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Long range geoid control through the European GPS traverse: Final results

The European north-south Global Positioning System (GPS)-traverse proposed by IAG SSG 3.88, should control and improve the European geoid. This traverse follows first order leveling lines, included in the United European Leveling Network. From May to August 1986 and in July 1987, the central and northern part of this traverse (approx. 3000 km) was observed using up to four TI 4100 receivers, covering Austria, Federal Republic of Germany, Denmark, Sweden and Norway. Both traverse parts contain 71 stations with distances of about 50 km. In addition, 8 stations have been occupied for overlapping connections, and traverse links were established for connecting the fundamental stations Wettzell (VLBI and SLR) and Onsala (VLBI). Final results show a GPS observation precision of a few cm for loops of some 100 km circumference. After transformation of the GPS results to geoid heights using the leveled heights, comparisons with different existing gravimetric geoid determinations including geopotential models were performed. In addition, new geopotential models complete to degree and order 360 tailored to gravity data in Europe, and gravimetric geoid solutions using 6 x 10' mean gravity anomalies were investigated. The comparison with GPS and leveling yields rms discrepancies of + or - 0.1...0.2 m over 1000 km traverse sections for the best solutions, but a strong slope is existing in Sweden and southern Norway in almost all solutions, which is probably caused by systematic errors in the available gravity data for Scandinavia. This is confirmed by a new geoid computation at the Danish Geodetic Institute where the slope has disappeared. If this new solution is taken for the northern traverse section and the best solution for the central part, the rms discrepancy reduces to approximately + or - 0.2 m over 3000 km. Thus, a + or - 10 (exp 7) relative height accuracy seems to be achievable over long distances with the GPS/leveling and the gravimetric geoid calculation techniques, applied in this experiment.

Torge, W.↗

Liquid Crystal Films as Active Substrates for Nanoparticle Control

Organizing nanoparticles in a controlled way allows us to monitor their optical properties. It is particularly interesting to organize them on top of liquid crystal films to take advantage, in a second step, of the easy actuation of liquid crystals with external parameters such as temperature, electric fields, and so forth. We show that despite their fluidity, nematic and smectic films allow the formation of well-ordered hexagonal domains of gold spherical nanoparticles (AuNPs) at their surface, but we also show that both nematic films and AuNP domains impact each other. Using optical microscopy, atomic force microscopy (AFM), scanning electron microscopy (SEM), and spectrophotometry, we compare nematic, polymer-stabilized nematic, and smectic films with AuNP domains made of NPs of diameter 6 nm. On the liquid crystal films, depressions are revealed below the AuNP domains, whereas the AuNP domains appear well-organized but with a hexagonal period shortened with respect to AuNP monolayers formed on hard substrates. We interpret these features by the anchoring tilt imposed by the AuNP domains on the liquid crystal molecules. The smectic-A layers characteristic of the nematic surface transform into smecticC layers, which induce the formation of depression. Here, the energy penalty associated with the local smectic-A/smectic-C transition induces the shortening of the AuNP domain period in order to decrease the AuNP domain surface. The observed large depth of the polymer-stabilized nematic depressions below AuNP domains may be explained either by an increased size of the polymer-stabilized smectic layers close to the surface or by an increased number of polymer-stabilized smectic liquid crystal smectic layers close to the surface with respect to pure nematic films.

