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At least 613 records · Page 34

Prediction of Weather Impacted Airport Capacity using Ensemble Learning

Ensemble learning with the Bagging Decision Tree (BDT) model was used to assess the impact of weather on airport capacities at selected high-demand airports in the United States. The ensemble bagging decision tree models were developed and validated using the Federal Aviation Administration (FAA) Aviation System Performance Metrics (ASPM) data and weather forecast at these airports. The study examines the performance of BDT, along with traditional single Support Vector Machines (SVM), for airport runway configuration selection and airport arrival rates (AAR) prediction during weather impacts. Testing of these models was accomplished using observed weather, weather forecast, and airport operation information at the chosen airports. The experimental results show that ensemble methods are more accurate than a single SVM classifier. The airport capacity ensemble method presented here can be used as a decision support model that supports air traffic flow management to meet the weather impacted airport capacity in order to reduce costs and increase safety.

Weather impact↗

Predictive Chemical Kinetic Modeling: Where We Succeed, Where We Struggle, and What Comes Next

Chemical kinetic modeling plays a foundational role in fields ranging from energy to environmental science, pharmaceuticals, and advanced materials. The past two decades have seen remarkable progress, particularly in modeling gas-phase reactions for thermochemical processes, leading to impactful industrial applications such as steam cracking and air quality management. However, new challenges are emerging. The successful development of systematic methodologies for the description of gas-phase kinetics opens the possibility to apply the same approach to the study of more challenging systems. Here, we review recent advances, including ab initio transition state theory-based master equation estimation of elementary rates, automated mechanism generation, machine-learning-assisted kinetics, and uncertainty quantification, and discuss the advances needed to apply the same methodological approach in areas such as heterogeneous catalysis, electrochemistry, liquid-phase and solid-state reactivity, and multiscale model integration. We advocate for the development of targeted tools, especially methods that go beyond empirical tuning toward first-principles-based predictions. We highlight the need for accessible software and AIaugmented workflows to democratize modeling for industry and academia alike. In this perspective, we call attention to not only what has worked but also what remains unsolved, advocating to avoid overemphasizing successes in scientific works at the expense of realism. The next decade should focus on predictive capability, physical accuracy, and community infrastructure (e.g., databases and services) to enable innovation across diverse fields. We argue that kinetic modeling, properly equipped, can accelerate discovery far beyond its traditional domains.

ab initio calculations↗

Rapid characterization of MSW and RDF feedstocks for waste-to-energy process using LIBS and ML techniques

The heterogeneity in the composition of municipal solid wastes (MSW) poses significant challenges in the production of biofuel and bioproducts. This research aims to enhance the accuracy and efficiency of waste analysis and characterization by introducing a fast characterization approach for MSW-derived refuse-derived fuels (RDF) by combining Laser-Induced Breakdown Spectroscopy (LIBS) with advanced machine learning (ML) techniques. The approach combines data pre-processing of LIBS spectra of RDF, and the development of ML models trained on domain and theory-based spectral features for predicting process parameters. These models are adept at predicting key process parameters like High Heating Value (HHV), carbon content, and volatile matter. This approach can achieve an average RRMSE of 2.13% and R 2 of 0.98 or higher for all considered parameters on testing data. This work demonstrates significant potential for improving waste sorting, processing efficiency, and environmental compliance over traditional labor- and time-intensive laboratory waste analysis and characterization.

09 BIOMASS FUELS↗

Femtosecond pulse parameter estimation from photoelectron momenta using machine learning

Abstract Deep learning models have provided huge interpretation power for image-like data. Specifically, convolutional neural networks (CNNs) have demonstrated incredible acuity for tasks such as feature extraction or parameter estimation. Here we test CNNs on strong-field ionization photoelectron spectra, training on theoretical data sets to ‘invert’ experimental data. Pulse characterization is used as a ‘testing ground’, specifically we retrieve the laser intensity, where ‘traditional’ measurements typically lead to 20% uncertainty. We report on crucial data augmentation techniques required to successfully train on theoretical data and return consistent results from experiments, including accounting for detector saturation. The same procedure can be repeated to apply CNNs in a range of scenarios for strong-field ionization. Using a predictive uncertainty estimation, reliable laser intensity uncertainties of a few percent can be extracted, which are consistently lower than those given by traditional techniques. Using interpretability methods can reveal parts of the distribution that are most sensitive to laser intensity, which can be directly associated with holographic interferences. The CNNs employed provide an accurate and convenient ways to extract parameters, and represent a novel interpretational tool for strong-field ionization spectra.

