Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “analysis and visualization”

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 1,153 records · Page 64
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Digital Twin for Chemical Science (DTCS) v0.01

Directly visualizing the trajectories of chemistry can unravel novel insights into the behavior of catalysts, gas phase reactions, photo-induced dynamics, and building blocks for quantum information processing. The ability of explicitly identifying, tracking, and tagging the exchange of matter, hence the annihilation and creation of new chemical species, can be best realized through a close coupling of theory and experiment. While the synchrotron-based characterization facilities propelled rapidly in its hardware, providing higher brightness, better resolution, and more precision, the software infrastructure is lagging. We developed DTCS (Digital Twin for Chemical Science) v.01, a central platform that faithfully mimics advanced instrumentations in Scientific User Facilities, by solving a variety of technical challenges in data acquisition, analysis, and model-driven interpretation. Rooted in physics and accelerated by AI, we validated this concept by direct comparison with precise experimental X-ray Photoelectron Spectroscopy (XPS) observations using a ubiquitous metal-water interfacial scenario, i.e., Ag/H2O as our main narrative. The DTCS v.01 input mirrors how the bench chemists work, with the output directly linked to the end station computer, thereby providing a user-friendly, knowledge-driven, and accessible user experience with mechanistic insights standardized in a way that are ready to be published, versioned, and transferred flexibly.

Qian, Jin↗
DOE OSTI2023

Examining phase separation and crystallization in glasses with X-ray nano-computed tomography

X-ray nano-computed tomography (nano-CT) is a powerful technique to characterize and visualize 3 dimensional (3D) phenomena in complex glasses at the nanoscale. This technique can offer a unique opportunity to explore the intricate morphology of multicomponent glass and glass-ceramic samples, due to its low X-ray energy and high spatial resolution (down to 50 nm). In the current demonstration paper, nano-CT provided insight into crystallization and phase separation, as well as a variety of other phenomena, including corrosion, fracture, and porosity. At scales ranging from 100 to 20 μm, the microstructures of phase separation in borosilicate, complex silicate, and chalcogenide glass compositions were examined. In addition, crystallites present in simulant nuclear waste glasses, volcanic glasses, and other related samples were explored. Nano-CT analysis can add to the understanding of (1) the formation processes, (2) distributions, interactions, and compositions of phases, and (3) the mechanisms, structures, and growth of crystallization and phase separation. Nano-CT offers wide potential in the field of glass science, especially when (1) common characterization methods are insufficient, (2) simple sample preparation is required, (3) 3D rendering is needed, or (4) compelling images of small, complex features are desired.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Tuning MXene Surface Terminations for Strategic Control of Physical Properties

Scientific Achievement • Ti3C2Tx surfaces with a higher hydroxyl group concentration play a pivotal role in surface properties and were found to be thermodynamically stable. • From the electronic bonding analysis, the charge density difference and electron localization function demonstrated a significant electron localization at the hydroxyl group, which results in a locally induced dipole on the surface. • A large tunability in the work function is found from different concentrations of functional groups on the surface which can be controlled by the concentration of HF used for etching of the MAX phase to produce the resulting MXene. Research Details • The influence of termination group distribution on the surface of Ti3C2Tx MXenes from various etching concentrations of HF was evaluated • The work functions of Ti3C2Tx MXenes with differing concentrations of functional groups were determined • The influence of termination group clustering on the surface of Ti3C2Tx MXenes was investigated by visualization of the electron localization function and charge density difference

Ward, Patrick A.↗
DOE OSTI2022

Quantifying fish otolith mineralogy for trace-element chemistry studies

Otoliths are frequently used to infer environmental conditions or fish life history events based on trace-element concentrations. However, otoliths can be comprised of any one or combination of the three most common polymorphs of calcium carbonate - aragonite, calcite, and vaterite - which can affect the ecological interpretation of otolith trace-element results. Previous studies have reported heterogeneous calcium carbonate compositions between left and right otoliths but did not provide quantitative assessments of polymorph abundances. In this study, neutron diffraction and Raman spectroscopy were used to identify and quantify mineralogical compositions of Chinook salmon Oncorhynchus tshawytscha otolith pairs. We found mineralogical compositions frequently differed between otoliths in a pair and accurate calcium carbonate polymorph identification was rarely possible by visual inspection alone. The prevalence of multiple polymorphs in otoliths is not well-understood, and future research should focus on identifying otolith compositions and investigate how variations in mineralogy affect trace-element incorporation and potentially bias environmental interpretations.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2022

