•The paper considers the calibration of a code from high-dimensional observations.•Extensions of the Gaussian process regression to the multivariate case are presented.•An adaptive sampling framework ...is introduced to solve the inference problem.•Two real-life applications are presented to illustrate the proposed methodology.
Simulation plays a major role in the conception, the optimization and the certification of complex systems. Of particular interest here is the calibration of the parameters of computer models from high-dimensional physical observations. When the run times of these computer codes is high, this work focuses on the numerical challenges associated with the statistical inference. In particular, several adaptations of the Gaussian Process Regression (GPR) to the high-dimensional or functional output case are presented for the emulation of computer codes from limited data. Then, an adaptive procedure is detailed to minimize the calibration parameters uncertainty at the minimal computational cost. The proposed method is eventually applied to two applications that are based on dynamic simulators.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK, ZRSKP
Due to the performance and certification criteria, complex mechanical systems have to taken into account several constraints, which can be associated with a series of performance functions. Different ...software are generally used to evaluate such functions, whose computational cost can vary a lot. In conception or reliability analysis, we thus are interested in the identification of the boundaries of the domain where all these constraints are satisfied, at the minimal total computational cost. To this end, the present work proposes an iterative method to maximize the knowledge about these limits while trying to minimize the required number of evaluations of each performance function. This method is based first on Gaussian process surrogate models that are defined on nested sub-spaces, and second, on an original selection criterion that takes into account the computational cost associated with each performance function. After presenting the theoretical basis of this approach, this paper compares its efficiency to alternative methods on an example.
•An iterative method to identify the limits of a system is proposed.•The method is based on nested Gaussian process surrogate models.•A new selection criterion that is adapted to the system case is presented.•The interest of the method is illustrated on an analytical example.
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This paper addresses the issue of guaranteeing the good functioning of physical systems using expensive simulators. More precisely, it is interested in the construction of bounds allowing to majorize ...with a specified confidence the probability of occurrence of undesired events. In this context, this paper presents two algorithms: a first one allowing to build a bound higher than this probability at a fixed number of simulator evaluations; a second one allowing to reduce as much as possible this bound by adding in an optimized way new simulator evaluations. The efficiency of these algorithms is finally illustrated through the analysis of several test functions.
•The paper considers the reliability analysis of systems modeled by costly simulators.•A method is proposed to bound the failure probability from above.•It couples order statistics, kriging, and a dedicated Poisson process.•An adaptive procedure is proposed to sequentially improve the quality of the bound.
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Context.
The Event Horizon Telescope (EHT) collaboration recently obtained the first images of the surroundings of the supermassive compact object M87* at the center of the galaxy M87. This provides ...a fascinating probe of the properties of matter and radiation in strong gravitational fields. It is important to determine from the analysis of these results what can and cannot be inferred about the nature of spacetime around M87*
Aims.
We want to develop a simple analytic disk model for the accretion flow of M87*. Compared to general-relativistic magnetohydrodynamic models, this new approach has the advantage that it is independent of the turbulent character of the flow and is controlled by only a few easy-to-interpret, physically meaningful parameters. We want to use this model to predict the image of M87*, assuming that it is either a Kerr black hole or an alternative compact object.
Methods.
We computed the synchrotron emission from the disk model and propagate the resulting light rays to the far-away observer by means of relativistic ray tracing. Such computations were performed assuming different spacetimes, such as Kerr, Minkowski, nonrotating ultracompact star, rotating boson star, or Lamy spinning wormhole. We performed numerical fits of these models to the EHT data.
Results.
We discuss the highly lensed features of Kerr images and show that they are intrinsically linked to the accretion-flow properties and not only to gravitation. This fact is illustrated by the notion of the secondary ring, which we introduce. Our model of a spinning Kerr black hole predicts mass and orientation consistent with the EHT interpretation. The non-Kerr images result in a similar quality of numerical fits and may appear very similar to Kerr images, once blurred to the EHT resolution. This implies that a strong test of the Kerr spacetime may be out of reach with the current data. We note that future developments of the EHT could alter this situation.
Conclusions.
Our results show the importance of studying alternatives to the Kerr spacetime to be able to test the Kerr paradigm unambiguously. More sophisticated treatments of non-Kerr spacetimes and more advanced observations are needed to proceed further in this direction.
