386 research outputs found
Enforcing Dirichlet boundary conditions in physics-informed neural networks and variational physics-informed neural networks
In this paper, we present and compare four methods to enforce Dirichlet
boundary conditions in Physics-Informed Neural Networks (PINNs) and Variational
Physics-Informed Neural Networks (VPINNs). Such conditions are usually imposed
by adding penalization terms in the loss function and properly choosing the
corresponding scaling coefficients; however, in practice, this requires an
expensive tuning phase. We show through several numerical tests that modifying
the output of the neural network to exactly match the prescribed values leads
to more efficient and accurate solvers. The best results are achieved by
exactly enforcing the Dirichlet boundary conditions by means of an approximate
distance function. We also show that variationally imposing the Dirichlet
boundary conditions via Nitsche's method leads to suboptimal solvers.Comment: 22 pages, 45 figure
Efficient computation of bifurcation diagrams with a deflated approach to reduced basis spectral element method
The majority of the most common physical phenomena can be described using partial differential equations (PDEs). However, they are very often characterized by strong nonlinearities. Such features lead to the coexistence of multiple solutions studied by the bifurcation theory. Unfortunately, in practical scenarios, one has to exploit numerical methods to compute the solutions of systems of PDEs, even if the classical techniques are usually able to compute only a single solution for any value of a parameter when more branches exist. In this work, we implemented an elaborated deflated continuation method that relies on the spectral element method (SEM) and on the reduced basis (RB) one to efficiently compute bifurcation diagrams with more parameters and more bifurcation points. The deflated continuation method can be obtained combining the classical continuation method and the deflation one: the former is used to entirely track each known branch of the diagram, while the latter is exploited to discover the new ones. Finally, when more than one parameter is considered, the efficiency of the computation is ensured by the fact that the diagrams can be computed during the online phase while, during the offline one, one only has to compute one-dimensional diagrams. In this work, after a more detailed description of the method, we will show the results that can be obtained using it to compute a bifurcation diagram associated with a problem governed by the Navier-Stokes equations
Updating the orbital ephemeris of the dipping source XB 1254-690 and the distance to the source
XB 1254-690 is a dipping low mass X-ray binary system hosting a neutron star
and showing type I X-ray bursts. We aim at obtaining more accurate orbital
ephemeris and at constraining the orbital period derivative of the system for
the first time. In addition, we want to better constrain the distance to the
source in order to locate the system in a well defined evolutive scenario. We
apply for the first time an orbital timing technique to XB 1254-690, using the
arrival times of the dips present in the light curves that have been collected
during 26 years of X-ray pointed observations performed from different space
missions. We estimate the dip arrival times using a statistical method that
weights the count-rate inside the dip with respect to the level of the
persistent emission outside the dip. We fit the obtained delays as a function
of the orbital cycles both with a linear and a quadratic function. We infer the
orbital ephemeris of XB 1254-690 improving the accuracy of the orbital period
with respect to previous estimates. We infer a mass of M
M for the donor star, in agreement with the estimations already
present in literature, assuming that the star is in thermal equilibrium while
it transfers part of its mass via the inner Lagrangian point, and assuming a
neutron star mass of 1.4 M. Using these assumptions, we also
constrain the distance to the source, finding a value of 7.6 kpc.
Finally, we discuss the evolution of the system suggesting that it is
compatible with a conservative mass transfer driven by magnetic braking.Comment: 13 pages, 5 figures, accepted for publication in Research in
Astronomy and Astrophysics (RAA
New orbital ephemerides for the dipping source 4U 1323-619: constraining the distance to the source
4U 1323-619 is a low mass X-ray binary system that shows type I X-ray bursts
and dips. The most accurate estimation of the orbital period is 2.941923(36)
hrs and a distance from the source that is lower than 11 kpc has been proposed.
We aim to obtain the orbital ephemeris, the orbital period of the system, as
well as its derivative to compare the observed luminosity with that predicted
by the theory of secular evolution. We took the advantage of about 26 years of
X-ray data and grouped the selected observations when close in time. We folded
the light curves and used the timing technique, obtaining 12 dip arrival times.
We fit the delays of the dip arrival times both with a linear and a quadratic
function. We locate 4U 1323-619 within a circular area centred at RA (J2000)=
201.6543\degree and DEC (J2000)= -62.1358\degree with an associated error of
0.0002\degree, and confirm the detection of the IR counterpart already
discussed in literature. We estimate an orbital period of P=2.9419156(6) hrs
compatible with the estimations that are present in the literature, but with an
accuracy ten times higher. We also obtain a constraint on the orbital period
derivative for the first time, estimating
s/s. Assuming that the companion star is in thermal equilibrium in the lower
main sequence, and is a neutron star of 1.4 M, we infer a mass of
0.280.03 M for the companion star. Assuming a distance of 10
kpc, we obtained a luminosity of (4.30.5) erg s,
which is not in agreement with what is predicted by the theory of secular
evolution. Using a 3D extinction map of the K radiation in our Galaxy, we
obtain a distance of 4.2 kpc at 68\% confidence level.
