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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.

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At least 1,387 records · Page 77
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

QC-GN 2 oMS 2 : a Graph Neural Net for High Resolution Mass Spectra Prediction

Predicting the mass spectrum of a molecular ion is often accomplished via three generalized approaches: rules-based methods for bond breaking, deep learning, or quantum chemical (QC) modeling. Rules-based approaches are often limited by the conditions for different chemical subspaces and perform poorly under chemical regimes with few defined rules. QC modeling is theoretically robust but requires significant amounts of computational time to produce a spectrum for a given target. Among deep learning techniques, graph neural networks (GNNs) have performed better than previous work with fingerprint-based neural networks in mass spectra prediction. To explore this technique further, we investigate the effects of including quantum chemically derived information as edge features in the GNN to increase predictive accuracy. The models we investigated include categorical bond order, bond force constants derived from extended tight-binding (xTB) quantum chemistry, and acyclic bond dissociation energies. Throughout this work, we evaluated these models against a control GNN with no edge features in the input graphs. Bond dissociation enthalpies yielded the best improvement with a cosine similarity score of 0.462 relative to the baseline model (0.437). In this work we also apply dynamic graph attention which improves performance on benchmark problems and supports the inclusion of edge features. Between implementations, we investigate the nature of the molecular embedding for spectra prediction and discuss the recognition of fragment topographies in distinct chemistries for further development in tandem mass spectrometry prediction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Opportunities in AI/ML for the Rubin LSST Dark Energy Science Collaboration

The Vera C. Rubin Observatory's Legacy Survey of Space and Time (LSST) will produce unprecedented volumes of heterogeneous astronomical data (images, catalogs, and alerts) that challenge traditional analysis pipelines. The LSST Dark Energy Science Collaboration (DESC) aims to derive robust constraints on dark energy and dark matter from these data, requiring methods that are statistically powerful, scalable, and operationally reliable. Artificial intelligence and machine learning (AI/ML) are already embedded across DESC science workflows, from photometric redshifts and transient classification to weak lensing inference and cosmological simulations. Yet their utility for precision cosmology hinges on trustworthy uncertainty quantification, robustness to covariate shift and model misspecification, and reproducible integration within scientific pipelines. This white paper surveys the current landscape of AI/ML across DESC's primary cosmological probes and cross-cutting analyses, revealing that the same core methodologies and fundamental challenges recur across disparate science cases. Since progress on these cross-cutting challenges would benefit multiple probes simultaneously, we identify key methodological research priorities, including Bayesian inference at scale, physics-informed methods, validation frameworks, and active learning for discovery. With an eye on emerging techniques, we also explore the potential of the latest foundation model methodologies and LLM-driven agentic AI systems to reshape DESC workflows, provided their deployment is coupled with rigorous evaluation and governance. Finally, we discuss critical software, computing, data infrastructure, and human capital requirements for the successful deployment of these new methodologies, and consider associated risks and opportunities for broader coordination with external actors.

Aubourg, Eric [APC, Paris] (ORCID:000000025592023X↗
DOE OSTI2024

STSR-INR: Spatiotemporal super-resolution for multivariate time-varying volumetric data via implicit neural representation

Implicit neural representation (INR) has surfaced as a promising direction for solving different scientific visualization tasks due to its continuous representation and flexible input and output settings. We present STSR-INR, an INR solution for generating simultaneous spatiotemporal super-resolution for multivariate time-varying volumetric data. Inheriting the benefits of the INR-based approach, STSR-INR supports unsupervised learning and permits data upscaling with arbitrary spatial and temporal scale factors. Unlike existing GAN- or INR-based super-resolution methods, STSR-INR focuses on tackling variables or ensembles and enabling joint training across datasets of various spatiotemporal resolutions. Here we achieve this capability via a variable embedding scheme that learns latent vectors for different variables. In conjunction with a modulated structure in the network design, we employ a variational auto-decoder to optimize the learnable latent vectors to enable latent-space interpolation. To combat the slow training of INR, we leverage a multi-head strategy to improve training and inference speed with significant speedup. We demonstrate the effectiveness of STSR-INR with multiple scalar field datasets and compare it with conventional tricubic+linear interpolation and state-of-the-art deep-learning-based solutions (STNet and CoordNet).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Anisotropic interactions for continuum modeling of protein–membrane systems