Deep Active Learning for Solvability Prediction in Power Systems

Traditional methods for solvability region analysis can only have inner approximations with inconclusive conservatism and handle limited types of power flow models. In this letter, we propose a deep active learning framework for solvability prediction in power systems. Compared with passive learning where the training is performed after all instances are labeled, active learning selects most informative instances to be labeled and therefore significantly reduces the size of the labeled dataset for training. In the active learning framework, the acquisition functions, which correspond to different sampling strategies, are defined in terms of the on-the-fly posterior probability from the classifier. First, the IEEE 39-bus system is employed to validate the proposed framework, where a two-dimensional case is illustrated to visualize the effectiveness of the sampling method followed by the high-dimensional numerical experiments. Then, the Northeast Power Coordinating Council (NPCC) 140-bus system is used to validate the performance on large-scale power systems.

42 ENGINEERING↗
DOE OSTI2024

Nanoscale elemental and morphological imaging of nitrogen-fixing cyanobacteria

Nitrogen-fixing cyanobacteria bind atmospheric nitrogen and carbon dioxide using sunlight. This experimental study focused on a laboratory-based model system, Anabaena sp., in nitrogen-depleted culture. When combined nitrogen is scarce, the filamentous prokaryotes reconcile photosynthesis and nitrogen fixation by cellular differentiation into heterocysts. To better understand the influence of micronutrients on cellular function, 2D and 3D synchrotron X-ray fluorescence mappings were acquired from whole biological cells in their frozen-hydrated state at the Bionanoprobe, Advanced Photon Source. To study elemental homeostasis within these chain-like organisms, biologically relevant elements were mapped using X-ray fluorescence spectroscopy and energy-dispersive X-ray microanalysis. Higher levels of cytosolic K + , Ca 2+ , and Fe 2+ were measured in the heterocyst than in adjacent vegetative cells, supporting the notion of elevated micronutrient demand. P-rich clusters, identified as polyphosphate bodies involved in nutrient storage, metal detoxification, and osmotic regulation, were consistently co-localized with K + and occasionally sequestered Mg 2+ , Ca 2+ , Fe 2+ , and Mn 2+ ions. Machine-learning-based k-mean clustering revealed that P/K clusters were associated with either Fe or Ca, with Fe and Ca clusters also occurring individually. In accordance with XRF nanotomography, distinct P/K-containing clusters close to the cellular envelope were surrounded by larger Ca-rich clusters. The transition metal Fe, which is a part of nitrogenase enzyme, was detected as irregularly shaped clusters. The elemental composition and cellular morphology of diazotrophic Anabaena sp. was visualized by multimodal imaging using atomic force microscopy, scanning electron microscopy, and fluorescence microscopy. This paper discusses the first experimental results obtained with a combined in-line optical and X-ray fluorescence microscope at the Bionanoprobe.

Anabaena sp↗
DOE OSTI2021

COVID-19, An Exercise in Data Governance at Sandia National Laboratories

In April of 2020, Sandia National Laboratories had an urgent need to identify and manage the data that could be used to create mobile applications, models, reports, and visualizations to assist management in safely bringing the workforce onsite during the COVID-19 pandemic. Multiple divisions volunteered to design and build software solutions; meanwhile, requests for new data sources, including duplicate requests, were inundating Information Technology (IT) and data owners. The Enterprise Data Governance Team was assigned to resolve obtaining and accessing new sources of data in an accelerated timeframe. Through successful collaboration with multiple stakeholders and domain owners across Sandia, the Enterprise Data Governance Team rapidly developed a centralized data strategy and solution for use in safeguarding the Sandia workforce during the COVID-19 pandemic. This foundation enabled teams to successfully develop solutions, including reports for executives and management as well as the data for modeling and scientific analysis.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗
DOE OSTI2022

Summary of NDC Capacity Building Workshop and Regional Seismic Travel Time (RSTT) in combination with Data Sharing and Integration Training

