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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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Application of prophage sequence analysis to investigate a disease outbreak involving Salmonella Adjame, a rare serovar and implications for the population structure

Introduction Outbreak investigation of foodborne salmonellosis is hindered when the food source is contaminated by multiple strains of Salmonella , creating difficulties matching an incriminated organism recovered from patients with the specific strain in the suspect food. An outbreak of the rare Salmonella Adjame was caused by multiple strains of the organism as revealed by single-nucleotide polymorphism (SNP) variation. The use of highly discriminatory prophage analysis to characterize strains of Salmonella should enable a more precise strain characterization and aid the investigation of foodborne salmonellosis. Methods We have carried out genomic analysis of S. Adjame strains recovered during the course of a recent outbreak and compared them with other strains of the organism ( n = 38 strains), using SNPs to evaluate strain differences present in the core genome, and prophage sequence typing (PST) to evaluate the accessory genome. Phylogenetic analyses were performed using both total prophage content and conserved prophages. Results The PST analysis of the S. Adjame isolates showed a high degree of strain heterogeneity. We observed small clusters made up of 2-6 isolates ( n = 27) and singletons ( n = 11) in stark contrast with the three clusters observed by SNP analysis. In total, we detected 24 prophages of which only four were highly prevalent, namely: Entero_p88 (36/38 strains), Salmon_SEN34 (35/38 strains), Burkho_phiE255 (33/38 strains) and Edward_GF (28/38 strains). Despite the marked strain diversity seen with prophage analysis, the distribution of the four most common prophages matched the clustering observed using core genome. Discussion Mutations in the core and accessory genomes of S. Adjame have shed light on the evolutionary relationships among the Adjame strains and demonstrated a convergence of the variations observed in both fractions of the genome. We conclude that core and accessory genomes analyses should be adopted in foodborne bacteria outbreak investigations to provide a more accurate strain description and facilitate reliable matching of isolates from patients and incriminated food sources. The outcomes should translate to a better understanding of the microbial population structure and an 46 improved source attribution in foodborne illnesses.

Gao, Ruimin↗
DOE OSTI2020

Radiation and Polarization Signatures from Magnetic Reconnection in Relativistic Jets. I. A Systematic Study

Blazars are relativistic magnetized plasma outflows from supermassive black holes that point very close to our line of sight. Their emission is nonthermal-dominated and highly variable across the entire electromagnetic spectrum. Relativistic magnetic reconnection has been proposed as the driver of particle acceleration during blazar flares. While recent particle-in-cell (PIC) simulations have self-consistently studied the evolution of magnetic reconnection and particle acceleration therein, the resulting radiation signatures have not been systematically explored. In particular, the polarization signatures, which directly reflect the characteristic strongly dynamical evolution of magnetic field during reconnection, have not been carefully investigated. In this paper, we present a systematic study of radiation and polarization signatures arising from magnetic reconnection in blazars, based on combined PIC and polarized radiation transfer simulations with various physical parameters. We identify a harder-when-brighter trend in the spectral evolution. Moreover, higher-frequency bands (ultraviolet to X-ray) tend to flare earlier than lower-frequency bands (infrared to optical) in the synchrotron spectral component. Most importantly, polarization signatures appear more variable with higher frequencies. We find that the variation in temporal polarization depends strongly on the guide field strength. Specifically, reconnection with a significant guide field component leads to a very high polarization degree that contradicts typical blazar observations, while large polarization angle rotations are unique signatures of magnetic reconnection between nearly antiparallel magnetic field lines. These rotations are at least 90° and can extend to >180°, and they may be in either direction. Furthermore, these results imply that blazars that have shown large polarization angle rotations intrinsically have more nearly antiparallel magnetic field morphology.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Constraints on the Electromagnetic Counterpart of the Neutron-star–Black-hole Merger GW200115