In this work, a model for anisotropic interactions between proteins and cellular membranes is proposed for large-scale continuum simulations. The framework of the model is based on dynamic density functional theory, which provides a formalism to describe the lipid densities within the membrane as continuum fields while still maintaining the fidelity of the underlying molecular interactions. Within this framework, we extend recent results to include the anisotropic effects of protein–lipid interactions. As applications, we consider two membrane proteins of biological interest: a RAS–RAF complex tethered to the membrane and a membrane embedded G protein-coupled receptor. A strong qualitative and quantitative agreement is found between the numerical results and the corresponding molecular dynamics simulations. Combining the scope of continuum level simulations with the details from molecular level particle simulations enables research into protein–membrane behaviors at a more biologically relevant scale, which crucially can also be accessed via experiment.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRSDate not supplied

High dimensional similarity search with quantum assisted variational autoencoder

Recent progress in quantum algorithms and hardware is indicator of the potential importance of quantum computing in the next future. However, finding suitable application areas remains an active area of research. Quantum machine learning [1] is touted as a potential approach to demonstrate quantum advantage within both the gate-model [2,3] and the adiabatic [4,5] schemes. For instance, the Quantum-assisted Variational Autoencoder (QVAE) [6] has been proposed as a quantum enhancement to the discrete VAE [7]. We extend on previous work and study the real-world applicability of a QVAE, specifically, for similarity search in large-scale high dimensional datasets. While similarity search algorithms are available for low dimensional datasets, scaling to billion-scale datasets with thousands of dimensions is non-trivial. We show how the latent-space representation of a QVAE can be used to construct a space-efficient search index. We back up our claims by experimental results which show a correlation between the Hamming distance in the embedded space and the Euclidean distance in the original space on the Moderate Resolution Imaging Spectroradiometer (MODIS) dataset. Further, we show real-world speedups compared to linear search and demonstrate memory efficient scaling to large-scale datasets.

Nicholas D Gao↗
DOE OSTI2023

Study of The Compression of an Imploding Plasma and the Magnetic- Field Flux Using Advanced, Non-Intrusive, Spectroscopic Techniques

The main motivation of the project was to measure the magnetic field in pulsed power driven plasma compression using advanced non-intrusive spectroscopic techniques. The strength of the project is that it encompasses a combination of laboratory experiments with diagnostics for both the magnetic field and plasma properties and computational modeling. The following issues were addressed: (1) Plasma and magnetic field dynamics, (2) Field compression and diffusion, (3) Energy balance in the system, (4) Onset of instabilities, and (5) Correlation of the plasma and field evolutions with the initial conditions. The unique feature of the research was the use of advanced spectroscopy to measure both the magnetic field and various plasma properties in multiple locations using both side-on and end-on views, simultaneously. The experimental system allowed for imploding different gas mixtures (which facilitated local measurements) and for flexibility in modifying the initial conditions. Two current generators were used with significantly different current rise times (200 ns and 1.6 µs) but at the same current level of 400 kA. The slower pulsed power generator (at rise time 1.6 µs) was based at the Weizmann Institute of Science (WIS) and imploded plasma into which an axial magnetic field (up to 1 T) was initially embedded. The faster current rise time generator (at rise time 200 ns) based at University of California San Diego (UCSD) was used for plasma parameter studies initially, with collaborative efforts we successfully implemented the advanced spectroscopy techniques at UC San Diego. One graduate student (Nick Aybar) and a postdoctoral scholar (Maylis Dozeries) were trained. They both are based at the Lawrence Livermore National Laboratory now.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1997