The NNSA Seismic Cooperation Program (SCP) sponsored Stephen Myers (LLNL), Michael Begnaud (LANL), Brian Young (SNL) and Istvan Bondar (Research Center for Astronomy and Earth Sciences, Hungary) to serve as a presenters/trainers at the “NDC Capacity Building Workshop and Regional Seismic Travel Time (RSTT) in combination with Data Sharing and Integration Training” September 4-8 2022 in Muscat, Oman (See Appendix A for the agenda). The workshop and training (workshop from here forward) was organized by the Comprehensive Nuclear-Test-Ban Treaty Organization (CTBTO) Provisional Technical Secretariat (PTS). The first half of the week was devoted to NDC workshop activities, and the second half was devoted to RSTT training. Fifty-five participants from 27 countries and the CTBTO-PTS attended the 5-day workshop (See Appendix B for list of participants and countries of origin). Presentations from the PTS described the International Monitoring System (IMS), International Data Centre (IDC) products, and metrics of regional data utilization. Contributed presentations from each country’s scientists included descriptions of regional and national networks, methods of data analysis, and needs for material and technical assistance. Training included an overview of the RSTT method and instruction on how to locate seismic events with the iLoc program, which utilizes RSTT travel times to reduce bias in event location estimates. Methods of seismic tomography and the need for a high-quality tomographic set, including seismological “ground truth”, were emphasized. Seismological “ground truth” or “GT” is a term that has come to mean both events with known location and events with well-characterized locations that are estimated using seismological data, typically with epicenter accuracy of 5 km or better. Notably, the instructional platform has migrated from UNIX shell scripts to Jupyter Notebooks. Jupyter Notebooks have the advantage being more visually intuitive, including display of graphics within the notebook. Each notebook includes every processing step that participants need to reproduce the entire exercise.

58 GEOSCIENCES↗
DOE OSTI2023

Investigation of Nanoparticle Degradation in Hydrogen Fuel Cell Systems through Automated Electron Microscopy

Proton exchange membrane fuel cells (PEMFC) are promising devices for the deployment of hydrogen-powered heavy-duty vehicles, providing a higher efficiency for similar driving range and fueling time than the existing ones. However, PEMFCs still encounter durability challenges mainly due to catalyst degradation in the cathode. Mitigating these performance losses requires a better understanding of the degradation mechanisms under heavy-duty accelerated stress tests (ASTs) [1]. Scanning transmission electron microscopy (STEM) combined with energy dispersive X-ray spectroscopy (EDS) are key tools for the analysis of Pt and PtCo nanoparticle size, spatial distribution and composition [2]. Electron tomography is also used to determine the rate and type of degradation of catalyst nanoparticles as a function of their position on the carbon support. In this work, automated data acquisition software, paired with a custom Python code, have been used to study the effect of different accelerated stress tests (ASTs) on nanoparticle coarsening [2]. Figure 1 shows high-angle annular dark-field (HAADF)-STEM images and EDS maps comparing the cathodes of membrane electrode assemblies (MEAs) following an electrocatalyst AST performed under H2/N2 with that of the heavy-duty AST performed under H2/air. We will discuss how AST conditions affect considerably the spatial distribution of the nanoparticles across the electrode between the membrane and microporous layer. Although the median particle size increased more in the MEA aged under the heavy-duty AST, as determined using a high-throughput image analysis, the quantitative EDS measurements demonstrate that the electrocatalyst AST resulted in more Pt and Co dissolution from the cathode, which is another important indicator of electrocatalyst degradation. We will further present the impact of the relative humidity (% RH) on the degradation mechanisms demonstrated using the same approach. Electron tomography has been used to distinguish the Pt nanoparticles residing on the carbon support surface (exterior) from those within the pore structure (interior) in order to determine the relative stability of interior and exterior nanoparticles. As shown in Figure 2, we will compare the Pt catalyst particle size at the beginning of test (BOT) and end of test (EOT), and discuss the importance of automating the electron tomography workflow, i.e. acquisition, reconstruction, and visualization, to increase sampling and determine the standard deviation of these measurement. The outlook for utilizing low-dose cryo-tomography for limiting damage to the catalyst, support, and especially proton-conducting ionomer will also be discussed [3].

