Search NASA⌕ Search

SEARCH · Search NASA

Results for “Advanced GPC”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRSDate not supplied

Experimental Testing of Advanced Generalized Predictive Control for Stability Augmentation and Vibration Reduction of Tiltrotor Aircraft

Generalized Predictive Control (GPC) is an advanced form of an adaptive control algorithm that uses experimentally acquired data to determine the input-output relationship of complex systems through a process called system identification (system ID). GPC has historically been applied to wind tunnel tests of dynamically-scaled tiltrotor aircraft for stability augmentation and vibration reduction since the complex nature of these dynamic systems does not lend itself well to traditional control theory. Advanced GPC (AGPC) improves upon traditional GPC by enabling self-adaptation as conditions change from those used to acquire the system ID and controller performance would normally erode. The present research expands upon previous analytical development and demonstration of AGPC with experimental demonstration. To support AGPC, this present work also identifies and describes figures of merit that define a good working controller and quantifies the uniqueness of the control inputs and quality of the system ID parameters. The present research demonstrates that AGPC consistently performs better than traditional GPC and can successfully adapt to changing conditions.

Active Controls↗
NASA NTRSDate not supplied

Experimental Testing of Advanced Generalized Predictive Control for Stability Augmentation and Vibration Reduction of Tiltrotor Aircraft

Generalized Predictive Control (GPC) is an advanced form of an adaptive control algorithm that uses experimentally acquired data to determine the input-output relationship of complex systems through a process called system identification (system ID). GPC has historically been applied to wind tunnel tests of dynamically-scaled tiltrotor aircraft for stability augmentation and vibration reduction since the complex nature of these dynamic systems does not lend itself well to traditional control theory. Advanced GPC (AGPC) improves upon traditional GPC by enabling self-adaptation as conditions change from those used to acquire the system ID and controller performance would normally erode. The present research expands upon previous analytical development and demonstration of AGPC with experimental demonstration. To support AGPC, this present work also identifies and describes figures of merit that define a good working controller and quantifies the uniqueness of the control inputs and quality of the system ID parameters. The present research demonstrates that AGPC consistently performs better than traditional GPC and can successfully adapt to changing conditions.

Active Controls↗
NASA NTRSDate not supplied

Generalized Predictive Control for Active Stability Augmentation and Vibration Reduction on an Aeroelastic Tiltrotor Model

Tiltrotor aircraft are defining the state-of-the-art in vertical lift technology as they have the potential to greatly expand rotary-wing operational boundaries. However, they are often limited in forward flight speed due to complex coupled rotor and wing dynamic instabilities. The U.S. Army and NASA have been developing a new wind tunnel model, the TiltRotor Aeroelastic Stability Testbed(TRAST), to test proprotors in the NASA Langley Research Center Transonic Dynamics Tunnel (TDT) to investigate aeroelastic stability in cruise. The test is intended to provide high-quality research data for analytical tool development and validation. In addition, the TRAST model will support, develop, and mature new technologies for the design of advanced proprotor aircraft. Stability augmentation and vibration reduction during testing is planned with the use of an active control methodology known as Generalized Predictive Control(GPC). GPC is an autoregressive control law that experimentally acquires a system identification to derive the input-output relation of controls and corresponding sensors. This type of control law is especially useful for complex dynamic interactions that are difficult to explicitly model such as proprotor pylon instability, often referred to as whirl flutter. GPC has been successfully employed on other tiltrotor vehicles to suppress whirl flutter instabilities and vibrations. To aid in the characterization of the wind-tunnel model and in tool development, an analytical representation of the wind-tunnel model was developed using the rotorcraft comprehensive analysis system (RCAS) that simulates structural dynamics and aerodynamics. RCAS was used to derive state-space estimates of the physical plant at various flight conditions to test control law effectiveness. This paper will present an overview of the test article development, a description of RCAS, an explanation of the GPC methodology, and results of GPC being applied to state-space plant estimates of the TRAST model. In these simulations, GPC was effective at stabilizing the aircraft beyond the whirl-flutter boundary while simultaneously reducing vibrations across the flight regime. Additionally, a modern advancement to GPC, termed advanced GPC (AGPC), is introduced that enables a self-adapting system identification. Preliminary results show that AGPC is successful at self-correction as the plant changes from what was used for system identification.