The Accuracy of Saccadic and Perceptual Decisions in Visual Search

Saccadic eye movements during search for a target embedded in noise are suboptimally guided by information about target location. Our goal is to compare the spatial information used to guide the saccades with that used for the perceptual decision. Three observers were asked to determine the location of a bright disk (diameter = 21 min) in white noise (signal-to-noise ratio = 4.2) from among 10 possible locations evenly spaced at 5.9 deg eccentricity. In the first of four conditions, observers used natural eye movements. In the three remaining conditions, observers fixated a central cross at all times. The fixation conditions consisted of three different presentation times (100, 200, 300 msec), each followed by a mask. Eye-position data were collected, with a resolution of (approximately) 0.2 deg. In the natural viewing condition, we measured. the accuracy with respect to the target and the latency of the first saccade. In the fixation conditions, we discarded trials in which observers broke fixation. Perceptual performance was computed for all conditions. Averaged across observers, the first saccade was correct (closest to the target location) for 56 +/- (SD) % of trials (chance = 10 %) and occurred after a latency of 313 +/- 56 msec. Perceptual performance averaged 53 +/- 4, 63 +/- 4, 65 +/- 2 % correct at 100, 200, and 300 msec, respectively. For the signal-to-noise ratio used, at the time of initiation of the first saccade, there is little difference between the amount of information about target location available to the perceptual and saccadic systems.

Eckstein, Miguel P.↗
DOE OSTI2023

Experimental and numerical investigation of proppant embedment and conductivity reduction within a fracture in the Caney Shale, Southern Oklahoma, USA

The current worldwide energy supply is insufficient to meet the rising demand. As a result, the energy prices are expected to keep soaring despite the recent increases in a variety of renewable energy resources. Although not renewable, shale oil and gas — “unconventional” hydrocarbon resources are relatively clean forms of energy resources, which still hold a vast share of the energy market. For many oil and gas companies, meeting profitable production goals from shale reservoirs is sometimes challenging, due to the loss of fracture conductivity and premature declines in the production. In this paper we investigate the stress-dependent changes in the hydraulic conductivity of proppant-filled fractures and mechanical fracture–proppant interactions in Caney Shale, a calcareous, organic-rich mudrock, through laboratory experiments and numerical modeling. American Petroleum Institute (API) fracture conductivity tests were conducted using 2% KCl on five locations within the Caney Shale that consisted of selecting three brittle (reservoir) zones and two ductile zones. Confining pressures ranged from 1,000 psi to 12,000 psi at 210 °F. Conductivity, permeability as well as embedment were measured during the test. Also, an additional, laboratory in-situ visualization test was conducted to examine the detailed proppant-shale matrix interaction under elevated stress (3,920 psi effective stress) and temperature (252 °F), with a synthetic reservoir fluid. Our experimental results have confirmed that improved fracture conductivity is attributed to proppant size, and that the increase in porosity of the proppant pack, closure pressure changes and the reduction in fracture conductivity are a function of many factors such as fracture closure stress.

04 OIL SHALES AND TAR SANDS↗
DOE OSTI2024

Transferring predictions of formation energy across lattices of increasing size*

In this study, we show the transferability of graph convolutional neural network (GCNN) predictions of the formation energy of the nickel-platinum solid solution alloy across atomic structures of increasing sizes. The original dataset was generated with the large-scale atomic/molecular massively parallel simulator using the second nearest-neighbor modified embedded-atom method empirical interatomic potential. Geometry optimization was performed on the initially randomly generated face centered cubic crystal structures and the formation energy has been calculated at each step of the geometry optimization, with configurations spanning the whole compositional range. Using data from various steps of the geometry optimization, we first trained our open-source, scalable implementation of GCNN called HydraGNN on a lattice of 256 atoms, which accounts well for the short-range interactions. Using this data, we predicted the formation energy for lattices of 864 atoms and 2048 atoms, which resulted in lower-than-expected accuracy due to the long-range interactions present in these larger lattices. We accounted for the long-range interactions by including a small amount of training data representative for those two larger sizes, whereupon the predictions of HydraGNN scaled linearly with the size of the lattice. Therefore, our strategy ensured scalability while reducing significantly the computational cost of training on larger lattice sizes.

