Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “persistent current”

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 91 records · Page 5

Precision current regulator for NMR electromagnets

When using electromagnets or non-persistent superconducting magnets, the field stability can be directly proportional to the current stability. We present in this report a simple design for a current regulator based upon a high-precision, dc-dc fluxgate transformer. The output current and NMR frequency are stabilized by about a factor of 50, over times of order one hour. The method can be applied to essentially any current supply.

59 BASIC BIOLOGICAL SCIENCES↗

Fredkin Staircase: An Integrable System with a Finite-Frequency Drude Peak

We introduce and explore an interacting integrable cellular automaton, the Fredkin staircase, that lies outside the existing classification of such automata, and has a structure that seems to lie beyond that of any existing Bethe-solvable model. The Fredkin staircase has two families of ballistically propagating quasiparticles, each with infinitely many species. Despite the presence of ballistic quasiparticles, charge transport is diffusive in the d.c. limit, albeit with a highly non- gaussian dynamic structure factor. Remarkably, this model exhibits persistent temporal oscillations of the current, leading to a delta-function singularity (Drude peak) in the a.c. conductivity at nonzero frequency. Here, we analytically construct an extensive set of operators that anticommute with the time-evolution operator; the existence of these operators both demonstrates the integrability of the model and allows us to lower-bound the weight of this finite-frequency singularity.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Application of electron beam technology to decompose persistent emerging drinking water contaminants: poly- and perfluoroalkyl substances (PFAS) and 1,4-Dioxane

Poly- and perfluoroalkyl substances (PFAS) and 1,4-dioxane are persistent emerging contaminants that are currently under consideration for federal and state-specific regulations in drinking water. Both PFAS and 1,4-dioxane are highly resistant to degradation and are not effectively removed by conventional drinking water treatment systems. Results from the Unregulated Contaminant Monitoring Rule 3 survey showed that >540 sites across the nation are contaminated with both PFAS and 1,4-dioxane. Hence, there is a need to identify technologies that can effectively remove both these contaminants. Water treatment via electron beam (e-beam) has been proven effective at treating a wide range of contaminants, including perfluorooctane sulfonate (PFOS), perfluorooctanoate (PFOA), polychlorinated biphenyls, and trichloroethylene. While the e-beam process is often considered similar to advanced oxidation processes (AOPs), e-beam technology is unique in that it produces both highly oxidizing and reducing species at the same time. The specific objectives of this study were to: (i) determine the effectiveness of 9 MeV electrons provided by the Fermilab’s Accelerator Application Development and Demonstration (A2D2) tool to decompose PFAS and 1,4-dioxane; (ii) assess the formation of byproducts during water treatment; (iii) apply the optimized treatment to field groundwater samples contaminated with PFAS and 1,4-dioxane, and (iv) assess the energy demands for the treatment of these contaminants using e-beam. Results from this study showed that e-beam is effective in treating both 1,4-dioxane and PFAS. Complete degradation of 1,4-dioxane was observed at a dose of 5 kGy for an initial concentration of up to 1 ppm without the need for any sample modification. The electrical energy per order (EEo) for treatment of 1,4-dioxane ranged from 0.46 to 0.72 kWh/m 3 /order and was comparable and even lower, in some cases, than other AOP technologies. Alkaline conditions (pH 13) and low dissolved oxygen concentration (2 mg/L) highly favored the treatment of PFAS by e-beam. Greater than 90% removal of PFOA and PFOS from an initial concentration of 100 to 500 ppb was achieved at a dose of 250 kGy and 500 kGy, respectively, under optimized conditions. The degradation efficiency was not significantly changed when treating other PFAS of fluorinated carbon chain length of 5 to 7 individually at 250 kGy with a removal ranging from 85¬–99% for different compounds. Short chain PFAS (perfluorobutanoate: PFBA and perfluorobutane sulfonate: PFBS) did not degrade under the same conditions at 250 kGy, but 70 to 99% degradation was observed at a higher dose of 1000 kGy. Short chain PFAS (perfluorohexanoate: PFHxA (C5) and perfluoroheptanoate: PFHpA (C6)) were detected after treatment of PFOA, but not after PFOS treatment. Inability to close the mass balance through targeted analysis suggests the presence of other intermediates not detectable by available analytical methods. When treating PFAS mixture containing ten compounds at equimolar concentration of 0.05 µM each, preferential degradation of polyfluorinated compound (6:2 fluorotelomer sulfonate or 6:2 FTS) followed by C8 and C7 compounds was observed as a function of increasing e-beam dose. About 30% degradation of ΣPFAS was observed at 250 kGy and no further removal was observed up to a dose of 1000 kGy. C4 to C6 PFASs showed no degradation, while C3 PFAS (PFBS) showed an increase in concentration by 34% at 1000 kGy due to formation from the breakdown of other long chain PFAS. These results suggested that (a) the reaction kinetics is likely different for different PFAS based on chain length, functional group, and the degree of fluorination of the carbon chain, and (b) there may be intermediates generated from the degradation of 6:2 FTS and C7/C8 compounds that can potentially scavenge hydrated electrons needed for reaction with the untreated PFAS molecules. Treatment of three PFAS-contaminated groundwater samples from two US states showed similar trends as observed in the treatment of equimolar PFAS mixtures. Up to 71% removal of ΣPFAS was achieved in real groundwater samples at 750 kGy and data trend suggested that higher degradation is feasible if higher doses (>1MGy) are applied to treat field samples to overcome matrix effects and competing species. Calculated EEo for PFAS ranged from as low as ~48 to 1081 kWh/m 3 /order depending on the type of PFAS treated. These values are comparable and even lower, in some cases, than other destructive technologies employed for PFAS treatment such as ultrasound, plasma, and photochemical treatment. The results from this study indicate e-beam is a promising approach under favorable conditions and should be explored further as an end-of-train treatment option for PFAS destruction.

