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DOE OSTI2018

Dynamics in the Plastic Crystalline Phases of Cyclohexanol and Cyclooctanol Studied by Quasielastic Neutron Scattering

Plastic crystals are a promising candidate for solid state ionic conductors. In this work, quasielastic neutron scattering is employed to investigate the center of mass diffusive motions in two types of plastic crystalline cyclic alcohols: cyclohexanol and cyclooctanol. Two separate motions are observed which are attributed to long-range translational diffusion (α-process) and cage rattling (fast β-process). Residence times and diffusion coefficients are calculated for both processes, along with the confinement distances for the cage rattling. In addition, a binary mixture of these two materials is measured to understand how the dynamics change when a second type of molecule is added to the matrix. Furthermore, it is observed that, upon the addition of the larger cyclooctanol molecules into the cyclohexanol solution, the cage size decreases, which causes a decrease in the observed diffusion rates for both the α- and fast β-processes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2019

Signatures of tunable superconductivity in a trilayer graphene moiré superlattice

Understanding the mechanism of high-transition-temperature (high-T c ) superconductivity is a central problem in condensed matter physics. It is often speculated that high-Tc superconductivity arises in a doped Mott insulator1 as described by the Hubbard model 2,3,4 . An exact solution of the Hubbard model, however, is extremely challenging owing to the strong electron–electron correlation in Mott insulators. Therefore, it is highly desirable to study a tunable Hubbard system, in which systematic investigations of the unconventional superconductivity and its evolution with the Hubbard parameters can deepen our understanding of the Hubbard model. Here we report signatures of tunable superconductivity in an ABC-trilayer graphene (TLG) and hexagonal boron nitride (hBN) moiré superlattice. Unlike in ‘magic angle’ twisted bilayer graphene, theoretical calculations show that under a vertical displacement field, the ABC-TLG/hBN heterostructure features an isolated flat valence miniband associated with a Hubbard model on a triangular superlattice 5,6 where the bandwidth can be tuned continuously with the vertical displacement field. Upon applying such a displacement field we find experimentally that the ABC-TLG/hBN superlattice displays Mott insulating states below 20 kelvin at one-quarter and one-half fillings of the states, corresponding to one and two holes per unit cell, respectively. Upon further cooling, signatures of superconductivity (‘domes’) emerge below 1 kelvin for the electron- and hole-doped sides of the one-quarter-filling Mott state. The electronic behaviour in the ABC-TLG/hBN superlattice is expected to depend sensitively on the interplay between the electron–electron interaction and the miniband bandwidth. By varying the vertical displacement field, we demonstrate transitions from the candidate superconductor to Mott insulator and metallic phases. Our study shows that ABC-TLG/hBN heterostructures offer attractive model systems in which to explore rich correlated behaviour emerging in the tunable triangular Hubbard model.

36 MATERIALS SCIENCE↗

NASA NTRS1999

Development of CDZNTE Detectors for Low-Energy Gamma-Ray Astronomy

Under this grant the UC Berkeley PI, K. Hurley, joined a Goddard-led effort to develop large area, multi-pixel Cadmium-Zinc-Telluride (CdZnTe, or CZT) detectors for gamma-ray astronomy. His task was to advise the project of new developments in the area of cosmic gamma-ray bursts, in order to focus the detector development effort on the construction of an instrument which could be deployed on a spacecraft to localize and measure the energy spectra of bursts with good angular and energy resolution, respectively. UC Berkeley had no hardware role in this proposal. The result of this effort was the production, at Goddard, of five CZT prototype modules. A proposal was written for SWIFT, a MIDEX mission to study cosmic gamma-ray bursts. One experiment aboard SWIFT is the Burst Arcminute Telescope (BAT), which consists of a 5200 sq cm hard X-ray detector and a coded mask. The detector comprises 256 CZT modules, each containing 128 4 x 4 x 2 mm CZT detectors. Each detector is read out using an ASIC. The angular resolution achieved with this mask/array combination is 22 arcminutes, and a strong gamma-ray burst can be localized to an accuracy of 4 arcminutes in under 10 seconds. The energy resolution is typically 5 keV FWHM at 60 keV, and the energy range is 10 - 150 keV. The BAT views 2 steradians, and its sensitivity is such that the instrument can detect 350 gamma-ray burst/year, localizing 320 of them to better than 4 arcminute accuracy. The BAT concept therefore met the science goals for gamma-ray bursts. The UCB effort in the SWIFT proposal included the scientific objectives for gamma-ray bursts, and the assembly of a team of optical and radio observers who would use the BAT data to perform rapid multi-wavelength searches for the counterparts to bursts. This proposal was submitted to NASA and peer-reviewed. In January 1999 it was one of five such proposals selected for a Phase A study. This study was completed in June, and SWIFT was formally presented to NASA in September. It appeared that a final selection of two MIDEX missions for flight was imminent. However, the final selection was deferred at the last minute due to the uncertainty in NASA's OSS budget.