We report the results of our follow-up campaign for the neutron-star—black-hole (NSBH) merger GW200115 detected during the O3 run of the Advanced LIGO and Advanced Virgo detectors. We obtained wide-field observations with the Deca-Degree Optical Transient Imager covering ~20% of the total probability area down to a limiting magnitude of w = 20.5 AB at ~23 hr after the merger. Our search for counterparts returns a single candidate (AT2020aeo), likely not associated with the merger. In total, only 25 sources of interest were identified by the community and later discarded as unrelated to the GW event. We compare our upper limits with the emission predicted by state-of-the-art kilonova simulations and disfavor high-mass ejecta (>0.1 M⊙), indicating that the spin of the system is not particularly high. By combining our optical limits with gamma-ray constraints from Swift and Fermi, we disfavor the presence of a standard short-duration burst for viewing angles ≲15° from the jet axis. Our conclusions are, however, limited by the large localization region of this GW event, and accurate prompt positions remain crucial to improving the efficiency of follow-up efforts.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Neutrino many-body flavor evolution: The full Hamiltonian

We study neutrino flavor evolution in the quantum many-body approach using the full neutrino-neutrino Hamiltonian, including the usually neglected terms that mediate nonforward scattering processes. Working in the occupation number representation with plane waves as single-particle states, we explore the time evolution of simple initial states with up to N = 10 neutrinos. We discuss the time evolution of the Loschmidt echo, one body flavor and kinetic observables, and the one-body entanglement entropy. For the small systems considered, we observe “thermalization” of both flavor and momentum degrees of freedom on comparable time scales, with results converging towards expectation values computed within a microcanonical ensemble. We also observe that the inclusion of nonforward processes generates a faster flavor evolution compared to the one induced by the truncated (forward) Hamiltonian. Published by the American Physical Society 2024

Cirigliano, Vincenzo (ORCID:000000029056754X)↗
DOE OSTI2020

Magnetic structure and exchange interactions in the layered semiconductor CrPS 4

Compounds with two-dimensional (2D) layers of magnetic ions weakly connected by van der Waals bonding offer routes to enhance quantum behavior, stimulating both fundamental and applied interest. CrPS 4 is one such magnetic van der Waals material, however, it has undergone only limited investigation. Here we present a comprehensive series of neutron scattering measurements to determine the magnetic structure and exchange interactions. The observed magnetic excitations allow a high degree of constraint on the model parameters not normally associated with measurements on a powder sample. The results demonstrate the 2D nature of the magnetic interactions, while also revealing the importance of interactions along 1D chains within the layers. The subtle role of competing interactions is observed, which manifest in a nontrivial magnetic transition and a tunable magnetic structure in a small applied magnetic field through a spin-flop transition. Our results on the bulk compound provide insights that can be applied to an understanding of the behavior of reduced layer CrPS 4 .

36 MATERIALS SCIENCE↗
DOE OSTI2022

Limits on X-Ray Polarization at the Core of Centaurus A as Observed with the Imaging X-Ray Polarimetry Explorer

We present measurements of the polarization of X-rays in the 2–8 keV band from the nucleus of the radio galaxy Centaurus A (Cen A), using a 100 ks observation from the Imaging X-ray Polarimetry Explorer (IXPE). Nearly simultaneous observations of Cen A were also taken with the Swift, NuSTAR, and INTEGRAL observatories. No statistically significant degree of polarization is detected with IXPE. These observations have a minimum detectable polarization at 99% confidence (MDP 99 ) of 6.5% using a weighted, spectral model-independent calculation in the 2–8 keV band. The polarization angle ψ is consequently unconstrained. Spectral fitting across three orders of magnitude in X-ray energy (0.3–400 keV) demonstrates that the SED of Cen A is well described by a simple power law with moderate intrinsic absorption (N H ~ 10 23 cm -2 ) and a Fe Kα emission line, although a second unabsorbed power law is required to account for the observed spectrum at energies below 2 keV. This spectrum suggests that the reprocessing material responsible for this emission line is optically thin and distant from the central black hole. Our upper limits on the X-ray polarization are consistent with the predictions of Compton scattering, although the specific seed photon population responsible for the production of the X-rays cannot be identified. The low polarization degree, variability in the core emission, and the relative lack of variability in the Fe Kα emission line support a picture where electrons are accelerated in a region of highly disordered magnetic fields surrounding the innermost jet.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Efficacy of SCMs to mitigate ASR in systems with higher alkali contents assessed by pore solution method