tiltrotor↗
NASA NTRS1989

Molecular weight characterization of advanced thermoplastic resins

Analytical techniques including low angle laser light scattering photometry (LALLS), differential viscometry (DV), gel permeation chromatography (GPC), GPC-LALLS and GPC-DV, were used to characterize the molecular weight and molecular weight distribution of several advanced thermoplastics. A discussion is presented of various molecular-weight-related parameters obtained by these techniques on an experimental polyimide and poly(arylene ether ketone) and a commercially available polysulfone. Where possible, these parameters are correlated with processability and selected mechanical properties. The molecular weight was found to vary during the thermal conversion of poly(amic acid) to polyimide. However, no change in composition of the polysulfone was noted in response to various processing procedures.

Young, Philip R.↗
NASA NTRS2012

A Jet Break in the X-ray Light Curve of Short GRB 111020A: Implications for Energetics and Rates

We present broadband observations of the afterglow and environment of the short GRB 111020A. An extensive X-ray light curve from Swift/XRT, XMM-Newton, and Chandra, spanning approx.100 s to 10 days after the burst, reveals a significant break at (delta)t approx. = 2 days with pre- and post-break decline rates of (alpha)X,1 approx. = -0.78 and (alpha)X,2 < or approx. 1.7, respectively. Interpreted as a jet break, we infer a collimated outflow with an opening angle of (theta)j approx. = 3deg - 8deg. The resulting beaming-corrected gamma-ray (10-1000 keV band) and blast-wave kinetic energies are (2-3) x 10(exp 48) erg and (0.3-2) x 10(exp 49) erg, respectively, with the range depending on the unknown redshift of the burst. We report a radio afterglow limit of <39 micro-Jy (3(sigma)) from Expanded Very Large Array observations that, along with our finding that v(sub c) < v(sub X), constrains the circumburst density to n(sub 0) approx.0.01 0.1/cu cm. Optical observations provide an afterglow limit of i > or approx.24.4 mag at 18 hr after the burst and reveal a potential host galaxy with i approx. = 24.3 mag. The subarcsecond localization from Chandra provides a precise offset of 0".80+/-0".11 (1(sigma))from this galaxy corresponding to an offset of 5.7 kpc for z = 0.5-1.5. We find a high excess neutral hydrogen column density of (7.5+/-2.0) x 10(exp 21)/sq cm (z = 0). Our observations demonstrate that a growing fraction of short gamma-ray bursts (GRBs) are collimated, which may lead to a true event rate of > or approx.100-1000 Gpc(sup -3)/yr, in good agreement with the NS-NS merger rate of approx. = 200-3000 Gpc(sup -3)/ yr. This consistency is promising for coincident short GRB-gravitational wave searches in the forthcoming era of Advanced LIGO/VIRGO.

Fong, W.↗
NASA NTRS2016

Binary Black Hole Mergers in the First Advanced LIGO Observing Run

The first observational run of the Advanced LIGO detectors, from September 12, 2015 to January 19, 2016, saw the first detections of gravitational waves from binary black hole mergers. In this paper we present full results from a search for binary black hole merger signals with total masses up to 100M solar mass and detailed implications from our observations of these systems. Our search, based on general-relativistic models of gravitational wave signals from binary black hole systems, unambiguously identified two signals, GW150914 and GW151226, with a significance of greater than 5 alpha over the observing period. It also identified a third possible signal, LVT151012, with substantially lower significance, which has a 87 probability of being of astrophysical origin. We provide detailed estimates of the parameters of the observed systems. Both GW150914 and GW151226 provide an unprecedented opportunity to study the two-body motion of a compact-object binary in the large velocity, highly nonlinear regime. We do not observe any deviations from general relativity, and place improved empirical bounds on several high-order post-Newtonian coefficients. From our observations we infer stellar-mass binary black hole merger rates lying in the range 9-240 Gpc-3 yr-1. These observations are beginning to inform astrophysical predictions of binary black hole formation rates, and indicate that future observing runs of the Advanced detector network will yield many more gravitational wave detections.