Gehrels, N.↗

NASA NTRS1997

Risk Management of NASA Projects

Various NASA Langley Research Center and other center projects were attempted for analysis to obtain historical data comparing pre-phase A study and the final outcome for each project. This attempt, however, was abandoned once it became clear that very little documentation was available. Next, extensive literature search was conducted on the role of risk and reliability concepts in project management. Probabilistic risk assessment (PRA) techniques are being used with increasing regularity both in and outside of NASA. The value and the usage of PRA techniques were reviewed for large projects. It was found that both civilian and military branches of the space industry have traditionally refrained from using PRA, which was developed and expanded by nuclear industry. Although much has changed with the end of the cold war and the Challenger disaster, it was found that ingrained anti-PRA culture is hard to stop. Examples of skepticism against the use of risk management and assessment techniques were found both in the literature and in conversations with some technical staff. Program and project managers need to be convinced that the applicability and use of risk management and risk assessment techniques is much broader than just in the traditional safety-related areas of application. The time has come to begin to uniformly apply these techniques. The whole idea of risk-based system can maximize the 'return on investment' that the public demands. Also, it would be very useful if all project documents of NASA Langley Research Center, pre-phase A through final report, are carefully stored in a central repository preferably in electronic format.

Sarper, Hueseyin↗

DOE OSTI2019

Radioablation by Image-Guided (HDR) Brachytherapy and Transarterial Chemoembolization in Hepatocellular Carcinoma: A Randomized Phase II Trial

Background and Aims: The aim of this single-center, open-label phase II study was to assess the efficacy of image-guided high-dose-rate (HDR) brachytherapy (iBT) compared with conventional transarterial embolization (cTACE) in unresectable hepatocellular carcinoma. Methods: Seventy-seven patients were treated after randomization to iBT or cTACE, as single or repeated interventions. Crossover was allowed if clinically indicated. The primary endpoint was time to untreatable progression (TTUP). Eligibility criteria included a Child–Pugh score of ≤ 8 points, absence of portal vein thrombosis (PVT) at the affected liver lobe, and ≤ 4 lesions. Survival was analyzed by using the Cox proportional hazard model with stratification for Barcelona Clinic Liver Cancer (BCLC) stages. Results: Twenty patients were classified as BCLC-A (iBT/cTACE 8/12), 35 as BCLC-B (16/19), and 22 as BCLC-C (13/9). The 1-, 2-, and 3-year TTUP probabilities for iBT compared with cTACE were 67.5% versus 55.2%, 56.0% versus 27.4%, and 29.5% versus 11.0%, respectively, with an adjusted hazard ratio (HR) of 0.49 (95% confidence interval 0.27–0.89; p = 0.019). The 1-, 2-, and 3-year TTPs for iBT versus cTACE were 56.0% versus 28.2%, 23.9% versus 6.3%, and 15.9% versus 6.3%, respectively, with an adjusted HR of 0.49 (0.29–0.85; p = 0.011). The 1-, 2-, and 3-year OS rates were 78.4% versus 67.7%, 62.0% versus 47.3%, and 36.7% versus 27.0%, respectively, with an adjusted HR of 0.62 (0.33–1.16; p = 0.136). Conclusions: This explorative phase II trial showed a superior outcome of iBT compared with cTACE in hepatocellular carcinoma and supports proceeding to a phase III trial.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

NASA NTRS1968

Concepts for a theoretical and experimental study of lifting rotor random loads and vibrations, Phase 2

A comparison with NASA conducted simulator studies has shown that the approximate digital method for computing rotor blade flapping responses to random inputs, tentatively suggested in Phase I Report, gives with increasing rotor advance ratio the wrong trend. Consequently, three alternative methods of solution have been considered and are described: (1) an approximate method based on the functional relation between input and output double frequency spectra, (2) a numerical method based on the system responses to deterministic inputs and (3) a perturbation approach. Among these the perturbation method requires the least amount of computation and has been developed in two forms - the first form to obtain the response correlation function and the second for the time averaged spectra of flapping oscillations.

Hohenemser, K. H.↗

NASA NTRS1991

Crystallization of the glassy grain boundary phase in silicon nitride ceramics

The role was studied of the intergranular glassy phase in silicon nitride as-processed with yttria as a sintering aid. The microstructure, crystallization, and viscosity of the glassy phase were areas studied. Crystallization of the intergranular glassy phase to more refractory crystalline phases should improve the high temperature mechanical properties of the silicon nitride. The addition of a nucleating agent will increase the rate of crystallization. The measurement of the viscosity of the glassy phase will permit the estimation of the high temperature deformation of the silicon nitride.