Szołdra, Tomasz (ORCID:0000000228970506)↗

Reservoir Computing as a Tool for Climate Predictability Studies

Reduced-order dynamical models play a central role in developing our understanding of predictability of climate irrespective of whether we are dealing with the actual climate system or surrogate climate models. In this context, the linear inverse modeling (LIM) approach, by capturing a few essential interactions between dynamical components of the full system, has proven valuable in providing insights into predictability of the full system. We demonstrate that reservoir computing (RC), a form of learning suitable for systems with chaotic dynamics, provides an alternative nonlinear approach that improves on the predictive skill of the LIM approach. We do this in the example setting of predicting sea surface temperature in the North Atlantic in the preindustrial control simulation of a popular earth system model, the Community Earth System Model so that we can compare the performance of the new RC-based approach with the traditional LIM approach both when learning data are plentiful and when such data are more limited. The improved predictive skill of the RC approach over a wide range of conditions—larger number of retained EOF coefficients, extending well into the limited data regime, etc.—suggests that this machine-learning technique may have a use in climate predictability studies. While the possibility of developing a climate emulator—the ability to continue the evolution of the system on the attractor long after failing to be able to track the reference trajectory—is demonstrated in the Lorenz-63 system, it is suggested that further development of the RC approach may permit such uses of the new approach in more realistic predictability studies.

54 ENVIRONMENTAL SCIENCES↗

New Era Towards Autonomous Additive Manufacturing: A Review of Recent Trends and Future Perspectives

Abstract The Additive Manufacturing (AM) landscape has significantly transformed in alignment with Industry 4.0 principles, primarily driven by the integration of Artificial Intelligence (AI) and Digital Twin (DT). However, current Intelligent Additive Manufacturing (IAM) systems face limitations such as fragmented AI tool usage and suboptimal human-machine interaction (HMI). This paper reviews existing IAM solutions, emphasizing control, monitoring, process autonomy, and end-to-end integration, and identifies key limitations, such as the absence of a high-level controller for global decision-making. To address these gaps, we propose a transition from IAM to Autonomous Additive Manufacturing (AAM), featuring a hierarchical framework with four integrated layers: knowledge, generative solution, operational, and cognitive. In the cognitive layer, AI agents notably enable machines to independently observe, analyze, plan, and execute operations that traditionally require human intervention. These capabilities streamline production processes and expand the possibilities for innovation, particularly in sectors like in-space manufacturing (ISM). Additionally, this paper discusses the role of AI in self-optimization and lifelong learning, positing that the future of AM will be characterized by a symbiotic relationship between human expertise and advanced autonomy, fostering a more adaptive, resilient manufacturing ecosystem.

Fan, Haolin↗

Rapid Electrochemical Diagnosis of Battery Health and Safety from Cells to Modules

Rapid electrochemical diagnosis of battery health and failure is critical for ensuring reliable battery performance and battery safety. Traditional battery health diagnostics such as capacity measurements and DC pulse tests are reliable and well-understood, however, these measurements of battery capacity and resistance do not capture all aspects of battery degradation. Other aspects of degradation, such as electrolyte decomposition, lithium-plating, and particle cracking are difficult to detect electrochemically but are crucial to measure to get a full picture of battery safety and flag out potential failures. In this work, lab- and field-aged commercial lithium-ion batteries and modules of various chemistries and formats are tested using a variety of traditional electrochemical characterization methods as well as using 2-minute pseudo-random DC pulse sequences at rest and during charge/discharge. The electrochemical measurements are compared to physical cell measurements, cell efficiency, drive cycle performance, physical and thermal heterogeneity, and qualitative safety metrics using statistical and machine-learning methods to discover if a comprehensive "battery health map" can be accurately identified using only rapid DC measurements.