Amichi, Lynda↗
DOE OSTI2022

Dynamic fracture of glass fiber-reinforced ductile polymer matrix composites and loading rate effect

Here, the dynamic fracture of S-2 glass fiber-reinforced polymer matrix composites (FRPMCs) was investigated in this study. The matrix ductility was improved by a recently developed network topology modification technique via mixing partially reacted substructures (mPRS). The composite material was manufactured and characterized by micro-CT scanning and scanning electron microscopy (SEM). Dynamic single-edge notched bending (d-SENB) experiments were performed on the composites by using a modified split-Hopkinson pressure bar. Each specimen’s fracture process was visualized by ultrafast X-ray imaging. Such in-situ radiography enabled identifying the damage initiation below 50-micron scale and inspecting its propagation through the internal structures of opaque composites, thereby accurately quantifying the composites’ mechanical properties. Furthermore, the identical d-SENB experiments were designed and the digital image correlation (DIC) was employed to monitor the stress wave propagation on the composite specimens. The force and deflection measurements were modified and correlated to the physical damage processes. Besides, quasi-static SENB experiments were conducted to identify the loading rate effects on the composites’ fracture behaviors. The force and deflection history, bending stiffness, energy dissipation, and fracture toughness at different loading rates were quantified and compared. Finally, post-fracture analysis by micro-CT scanning and SEM provided physical observations on the variation of the fracture morphology by different loading rates.

42 ENGINEERING↗
DOE OSTI2023

Automated phase segmentation and quantification of high-resolution TEM image for alloy design

In the alloy design and development process, a wealth of atomically resolved structural high-resolution transmission electron microscopy (HRTEM) images are produced. Identifying the different nano-precipitate phases and tracking their evolution under various compositions and during manufacturing or post-processing requires hundreds of HRTEM images and thousands of precipitates. The nanoscopic phase information labeling and analysis purely relies on humans are prohibitively costly and time-consuming, sometimes not reliable because of the lack of authoritative knowledge. Here, in this work, we develop a novel unsupervised machine learning approach coupled with adaptive computer vision techniques with features in the Fourier space to automatically determine the number of phases and segment/quantify the phases with nanoscale resolution, allowing for quantitative correlation between nanostructure formation, processing and functional properties. To automate the phase extraction/quantification and ascertain its applicability, we have applied the developed framework to the HRTEM images from several alloy systems, processing conditions, image magnifications, and phase types and morphologies (precipitates, nano-twins, stacking faults, crystalline matrix, and amorphous structures) for verification. This study paves the road for compression, visualization, and translation of raw image structural data into physically relevant information in real-time with minimal human supervision. It shows the promise of enabling high-throughput materials characterization for the acceleration of alloy manufacturing and design.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Synthetic Scientific Image Generation with VAE, GAN, and Diffusion Model Architectures

Generative AI (genAI) has emerged as a powerful tool for synthesizing diverse and complex image data, offering new possibilities for scientific imaging applications. This review presents a comprehensive comparative analysis of leading generative architectures, ranging from Variational Autoencoders (VAEs) to Generative Adversarial Networks (GANs) on through to Diffusion Models, in the context of scientific image synthesis. We examine each model's foundational principles, recent architectural advancements, and practical trade-offs. Our evaluation, conducted on domain-specific datasets including microCT scans of rocks and composite fibers, as well as high-resolution images of plant roots, integrates both quantitative metrics (SSIM, LPIPS, FID, CLIPScore) and expert-driven qualitative assessments. Results show that GANs, particularly StyleGAN, produce images with high perceptual quality and structural coherence. Diffusion-based models for inpainting and image variation, such as DALL-E 2, delivered high realism and semantic alignment but generally struggled in balancing visual fidelity with scientific accuracy. Importantly, our findings reveal limitations of standard quantitative metrics in capturing scientific relevance, underscoring the need for domain-expert validation. We conclude by discussing key challenges such as model interpretability, computational cost, and verification protocols, and discuss future directions where generative AI can drive innovation in data augmentation, simulation, and hypothesis generation in scientific research.