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The role of simulation keeps increasing for the reliability analysis of complex systems. Most of the time, these analyses can be reduced to estimating the probability of occurrence of an undesirable ...event, also called failure probability, using a stochastic model of the system. If the considered event is rare, sophisticated sample-based procedures are generally introduced to get a relevant estimate of the failure probability. Based on the samples constructed for the evaluation of this estimate, this work considers two types of reliability-oriented sensitivity indices (ROSI). The first ones are introduced to identify the model inputs whose variability has to be reduced in priority to decrease this probability. The second ones are used to find the model inputs whose distribution has to be particularly well-characterized for the available estimate to be realistic. It is also shown how these ROSI can be derived when the true model is approximated by a surrogate model. In particular, an innovative procedure is proposed to take into account the surrogate model uncertainty in the estimation of these ROSI. The proposed approach is then applied to the reliability analysis of a series of numerical and industrial examples.
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EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OBVAL, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
Context. The first observations of the GRAVITY instrument obtained in 2016, have shown that it should become possible to probe the spacetime close to the supermassive black hole Sagittarius A* (Sgr ...A*) at the Galactic center by using accurate astrometric positions of the S2 star. Aims. The goal of this paper is to investigate the detection by GRAVITY of different relativistic effects affecting the astrometric and/or spectroscopic observations of S2 such as the transverse Doppler shift, the gravitational redshift, the pericenter advance and higher-order general relativistic (GR) effects, in particular the Lense-Thirring effect due to the angular momentum of the black hole. Methods. We implement seven stellar-orbit models to simulate both astrometric and spectroscopic observations of S2 beginning near its next pericenter passage in 2018. Each model takes into account a certain number of relativistic effects. The most accurate one is a fully GR model and is used to generate the mock observations of the star. For each of the six other models, we determine the minimal observation times above which it fails to fit the observations, showing the effects that should be detected. These threshold times are obtained for different astrometric accuracies as well as for different spectroscopic errors. Results. Transverse Doppler shift and gravitational redshift can be detected within a few months by using S2 observations obtained with pairs of accuracies (σA,σV) = (10−100 μas, 1−10 km s-1) where σA and σV are the astrometric and spectroscopic accuracies, respectively. Gravitational lensing can be detected within a few years with (σA,σV) = (10 μas, 10 km s-1). Pericenter advance should be detected within a few years with (σA,σV) = (10 μas, 1−10 km s-1). Cumulative high-order photon curvature contributions, including the Shapiro time delay, affecting spectroscopic measurements can be observed within a few months with (σA,σV) = (10 μas, 1 km s-1). By using a stellar-orbit model neglecting relativistic effects on the photon path except the major contribution of gravitational lensing, S2 observations obtained with accuracies (σA,σV) = (10 μas, 10 km s-1), and a black hole angular momentum (a,i′,Ω′) = (0.99,45°,160°), the 1σ error on the spin parameter a is of about 0.4, 0.2, and 0.1 for a total observing run of 16, 30, and 47 yr, respectively. The 1σ errors on the direction of the angular momentum reach σi′ ≈ 25° and σΩ′ ≈ 40° when considering the three orbital periods run. We found that the uncertainties obtained with a less spinning black hole (a = 0.7) are similar to those evaluated with a = 0.99. Conclusions. The combination of S2 observations obtained with the GRAVITY instrument and the spectrograph SINFONI (Spectrograph for INtegral Field Observations in the Near Infrared) also installed at the VLT (Very Large Telescope) will lead to the detection of various relativistic effects. Such detections will be possible with S2 monitorings obtained within a few months or years, depending on the effect. Strong constraints on the angular momentum of Sgr A* (e.g., at 1σ = 0.1) with the S2 star will be possible with a simple stellar-orbit model without using a ray-tracing code but with approximating the gravitational lensing effect. However, long monitorings are necessary, and we thus must rely on the discovery of closer-in stars near Sgr A* if we want to efficiently constrain the black hole parameters with stellar orbits in a short time, or monitor the flares if they orbit around the black hole.