ADVANCED PROPULSION SYSTEMS,ENERGY STORAGE↗

Using Machine Learning to Predict Cloud Turbulent Entrainment–Mixing Processes

Different turbulent entrainment–mixing mechanisms between clouds and environment are essential to cloud–related processes; however, accurate representation of entrainment–mixing in weather/climate models still poses a challenge. This study exploits the use of machine learning (ML) to address this challenge. Four ML (Light Gradient Boosting Machine [LGB], eXtreme Gradient Boosting, Random Forest, and Support Vector Regression) are examined and compared. It is found that LGB performs best, and thus is selected to understand the impact of entrainment–mixing on microphysics using simulation data from Explicit Mixing Parcel Model. Compared with traditional parameterizations, the trained LGB provides more accurate microphysical properties (number concentration and cloud droplet spectral dispersion). The partial dependences of predicted microphysics on features exhibit a strong alignment with physical mechanisms and expectations, as determined by the interpreting method, thus overcoming the limitations of the “black box” scheme. The underlying mechanisms are that the smaller number concentration and larger spectral dispersion correspond to more inhomogeneous entrainment–mixing. Specifically, number concentration after entrainment–mixing is positively correlated with adiabatic number concentration and liquid water content affected by entrainment–mixing, and inversely correlated with adiabatic volume mean radius. Spectral dispersion after entrainment–mixing is negatively correlated with liquid water content affected by entrainment–mixing, turbulent dissipation rate and relative humidity of entrained air. Sensitivity analysis further suggests that number concentration is mainly determined by cloud microphysical properties whereas spectral dispersion is influenced by both cloud microphysical properties and environmental variables. The results indicate that the LGB scheme has the potential to enhance the representation of entrainment–mixing in weather/climate models.

54 ENVIRONMENTAL SCIENCES↗

Cyber threat assessment of machine learning driven autonomous control systems of nuclear power plants

We report advanced cyber-attacks against critical infrastructure and the energy sector are becoming more common. With the invention of autonomous control systems (ACS) within advanced nuclear reactor designs, system designers, reactor operators, and regulators must consider cybersecurity during the design and operational phases. This article provides a cyber threat assessment of machine learning (ML)-based digital twinning (DT) technologies in the context of advanced reactor ACS. A cyber–physical testbed was created to emulate nuclear reactor digital instrumentation and controls (I&C) and act as a basis for the ACS. The ACS was designed as two plant-level DTs predicting reactor malfunctions and determining control actions and two component-level DTs responsible for classifying component states and forecasting component inputs and outputs (I/O). Two duplicate ACS designs– one using a traditional ML framework and one using an automated ML (AutoML) framework– were created and tested against cyber-attacks on training data, real-time process data, and ML model architectures to determine their respective qualitative cyber-risk in terms of likelihood and impact. Both frameworks showed similar cyber-resilience against training, real-time, and ML architecture attacks, proving that neither is inherently more secure. Recommended safeguard and security measures are posed to system designers, reactor operators, and regulators to maintain the cybersecurity of ML-based DT technologies such as ACS, prompting a holistic view of shared responsibility for maintaining cyber-secure ML-based systems.

99 GENERAL AND MISCELLANEOUS↗

Multi-system analysis of offshore geologic carbon storage: a review of open-source data science solutions

Geologic carbon storage projects are maturing worldwide and the footprint of deployment in the offshore is expanding. At present, there are ten projects in operation or that have been completed, more than 50 in construction and development, and dozens of characterization studies completed or underway. Offshore geologic carbon storage offers potential benefits over onshore geologic carbon storage. These offshore projects are generally remote in location, distant from population centers, and avoid complicated pore space rights while having abundant prospective storage potential. Some offshore fields targeted for carbon storage have comparatively fewer prior borehole penetrations except for areas that have been explored for petroleum production, minimizing potential issues such as pressure interference and infrastructure impacts. Yet offshore geologic carbon storage projects face distinctive technical and economic challenges, such as seafloor geohazards (e.g., seabed instability), expensive maritime transport, and meteorological-oceanographic conditions that can damage infrastructure and impact operations. Analytical capabilities and improved computational speeds have advanced engineering, earth and energy sciences in the wake of the arrival of modern data science over the last decade. These advancements have created an opportunity for integrated, multi-systems modeling approaches utilizing artificial intelligence and machine learning that are no longer limited by computational issues. Analytical tools developed alongside this advancement in data science can be leveraged to calibrate the potential advantages and challenges of carbon storage operations in the offshore. New methods and approaches that incorporate data science to analyze multiple aspects of engineered and natural systems can provide insights that complement the characterization and onsite engineering that traditional commercial and operational software addresses. These new methods and approaches can potentially improve the outcome of energy operations and carbon storage. Providing multi-system, science-driven data analytics enhances the knowledge base that offshore developers, operators, and regulatory bodies may draw from to improve offshore site selection and operational efficiency. Here, we provide a brief synopsis of geologic carbon storage efforts to date, an overview of the engineered and natural systems involved in offshore geologic carbon storage, and a review of publicly available, open-source, offshore and/or carbon storage related data- and science-driven tools developed by 2010 or later that are suitable for screening and assessing regions for offshore geologic carbon storage.