This study demonstrates the efficacy of supplementary cementitious materials (SCMs) to mitigate alkali-silica reaction (ASR) even when used in conjunction with cement of higher alkali contents (up to 1% Na{sub 2}O{sub eq}). The expansion of concrete prisms was studied immersed in simulated pore solution in order to address the limitations of conventional ASR testing methods, accelerated mortar bar test (AMBT) and concrete prism test (CPT). Expansion results demonstrate that 25% fly ash and 50% slag are both sufficient to mitigate ASR even with cements with alkali content up to 1% Na{sub 2}O{sub eq} and that the pore solution method is a viable alternative ASR testing method. Massive amounts of ASR products (~20 μm thickness) were observed in concretes without SCMs consistent with high degree of expansion and extensive cracking. Small amounts of ASR products (≤5 μm thickness) were also observed in concrete with SCMs despite absence of significant expansion.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Numerical simulation of vortex-induced vibration response of a single IEA 10-MW wind turbine blade

Three-dimensional simulation of vortex-induced vibration (VIV) of a single International Energy Agency (IEA) 10-MW reference wind turbine blade with a length of 97.325 m is performed using the ExaWind stack, an open-source suite of codes. This study aims to illustrate the spanwise VIV response characteristics and cross-validate the results with an existing commercial framework. Five near-body meshes and three time steps are selected for the convergence study. To improve computational efficiency, several VIV triggering methods are also compared to shorten the VIV development period. The ExaWind-based VIV simulation strategy for a single IEA 10-MW blade is determined. First, the modal shape is validated against published results. Then, spanwise VIV responses of four blade configurations under a fixed and varied incoming flow velocity are analyzed. Results show that the VIV response is dominated by the first edgewise (second overall) mode. Little first-mode contributions appear near the second-mode node, producing a pi phase jump, and a higher harmonics response occurs near the blade root. Rotational degrees of freedom are minor compared with translational motion. The response versus reduced velocity is analyzed, showing a two-branch behavior similar to that of VIV for a bluff cylinder. Across all tested cases, the dominant frequency remains locked to the natural frequency of the second mode with no observed desynchronization. A mild deviation is observed for the case of 90-degree pitch and 310-degree azimuth rotation near a reduced velocity of 6, which will be examined with additional cases in future work. These findings indicate that severe VIV responses can arise under specific configurations and flow conditions, thereby increasing the potential for VIV fatigue damage and requiring greater attention during operation.

17 WIND ENERGY↗
DOE OSTI2021

Studying the effect of the upper internal structure design on thermal stratification in sodium fast reactors

Thermal stratification and mixing in large reactor pools can pose significant issues with regard to operation and safety of nuclear plants. While significant work has been done in this area on light water reactors it is more critical for sodium reactors and there is far less data with regard to low Prandtl number fluids. Here this paper focuses on the effect of the upper internal structure on the formation of thermal stratification in a scaled sodium fast reactor upper plenum. Six different upper internal structure configurations were tested to observe the effect on thermal stratification. The degree of stratification was quantified using the stratification number. Each configuration was tested from low to high flow rates at a temperature difference of 50 and 100 °C. Over this broad array of testing, it was observed that higher flow rates, more porosity in the upper internal structure design, and a smaller temperature difference yielded a lower degree of stratification. This information can be used to aid in the design of the upper internal structure in a sodium fast reactor. Furthermore, this high resolved temperature data can be used to verify models under prototypic low Prandtl numbers.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Spectroscopy of the T = 2 mirror nuclei 48 Fe/ 48 Ti using mirrored knockout reactions

A sequence of excited states has been established for the first time in the proton-rich nucleus 48 Fe (Z=26, N=22). The technique of mirrored (i.e. analogue) one-nucleon knockout reactions was applied, in which the T z = ±2 mirror pair, 48 Fe/ 48 Ti were populated via one-neutron/one-proton knockout from the secondary beams 49 Fe/ 49 V, respectively. The analogue properties of the reactions were used to help establish the new level scheme of 48 Fe. The inclusive and exclusive cross sections were determined for the populated states. Large differences between the cross sections for the two mirrored reactions were observed and have been interpreted in terms of different degrees of binding of the mirror nuclei and in the context of the recent observations of suppression of spectroscopic strength as a function of nuclear binding, for knockout reactions on light solid targets. Mirror energy differences (MED) have been determined between the analogue T = 2 states and compared with the shell model predictions. MED for this mirror pair, due to their location in the shell, are especially sensitive to excitations out of the f 7/2 shell, and present a stringent test of the shell-model prescription.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

