to within ~20%, for
rapidly rotating cores. For most waveforms, the nearest known degree of
precollapse differential rotation is correctly inferred by both our matched
filtering analysis and an alternative Bayesian model selection approach. We
test our results for robustness against systematic uncertainties by injecting
waveforms from simulations using a different EOS and and variations in the
electron fraction in the inner core. The results of these tests show that these
uncertainties significantly reduce the accuracy with which the total angular
momentum and its precollapse distribution can be inferred from observations.Comment: 22 pages, 16 figure
Correlated Gravitational Wave and Neutrino Signals from General-Relativistic Rapidly Rotating Iron Core Collapse
We present results from a new set of 3D general-relativistic hydrodynamic
simulations of rotating iron core collapse. We assume octant symmetry and focus
on axisymmetric collapse, bounce, the early postbounce evolution, and the
associated gravitational wave (GW) and neutrino signals. We employ a
finite-temperature nuclear equation of state, parameterized electron capture in
the collapse phase, and a multi-species neutrino leakage scheme after bounce.
The latter captures the important effects of deleptonization, neutrino cooling
and heating and enables approximate predictions for the neutrino luminosities
in the early evolution after core bounce. We consider 12-solar-mass and
40-solar-mass presupernova models and systematically study the effects of (i)
rotation, (ii) progenitor structure, and (iii) postbounce neutrino leakage on
dynamics, GW, and, neutrino signals. We demonstrate, that the GW signal of
rapidly rotating core collapse is practically independent of progenitor mass
and precollapse structure. Moreover, we show that the effects of neutrino
leakage on the GW signal are strong only in nonrotating or slowly rotating
models in which GW emission is not dominated by inner core dynamics. In rapidly
rotating cores, core bounce of the centrifugally-deformed inner core excites
the fundamental quadrupole pulsation mode of the nascent protoneutron star. The
ensuing global oscillations (f~700-800 Hz) lead to pronounced oscillations in
the GW signal and correlated strong variations in the rising luminosities of
antineutrino and heavy-lepton neutrinos. We find these features in cores that
collapse to protoneutron stars with spin periods <~ 2.5 ms and rotational
energies sufficient to drive hyper-energetic core-collapse supernova
explosions. Hence, joint GW + neutrino observations of a core collapse event
could deliver strong evidence for or against rapid core rotation. [abridged]Comment: 29 pages, 14 figures. Replaced with version matching published
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