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The star S2 orbiting the compact radio source Sgr A* is a precision probe of the gravitational field around the closest massive black hole (candidate). Over the last 2.7 decades we have monitored the ...star’s radial velocity and motion on the sky, mainly with the SINFONI and NACO adaptive optics (AO) instruments on the ESO VLT, and since 2017, with the four-telescope interferometric beam combiner instrument GRAVITY. In this Letter we report the first detection of the General Relativity (GR) Schwarzschild Precession (SP) in S2’s orbit. Owing to its highly elliptical orbit (
e
= 0.88), S2’s SP is mainly a kink between the pre-and post-pericentre directions of motion ≈±1 year around pericentre passage, relative to the corresponding
Kepler
orbit. The superb 2017−2019 astrometry of GRAVITY defines the pericentre passage and outgoing direction. The incoming direction is anchored by 118 NACO-AO measurements of S2’s position in the infrared reference frame, with an additional 75 direct measurements of the S2-Sgr A* separation during bright states (“flares”) of Sgr A*. Our 14-parameter model fits for the distance, central mass, the position and motion of the reference frame of the AO astrometry relative to the mass, the six parameters of the orbit, as well as a dimensionless parameter
f
SP
for the SP (
f
SP
= 0 for Newton and 1 for GR). From data up to the end of 2019 we robustly detect the SP of S2,
δ
ϕ
≈ 12′ per orbital period. From posterior fitting and MCMC Bayesian analysis with different weighting schemes and bootstrapping we find
f
SP
= 1.10 ± 0.19. The S2 data are fully consistent with GR. Any extended mass inside S2’s orbit cannot exceed ≈0.1% of the central mass. Any compact third mass inside the central arcsecond must be less than about 1000
M
⊙
.
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Scalar field effects on the orbit of S2 star Amorim, A; Bauböck, M; Benisty, M ...
Monthly notices of the Royal Astronomical Society,
11/2019, Volume:
489, Issue:
4
Journal Article
Peer reviewed
Open access
ABSTRACT
Precise measurements of the S-stars orbiting SgrA* have set strong constraints on the nature of the compact object at the centre of the Milky Way. The presence of a black hole in that region ...is well established, but its neighbouring environment is still an open debate. In that respect, the existence of dark matter in that central region may be detectable due to its strong signatures on the orbits of stars: the main effect is a Newtonian precession which will affect the overall pericentre shift of S2, the latter being a target measurement of the GRAVITY instrument. The exact nature of this dark matter (e.g. stellar dark remnants or diffuse dark matter) is unknown. This article assumes it to be a scalar field of toroidal distribution, associated with ultralight dark matter particles, surrounding the Kerr black hole. Such a field is a form of ‘hair’ expected in the context of superradiance, a mechanism that extracts rotational energy from the black hole. Orbital signatures for the S2 star are computed and shown to be detectable by GRAVITY. The scalar field can be constrained because the variation of orbital elements depends both on the relative mass of the scalar field to the black hole and on the field mass coupling parameter.
GYOTO, a general relativistic ray-tracing code, is presented. It aims at computing images of astronomical bodies in the vicinity of compact objects, as well as trajectories of massive bodies in ...relativistic environments. This code is capable of integrating the null and timelike geodesic equations not only in the Kerr metric, but also in any metric computed numerically within the 3+1 formalism of general relativity. Simulated images and spectra have been computed for a variety of astronomical targets, such as a moving star or a toroidal accretion structure. The underlying code is an open source and freely available. It is user-friendly, quickly handled and very modular so that extensions are easy to integrate. Custom analytical or numerical metrics and astronomical targets can be implemented in C++ plug-in extensions independent from the main code.
Vinyl triazenes were obtained by enantioselective 2+2 cycloaddition reactions of bicyclic alkenes with 1‐alkynyl triazenes in the presence of a RuII catalyst with a chiral cyclopentadienyl ligand. ...These triazenes serve as unique vinyl cation surrogates. Under acidic conditions, the triazene functionality can be replaced with a variety of groups, including halides, alkoxides, sulfoxides, amides, arenes, and heteroarenes, thus providing efficient access to a pool of chiral polycyclic compounds.
In with the new, in with the Nu: 1‐Alkynyl triazenes and bicyclic alkenes underwent enantioselective 2+2 cycloaddition catalyzed by a chiral cyclopentadienyl RuII complex to give vinyl triazenes. The triazene functionality was readily replaced with a variety of nucleophiles, including halides, alkoxides, sulfoxides, amides, arenes, and heteroarenes, thus providing efficient access to a wide range of chiral polycyclic compounds.
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