(Abridged)Comment: 10 pages, 8 figures, accepted for publication in Astronomy &
Astrophysic
Study of the reflection spectrum of the LMXB 4U 1702-429
The source 4U 1702-429 (Ara X-1) is a low-mass X-ray binary system hosting a
neutron star. Albeit the source is quite bright ( erg s)
its broadband spectrum has never been studied. Neither dips nor eclipses have
been observed in the light curve suggesting that its inclination angle is
smaller than 60.We analysed the broadband spectrum of 4U 1702-429 in
the 0.3-60 keV energy range, using XMM-Newton and INTEGRAL data, to constrain
its Compton reflection component if it is present. After excluding the three
time intervals in which three type-I X-ray bursts occurred, we fitted the joint
XMM-Newton and INTEGRAL spectra obtained from simultaneous observations. A
broad emission line at 6.7 keV and two absorption edges at 0.87 and 8.82 keV
were detected. We found that a self-consistent reflection model fits the 0.3-60
keV spectrum well. The broadband continuum is composed of an emission component
originating from the inner region of the accretion disc, a Comptonised direct
emission coming from a corona with an electron temperature of
keV and an optical depth , and, finally, a reflection
component. The best-fit indicates that the broad emission line and the
absorption edge at 8.82 keV, both associated with the presence of \ion{Fe}{xxv}
ions, are produced by reflection in the region above the disc with a ionisation
parameter of . We have inferred that the inner radius,
where the broad emission line originates, is km, and the inner
radius of the accretion disc is km. (Abridged)Comment: 9 pages, 9 figures, accepted for publication by A&
Testing Rate Dependent corrections on timing mode EPIC-pn spectra of the accreting Neutron Star GX 13+1
When the EPIC-pn instrument on board XMM-Newton is operated in Timing mode,
high count rates (>100 cts/s) of bright sources may affect the calibration of
the energy scale, resulting in a modification of the real spectral shape. The
corrections related to this effect are then strongly important in the study of
the spectral properties. Tests of these calibrations are more suitable in
sources which spectra are characterised by a large number of discrete features.
Therefore, in this work, we carried out a spectral analysis of the accreting
Neutron Star GX 13+1, which is a dipping source with several narrow absorption
lines and a broad emission line in its spectrum. We tested two different
correction approaches on an XMM-Newton EPIC-pn observation taken in Timing
mode: the standard Rate Dependent CTI (RDCTI or epfast) and the new, Rate
Dependent Pulse Height Amplitude (RDPHA) corrections. We found that, in
general, the two corrections marginally affect the properties of the overall
broadband continuum, while hints of differences in the broad emission line
spectral shape are seen. On the other hand, they are dramatically important for
the centroid energy of the absorption lines. In particular, the RDPHA
corrections provide a better estimate of the spectral properties of these
features than the RDCTI corrections. Indeed the discrete features observed in
the data, applying the former method, are physically more consistent with those
already found in other Chandra and XMM-Newton observations of GX 13+1.Comment: Accepted for publication in MNRAS; 10 pages, 8 figure
Global QSAR models of skin sensitisers for regulatory purposes
Abstract Background The new European Regulation on chemical safety, REACH, (Registration, Evaluation, Authorisation and Restriction of CHemical substances), is in the process of being implemented. Many chemicals used in industry require additional testing to comply with the REACH regulations. At the same time EU member states are attempting to reduce the number of animals used in experiments under the 3 Rs policy, (refining, reducing, and replacing the use of animals in laboratory procedures). Computational techniques such as QSAR have the potential to offer an alternative for generating REACH data. The FP6 project CAESAR was aimed at developing QSAR models for 5 key toxicological endpoints of which skin sensitisation was one. Results This paper reports the development of two global QSAR models using two different computational approaches, which contribute to the hybrid model freely available online. Conclusions The QSAR models for assessing skin sensitisation have been developed and tested under stringent quality criteria to fulfil the principles laid down by the OECD. The final models, accessible from CAESAR website, offer a robust and reliable method of assessing skin sensitisation for regulatory use.</p
A possible cyclotron resonance scattering feature near 0.7 keV in X1822-371
We analyse all available X-ray observations of X1822-371 made with
XMM-Newton, Chandra, Suzaku and INTEGRAL satellites. The observations were not
simultaneous. The Suzaku and INTEGRAL broad band energy coverage allows us to
constrain the spectral shape of the continuum emission well. We use the model