36 MATERIALS SCIENCE↗
DOE OSTI2025

TRUST Sensors in Environments: Thermocouples (SE-TC), Release FY25

The Delivery Environments Testbeds to Reduce Uncertainty in Simulations and Tests (TRUST) project is a broad project intended to analyze simplified problems experimentally and with modeling and simulation. The purpose of analyzing these simplified problems is to extend solution methods to more complex problems, as well as understand deficiencies and gaps in knowledge of methods currently used in more complex analyses. The TRUST project encompasses several smaller testbeds intended to isolate individual phenomena. The testbed under consideration in this report is the Sensors in Environments: Thermocouples testbed. In previous years, the purpose of this testbed was to quantify uncertainty of thermocouple sensors. To accomplish this, an aluminum plate was placed in a thermal chamber and subject to various types of thermal loading. Thermocouples were placed in various locations on the aluminum plate in various configurations (e.g., embedded in the plate, placed under Kapton tape), and an effort was made to quantify uncertainty in these measurements. Finite element simulations were performed to investigate how sensitive these measurements were to parameters such as the boundary conditions on the plate and material properties. However, a fundamental source of uncertainty in this analysis was the convective heat transfer from the plate. Convective heat transfer is a complex physical phenomenon comprised of a number of interacting sub-processes and is difficult to predict accurately a priori. As such, the main purpose of this testbed in FY25 was to better understand, both experimentally and numerically, the convective heat transfer from the plate. This is a highly applicable problem to several more complex problems, as convective heat transfer occurs in nearly all problems where a body is moving through air. Numerically, this required a two-step approach. First, the air flow in the thermal chamber was in vestigated using computational fluid dynamics. The commercial solver Fluent was used to perform these simulations. From these simulations, a heat transfer coefficient over the surface of the plate was calculated. This heat transfer was then used as boundary conditions for finite element heat transfer simulations within the plate, which were performed using Abaqus. Significant effort was devoted to automating the handoff between these two solvers. Experimentally, previous thermocouple results in the plate were used to validate the time-dependent thermal profiles produced from Abaqus. Further experimental efforts were performed both to help validate the Fluent simulations and to inform its boundary conditions. For example, hot-wire anemometers were used to measure the velocity in the chamber, which would be particularly useful in understanding the chamber inlet velocity. Thermocouple measurements were also taken in the chamber, instead of only on the plate, to serve as validation evidence for the Fluent simulations. Numerical results showed that the Fluent to Abaqus workflow matched previous plate thermocouple measurements well. This type of handoff is useful for more complex experiments, or those that are not able to be examined in as great of detail as this testbed, as it was performed without any experimental input. Experimental results, however, were more mixed. The anemometers proved unreliable, with inconsistent measurements across all anemometers, even at locations that were nearly identical. On the other hand, the thermocouples provided a relatively rich view of the temperature field in the chamber.

42 ENGINEERING↗
NASA NTRS2002

Flow-Field Measurement of Device-Induced Embedded Streamwise Vortex on a Flat Plate

Detailed flow-field measurements were performed downstream of a single vortex generator (VG) using an advanced Stereo Digital Particle Image Velocimetry system. Thc passive flow-control devices examined consisted of a low-profile VG with a device height, h, approximately equal to 20 percent of the boundary-layer thickness, sigma, and a conventional VG with h is approximately sigma. Flow-field data were taken at twelve cross-flow planes downstream of the VG to document and quantify the evolution of embedded streamwise vortex. The effects of device angle of attack on vortex development downstream were compared between the low-profile VG and the conventional VG. Key parameters including vorticity, circulation, trajectory, and half-life radius - describing concentration, strength, path, and size, respectively--of the device-induced streamwise vortex were extracted from the flow-field data. The magnitude of maximum vorticity increases as angle of attack increases for the low-profile VG, but the trend is reversed for the conventional VG, probably due to flow stalling around the larger device at higher angles of attack. Peak vorticity and circulation for the low-profile VG decays exponentially and inversely proportional to the distance downstream from the device. The device-height normalized vortex trajectories for the low-profile VG, especially in the lateral direction, follow the general trends of the conventional VG. The experimental database was used to validate the predictive capability of computational fluid dynamics (CFD). CFD accurately predicts the vortex circulation and path; however, improvements are needed for predicting the vorticity strength and vortex size.