artificial intelligence↗

Predicting impurity spectral functions using machine learning

The Anderson Impurity Model (AIM) is a canonical model of quantum many-body physics. Here we investigate whether machine learning models, both neural networks (NN) and kernel ridge regression (KRR), can accurately predict the AIM spectral function in all of its regimes, from empty orbital, to mixed valence, to Kondo. To tackle this question, we construct two large spectral databases containing approximately 410 000 and 600 000 spectral functions of the single-channel impurity problem. We show that the NN models can accurately predict the AIM spectral function in all of its regimes, with pointwise mean absolute errors down to 0.003 in normalized units. We find that the trained NN models outperform models based on KRR and enjoy a speedup on the order of 10 5 over traditional AIM solvers. Finally, the required size of the training set of our model can be significantly reduced using farthest point sampling in the AIM parameter space, which is important for generalizing our method to more complicated multichannel impurity problems of relevance to predicting the properties of real materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Bridging the time scale in exascale computing of chemical systems (Final Technical Report)

This report summarizes the work carried out with support of the United States Department of Energy under Award DE-SC0019441. The theme of this project was to develop and apply methods that allowed for the acceleration of atomistic calculations, particularly in challenging areas such as multiphase systems, electrified interfaces, uncertainty estimation, and applications requiring chemical accuracy, which tend to be applications where simulation time is severely bottlenecked by the computational time requirements. Much of the focus was on the application of emerging machine-learning methodologies, although a wide range of methodologies were employed. This report has two major sections. The first focuses on the methodological advances themselves. Within this part, we report a number of major advances, a few examples of which are described here. We report the first machine-learning scheme for the acceleration of electronically grand-canonical calculations (that is, those applicable to electrochemistry). We report new methods of performing transfer learning, in which physics-based priors can be used to provide predictions, often with uncertainty estimates, of images well outside of training sets; we also offer ways to fine-tune these transfer-learning models. We provide a new systematic means to generate and apply minimal training data sets to very large (10,000’s of atoms) systems, with only small training sets appropriate for electronic structure. We developed new methodologies to integrate surface vibrations into surface adsorption calculations. We made advances to the applicability of diffusion Monte Carlo methods to allow (learned) force prediction, finite-size error correction, and force-free means of searching for transition states. We integrated machine-learned atomistic predictions into mechanism generation codes. Additionally, we released new software including AmpTorch, a modernized version of our original atomistic machine-learning code Amp. The second part of this report focuses on the scientific applications that accompanied, and were often enabled by, the methodological advances described earlier. A few examples follow, but full details are in the individual chapters of the report. For example, we developed a general theory of phonon-induced friction on molecular adsorbates. We showed fundamentally how solvent influences the adsorption and desorption process and how it differs from the processes typically involved at the solid–gas interface, making aqueous-phase and electrocatalysis different from traditional thermocatalysis. We examined how metal–insulator and magnetic transitions can be probed, and accelerated exciton dynamics via Frenkel Hamiltonian parameters. We showed that the nearsighted force-training approach, developed within this project, can predict both the stability and reactivity of large nanoparticles, and can also lead to insights on catalyst coverage on binding energies and entropies. These applied studies, which generally integrated with our method development, allowed us to push forward the theoretical understanding of several reaction classes.