1,4-Dioxane↗

Crystal Engineering of Hydrogen Bonding for Direct Air Capture of CO2: A Quantum Crystallography Perspective

Rising atmospheric CO2 levels demand efficient and sustainable carbon capture solutions. Direct air capture (DAC) via crystallizing hydrogen-bonded frameworks such as carbonate salts has emerged as a promising approach. This review explores the potential of crystal engineering, in tandem with advanced quantum crystallography techniques and computational modeling, to unlock the full potential of DAC materials. We examine the critical role of hydrogen bonding and other noncovalent interactions within a family of bis-guanidines that governs the formation of carbonate salts with high CO2 capture capacity and low regeneration energies for utilization. Quantum crystallography and charge density analysis prove instrumental in elucidating these interactions. A case study of a highly insoluble carbonate salt of a 2,6-pyridine-bis-(iminoguanidine) exemplifies the effectiveness of these approaches. However, challenges remain in the systematic and precise determination of hydrogen atom positions and atomic displacement parameters within DAC materials using quantum crystallography, and limitations persist in the accuracy of current energy estimation models for hydrogen bonding interactions. Future directions lie in exploring diverse functional groups, designing advanced hydrogen-bonded frameworks, and seamlessly integrating experimental and computational modeling with machine learning. This synergistic approach promises to propel the design and optimization of DAC materials, paving the way for a more sustainable future.

36 MATERIALS SCIENCE↗

Structure and evolution of the large scale solar and heliospheric magnetic fields

Structure and evolution of large scale photospheric and coronal magnetic fields in the interval 1976-1983 were studied using observations from the Stanford Solar Observatory and a potential field model. The solar wind in the heliosphere is organized into large regions in which the magnetic field has a componenet either toward or away from the sun. The model predicts the location of the current sheet separating these regions. Near solar minimum, in 1976, the current sheet lay within a few degrees of the solar equator having two extensions north and south of the equator. Soon after minimum the latitudinal extent began to increase. The sheet reached to at least 50 deg from 1978 through 1983. The complex structure near maximum occasionally included multiple current sheets. Large scale structures persist for up to two years during the entire interval. To minimize errors in determining the structure of the heliospheric field particular attention was paid to decreasing the distorting effects of rapid field evolution, finding the optimum source surface radius, determining the correction to the sun's polar field, and handling missing data. The predicted structure agrees with direct interplanetary field measurements taken near the ecliptic and with coronameter and interplanetary scintillation measurements which infer the three dimensional interplanetary magnetic structure. During most of the solar cycle the heliospheric field cannot be adequately described as a dipole.