Generative Adversarial Networks↗
DOE OSTI2020

The Gemini Planet Imager Exoplanet Survey: Dynamical Mass of the Exoplanet β Pictoris b from Combined Direct Imaging and Astrometry

Herein, we present new observations of the planet β Pictoris b from 2018 with the Gemini Planet Imager (GPI), the first GPI observations following conjunction. Based on these new measurements, we perform a joint orbit fit to the available relative astrometry from ground-based imaging, the Hipparcos Intermediate Astrometric Data (IAD), and the Gaia DR2 position, and demonstrate how to incorporate the IAD into direct imaging orbit fits. We find a mass consistent with predictions of hot-start evolutionary models and previous works following similar methods, though with larger uncertainties: $12.8^{+5.3}_{–3.2} M_{Jup}$. Our eccentricity determination of ${0.12}_{-0.03}^{+0.04}$ disfavors circular orbits. We consider orbit fits to several different imaging data sets, and find generally similar posteriors on the mass for each combination of imaging data. Our analysis underscores the importance of performing joint fits to the absolute and relative astrometry simultaneously, given the strong covariance between orbital elements. Time of conjunction is well-constrained within 2.8 days of 2017 September 13, with the star behind the planet's Hill sphere between 2017 April 11 and 2018 February 16 (±18 days). Following the recent radial velocity detection of a second planet in the system, β Pic c, we perform additional two-planet fits combining relative astrometry, absolute astrometry, and stellar radial velocities. These joint fits find a significantly smaller mass (8.0 ± 2.6 M Jup) for the imaged planet β Pic b, in a somewhat more circular orbit. We expect future ground-based observations to further constrain the visual orbit and mass of the planet in advance of the release of Gaia DR4.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

CO 2 Storage Site Screening Platform Development and CO 2 Storage Resource Analysis in SECARB Offshore Reservoirs Using SAS Viya

A major goal of the SECARB Offshore Partnership (DE-FE0031557) is to screen deep saline aquifers and hydrocarbon reservoirs in the central Gulf of Mexico for CO 2 sequestration and CO 2 -enhanced oil and gas recovery (EOR/EGR) and estimate the corresponding CO 2 storage resources for select reservoirs. CO 2 storage potential associated with offshore CO 2 -EOR is considerable and likely represents “low hanging fruit” for near-term CO 2 storage given the in-place infrastructure in the region. It is for these reasons that this assessment focuses on oil and gas fields. To this end, three major objectives have been completed and include (1) managing geological data derived from different sources, (2) building a reservoir screening platform for CO 2 storage, and (3) ranking the reservoirs based on the estimated CO 2 storage resources. The SAS ® Viya platform was used for data management and analytics. The Viya platform is a cloud service platform that provides data integration, data management, quick analytics, data visualization, machine learning functions, and application programming interfaces (APIs) for multi-programming languages. Different sources of data containing geologic information, reservoir properties, and EOR/EGR information were collected, cleaned, formatted, and loaded into the SAS ® Viya platform for evaluation. The major geological characteristics of both shelf and deep-water areas of the central Gulf were examined and compared to define the appropriate reservoir screening criteria. Next, a CO 2 storage site screening system was built in the SAS ® Viya platform with the pre-defined criteria. Finally, the CO 2 storage resources of the screened reservoirs were calculated and reported at the BOEM field level to identify fields with the highest estimated CO 2 storage resource. The fields with the largest total estimated CO 2 storage resource are located in the Mississippi Canyon protraction area. Due to proximity to the Mississippi Delta (indicative of less infrastructure) and large estimated CO 2 storage resources, future development activities may wish to focus efforts in the Mississippi Canyon protraction area.