36 MATERIALS SCIENCE↗

SIM Configuration Evolution

The Space Interferometry Mission (SIM) is a space-based 10 m baseline Michelson interferometer. Planned for launch in 2005 aboard a Delta III launch vehicle, or equivalent, its primary objective is to measure the positions of stars and other celestial objects with an unprecedented accuracy of 4 micro arc seconds. With such an instrument, tremendous advancement can be expected in our understanding of stellar and galactic dynamics. Using triangulation from opposite sides of the orbit around the sun (i.e. by using parallax) one can measure the distance to any observable object in our galaxy. By directly measuring the orbital wobble of nearby stars, the mass and orbit of planets can be determined over a wide range of parameters. The distribution of velocity within nearby galaxies will be measurable. Observations of these and other objects will improve the calibration of distance estimators by more than an order of magnitude. This will permit a much better determination of the Hubble Constant as well as improving our overall understanding of the evolution of the universe. SIM has undergone several transformations, especially over the past year and a half since the start of Phase A. During this phase of a project, it is desirable to perform system-level trade studies, so the substantial evolution of the design that has occurred is quite appropriate. Part of the trade-off process has addressed two major underlying architectures: SIM Classic; and Son of SIM. The difference between these two architectures is related to the overall arrangement of the optical elements and the associated metrology system. Several different configurations have been developed for each architecture. Each configuration is the result of design choices that are influenced by many competing considerations. Some of the more important aspects will be discussed. The Space Interferometry Mission has some extremely challenging goals: millikelvin thermal stability, nanometer stabilization of optics, picometer measurement of wavefront, and others. In order to meet these goals, a significant amount of technological development is required. Although there has been a program operating for about a decade developing technologies specifically to address the challenges of space-based interferometry, there still remains a tremendous effort to achieve the incredible accuracy required of SIM. The projected viability of some of these areas has influenced design choices during the evolution of the many configurations that have been developed. For instance, the perceived complexity of the IR laser metrology system used to measure and control the positions of key optical elements was the strongest discriminator between the two architectures, and led to a decision to select SOS rather than Classic in early 1998. More recently, an appreciation of the sensitivity to beam-walk within the SOS architecture is forcing a reconsideration of that decision. At the time of submission of this abstract, there is some hope that a full-aperture metrology system may alleviate this issue. In addition to describing the current configuration of SIM, the influence of a few selected areas on the evolution of the configuration will be discussed.

Aaron, Kim M.↗

Evidence of distinct nonpolar/polar ordering at long/short ranges in relaxor ferroelectrics

Distinct atomic nonpolar/polar ordering is determined at long, intermediate, and short ranges using synchrotron x-ray diffraction, Raman scattering, and pair distribution function data in K 0.5 Na 0.5 NbO 3 -doped BaTiO 3 -based relaxor ferroelectrics, viz., (1 - x) Ba 0.9 Sr 0.1 TiO 3 -x KNN 50. Two different polar phases with distinct symmetries are identified at short/intermediate ranges for x = 0.10, where a monoclinic phase at short ranges gradually transforms into a rhombohedral phase at intermediate ranges. Here, in contrast, a nonpolar phase with average cubic symmetry is found to be stable at long ranges for a wide temperature range (100 ≤ T ≤ 500 K). The polar behavior of short/intermediate-range ordering is quantified in terms of the amplitude of ferroelectric phonon mode $Γ^-_4$ (q = 0, 0, 0) (which corresponds to the zone center of the cubic Brillouin zone). The amplitude of the $Γ^-_4$ phonon mode increases with decreasing temperature, suggesting the enhancement of ferroelectric polarization at short/intermediate ranges on lowering temperatures. Enhanced ferroelectric polarization at low temperature is also visible and evident by ferroelectrostriction and is quantified by the increase in magnitude of spontaneous volume ferroelectrostriction. Consequently, Zero thermal expansion is observed at low temperatures.

36 MATERIALS SCIENCE↗

Uncertainty-aware molecular dynamics from Bayesian active learning for phase transformations and thermal transport in SiC

Abstract Machine learning interatomic force fields are promising for combining high computational efficiency and accuracy in modeling quantum interactions and simulating atomistic dynamics. Active learning methods have been recently developed to train force fields efficiently and automatically. Among them, Bayesian active learning utilizes principled uncertainty quantification to make data acquisition decisions. In this work, we present a general Bayesian active learning workflow, where the force field is constructed from a sparse Gaussian process regression model based on atomic cluster expansion descriptors. To circumvent the high computational cost of the sparse Gaussian process uncertainty calculation, we formulate a high-performance approximate mapping of the uncertainty and demonstrate a speedup of several orders of magnitude. We demonstrate the autonomous active learning workflow by training a Bayesian force field model for silicon carbide (SiC) polymorphs in only a few days of computer time and show that pressure-induced phase transformations are accurately captured. The resulting model exhibits close agreement with both ab initio calculations and experimental measurements, and outperforms existing empirical models on vibrational and thermal properties. The active learning workflow readily generalizes to a wide range of material systems and accelerates their computational understanding.