Hoeksema, J. T.↗

Energetic charged-particle phenomena in the Jovian magnetosphere - First results from the Ulysses COSPIN collaboration

The Ulysses spacecraft made the first exploration of the region of Jupiter's magnetosphere at high Jovigraphic latitudes on the dusk side and reached higher magnetic latitudes on the day side than any previous mission to Jupiter. The cosmic and solar particle investigations (COSPIN) instrumentation achieved a remarkably well integrated set of observations of energetic charged particles in the energy ranges of about 1 to 170 megaelectron volts for electrons and 0.3 to 20 megaelectron volts for protons and heavier nuclei. The new findings include an apparent polar cap region in the northern hemisphere in which energetic charged particles following Jovian magnetic field lines may have direct access to the interplanetary medium; high-energy electron bursts on the dusk side that are apparently associated with field-aligned currents and radio burst emissions; persistence of the global 10-hour relativistic electron 'clock' phenomenon throughout Jupiter's magnetosphere; on the basis of charged-particle measurements, apparent dragging of magnetic field lines at large radii in the dusk sector toward the tail; and consistent outflow of megaelectron volt electrons and large-scale departures from corotation for nucleons.

Simpson, J. A.↗

Density fluctuations in solar wind flow types at 1 AU: Comparison to Doppler scintillation measurements

Density fluctuations with periods 10 minutes to 1 hour have been investigated in ISEE 3 plasma measurements of solar wind flows at l AU. Coronal hole, interstream, plasma sheet, coronal mass ejection, and interaction region flow types are considered. The ISEE 3 results support the interpretation of the large-scale variations in density fluctuations observed by Doppler scintillation measurement techniques inside 0.2 AU. The highest absolute and relative density fluctuations occur ahead of and within the plasma from coronal mass ejections, with the maximum values occurring between the associated interplanetary shocks and the driver gas. For the quasi-stationary solar wind, density and relative density fluctuations are highest around the heliospheric current sheet and lowest in the high-speed coronal flow. Superposed epoch analysis shows that the region of enhanced density fluctuations and its abrupt boundaries observed in the vicinity of the heliospheric current sheet near the Sun persists to l AU, providing further support for the filamentary nature of the extensions of coronal streamers. The results of this study confirm the advantages of using density fluctuations rather than density as a tracer of solar wind flows with differing origins at the Sun and as a detector of propagating interplanetary disturbances.

Huddleston, D. E.↗

Dynamics of the Cold Water Event off the Southeast Coast of the United States in the Summer of 2003: An Application of NASA's Remote Sensing Data to Coastal Studies

The Moderate Resolution Imaging Spectroradiometer (MODIS) instruments onboard of Terra and Aqua satellites provide, for the first time, concurrent measurements of sea surface temperature (SST) and ocean color, which are suitable for coastal upwelling studies. The accuracy, the 1-km spatial resolution, and the almost complete daily coverage of the MODIS data compared with historical measurements make it advantageous for resolving important coastal fronts of chlorophyll concentration and temperature. The cold SST anomaly during summer 2003 off the coast of the South Atlantic Bight is an event that is comprehensively covered by NASA's MODIS and SeaWinds satellite observations. These data combined with in situ tide gauge, mooring, and ship measurements can be used to identify important dynamics responsible for the anomalous cold water event. The analysis of the data suggests that coastal upwelling occurs in the climatological summer forced by the climatological southerlies over the South Atlantic Bight area in summer. However, the strong buoyancy barrier in summer prevents the cold water below the thermocline from reaching the ocean surface. In summer 2003, the southwesterlies in July through August were extraordinarily strong and persistent, which generated the upwelling currents strong enough to overcome the buoyancy resistance. The results of this analysis demonstrate the possibility of monitoring and forecasting the event using combination of the satellite and in situ observations. The MODIS data are archived and distributed by the NASA's Goddard Earth Science (GES) Distributed Active Archive Center (DAAC). The data can be accessed via the URL http://wwv.daac.gsfc.nasa.gov/MODIS.