Abbott, B. P.↗
NASA NTRS2016

Supplement: The Rate of Binary Black Hole Mergers Inferred from Advanced LIGO Observations Surrounding GW150914

This article provides supplemental information for a Letter reporting the rate of (BBH) coalescences inferred from 16 days of coincident Advanced LIGO observations surrounding the transient (GW) signal GW150914. In that work wereported various rate estimates whose 90% confidence intervals fell in the range 2600 Gpc(exp -3) yr(exp -1). Here we givedetails on our method and computations, including information about our search pipelines, a derivation of ourlikelihood function for the analysis, a description of the astrophysical search trigger distribution expected frommerging BBHs, details on our computational methods, a description of the effects and our model for calibrationuncertainty, and an analytic method for estimating our detector sensitivity, which is calibrated to our measurements.

gravitational waves – stars: black holes↗
NASA NTRS2019

Search for Intermediate Mass Black Hole Binaries in the First and Second Observing Runs of the Advanced LIGO and VIRGO Network

Gravitational-wave astronomy has been firmly established with the detection of gravitational waves from the merger of ten stellar-mass binary black holes and a neutron star binary. This paper reports on the all-sky search for gravitational waves from intermediate mass black hole binaries in the first and second observing runs of the Advanced LIGO and Virgo network. The search uses three independent algorithms: two based on matched filtering of the data with waveform templates of gravitational-wave signals from compact binaries, and a third, model-independent algorithm that employs no signal model for the incoming signal. No intermediate mass black hole binary event is detected in this search. Consequently, we place upper limits on the merger rate density for a family of intermediate mass black hole binaries. In particular, we choose sources with total masses 𝑀=𝑚1+𝑚2∈[120,800] 𝑀⊙ and mass ratios 𝑞=𝑚2/𝑚1∈[0.1,1.0]. For the first time, this calculation is done using numerical relativity waveforms (which include higher modes) as models of the real emitted signal. We place a most stringent upper limit of 0.20 Gpc−3 yr−1 (in comoving units at the 90% confidence level) for equal-mass binaries with individual masses 𝑚1,2=100 𝑀⊙ and dimensionless spins 𝜒1,2=0.8 aligned with the orbital angular momentum of the binary. This improves by a factor of ∼5 that reported after Advanced LIGO’s first observing run.

B. P. Abbott↗
DOE OSTI2025

Physics-Based Limiter Redesign and Bit Performance Analysis at The Geysers

As part of a U.S. DOE Geothermal Technologies Office funding opportunity, Geysers Power Company, LLC (GPC), an indirect subsidiary of Calpine Corporation, partnered with Sandia National Labs, EGI at the University of Utah, and Texas A&M University to demonstrate increased drilling performance at The Geysers Geothermal Field. The performance target in the drilling demonstrations is at least a 25% improvement in rates of penetration, with increased footage on bottom for each bit coupled with increased bit life and time drilling. The project leverages advances in oil and gas drilling technologies including PDC bits, along with the physics-based limiter redesign techniques championed in drilling demonstrations conducted at the Utah FORGE geothermal site. The planned drilling demonstrations are being conducted as part of an existing drilling campaign intended to enhance reservoir utilization. The wells are typically drilled to the top of the reservoir with mud and then air-drilled to total depth (TD) through fractured zones at temperatures ≥ 450°F. A major goal of the project is to assess the effectiveness of implementing mechanical specific energy (MSE) and drilling dysfunction diagnosis and remediation in these challenging environments, as well as alternate rock reduction technologies. The first demonstration well has been completed, with 15 PDC bit runs in the 17.5”, 12.25” and 8.5” sections. Initial analysis shows ROP gains in all three sections, especially in the 17.5” and 12.25” sections, compared with conventional roller cone bit runs in the demonstration well and offset wells. However, in the 8.5” hole, wear and damage to the PDC bits resulted in relatively short bit runs. Analysis is underway to take advantage of the positive results and remediate the challenges. This paper provides updates on drilling activities conducted since the Phase 1 demonstration well at GDC-36 which was drilled from November 2023-January 2024. Additional analysis of the bit performance has been conducted. Furthermore, in subsequent wells drilled by GPC, PDC bits have been used extensively, building on the gains realized at GDC-36. GPC has continued to work with bit vendors to identify designs that last longer in the harsh, air-drilled 8.5” portions of the wells. Planning for the Phase 2 demonstration at Prati-44 is ongoing.