New physics contamination to precision luminosity measurements at future 𝑒 +⁢ 𝑒 − colliders

Several key observables of the high-precision physics program at future lepton colliders will critically depend on the knowledge of the absolute machine luminosity. The determination of the luminosity relies on the precise knowledge of some reference process, which is, in principle, not affected by unknown physics, so that its cross section can be computed within a well-established theory, like the Standard Model. Quantifying the uncertainties induced by possible new physics effects on such processes is, therefore, crucial. We present an investigation of light and heavy new physics contributions to the small-angle Bhabha process at future 𝑒 + ⁢𝑒 − colliders, and we discuss possible strategies to remove the contamination due to heavy degrees of freedom by relying on observables that are independent of the absolute luminosity.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Effects of spatial resolution on WRF v3.8.1 simulated meteorology over the central Himalaya

The sensitive ecosystem of the central Himalayan (CH) region, which is experiencing enhanced stress from anthropogenic forcing, requires adequate atmospheric observations and an improved representation of the Himalaya in the models. However, the accuracy of atmospheric models remains limited in this region due to highly complex mountainous topography. This article delineates the effects of spatial resolution on the modeled meteorology and dynamics over the CH by utilizing the Weather Research and Forecasting (WRF) model extensively evaluated against the Ganges Valley Aerosol Experiment (GVAX) observations during the summer monsoon. The WRF simulation is performed over a domain (d01) encompassing northern India at 15 km x 15 km resolution and two nests (d02 at 5 km x 5 km and d03 at 1 km x 1 km) centered over the CH, with boundary conditions from the respective parent domains. WRF simulations reveal higher variability in meteorology, e.g., relative humidity (RH = 70.3%-96.1%) and wind speed (WS = 1.1-4.2m s(-1)), compared to the ERA-Interim reanalysis (RH D 80.0%-85.0%, WS D 1.2-2.3m s(-1)) over northern India owing to the higher resolution. WRF-simulated temporal evolution of meteorological variables is found to agree with balloon-borne measurements, with stronger correlations aloft (r = 0.44-0.92) than those in the lower troposphere (r = 0.18-0.48). The model overestimates temperature (warm bias by 2.8 degrees C) and underestimates RH (dry bias by 6.4 %) at the surface in d01. Model results show a significant improvement in d03 (P = 827.6 hPa, T = 19.8 degrees C, RH = 92.3 %), closer to the GVAX observations (P = 801.4 hPa, T = 19.5 degrees C, RH = 94.7 %). Interpolating the output from the coarser domains (d01, d02) to the altitude of the station reduces the biases in pressure and temperature; however, it suppresses the diurnal variations, highlighting the importance of well-resolved terrain (d03). Temporal variations in near-surface P, T, and RH are also reproduced by WRF in d03 to an extent (r>0:5). A sensitivity simulation incorporating the feedback from the nested domain demonstrates the improvement in simulated P, T, and RH over the CH. Our study shows that the WRF model setup at finer spatial resolution can significantly reduce the biases in simulated meteorology, and such an improved representation of the CH can be adopted through domain feedback into regional-scale simulations. Interestingly, WRF simulates a dominant easterly wind component at 1 km x 1 km resolution (d03), which is missing in the coarse simulations; however, the frequency of southeasterlies remains underestimated. The model simulation implementing a highresolution (3 s) topography input (SRTM) improved the prediction of wind directions; nevertheless, further improvements are required to better reproduce the observed local-scale dynamics over the CH.