Yuan, Dongliang↗

Spreadsheets in Team X: Preserving Order in an Inherently Chaotic Environment

JPL is NASA's prime center for deep space missions. In response to the need to reduce the cost and time to complete early concept studies and proposals JPL created the first concurrent engineering team in the aerospace industry: Team X. Started in 1995, Team X has carried out over 800 studies, dramatically reducing the time and cost involved, and has been the model for other concurrent engineering teams both within NASA and throughout the larger aerospace community. Since its inception, the software backbone of this highly successful design team - engaged in examining some of NASA's cutting edge concepts - has been the unassuming spreadsheet. Over the years the Team X spreadsheet-based tools have evolved from simple standalone engineering models into a networked spreadsheet intensive system with real time parameter updating. Recent new capabilities include stochastic cost estimation and a graphical drag and drop block diagram that automatically populates the related spreadsheet parameters of cost, mass and power. This paper describes how the spreadsheet functions within Team X: its history, architecture, current capabilities, enabling strengths and persistent weaknesses. In addition, the verification methods and institutional oversight that have evolved as the Team X products became increasingly critical to Laboratory success are also discussed.

concurrent engineering↗

Colossal anisotropic absorption of spin currents induced by chirality

The chiral induced spin selectivity (CISS) effect, in which the structural chirality of a material determines the preference for the transmission of electrons with one spin orientation over that of the other, is emerging as a design principle for creating next-generation spintronic devices. CISS implies that the spin preference of chiral structures persists upon injection of pure spin currents and can act as a spin analyzer without the need for a ferromagnet. Here, we report an anomalous spin current absorption in chiral metal oxides that manifests a colossal anisotropic nonlocal Gilbert damping with a maximum-to-minimum ratio of up to 1000%. A twofold symmetry of the damping is shown to result from differential spin transmission and backscattering that arise from chirality-induced spin splitting along the chiral axis. These studies reveal the rich interplay of chirality and spin dynamics and identify how chiral materials can be implemented to direct the transport of spin current.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Corotating Birkeland currents in Jupiter's magnetosphere - An Io plasma-torus source

It is proposed that a persistent longitudinally asymmetric pattern of Birkeland (magnetic-field aligned) currents flow between the Jovian ionosphere and the plasma torus that encircles Jupiter near Io's orbit. A specific longitudinal sector of the torus (i.e., the active sector) contains more plasma and is therefore more massive than the rest of the torus. This asymmetry causes Birkeland currents to flow between Jupiter's ionosphere and the torus. The principal currents are confined to the longitude range of the active sector; an upper limit to their magnitude is approximately 5,000,000 A. Current flows upward from the ionosphere in the longitude range = 290 + or - 30 deg at the torus, which maps down the magnetic field lines in the northern hemisphere to a longitude range between 215 and 300 deg. Similarly, the downward Birkeland current, which flows between 230 + or - 30 deg at the torus, maps down to a longitude range within 180 and 215 deg at ionospheric heights in the northern hemisphere. The model also contains a possible weaker source in the southern hemisphere, removed approximately 180 deg in longitude from the primary northern-hemisphere source.

Dessler, A. J.↗

Driven resonant current amplification in self-organized plasma configurations with uniform λ and plasma pressure confinement

Driven resonant current amplification in uniform λ=$^{μoJ}_{B}$, self-organized plasma configurations with plasma pressure confinement is studied. This work extends previous analyses of force-free states (J ∥ B) to equilibria with plasma pressure gradients (∇P = J × B ≠ 0). An analytical treatment shows that in equilibria with uniform λ and a plasma pressure gradient that varies linearly with poloidal magnetic flux, driven resonances are either downshifted or upshifted from their force-free values. Additionally, a modification of off resonance current amplification is observed in pressure confining equilibria. Computational results add support to analytical predictions, and also include driven resonance behavior with equilibrium profiles not considered analytically. Furthermore, these results suggest not only persistence, but also modification of driven resonant current amplification in sustained spheromak configurations with plasma pressure confinement when compared to force-free states. By providing a basis for the existence of driven, high current amplification, pressure confining equilibria, this work provides insight into the accessibility of sustained spheromak states of most interest for potential fusion energy applications.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Characterization of YBa2Cu3O7, including critical current density Jc, by trapped magnetic field

Spatial distributions of persistent magnetic field trapped by sintered and melt-textured ceramic-type high-temperature superconductor (HTS) samples have been studied. The trapped field can be reproduced by a model of the current consisting of two components: (1) a surface current Js and (2) a uniform volume current Jv. This Js + Jv model gives a satisfactory account of the spatial distribution of the magnetic field trapped by different types of HTS samples. The magnetic moment can be calculated, based on the Js + Jv model, and the result agrees well with that measured by standard vibrating sample magnetometer (VSM). As a consequence, Jc predicted by VSM methods agrees with Jc predicted from the Js + Jv model. The field mapping method described is also useful to reveal the granular structure of large HTS samples and regions of weak links.