already proposed for this source, consisting of a Comptonised component
absorbed by interstellar matter and partially absorbed by local neutral matter,
and we added a Gaussian feature in absorption at keV. This addition
significantly improves the fit and flattens the residuals between 0.6 and 0.8
keV. We interpret the Gaussian feature in absorption as a cyclotron resonant
scattering feature (CRSF) produced close to the neutron star surface and derive
the magnetic field strength at the surface of the neutron star, G for a radius of 10 km. We derive the pulse period in the
EPIC-pn data to be 0.5928850(6) s and estimate that the spin period derivative
of X1822-371 is s/s using all available
pulse period measurements. Assuming that the intrinsic luminosity of
X1822-371is at the Eddington limit and using the values of spin period and spin
period derivative of the source, we constrain the neutron star and companion
star masses. We find the neutron star and the companion star masses to be M and M, respectively, for a
neutron star radius of 10 km.In a self-consistent scenario in which X1822-371
is spinning-up and accretes at the Eddington limit, we estimate that the
magnetic field of the neutron star is G for a
neutron star radius of 10 km. If our interpretation is correct, the Gaussian
absorption feature near 0.7 keV is the very first detection of a CRSF below 1
keV in a LMXB. (abridged)Comment: 14 pages, 12 figures, accepted for publication in A&
Signature of the presence of a third body orbiting around XB 1916-053
The ultra-compact dipping source \object{XB 1916-053} has an orbital period
of close to 50 min and a companion star with a very low mass (less than 0.1
M). The orbital period derivative of the source was estimated to be
s/s through analysing the delays associated with the
dip arrival times obtained from observations spanning 25 years, from 1978 to
2002. The known orbital period derivative is extremely large and can be
explained by invoking an extreme, non-conservative mass transfer rate that is
not easily justifiable. We extended the analysed data from 1978 to 2014, by
spanning 37 years, to verify whether a larger sample of data can be fitted with
a quadratic term or a different scenario has to be considered. We obtained 27
delays associated with the dip arrival times from data covering 37 years and
used different models to fit the time delays with respect to a constant period
model.We find that the quadratic form alone does not fit the data. The data are
well fitted using a sinusoidal term plus a quadratic function or,
alternatively, with a series of sinusoidal terms that can be associated with a
modulation of the dip arrival times due to the presence of a third body that
has an elliptical orbit. We infer that for a conservative mass transfer
scenario the modulation of the delays can be explained by invoking the presence
of a third body with mass between 0.10-0.14 M, orbital period around
the X-ray binary system of close to 51 yr and an eccentricity of . In a non-conservative mass transfer scenario we estimate that the
fraction of matter yielded by the degenerate companion star and accreted onto
the neutron star is , the neutron star mass is
M, and the companion star mass is 0.028 M. (Abridged)Comment: 13 pages, 9 figures. Accepted for publication in A&
GRO J1744-28: an intermediate B-field pulsar in a low mass X-ray binary
The bursting pulsar, GRO J1744-28, went again in outburst after 18
years of quiescence in mid-January 2014. We studied the broad-band, persistent,
X-ray spectrum using X-ray data from a XMM-Newton observation, performed almost
at the peak of the outburst, and from a close INTEGRAL observation, performed 3
days later, thus covering the 1.3-70.0 keV band. The spectrum shows a complex
continuum shape that cannot be modelled with standard high-mass X-ray pulsar
models, nor by two-components models. We observe broadband and peaked residuals
from 4 to 15 keV, and we propose a self-consistent interpretation of these
residuals, assuming they are produced by cyclotron absorption features and by a
moderately smeared, highly ionized, reflection component. We identify the
cyclotron fundamental at 4.7 keV, with hints for two possible harmonics
at 10.4 keV and 15.8 keV. The position of the cyclotron fundamental allows an
estimate for the pulsar magnetic field of (5.27 0.06) 10
G, if the feature is produced at its surface. From the dynamical and
relativistic smearing of the disk reflected component, we obtain a lower limit
estimate for the truncated accretion disk inner radius, ( 100 R),
and for the inclination angle (18-48). We also detect the
presence of a softer thermal component, that we associate with the emission
from an accretion disk truncated at a distance from the pulsar of 50-115 R.
From these estimates, we derive the magneto-spheric radius for disk accretion
to be 0.2 times the classical Alfv\'en radius for radial accretion.Comment: Accepted for publication in MNRA
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