36 MATERIALS SCIENCE↗

Probing the meta-stability of oxide core/shell nanoparticle systems at atomic resolution

Hybrid nanoparticles allow exploiting the interplay of confinement, proximity between different materials and interfacial effects. However, to harness their properties an in-depth understanding of their (meta)stability and interfacial characteristics is crucial. This is especially the case of nanosystems based on functional oxides working under reducing conditions, which may severely impact their properties. Here, the in-situ electron-induced selective reduction of Mn 3 O 4 to MnO is studied in magnetic Fe 3 O 4 /Mn 3 O 4 and Mn 3 O 4 /Fe 3 O 4 core/shell nanoparticles by means of high-resolution scanning transmission electron microscopy combined with electron energy-loss spectroscopy. Such in-situ transformation allows mimicking the actual processes in operando environments. A multi-stage image analysis using geometric phase analysis combined with particle image velocity enables direct monitoring of the relationship between structure, chemical composition and strain relaxation during the Mn 3 O 4 reduction. In the case of Fe 3 O 4 /Mn 3 O 4 core/shell the transformation occurs smoothly without the formation of defects. However, for the inverse Mn 3 O 4 /Fe 3 O 4 core/shell configuration the electron beam-induced transformation occurs in different stages that include redox reactions and void formation followed by strain field relaxation via formation of defects. This study highlights the relevance of understanding the local dynamics responsible for changes in the particle composition in order to control stability and, ultimately, macroscopic functionality.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Testing First-Order Logic Axioms in AutoCert

AutoCert [2] is a formal verification tool for machine generated code in safety critical domains, such as aerospace control code generated from MathWorks Real-Time Workshop. AutoCert uses Automated Theorem Provers (ATPs) [5] based on First-Order Logic (FOL) to formally verify safety and functional correctness properties of the code. These ATPs try to build proofs based on user provided domain-specific axioms, which can be arbitrary First-Order Formulas (FOFs). These axioms are the most crucial part of the trusted base, since proofs can be submitted to a proof checker removing the need to trust the prover and AutoCert itself plays the part of checking the code generator. However, formulating axioms correctly (i.e. precisely as the user had really intended) is non-trivial in practice. The challenge of axiomatization arise from several dimensions. First, the domain knowledge has its own complexity. AutoCert has been used to verify mathematical requirements on navigation software that carries out various geometric coordinate transformations involving matrices and quaternions. Axiomatic theories for such constructs are complex enough that mistakes are not uncommon. Second, adjusting axioms for ATPs can add even more complexity. The axioms frequently need to be modified in order to have them in a form suitable for use with ATPs. Such modifications tend to obscure the axioms further. Thirdly, speculating validity of the axioms from the output of existing ATPs is very hard since theorem provers typically do not give any examples or counterexamples.

Ahn, Ki Yung↗

Gravitational soft theorem from emergent soft gauge symmetries

We consider and derive the gravitational soft theorem up to the sub-subleading power from the perspective of effective Lagrangians. The emergent soft gauge symmetries of the effective Lagrangian provide a transparent explanation of why soft graviton emission is universal to sub-subleading power, but gauge boson emission is not. They also suggest a physical interpretation of the form of the soft factors in terms of the charges related to the soft transformations and the kinematics of the multipole expansion. The derivation is done directly at Lagrangian level, resulting in an operatorial form of the soft theorems. In order to highlight the differences and similarities of the gauge-theory and gravitational soft theorems, we include an extensive discussion of soft gauge-boson emission from scalar, fermionic and vector matter at subleading power.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

He bubble-induced phase transformation of W grain boundaries revealed by accelerated molecular dynamics

The growth of He bubbles and the resulting impact on the microstructural evolution of W are of paramount importance to the plasma-facing materials community due to the application of W in Tokamak fusion reactors. Using accelerated molecular dynamics (AMD) techniques, we outline the structural evolution of grain boundaries (GBs) caused by growing He bubbles. It is discovered that when an alternative, low energy, high density GB structure or phase is available, He bubbles can induce a progressive phase transformation of the GB to the higher density phase by the continual nucleation of W Frenkel pairs. Here, we find that the resulting W self-interstitials migrate to sites at the GB which are structurally related to the higher density phase, leading to the transformation. We discuss the implications of this progressive microstructural evolution on the growing He bubble and consider in general how He bubbles will impact the structural evolution of an arbitrary W GB. These findings of GB phase transformation are predicted to impact other damage events in W such as recrystallization, GB migration and defect segregation which must take these findings into account in order to accurately simulate a realistic W microstructure and hence extract experimentally meaningful data.