Singh, Jaydeep↗
DOE OSTI2025

Band-Selective Spin-Charge Separation across the Charge Density Wave Transition in Quasi-1D NbSe 3

Non-Fermi liquid (non-FL) phase is a pivotal enigma in understanding intriguing quantum phases in strongly correlated systems, such as high-temperature superconductivity. Tomonaga-Luttinger liquid (TLL) theory, designed for one-dimensional (1D) systems, serves as one of the microscopic frameworks that elucidates non-FL behavior. Despite its theoretical concreteness, comprehensive experimental verification has remained incomplete. In particular, addressing the persistence of the TLL nature within ordered phases, such as charge density wave (CDW), has posed a significant challenge. We report the observation of TLL characteristics across the CDW transitions in a quasi-1D material NbSe 3 using angle-resolved photoemission spectroscopy. Spin-charge separation, a disentanglement of spin and charge degrees of freedom of electrons, is clearly observed within the band, accompanied by the suppression of spectral weight following a power-law behavior with anticipated temperature scaling. Surprisingly, the spin-charge separation persists even below the CDW transition temperatures, indicating the validity of the TLL nature in the CDW phase. In conclusion, our findings offer a unique opportunity to explore the interplay between the TLL and ordered phases, which could be connected to the interplay between non-FL and ordered phases in strongly correlated systems.

1-dimensional systems↗
DOE OSTI2023

Noncommutative Bohnenblust–Hille inequalities

Abstract Bohnenblust–Hille inequalities for Boolean cubes have been proven with dimension-free constants that grow subexponentially in the degree (Defant et al. in Math Ann 374(1):653–680, 2019). Such inequalities have found great applications in learning low-degree Boolean functions (Eskenazis and Ivanisvili in Proceedings of the 54th annual ACM SIGACT symposium on theory of computing, pp 203–207, 2022). Motivated by learning quantum observables, a qubit analogue of Bohnenblust–Hille inequality for Boolean cubes was recently conjectured in Rouzé et al. (Quantum Talagrand, KKL and Friedgut’s theorems and the learnability of quantum Boolean functions, 2022. arXiv preprint arXiv:2209.07279 ). The conjecture was resolved in Huang et al. (Learning to predict arbitrary quantum processes, 2022. arXiv preprint arXiv:2210.14894 ). In this paper, we give a new proof of these Bohnenblust–Hille inequalities for qubit system with constants that are dimension-free and of exponential growth in the degree. As a consequence, we obtain a junta theorem for low-degree polynomials. Using similar ideas, we also study learning problems of low degree quantum observables and Bohr’s radius phenomenon on quantum Boolean cubes.

Volberg, Alexander↗
DOE OSTI2026

Weak Lensing Mass Calibration of the ACT DR5 Galaxy Clusters with the DES Year 3 Weak Lensing Data

We use weak gravitational lensing measurements from Year 3 Dark Energy Survey data to calibrate the masses of 443 galaxy clusters selected via the Sunyaev-Zel'dovich effect from Atacama Cosmology Telescope Data Release 5 maps of the cosmic microwave background. We incorporate redshift and SZ measurements for individual clusters into a hierarchical model for the stacked lensing signals and perform Bayesian analyses to constrain the hydrostatic mass bias of the clusters. Our treatment of systematic uncertainties includes a prescription for measuring and accounting for the weak lensing boost factor, consideration of a miscentering effect, as well as marginalization over uncertainties in the source galaxy photometric redshift distributions and shear calibration. The resultant constraints on the normalization of the mass-observable relation have a precision of approximately 7%, with the mean WL halo mass of M $_{500c}$ = 5.4 × 10$^{14}$ M $_{⊙}$. We measure the bias between the true cluster mass and the mass estimated from the SZ signal based on an X-ray-calibrated scaling relation assuming hydrostatic equilibrium, to be 1 - b = 0.74$^{+0.06}$ $_{-0.05}$ over the full sample. When splitting the clusters into high (z = 0.43-0.70) and low (z = 0.15-0.43) redshift bins, we measure 1 - b = 0.58$^{+0.06}$ $_{-0.05}$ and 0.81$^{+0.08}$ $_{-0.06}$, respectively. When introducing additional freedom in redshift and mass to the hydrostatic bias model, we find that 1 - b decreases with redshift (with the power law of -1.8$^{+0.5}$ $_{-0.6}$, 99.95% confidence), consistent with findings from other recent studies, while we do not find any significant trend in mass. We also demonstrate that our result is robust against various systematics such as a scale cut, priors on baryonic and miscentering parameters, and degree of scatter in mass-observable relation. The weak-lensing mass calibration presented in this study will be a useful tool for using the ACT clusters as probes of astrophysics, and as a step towards using their abundance as a cosmological probe.