02 PETROLEUM↗
DOE OSTI2023

Convolutional Neural Network for Segmenting Micro-X-ray Computed Tomography Images of Wood Cellular Structures

To further enhance the performance of wood products, improved tools are needed to study in situ cellular scale phenomena like mechanical deformations and moisture swelling. Micro-X-ray computed tomography (μXCT) using brilliant synchrotron light sources now has the spatial and temporal resolution for real-time visualization of phenomena in three-dimensional cellular structures. However, the tradeoff for speed includes the loss of intensity contrast between different types of materials within the imaged structure, such as cell wall and air in wood. This loss of contrast prevents traditional histogram-based segmentation methods from being used effectively. A new convolutional neural network (CNN) approach was therefore developed to segment fast μXCT images of wood into cell wall and air volumes. The fast μXCT and segmentation were demonstrated in the study of moisture swelling in loblolly pine (Pinus taeda) earlywood and latewood cellular structures conditioned at 0%, 33%, 75%, and 95% relative humidity (RH). The CNN segmentation results had a mean intersection over union (IoU) metric accuracy of 96%. Initial analysis of the swelling in the latewood revealed cell walls swelled about 25% when conditioned from 0% to 95% RH. Additionally, the widths of ray cell lumina in the transverse plane of latewood could be observed to increase at higher RH. The segmentation method presented here will facilitate future quantitative analyses in in situ μXCT studies of wood and other similar cellular materials.

Arzola-Villegas, Xavier (ORCID:0000000305369766)↗
DOE OSTI2022

Experimental Investigation of a Phase Change Material Charged Finned-Tube Heat Exchanger

Understanding different thermal performance aspects of phase change material heat exchangers (PCM-HX) is critical for designing future energy-efficient thermal energy storage systems. This paper presents an experimental performance analysis of a vertically oriented annular finned-tube PCM-HX in a cylindrical container tested under six different melting and solidification test conditions, varied by heat transfer fluid’s (HTF) inlet temperatures and flow directions. The PCM-HX structure with 20 evenly spaced fins was 3D printed in aluminum, and the PCM-HX container was 285 mm in height. The PCM-HX average porosity was 89.7%, where the PCM mass was 246.4 g. Water served as the HTF, and a PCM with a nominal phase change temperature of 35 °C was selected. Instead of opaque conventional insulation sheets, a combination of air-and-argon-filled see-through insulation cylinders was assembled with the PCM-HX to visualize the phase-change phenomena, while minimizing the uncertainties due to heat loss. In total, there were 78 T-type thermocouples installed in the test section which allows a more precise assessment of thermal mass and heat loss, which are often neglected in similar studies found in the literature. We validated the reliability of the test facility as the repeated test results had negligible deviations under the same test conditions. The energy balances between the estimated theoretical and experimentally calculated PCM storage, considering heat loss and thermal mass, were within ±9% deviation for all test conditions. From the experimental investigations, we made several following observations. It was found that the melting pattern of the finned-tube PCM-HX with small gaps between the container wall and the fins was largely affected by the HTF flow directions, unlike the typical straight annular tube PCM-HX. For effective charging and discharging processes, a combination of upward melting and downward solidification is recommended to shorten the test duration. However, an upward solidification should be considered to minimize the cavity formation between the fins caused by the PCM volume contraction during the solidification process.

25 ENERGY STORAGE↗
DOE OSTI2024

Solving the Orszag–Tang vortex magnetohydrodynamics problem with physics-constrained convolutional neural networks

We study the 2D Orszag–Tang vortex magnetohydrodynamics (MHD) problem through the use of physics-constrained convolutional neural networks (PCNNs) for forecasting the density, ρ, and the magnetic field, B, as well as the prediction of B given the velocity field v of the fluid. In addition to translation equivariance from the convolutional architecture, other physics constraints were embedded: absence of magnetic monopoles, non-negativity of ρ, use of only relevant variables, and the periodic boundary conditions of the problem. The use of only relevant variables and the hard constraint of non-negative ρ were found to facilitate learning greatly. The divergenceless condition ∇·B=0 was implemented as a hard constraint up to machine precision through the use of a magnetic potential to define B=∇×A. Residual networks and data augmentation were also used to improve performance. This allowed for some of the residual models to function as surrogate models and provide reasonably accurate simulations. For the prediction task, the PCNNs were evaluated against a physics-informed neural network, which had the ideal MHD induction equation as a soft constraint. Several models were able to generate highly accurate fields, which are visually almost indistinguishable and have low mean squared error. Only methods with built-in hard constraints produced physical fields with ∇·B=0. The use of PCNNs for MHD has the potential to produce physically consistent real-time simulations to serve as virtual diagnostics in cases where inferences must be made with limited observables.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