Yao, Chung-Sheng↗
DOE OSTI2026

Predicting U 3 O 8 powder processing conditions: An AI/ML approach analyzing deep learning embeddings of SEM micrographs

High-resolution SEM images of uranium-oxide powders encode micro- and nanoscale clues to their synthesis route and calcination temperature. We trained a ResNet-50 model on 11 commercial-scale U₃O₈ classes, ammonium diuranate (ADU) or uranyl peroxide (H₂O₂) precursors calcined at temperatures ranging from 400 to 750 °C and added a 256-D projection head before the classifier to analyze the learned representation. The best of eight seeds reached 92.4 % accuracy on reserved testing data, but our focus is the structure of the embedding space rather than the accuracy and labels. We quantify class relatedness in the original 256-D space using centroid similarity and distributional distances, and we use Uniform Manifold Approximation Projection (UMAP) for visualization. ‘Unknown’ images from different preparation methods, SEM operators, and from the literature localized near the expected classes under a nearest-centroid analysis without retraining, as well as clustered in similar UMAP space. In conclusion, this embedding-centered workflow complements black-box classification by providing quantitative, similarity-based comparisons of U₃O₈ morphologies and reduces storage space by up to 98 % for image data used in millisecond vector search comparisons.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Accuracy of ghost rotationally invariant slave-boson and dynamical mean field theory as a function of the impurity-model bath size

Here, we compare the accuracy of the ghost rotationally invariant slave-boson (g-RISB) theory and dynamical mean field theory (DMFT) on the single-band Hubbard model, as a function of the number of bath sites in the embedding impurity Hamiltonian. Our benchmark calculations confirm that the accuracy of g-RISB can be systematically improved by increasing the number of bath sites, similar to DMFT. With a few bath sites, we observe that g-RISB is systematically more accurate than DMFT for the ground-state observables. On the other hand, the relative accuracy of these methods is generally comparable for the quasiparticle weight and the spectral function. As expected, we observe that g-RISB satisfies the variational principle in infinite dimensions, as the total energy decreases monotonically towards the exact value as a function of the number of bath sites, suggesting that the g-RISB wave function may approach the exact ground state in infinite dimensions. Our results suggest that the g-RISB is a promising method for first-principles simulations of strongly correlated matter, which can capture the behavior of both static and dynamical observables, at a relatively low computational cost.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1991

Investigation of vortex development on a pitching slender body of revolution

A computational study of the unsteady flow about a pitching 3.5 caliber tangent ogive forebody is presented. The flow is simulated using the full 3D unsteady Navier-Stokes equations and a time-accurate implicit algorithm. Comparison to available experimental data for a steady 20 deg case is presented as validation. Effects of grid resolution and a comparison of solutions using full Navier-Stokes and the thin-layer approximation are included. The forebody is simulated in a 'pitch-up to 20 deg and hold' maneuver, and two different pitch axis locations are used in the study. Examination of the unsteady vorticity field for the pitch-up cases reveals the formation of strong shear layers as the body decelerates, and their roll-up into vortical structures in a process similar to that observed in airfoil dynamic stall. Pronounced vortex/surface interactions are seen which produce multiple secondary separation regions, ejection of vorticity from the surface, and embedded regions of high suction.

Stanek, M. J.↗
DOE OSTI2024

HybridSystemsSimulations.jl - Solving the Merchant Collocated Facilities with JuMP

The development of new clean-generation technologies also leads to new plant-level architectures that combine several generation and storage assets behind the point of connection. These co-located generation resources (Hybrid Systems) primarily operate as merchant assets that employ automated market bidding models and internal Energy Management Systems (EMS) to comply with the operator's signals. Formulating an optimal bidding model requires embedding the EMS control model into the bidding algorithm, resulting in a bi-level optimization problem. In this presentation, we first showcase using JuMP to formulate and solve this problem effectively for multiple merchant systems and the bidding outcomes considering different model formulations. Second, the bidding outcomes are later integrated into a PowerSimulations.jl (also built with JuMP) simulation to study the system-level effects of the various merchant bidding and the interactions between market-clearing models and the embedded EMS model. We will showcase simulations conducted in the RTS system considering different levels of merchant hybrid systems participation. The presentation provides the following specific insights on JuMP usage: 1) the Formulation of specialized bi-level problems with custom cuts to solve the merchant hybrid system bidding problem; 2) the integration of a modular model within a complex simulation workflow supported by JuMP in PowerSimulations.jl; 3) Accelerating the solution of power systems operations simulation that employ agent optimization problems using JuMP.