15 GEOTHERMAL ENERGY↗
NASA NTRS2019

Search for Subsolar Mass Ultracompact Binaries in Advanced LIGO’s Second Observing Run

We present a search for subsolar mass ultracompact objects in data obtained during Advanced LIGO’s second observing run. In contrast to a previous search of Advanced LIGO data from the first observing run, this search includes the effects of component spin on the gravitational waveform. We identify no viable gravitational-wave candidates consistent with subsolar mass ultracompact binaries with at least one component between 0.2 𝑀 ⊙ –1.0 𝑀 ⊙ . We use the null result to constrain the binary merger rate of (0.2 𝑀 ⊙ , 0.2 𝑀 ⊙ ) binaries to be less than 3.7×10 5 Gpc −3 yr −1 and the binary merger rate of (1.0 𝑀 ⊙ , 1.0 𝑀 ⊙ ) binaries to be less than 5.2×10 3 Gpc −3 yr −1 . Subsolar mass ultracompact objects are not expected to form via known stellar evolution channels, though it has been suggested that primordial density fluctuations or particle dark matter with cooling mechanisms and/or nuclear interactions could form black holes with subsolar masses. Assuming a particular primordial black hole (PBH) formation model, we constrain a population of merging 0.2 𝑀 ⊙ black holes to account for less than 16% of the dark matter density and a population of merging 1.0 𝑀 ⊙ black holes to account for less than 2% of the dark matter density. We discuss how constraints on the merger rate and dark matter fraction may be extended to arbitrary black hole population models that predict subsolar mass binaries.

B. P. Abbott↗
DOE OSTI2023

Enabling Recycling of Composites: Understanding the Impacts of Multiple Thermal Processing Cycles

When considering the utilization of recycled short carbon fiber feedstock materials for advanced manufacturing, understanding the material degradation behavior is essential in determining how many times a composite material can be effectively reprocessed and remanufactured. This study characterizes the degradation behavior of short carbon fiber acrylonitrile butadiene (CF-ABS) that has been reprocessed five times with twin screw extrusion. Parallel plate rheology was completed to observe the degradation in complex viscosity of the recycled feedstock materials. Gel permeation chromatography (GPC) was utilized to characterize the changes in molecular weight distribution of the recycled materials as a result of thermal and mechanical degradation during the re-processing steps. Rheological characterization, GPC, and twin-screw processing data help inform the process optimizations required to process the recycled feedstock material. Successful characterization of the degradation behavior of short fiber composite feedstock materials aids in increased understanding of the lifespan of high value carbon fiber composite materials and aids in process optimization of recycled composite materials.

Walker, Roo↗
NASA NTRS2019

Search for Eccentric Binary Black Hole Mergers with Advanced LIGO and Advanced Virgo during Their First and Second Observing Runs

When formed through dynamical interactions, stellar-mass binary black holes (BBHs) may retain eccentric orbits (e > 0.1 at 10 Hz) detectable by ground-based gravitational-wave detectors. Eccentricity can therefore be used to differentiate dynamically formed binaries from isolated BBH mergers. Current template-based gravitational-wave searches do not use waveform models associated with eccentric orbits, rendering the search less efficient for eccentric binary systems. Here we present the results of a search for BBH mergers that inspiral in eccentric orbits using data from the first and second observing runs (O1 and O2) of Advanced LIGO and Advanced Virgo. We carried out the search with the coherent WaveBurst algorithm, which uses minimal assumptions on the signal morphology and does not rely on binary waveform templates. We show that it is sensitive to binary mergers with a detection range that is weakly dependent on eccentricity for all bound systems. Our search did not identify any new binary merger candidates. We interpret these results in light of eccentric binary formation models. We rule out formation channels with rates ≳100 Gpc−3 yr−1 for e > 0.1, assuming a black hole mass spectrum with a power-law index ≲2.