08 HYDROGEN↗

Recent advances in integrated hydrologic models: Integration of new domains

Over the past several decades, hydrologic models have advanced from independent models of the surface and subsurface to integrated models that can capture the terrestrial hydrologic cycle within one framework. In recent years, these coupled frameworks have seen the inclusion of biogeochemical processes, ecohydrology, sedimentation and erosion, cold region hydrology, anthropogenic activities, and atmospheric processes. This expansion is the result of increased computational, data, and modeling capabilities and capacities, as well as improved understanding of the processes that drive these integrated systems. Here, in this study, we review these recent advances to integrate new processes and systems into existing terrestrial hydrologic models and highlight the significant challenges and opportunities that remain. We identify that with so many models currently available and in development, selecting the most appropriate model is difficult, and we suggest a path for new or novice modelers to find the most appropriate code based on their needs. In addition, data required to parameterize and calibrate these models can often constrain their applicability and usefulness. However, advances in environmental sensors and measurement technology, in addition to data assimilation of non-traditional data (e.g. remote sensing, qualitative data) are providing new ways of addressing this issue. As we expand hydrologic models to integrate more processes and systems, our computational demands also increase. Recent and emerging advances in computational platforms, including cloud and quantum computing, in addition to the use of machine learning to capture some processes, will continue to support the use of increasingly larger and more complex, process-based models. Finally, we highlight that it is critical to develop state-of-the-science models that are accessible to all model users, not just those applied for research and development. We encourage continued development of diverse modeling platforms, considering the user needs, data availability, and computational resources.

54 ENVIRONMENTAL SCIENCES↗

An Ensemble of Bayesian Neural Networks for Exoplanetary Atmospheric Retrieval

Machine learning (ML) is now used in many areas of astrophysics, from detecting exoplanets in Kepler transit signals to removing telescope systematics. Recent work demonstrated the potential of using ML algorithms for atmospheric retrieval by implementing a random forest (RF) to perform retrievals in seconds that are consistent with the traditional, computationally expensive nested-sampling retrieval method. We expand upon their approach by presenting a new ML model, plan-net, based on an ensemble of Bayesian neural networks (BNNs) that yields more accurate inferences than the RF for the same data set of synthetic transmission spectra. We demonstrate that an ensemble provides greater accuracy and more robust uncertainties than a single model. In addition to being the first to use BNNs for atmospheric retrieval, we also introduce a new loss function for BNNs that learns correlations between the model outputs. Importantly, we show that designing ML models to explicitly incorporate domain-specific knowledge both improves performance and provides additional insight by inferring the covariance of the retrieved atmospheric parameters. We apply plan-net to the Hubble Space Telescope Wide Field Camera 3 transmission spectrum for WASP-12b and retrieve an isothermal temperature and water abundance consistent with the literature. We highlight that our method is flexible and can be expanded to higher resolution spectra and a larger number of atmospheric parameters.

Adam D. Cobb↗

Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems

In this work, we present Lift & Learn, a physics-informed method for learning low-dimensional models for large-scale dynamical systems. The method exploits knowledge of a system’s governing equations to identify a coordinate transformation in which the system dynamics have quadratic structure. This transformation is called a lifting map because it often adds auxiliary variables to the system state. The lifting map is applied to data obtained by evaluating a model for the original nonlinear system. This lifted data is projected onto its leading principal components, and low-dimensional linear and quadratic matrix operators are fit to the lifted reduced data using a least-squares operator inference procedure. Analysis of our method shows that the Lift & Learn models are able to capture the system physics in the lifted coordinates at least as accurately as traditional intrusive model reduction approaches. This preservation of system physics makes the Lift & Learn models robust to changes in inputs. Numerical experiments on the FitzHugh–Nagumo neuron activation model and the compressible Euler equations demonstrate the generalizability of our model.