energy markets↗
NASA NTRS2013

SpaceCube Version 1.5

SpaceCube 1.5 is a high-performance and low-power system in a compact form factor. It is a hybrid processing system consisting of CPU (central processing unit), FPGA (field-programmable gate array), and DSP (digital signal processor) processing elements. The primary processing engine is the Virtex- 5 FX100T FPGA, which has two embedded processors. The SpaceCube 1.5 System was a bridge to the SpaceCube 2.0 and SpaceCube 2.0 Mini processing systems. The SpaceCube 1.5 system was the primary avionics in the successful SMART (Small Rocket/Spacecraft Technology) Sounding Rocket mission that was launched in the summer of 2011. For SMART and similar missions, an avionics processor is required that is reconfigurable, has high processing capability, has multi-gigabit interfaces, is low power, and comes in a rugged/compact form factor. The original SpaceCube 1.0 met a number of the criteria, but did not possess the multi-gigabit interfaces that were required and is a higher-cost system. The SpaceCube 1.5 was designed with those mission requirements in mind. The SpaceCube 1.5 features one Xilinx Virtex-5 FX100T FPGA and has excellent size, weight, and power characteristics [4×4×3 in. (approx. = 10×10×8 cm), 3 lb (approx. = 1.4 kg), and 5 to 15 W depending on the application]. The estimated computing power of the two PowerPC 440s in the Virtex-5 FPGA is 1100 DMIPS each. The SpaceCube 1.5 includes two Gigabit Ethernet (1 Gbps) interfaces as well as two SATA-I/II interfaces (1.5 to 3.0 Gbps) for recording to data drives. The SpaceCube 1.5 also features DDR2 SDRAM (double data rate synchronous dynamic random access memory); 4- Gbit Flash for storing application code for the CPU, FPGA, and DSP processing elements; and a Xilinx Platform Flash XL to store FPGA configuration files or application code. The system also incorporates a 12 bit analog to digital converter with the ability to read 32 discrete analog sensor inputs. The SpaceCube 1.5 design also has a built-in accelerometer. In addition, the system has 12 receive and transmit RS- 422 interfaces for legacy support. The SpaceCube 1.5 processor card represents the first NASA Goddard design in a compact form factor featuring the Xilinx Virtex- 5. The SpaceCube 1.5 incorporates backward compatibility with the Space- Cube 1.0 form factor and stackable architecture. It also makes use of low-cost commercial parts, but is designed for operation in harsh environments.

Geist, Alessandro↗
DOE OSTI2024

E(n)-Equivariant cartesian tensor message passing interatomic potential

Machine learning potential (MLP) has been a popular topic in recent years for its capability to replace expensive first-principles calculations in some large systems. Meanwhile, message passing networks have gained significant attention due to their remarkable accuracy, and a wave of message passing networks based on Cartesian coordinates has emerged. However, the information of the node in these models is usually limited to scalars, and vectors. In this work, we propose High-order Tensor message Passing interatomic Potential (HotPP), an E(n) equivariant message passing neural network that extends the node embedding and message to an arbitrary order tensor. By performing some basic equivariant operations, high order tensors can be coupled very simply and thus the model can make direct predictions of high-order tensors such as dipole moments and polarizabilities without any modifications. The tests in several datasets show that HotPP not only achieves high accuracy in predicting target properties, but also successfully performs tasks such as calculating phonon spectra, infrared spectra, and Raman spectra, demonstrating its potential as a tool for future research.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Voronoi cell analysis: The shapes of particle systems

Many physical systems can be studied as collections of particles embedded in space, often evolving in time. Natural questions arise concerning how to characterize these arrangements—are they ordered or disordered? If they are ordered, how are they ordered and what kinds of defects do they possess? Voronoi tessellations, originally introduced to study problems in pure mathematics, have become a powerful and versatile tool for analyzing countless problems in pure and applied physics. Here we explain the basics of Voronoi tessellations and the shapes that they produce and describe how they can be used to characterize many physical systems.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