B. P. Abbott↗
DOE OSTI2022

Valorization of bamboo biomass using combinatorial pretreatments

Current studies concerning liquid hot water pretreatment (LHWP) usually focus on cellulose saccharification or hemicellulose conversion, while the appropriate extraction and utilization of LHWP-induced lignin have not been addressed. To valorize whole biomass, here, in this study, a series of LHWP-based combinatorial pretreatments are proposed using advanced solvent systems. The first LHWP stage removed 73.74% of xylan at the optimized pretreatment severity (~4.0), at the same time preserving almost all the cellulose and lignin. As a result, 9.04 g L –1 xylo-oligosaccharides (XOSs) were obtained in the prehydrolyzate, representing 63.31% of the degraded xylan. The LHWP also caused the migration and partial degradation of the lignin which benefits the delignification in the second stage of pretreatment utilizing NaOH, deep eutectic solvent (DES) and 1,4-butanediol (BDO) under relatively mild conditions. The proposed combinatorial pretreatment significantly enhanced glucan conversion. The physiochemical structural properties of the untreated and pretreated substrates were investigated with XRD, FTIR, GPC, SEM, and Simons’ staining to understand the mechanisms of different combinatorial pretreatments for overcoming biomass recalcitrance and facilitating integrated biomass valorization. Finally, the physical and chemical properties of the regenerated lignins were analyzed. The results revealed that lignins from LHWP–NaOH pretreatment preserved most of the native β-O-4 structure (37.1%). Thus it could be used as an ideal method for the catalytic production of aromatic monomers. On the other hand, LHWP–DES pretreatment generated lignins with low molecular weight and high phenolic OH content, which is promising for synthesizing resins and antioxidants. In conclusion, the proposed combinatorial pretreatment established a reliable sequential pretreatment methodology for maximizing the output of bamboo biomass and may fit into different biorefinery configurations for various value-added products.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Advanced spectrometric methods for characterizing bio-oils to enable refineries to reduce fuel carbon intensity during co-processing

A promising approach for supplementing petroleum-derived fuels to support reductions in green-house gas emissions is to convert abundant biomass feedstocks into renewable carbon-rich oils using pyrolysis. However, the resultant bio-oils contain various oxygenated compounds that can impart acidity, chemical and thermal instability, and immiscibility with petroleum derived fuels, necessitating further upgrading to derive fuel blendstocks. Co-processing bio-oils and petroleum-derived liquids in existing refineries is a potentially near-term, cost-effective approach for upgrading bio-oils while reducing refinery carbon intensities. However, one cause for hesitation in co-processing bio-oils is limited comprehensive characterization and speciation of the bio-oil components. Advanced analytical techniques are currently under investigation to enable identification of elusive species in bio-oils, enabling researchers to develop strategies to mitigate catalyst deactivation agents and contaminants. This review provides a brief overview of several analytical methods commonly used to analyze bio-oils and their limitations. In addition, advanced techniques currently under development are discussed to further elucidate bio-oil components that may limit its end use. This will help inform the technical and economic feasibility of co-processing bio-oils with petroleum-derived liquids, therefore, improving the overall downstream processes for biofuels blendstock production.

09 BIOMASS FUELS↗
DOE OSTI2020

Synthesis and Characterization of Lignin-grafted-poly(ε-caprolactone) from Different Biomass Sources

Modification of lignin with poly(ε-caprolactone) is a promising approach to valorize industrial low-value lignins and to advance the bioeconomy. We have synthesized lignin grafted poly(ε-caprolactone) (lignin-g-PCL) copolymers via ring-opening polymerization of ε-caprolactone with different types of lignins of varying botanical sources (G-type pine lignin, S/G-type poplar lignin, and C-type Vanilla seeds lignin) and lignin extraction methods (Kraft and ethanol organosolv pulping). The lignin-g-PCL copolymer showed remarkably improved compatibility and dispersion in acetone, chloroform, and toluene in comparison to non-modified lignins. The structure and thermal properties of the lignin-g-PCL were investigated using Fourier-transform infrared spectroscopy (FTIR), 31 P nuclear magnetic resonance (NMR), 2D heteronuclear single quantum correlation (HSQC) NMR, gel permeation chromatography (GPC), and differential scanning calorimetry (DSC). Furthermore, we have found that all the technical lignins were reactive to the copolymerization reaction regardless of their plant source and isolation methods. The molecular weights of the synthesized lignin-g-PCL copolymers were positively correlated with the content of aliphatic lignin hydroxyls, suggesting that the copolymerization reaction tends to occur preferentially at the aliphatic hydroxyls rather than the phenolic hydroxyls of lignin. Thermal analyses of the lignin-g-PCL copolymers were studied, and in general, a reduction of melting temperature and crystallinity percentage in comparison to the neat PCL was observed. However, the thermal behavior of lignin-g-PCL copolymers varied depending on the lignin feedstocks employed in the copolymerization reaction.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