36 MATERIALS SCIENCE↗

Kinetics of amorphous defect phases measured through ultrafast nanocalorimetry

Recognition of the role of extended defects on local phase transitions has led to the conceptualization of the defect phase, localized thermodynamically stable interfacial states that have since been applied in a myriad of material systems to realize significant enhancements in material properties. Here, we explore the kinetics of grain boundary confined amorphous defect phases, utilizing the high temperature and scanning rates afforded by ultrafast differential scanning calorimetry to apply targeted annealing/quenching treatments at high rates capable of capturing the kinetic behavior. Four Al-based nanocrystalline alloys, including two binary systems, Al–Ni and Al–Y, and two ternary systems, Al–Mg–Y and Al–Ni–Y, are selected to probe the materials design space (enthalpy of mixing, enthalpy of segregation, chemical complexity) for amorphous defect phase formation and stability, with correlative transmission electron microscopy applied to link phase evolution and grain stability to nanocalorimetry signatures. A series of targeted isothermal annealing heat treatments is utilized to construct a Time–Temperature-Transformation curve for the Al–Ni system, from which a critical cooling rate of 2400 °C/s was determined for the grain boundary confined disordered-to-ordered transition. Finally, a thermal profile consisting of 1000 repeated annealing sequences was created to quantify the recovery of the amorphous defect phase following sequential annealing treatments, with results indicating remarkable microstructural stability after annealing at temperatures above 90% of the melting temperature. This work contributes to a deeper understanding of grain boundary localized thermodynamics and kinetics, with potential implications for the design and optimization of advanced materials with enhanced stability and performance.

Amorphous defect phases↗

RandONets: Shallow networks with random projections for learning linear and nonlinear operators

Deep neural networks have been extensively used for the solution of both the forward and the inverse problem for dynamical systems. However, their implementation necessitates optimizing a high-dimensional space of parameters and hyperparameters. This fact, along with the requirement of substantial computational resources, pose a barrier to achieving high numerical accuracy, but also interpretability. Here, to address the above challenges, we present Random Projection-based Operator Networks (RandONets): shallow networks with random projections and tailor-made numerical analysis methods that learn accurately and fast linear and nonlinear operators. Building on previous works, we prove that RandOnets are universal approximators of linear and nonlinear operators. Due to their simplicity, RandONets provide a one-step transformation of the input space, facilitating interpretability. For the evaluation of their performance, we focus on operators of PDEs. We show, that RandONets outperform by several orders of magnitude, both in terms of numerical approximation accuracy and computational cost, the “vanilla” DeepONets. Hence, we believe that our method will trigger further developments in the field of scientific machine learning, for the development of new ‘’light”schemes that will provide high accuracy while reducing dramatically the computational cost. A MATLAB toolbox for RandONets, including demos, is available on GitHub at https://github.com/GianlucaFabiani/RandONets.

Interpretable machine learning↗

Unraveling the formation mechanism of NaCoPO 4 polymorphs

Phosphate compounds are one of the attractive classes of cathodes for their potential application in rechargeable Na-ion batteries (NIBs) due to their high insertion voltages and stabilities. Unlike olivine-LiMPO 4 (M = Fe, Mn, Co, Ni) cathodes, maricite-NaMPO 4 phases are electrochemically inactive due to lack of sodium diffusion channels. Interestingly, cobalt bearing compounds exhibit rich polymorphism (α-, β-, ABW- and Red-NaCoPO 4 ). However, the preparation of NaCoPO 4 single phases is challenging due to their closer enthalpies of formation. In this study, we have attempted to understand the formation mechanism of NaCoPO 4 polymorphs during solid state reaction using two different cobalt precursors (Co(OH) 2 and CoCO 3 ). The temperature dependent in-situ powder X-ray Diffraction (PXRD) studies showed the formation of β-NaCoPO 4 at a much lower temperature compared to the one reported in the literature, whilst we have discovered a new high temperature polymorph gamma-NaCoPO 4 . The choice of precursors was also found to be important for the preparation of ABW-NaCoPO 4 , i.e., the rapid decomposition of Co(OH) 2 has resulted in its formation whilst the high stability of CoCO 3 prohibited the same. The order of the formation of the NaCoPO 4 polymorphs during heating was found to be ABW→β→α →$\gamma$. During normal cooling, gamma-NaCoPO 4 transformed primarily into alpha-polymorph whilst quenching in liquid N-2 resulted in the formation of β-NaCoPO 4 The as-synthesized beta- and ABW-NaCoPO 4 phases exhibited high sodium (de)-intercalation voltages (similar to 4.2 and 4.5 V vs. Na + /Na 0 , respectively), albeit with limited reversible capacities. This study is expected to open new avenues to harvest metastable polymorphs based on other transition metals (Fe, Mn and Ni).

