18,031 research outputs found
A note on the convexity number for complementary prisms
In the geodetic convexity, a set of vertices of a graph is
if all vertices belonging to any shortest path between two
vertices of lie in . The cardinality of a maximum proper convex
set of is the of . The
of a graph arises from the
disjoint union of the graph and by adding the edges of a
perfect matching between the corresponding vertices of and .
In this work, we we prove that the decision problem related to the convexity
number is NP-complete even restricted to complementary prisms, we determine
when is disconnected or is a cograph, and we
present a lower bound when .Comment: 10 pages, 2 figure
X-ray powder diffraction of high-absorption materials at the XRD1 beamline off the best conditions: Application to (Gd,Nd)5Si4 compounds
Representative compounds of the new family of magnetic materials Gd5-xNdxSi4
were analyzed by X-ray diffraction at the XRD1 beamline at LNLS. To reduce
X-ray absorption, thin layers of the powder samples were mounted outside the
capillaries and measured in Debye-Scherrer geometry as usual. The X-ray
diffraction analyses and the magnetometry results indicate that the behavior of
the magnetic transition temperature as a function of Nd content may be directly
related to the average of the four smallest interatomic distances between
different rare earth sites of the majority phase of each compound. The quality
and consistency of the results show that the XRD1 beamline is able to perform
satisfactory X-ray diffraction experiments on high-absorption materials even
off the best conditions.Comment: 12 pages, 3 figures, 3 table
Born-Infeld magnetars: larger than classical toroidal magnetic fields and implications for gravitational-wave astronomy
Magnetars are neutron stars presenting bursts and outbursts of X- and
soft-gamma rays that can be understood with the presence of very large magnetic
fields. Thus, nonlinear electrodynamics should be taken into account for a more
accurate description of such compact systems. We study that in the context of
ideal magnetohydrodynamics and make a realization of our analysis to the case
of the well-known Born-Infeld (BI) electromagnetism in order to come up with
some of its astrophysical consequences. We focus here on toroidal magnetic
fields as motivated by already known magnetars with low dipolar magnetic fields
and their expected relevance in highly magnetized stars. We show that BI
electrodynamics leads to larger toroidal magnetic fields when compared to
Maxwell's electrodynamics. Hence, one should expect higher production of
gravitational waves (GWs) and even more energetic giant flares from nonlinear
stars. Given current constraints on BI's scale field, giant flare energetics
and magnetic fields in magnetars, we also find that the maximum magnitude of
magnetar ellipticities should be . Besides, BI electrodynamics
may lead to a maximum increase of order of the GW energy radiated
from a magnetar when compared to Maxwell's, while much larger percentages may
arise for other physically motivated scenarios. Thus, nonlinear theories of the
electromagnetism might also be probed in the near future with the improvement
of GW detectors.Comment: 8 pages, no figures, accepted for publication in The European
Physical Journal C (EPJC
A grid of Synthetic Spectra for Hot DA White Dwarfs and Its Application in Stellar Population Synthesis
In this work we present a grid of LTE and non-LTE synthetic spectra of hot DA
white dwarfs (WDs). In addition to its usefulness for the determination of
fundamental stellar parameters of isolated WDs and in binaries, this grid will
be of interest for the construction of theoretical libraries for stellar
studies from integrated light. The spectral grid covers both a wide temperature
and gravity range, with 17,000 K <= T_eff <= 100,000 K and 7.0 <= log(g) <=
9.5. The stellar models are built for pure hydrogen and the spectra cover a
wavelength range from 900 A to 2.5 microns. Additionally, we derive synthetic
HST/ACS, HST/WFC3, Bessel UBVRI and SDSS magnitudes. The grid was also used to
model integrated spectral energy distributions of simple stellar populations
and our modeling suggests that DAs might be detectable in ultraviolet bands for
populations older than ~8 Gyr.Comment: to be published in The Astrophysical Journal Supplement Serie
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