Chen, In-Gann↗

The Growth of Protein Crystals Using McDUCK

Most of the current microgravity crystal growth hardware is optimized to produce crystals within the limited time available on orbit. This often results in the actual nucleation and growth process being rushed or the system not coming to equilibrium within the limited time available. Longer duration hardware exists, but one cannot readily pick out crystals grown early versus those which nucleated and grew more slowly. We have devised a long duration apparatus, the Multi-chamber Dialysis Unit for Crystallization Kinetics, or McDUCK. This apparatus-is a series of protein chambers, stacked upon a precipitant reservoir chamber. All chambers are separated by a dialysis membrane, which serves to pass small molecules while retaining the protein. The volume of the Precipitant chamber is equal to the sum of the volumes of the protein chamber. In operation, the appropriate chambers are filled with precipitant solution or protein solution, and the McDUCK is placed standing upright, with the precipitant chamber on the bottom. The precipitant diffuses upwards over time, with the time to reach equilibration a function of the diffusivity of the precipitant and the overall length of the diffusion pathway. Typical equilibration times are approximately 2-4 months, and one can readily separate rapid from slow nucleation and growth crystals. An advantage on Earth is that the vertical precipitant concentration gradient dominates that of the solute, thus dampening out solute density gradient driven convective flows. However, large Earth-grown crystals have so far tended to be more two dimensional. Preliminary X-ray diffraction analysis of lysozyme crystals grown in McDUCK have indicated that the best, and largest, come from the middle chambers, suggesting that there is an optimal growth rate. Further, the improvements in diffraction resolution have been better signal to noise ratios in the low resolution data, not an increase in resolution overall. Due to the persistently large crystals grown we are currently proposing McDUCK for the growth of macromolecule crystals for use in neutron diffraction studies.

Ewing, Felicia↗

Persistent meanders and eddies lead to quasi-steady Lagrangian transport patterns in a weak western boundary current

The Brazil Current (BC) is a weak western boundary current flowing along the Southwestern Atlantic Ocean. It is frequently described as a flow with intense mesoscale activity and relatively low volume transport between 5.0 and 10.0 Sv. We use a 13-year eddy-resolving primitive-equation simulation to show that the presence of persistent meanders and eddies leads to characteristic quasi-steady Lagrangian transport patterns, aptly extracted through climatological Lagrangian Coherent Structures (cLCS). The cLCS position the surface expression of the BC core along the 2000-m isobath, in excellent visual agreement with high resolution satellite sea-surface temperature and the model Eulerian mean velocity. The cLCS deformation pattern also responds to zonally persistent cross-shelf SSH transition from positive (high) values near coastline to low (negative) values between 200- and 2000-m and back to positive (high) offshore from the 2000-m isobath. Zonally-paired cyclonic and anticyclonic structures are embedded in this transition, also causing the cLCS to deform into chevrons. An efficient transport barrier is identified close to the 200-m isobath confirmed by limited inshore movement of drogued drifters and accurately indicated by an along slope maxima of climatological strength of attraction. We also show that the persistent cyclonic and anticyclonic structures may induce localized cross-shelf transport. Regions of low climatological strength of attraction coincide with large shelves and with stagnant synthetic trajectories. We also show that cLCS accurately depict trajectories initiated at the location of Chevron’s spill (November 2011) as compared to synthetic and satellite-tracked trajectories, and the outline of the oil from that accident. There is also an agreement between the large-scale oil slicks reaching the Brazilian beaches (from August 2019 to February 2020) and the strength of climatological attraction at the coast. Our work also clarifies the influence of persistent mesoscale structures on the regional circulation. The identification and quantitative description of climatological Lagrangian coherent structures is expected to improve the effectiveness of future emergency response to oil spills, contingency planning, rescue operations, larval and fish connectivity assessment, drifter launch strategies, waste pollutant and marine debris dispersion and destination.