Structural characterization of sugarcane lignins extracted from different protic ionic liquid pretreatments

Previous studies based on protic ionic liquids have shown them to be effective for extracting lignins from biomass. Moreover, ILs synthesized with amine cations can promote the insertion of nitrogen into lignin, favoring its valorization for industrial applications. Here, lignins extracted from sugarcane bagasse by eight different PILs were analyzed. Several techniques of characterization were employed (2D HSQC NMR, 31P NMR, GPC, Py-GC/MS, TGA, FTIR, and elemental analysis), seeking a deeper understanding of lignin structure post-PILS treatment. In particular, lignin obtained with acetate and lactate anions with monoethanolamonium cations showed similar structural compositions. Lignins obtained from ethylenediamonium cation combined anions acetate and lactate exhibited relatively higher molecular weights compared to the other lignins studied. The elemental analysis of these lignins further revealed the presence of nitrogen in their structures, suggesting that amination occurred. In this work we used PILs not yet reported in the literature for this purpose, and consequently obtained lignins with specific structures. Overall, our results demonstrated that depending on the PILs used, lignins with distinct properties could be obtained which might be used for value-added applications. This work covered new advances in elucidation of lignin chemical structure and opened a new path for lignin valorization.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2020

GW190521: A Binary Black Hole Merger with a Total Mass of 150 Mꙩ

On May 21, 2019 at 03:02:29 UTC Advanced LIGO and Advanced Virgo observed a short duration gravitational-wave signal, GW190521, with a three-detector network signal-to-noise ratio of 14.7, and an estimated false-alarm rate of 1 in 4900 yr using a search sensitive to generic transients. If GW190521 is from a quasicircular binary inspiral, then the detected signal is consistent with the merger of two black holes with masses of 85 (+21,−14) Mꙩ and 66 (+17,−18) Mꙩ (90% credible intervals). We infer that the primary black hole mass lies within the gap produced by (pulsational) pair-instability supernova processes, with only a 0.32% probability of being below 65 M⊙. We calculate the mass of the remnant to be 142 (+28,−16) Mꙩ, which can be considered an intermediate mass black hole (IMBH). The luminosity distance of the source is 5.3 (+2.4,−2.6) Gpc, corresponding to a redshift of 0.82 (+0.28,−0.34) . The inferred rate of mergers similar to GW190521 is 0.13 (+0.30,−0.11) Gpc^(−3) per yr.

R. Abbott↗
DOE OSTI2020

GW190521: A Binary Black Hole Merger with a Total Mass of 150 M ⊙

On May 21, 2019 at 03:02:29 UTC Advanced LIGO and Advanced Virgo observed a short duration gravitational-wave signal, GW190521, with a three-detector network signal-to-noise ratio of 14.7, and an estimated false-alarm rate of 1 in 4900 yr using a search sensitive to generic transients. If GW190521 is from a quasicircular binary inspiral, then the detected signal is consistent with the merger of two black holes with masses of 8 5 - 14 + 21 M ⊙ and 6 6 - 18 + 17 M ⊙ (90% credible intervals). We infer that the primary black hole mass lies within the gap produced by (pulsational) pair-instability supernova processes, with only a 0.32% probability of being below 65 M ⊙ . We calculate the mass of the remnant to be 14 2 - 16 + 28 M ⊙ , which can be considered an intermediate mass black hole (IMBH). The luminosity distance of the source is 5.3 - 2.6 + 2.4 Gpc , corresponding to a redshift of 0.82 - 0.34 + 0.28 . The inferred rate of mergers similar to GW190521 is 0.13 - 0.11 + 0.30 Gpc - 3 yr - 1 .

79 ASTRONOMY AND ASTROPHYSICS↗