25 ENERGY STORAGE↗

Functional composites by programming entropy-driven nanosheet growth

Here, nanomaterials must be systematically designed to be technologically viable. Driven by optimizing intermolecular interactions, current designs are too rigid to plug in new chemical functionalities and cannot mitigate condition differences during integration. Despite extensive optimization of building blocks and treatments, accessing nanostructures with the required feature sizes and chemistries is difficult. Programming their growth across the nano-to-macro hierarchy also remains challenging, if not impossible. To address these limitations, we should shift to entropy-driven assemblies to gain design flexibility, as seen in high-entropy alloys, and program nanomaterial growth to kinetically match target feature sizes to the mobility of the system during processing. In tis report, following a micro-then-nano growth sequence in ternary composite blends composed of block-copolymer-based supramolecules, small molecules and nanoparticles, we successfully fabricate high-performance barrier materials composed of more than 200 stacked nanosheets (125 nm sheet thickness) with a defect density less than 0.056 µm -2 and about 98% efficiency in controlling the defect type. Contrary to common perception, polymer-chain entanglements are advantageous to realize long-range order, accelerate the fabrication process (<30 min) and satisfy specific requirements to advance multilayered film technology. This study showcases the feasibility, necessity and unlimited opportunities to transform laboratory nanoscience into nanotechnology through systems engineering of self-assembly.

42 ENGINEERING↗

Machine learning surrogate models for Landau fluid closure

The first result of applying the machine/deep learning technique to the fluid closure problem is presented in this letter. As a start, three different types of neural networks (multilayer perceptron (MLP), convolutional neural network (CNN) and two-layer discrete Fourier transform (DFT) network) were constructed and trained to learn the well-known Hammett-Perkins Landau fluid closure in configuration space. We found that in order to train a well-preformed network, a minimum size of training data set is needed; MLP also requires a minimum number of neurons in the hidden layers equals to the degrees of freedom in Fourier space despite training data is fed in configuration space. Out of three models DFT performs the best for the clean data most likely due to the existence of nice Fourier expression for Hammett-Perkins closure but it is least robust with respect to input noise. Overall, with appropriate tuning and optimization, all three neural networks are able to accurately predict Hammett-Perkins closure and reproduce the inherit nonlocal feature, suggesting a promising path to calculate more sophisticated closures with the machine/deep learning technique.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Advanced Monitoring and Control in the ANL METL Facility Using an Engineering Digital Twin

The potential benefits of using an engineering digital twin to achieve greater autonomy for monitoring and control functions in advanced reactors was investigated for the Mechanisms Engineering Test Loop (METL) liquid sodium facility at Argonne National Laboratory. The METL sodium purification system served as a representative system as it requires significant human in-the-loop interaction to accomplish its design function. The objective was to demonstrate how real-time operation could be automated while preserving oversight of the operator for ensuring that the system design functions are met. A digital twin model of the purification system was developed for both the cold trap purification loop and plugging meter diagnostic loop using information from the METL piping and instrumentation diagram (P&ID). Automated monitoring and diagnosis of component degradation in the METL facility was demonstrated in tests using the PRO-AID health monitoring software with the digital twin model incorporated in the library of components. Component failures were introduced and were successfully diagnosed in real time. These tests serve to demonstrate an advanced monitoring capability able to differentiate sensor degradation from component degradation, to generate a rank ordering of probabilities of different failure mechanisms that serves to circumvent the false alarm problem with current anomaly detection methods, and how facility monitoring can be transformed from anomaly detection to identification of a specific fault. Automated control of the purification system was demonstrated through simulations that exercised a model predictive controller designed using the digital twin model. Results of these simulations compared favorably with experimental data showing very good reference tracking response with negligible overshoot. In conclusion, these pilot tests and simulations successfully demonstrated the use of a digital twin for improved automation of monitoring and control. It was shown how the digital twin enables switching between control modes from cold trap operation where impurities are removed to plugging meter operation where impurity concentrations are measured.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Even Higher-Level Synthesis: An Exploration of AI Hardware Accelerators using HLS4ML