Shin, T. [Carnegie Mellon U.] (ORCID:0000000263895↗
DOE OSTI2025

Partners in root nodule symbiosis respond uniquely to heavy metal stresses in a host genotype-dependent manner

Abstract The mutualistic symbiosis between legume roots and soil rhizobia culminates in the formation of root nodules, where nitrogen is fixed. Root nodule symbiosis is inhibited by heavy metal stress. In this study, we investigated the relative responses of the symbiotic partners to a non-essential heavy metal cadmium (Cd) and an essential heavy metal zinc (Zn) stress and identified patterns in gene expression. We performed dual transcriptomics in nodules, using theMedicago truncatula-Sinorhizobium melilotisymbiotic system. Phenotypes were measured in the wild-typeMedicago truncatulaand a mutant in anABCtransporter gene (Mtabcg36), which showed compromised nodule formation in control conditions and further after heavy metal treatment. We observed that the rhizobia were particularly sensitive to Zn in mutant nodules. The greatest degree of differential gene expression in the host plant were observed under Cd and Zn treatments in wild-type nodules. Most Cd-regulated host genes were also differentially regulated by Zn, revealing little discernment between an essential and a non-essential ion under increased exposure. Furthermore, the host response to both the stresses affected auxin and iron homeostasis genes in a host genotype-dependent manner. Our results suggested impaired cadmium export from the mutant nodules. These results have potential implications in agricultural management systems and bioremediation strategies.

Science & Technology - Other Topics↗
DOE OSTI2021

Repetitively pulsed nanosecond discharge plasma decay in propane–oxygen gas mixture in the presence of a heating electric field

Plasma decay in the afterglow of a repetitively pulsed nanosecond discharge in a stoichiometric propane–oxygen mixture was experimentally investigated when a weak heating DC electric field was applied and in its absence. The discharge was ignited at room gas temperature and a pressure of 1–2 Torr and was characterized by low specific energy inputs (<0.004 eV per molecule in one pulse). Using microwave interferometry, the temporal evolution of the electron density during plasma decay was studied, and the effective recombination coefficients were obtained from data processing. It was shown that the rate of plasma decay behaved in a non-monotonic manner with increasing degree of propane oxidation; at first the decay rate grew, then passed through a maximum, fell and saturated in the limit of a large (~2000) number of pulses. In this limit, the effect of the heating DC electric field on the plasma decay decreased with approaching chemical equilibrium. Numerical simulation of the observed effects was performed for low and high oxidation degrees of propane taking into account changes in the composition of positive ions in the plasma. Good agreement was obtained between measurements and calculations of the electron density during plasma decay in these cases. Here it was shown that the formation of cluster ions in the discharge afterglow plays a fundamental role. The plasma decay was controlled by electron recombination with hydrocarbon cluster ion at low oxidation degree of propane and with water cluster (hydrated) ions at high oxidation degree. A hypothesis was proposed to explain the observed nonmonotonic behavior of the plasma decay rate with an increase in the propane oxidation in the discharge, based on the formation of hydrated hydrocarbon ions C x H y + (H 2 O) k at moderate oxidation degrees.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Double holography in string theory

We develop the notion of double holography in Type IIB string theory realizations of braneworld models. The Type IIB setups are based on the holographic duals of 4d BCFTs comprising 4d N = 4 SYM on a half space coupled to 3d N = 4 SCFTs on the boundary. Based on the concrete BCFTs and their brane construction, we provide microscopic realizations of the intermediate holographic description, obtained by dualizing only the 3d degrees of freedom. Triggered by recent observations in bottom-up models, we discuss the causal structures in the full BCFT duals and intermediate descriptions. This confirms qualitative features found in the bottom-up models but suggests a refinement of their interpretation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