54 ENVIRONMENTAL SCIENCES↗

Programmable hydrogels by combining persistent and transient dynamic bonds

Out-of-equilibrium chemistry is currently being applied to polymer systems to mimic the autonomous behavior of biological materials. In this study, hydrogels with self-healing properties were developed that combine persistent crosslinks from dynamic metal-ligand coordination with transient crosslinks from dynamic anhydride bonds. Polymers containing terpyridine ligands and carboxylic acid groups were synthesized and crosslinked with divalent metal ions (Fe 2+ , Ni 2+ , Co 2+ , Zn 2+ , Cu 2+ ). The coordination bonds from terpyridine–metal coordination impart persistent stability, while transient anhydrides formed on treatment with 1-ethyl-3-(3-dimethylaminopropyl)carbodiimide hydrochloride (EDC) temporarily increase crosslink density. Distinct behaviors are observed depending on the choice of metal, with Ni 2+ forming robust, stable networks; Zn 2+ creating moderately dynamic gels; and Cu 2+ yielding highly dynamic, soft materials. Treatment with EDC increased storage moduli significantly, with transient effects lasting up to 280 min depending on the metal ion. Self-healing experiments demonstrated independent contributions from metal coordination and transient anhydrides, enabling recovery of stress and strain under varying conditions. Additionally, complex and reversible 2D stiffness patterns were generated by spatially controlled EDC treatment of Zn 2+ and Cu 2+ hydrogel films, demonstrating programmability and reusability.

Rajawasam, Chamoni W. H. [Miami University, Oxford↗

Rickettsia increases its infection and spread in whitefly populations by manipulating the defense patterns of the host plant

ABSTRACT The whitefly Bemisia tabaci is a destructive agricultural pest that frequently harbors various species of secondary symbionts including Rickettsia. Previous studies have revealed that the infection of Rickettsia can improve whitefly performance on food plants; however, to date, no evidence has shown, if, and how, Rickettsia manipulates the plant-insect interactions. In the current study, the effects of Rickettsia persistence on the induced plant defenses and the consequent performance of whitefly B. tabaci were investigated. Results revealed that Rickettsia can be transmitted into plants via whitefly feeding and remain alive within the cotton plants for at least 2 weeks. The different expression genes of cotton plants were mostly concentrated in the phytohormone signaling pathways, the marker genes of jasmonic-acid signaling pathway (AOC, AOS, LOX, MYC2) were significantly downregulated, while the marker genes of the salicylic-acid signaling pathway (WRKY70, PR-1) were upregulated. Biological experiments revealed that the fecundity of Rickettsia negative B. tabaci significantly increased when they fed on Rickettsia-persistent cotton plants. Taken together, we provide experimental evidence that the persistence of Rickettsia and its induced defense responses in cotton plants can increase the fitness of whitefly and, by this, Rickettsia may increase its infection and spread within its whitefly host.

Shi, Pei-Qiong↗

Statistical interpretation of sterile neutrino oscillation searches at reactors

A considerable experimental effort is currently under way to test the persistent hints for oscillations due to an eV-scale sterile neutrino in the data of various reactor neutrino experiments. The assessment of the statistical significance of these hints is usually based on Wilks’ theorem, whereby the assumption is made that the log-likelihood is χ 2 -distributed. However, it is well known that the preconditions for the validity of Wilks’ theorem are not fulfilled for neutrino oscillation experiments. In this work we derive a simple asymptotic form of the actual distribution of the log-likelihood based on reinterpreting the problem as fitting white Gaussian noise. From this formalism we show that, even in the absence of a sterile neutrino, the expectation value for the maximum likelihood estimate of the mixing angle remains non-zero with attendant large values of the log-likelihood. Our analytical results are then confirmed by numerical simulations of a toy reactor experiment. Finally, we apply this framework to the data of the Neutrino-4 experiment and show that the null hypothesis of no-oscillation is rejected at the 2.6 σ level, compared to 3.2 σ obtained under the assumption that Wilks’ theorem applies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