With the rise of artificial intelligence, the popularization of deep learning, and a constantly evolving industry, the demand for flexible and efficient tools has never been greater. As algorithms grow more complex, their runtime and energy consumption increase exponentially. Customized hardware accelerators, long used for specific mathematical operations, remain essential for managing modern applications' computational and power demands. Hardware accelerators can speed up complex computations by orders of magnitude, but their manual design and verification processes are often challenging and time-consuming. High-Level Synthesis (HLS) provides a solution by transforming high-level algorithm descriptions, typically written in C++ or SystemC, into synthesizable RTL suitable for hardware implementation. This approach reduces development time for RTL engineers while offering flexibility beyond what traditional handwritten RTL can provide. We extended this capability to the machine-learning domain with the open-source framework hls4ml, which allows neural networks trained in Python frameworks like Tensorflow or PyTorch to be synthesized into efficient hardware representations for the traditional FPGA and ASIC flows. This breakthrough addresses the growing need for reduced design turnaround and easy verification of ML hardware accelerators with low latency and power efficiency constraints. During this tutorial, we will demonstrate how Python complements HLS by simplifying the ML design process, bridging the gap between software and hardware development. Attendees will explore how we translate neural networks modeled in Python into fixed-point C++ models suitable for HLS workflows. We will dive into strategies like Value-Range Analysis and Quantization-Aware Training, which optimize these designs for deployment and evaluate their accuracy, power consumption, and energy efficiency. To exemplify these concepts, experts from Fermilab will share their experiences applying this technology to high-energy physics experiments, where real-time, low-latency processing is critical. Over the years, Fermilab engineers have demonstrated how deep neural networks, optimized for hardware using hls4ml, can meet the stringent requirements of trigger systems at the CERN Large Hadron Collider. These systems rely on rapid decision-making to process immense data volumes while retaining only the most relevant events for further analysis. The application of hls4ml has also been extended to innovative technologies like smart pixel arrays. These smart pixels integrate ML inference capabilities directly into sensor devices, enabling localized data processing at the pixel level. This approach drastically reduces the need to transmit raw data to external processing units, significantly decreasing power consumption and latency. By embedding neural networks within the pixel architecture, the smart pixels can identify and prioritize relevant data in real time, providing a highly efficient solution for edge computing in scenarios such as particle detectors and imaging systems. Fermilab's work highlights the potential of hardware-accelerated ML in scenarios where both speed and power efficiency are mission-critical. Through this tutorial, attendees will gain valuable insights into the challenges and solutions of deploying ML in hardware. Understanding how HLS and hls4ml streamline the development of neural network-based hardware accelerators is fundamental for the industry's future. Participants will learn how these technologies are shaping the future of AI and scientific computing.

Di Guglielmo, Giuseppe [Fermilab]↗

Joint observations of 4U1223-62 by the SAS-3 satellite and Columbia University proportional counter experiment on NASA rocket 26.054 UH

The pulsating X-ray binary 4U1223-62 and Vela X-1 were observed by Aerobee rocket-borne proportional counters. Valid X-ray events were telemetered and analyzed for possible flaring, quasiperiodic, and periodic pulsations, and for other nonstatistical behavior in the source. Both fast Fourier transform and autocorrelation programs were used. For several hours four days before and after the rocket flight, the SAS-3 satellite scanned the galactic plane in order to identify X-ray sources in the vicinity of 4U1223-62 and their intensities, and to provide positional accuracy of 0.25 for sources with intensity greater than 10% of the target. Observations of the source near the main peak of its pulsating period as defined by SAS-3 are discussed. There is no evidence of a spectral feature although twice as many photons were received as than from Vela X-1.

Novick, R.↗