97 MATHEMATICS AND COMPUTING↗

MS25: Materials Science-Focused Benchmark Data Set for Machine Learning Interatomic Potentials

Here, we present MS25, a benchmark data set for evaluating machine learning interatomic potentials (MLIPs) across diverse materials-relevant systems including MgO surfaces, liquid water, zeolites, a catalytic Pt surface reaction, high-entropy alloys (HEAs), and disordered Zr-oxides. Five MLIP architectures (MACE, NequIP, Allegro, MTP, and Torch-ANI) are trained and tested, focusing not only on traditional metrics (energies, forces, and stresses) but also explicitly validating derived physical observables such as lattice constants, volumes, and reaction barriers. We find that most models reach comparable accuracy on standard error metrics across the simple systems, although equivariant MLIPs offer 1.5–2× improvements over nonequivariant MLIPs in energy and force error for structurally complex or compositionally disordered environments such as HEAs and Zr–O systems. Our analysis highlights that low errors in energy and force predictions do not guarantee reliable observables, emphasizing the necessity of explicit validation. We demonstrate limitations in cross-framework transferability, as models trained on one zeolite framework (CHA) fail to reliably generalize to predictions of structurally distinct frameworks (e.g., MFI). Size-extensive tests show some dependence on system size for MgO, resulting from forced periodicity. The HEA and Zr–O data sets are identified as challenging tests for future benchmarks and MLIP model architecture developments as they show significant differentiation in error between MLIP architectures and are still relatively difficult at 1000 training images. Moving forward, we recommend that benchmarking efforts shift their focus from marginal accuracy improvements in energy and force errors toward identifying and understanding model failure modes, rigorously assessing transferability, and evaluating how their errors affect observable predictions. For researchers looking to choose an MLIP architecture, we suggest selecting equivariant MLIP architectures if the complexity of the system is a challenge. For simple materials problems, auxiliary features such as integration with molecular dynamics engines, trade-offs between computational data set generation cost vs MLIP inference speed, and framework integration may play a more important decision factor than small differences in error metrics that are unlikely to matter for production-level research.

chemical structure↗

Azo(xy) vs Aniline Selectivity in Catalytic Nitroarene Reduction by Intermetallics: Experiments and Simulations

Intermetallic nanoparticles are promising catalysts in hydrogenation and fuel cell technologies. Much is known about the ability of intermetallic nanoparticles to selectively reduce nitro vs alkene, alcohol, or halide functional groups; less is known about their selectivity toward aniline vs azo or azoxy condensation products that result from the reduction of a nitro group alone. Because azo(xy)arenes bear promise as dyes, chemical stabilizers, and building blocks to functional materials but can be difficult to isolate, developing high surface area nanoparticle catalysts that display azo(xy) selectivity is desirable. To address this question, we studied a family of nanocrystalline group 10 metal (Pd, Pt)- and group 14 metal (Ge, Sn, Pb)-containing intermetallics-Pd 2 Ge, Pd 2 Sn, Pd 3 Sn 2 , Pd 3 Pb, and PtSn-in the catalytic reduction of nitroarenes. In contrast to monometallic Au, Pt, and Pd nanoparticles and "random" PdxSn1 – x nanoalloys, which are selective for aniline, nanoparticles of atomically precise intermetallic Pd 2 Ge, Pd 2 Sn, Pd 3 Sn 2 , and PtSn prefer an indirect condensation pathway and have a high selectivity for the azo(xy) products. The only exception is Pd 3 Pb, the most active among the intermetallic nanoparticles studied here, which is instead selective for aniline. Employing a novel application of molecular dynamics-based on machine learned potentials within a DeePMD framework-to heterogeneous catalysis, we are able to identify key reaction species on the different types of catalysts employed, furthering our understanding of the unique selectivity of these materials. By demonstrating how intermetallic nanoparticles can be as active yet more selective than other more traditional catalysts, this work provides new physical insights and opens new opportunities in the use of these materials in other important chemical transformations and applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Velocity Extraction Using Complete Time-Domain Waveform Data and Audio Machine Learning

We developed a new machine learning-based tool for extracting information from interferometry measurements: MIDWAZE (Modular Interferometry Direct Waveform AnalyZEr). This paper showcases MIDWAZE’s ability to extract an object’s velocity information from Photonic Doppler Velocimetry (PDV) data at near-human accuracy with little to no human intervention. MIDWAZE can extract velocities roughly 350 times as fast as a human analyst "rushing" to complete their extractions, with similar extraction accuracy. MIDWAZE’s most outstanding feature is that it operates directly in waveform/temporal space, freeing analysis from certain limitations imposed by traditional spectrogram-based approaches and opening the way to "phase aware" PDV analysis. MIDWAZE also has limited ability to discriminate between different solid objects, which we develop as a first step towards automated discrimination of different kinds of objects such as ejecta clouds.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