Drummond, Charles H., III↗

NASA NTRS2005

Development of High Altitude UAV Weather Radars for Hurricane Research

A proposed effort within NASA called (ASHE) over the past few years was aimed at studying the genesis of tropical disturbances off the east coast of Africa. This effort was focused on using an instrumented Global Hawk UAV with high altitude (%Ok ft) and long duration (30 h) capability. While the Global Hawk availability remains uncertain, development of two relevant instruments, a Doppler radar (URAD - UAV Radar) and a backscatter lidar (CPL-UAV - Cloud Physics Lidar), are in progress. The radar to be discussed here is based on two previous high-altitude, autonomously operating radars on the NASA ER-2 aircraft, the ER-2 Doppler Radar (EDOP) at X-band (9.6 GHz), and the Cloud Radar System (CRS) at W- band (94 GHz). The nadir-pointing EDOP and CRS radars profile vertical reflectivity structure and vertical Doppler winds in precipitation and clouds, respectively. EDOP has flown in all of the CAMEX flight series to study hurricanes over storms such as Hurricanes Bonnie, Humberto, Georges, Erin, and TS Chantal. These radars were developed at Goddard over the last decade and have been used for satellite algorithm development and validation (TRMM and Cloudsat), and for hurricane and convective storm research. We describe here the development of URAD that will measure wind and reflectivity in hurricanes and other weather systems from a top down, high-altitude view. URAD for the Global Hawk consists of two subsystems both of which are at X-band (9.3-9.6 GHz) and Doppler: a nadir fixed-beam Doppler radar for vertical motion and precipitation measurement, and a Conical scanning radar for horizontal winds in cloud and at the surface, and precipitation structure. These radars are being designed with size, weight, and power consumption suitable for the Global Hawk and other UAV's. The nadir radar uses a magnetron transmitter and the scanning radar uses a TWT transmitter. With conical scanning of the radar at a 35" incidence angle over an ocean surface in the absence of precipitation, the surface return over a single 360 degree sweep over -25 h-diameter region provides information on the surface wind speed and direction within the scan circle. In precipitation regions, the conical scan with appropriate mapping and analysis provides the 3D structure of reflectivity beneath the plane and the horizontal winds. The use of conical scanning in hurricanes has recently been demonstrated for measuring inner core winds with the IWRAP system flying on the NOAA P3's. In this presentation, we provide a description of the URAD system hardware, status, and future plans. In addition to URAD, NASA SBIR activity is supporting a Phase I study by Remote Sensing Solutions and the University of Massachusetts for a dual-frequency IWRAP for a high altitude UAV that utilizes solid state transmitters at 14 and 35 GHz, the same frequencies that are planned for the radar on the Global Precipitation System satellite. This will be discussed elsewhere at the meeting.

Heymsfield, Gerald↗

DOE OSTI2020

cm 2 -Scale Synthesis of MoTe 2 Thin Films with Large Grains and Layer Control

Owing to the small energy differences between its polymorphs, MoTe 2 can access a full spectrum of electronic states from the 2H semiconducting state to the 1T' semimetallic state and from the T d Weyl semimetallic state to the superconducting state in the 1T' and T d phase at low temperature. Thus, it is a model system for phase transformation studies as well as quantum phenomena such as the quantum spin Hall effect and topological superconductivity. Careful studies of MoTe 2 and its potential applications require large-area MoTe 2 thin films with high crystallinity and thickness control. Here, we present cm 2 -scale synthesis of 2H-MoTe 2 thin films with layer control and large grains that span several microns. Layer control is achieved by controlling the initial thickness of the precursor MoO x thin films, which are deposited on sapphire substrates by atomic layer deposition and subsequently tellurized. Despite the van der Waals epitaxy, the precursor–substrate interface is found to critically determine the uniformity in thickness and grain size of the resulting MoTe 2 films: MoTe 2 grown on sapphire show uniform films while MoTe 2 grown on amorphous SiO 2 substrates form islands. Furthermore, this synthesis strategy decouples the layer control from the variabilities of growth conditions for robust growth results and is applicable to growing other transition-metal dichalcogenides with layer control.

2D materials↗

NASA NTRS2019

A Global Climatology of Extratropical Transition Part II: Statistical Performance of the Cyclone Phase Space

This study analyzes the differences between an objective, automated identification of tropical cyclones (TCs) that undergo extratropical transition (ET), and the designation of ET determined subjectively by human forecasters in best-track data in all basins globally. The objective identification of ET is based on the cyclone phase space (CPS), calculated from the Japanese 55-year Reanalysis (JRA-55) or the ECMWF Interim Reanalysis (ERA-Interim). The resulting classification into “ET storms” and “non-ET storms” underlies the global climatology of ET presented in Part I of this study. Here, the authors investigate how well the CPS classifications agree with those in the best-track records calculated from JRA-55 or from ERA-Interim data. According to F1 scores and Matthews correlation coefficients (MCCs), the classification of ET storms in the CPS agrees best with the best-track classification in the Western North Pacific (MCC > 0.7) and the North Atlantic (MCC > 0.5). In other basins, the correlation between the CPS classification and the best-track classification is only slightly higher than that of a random classification. The JRA-55 classification achieves higher performance scores than does the ERA-Interim classification, and the differences are statistically significant in all basins. The lower performance of ERA-Interim is mainly due to a higher false alarm rate, particularly in the Eastern North Pacific. Overall, the results show that while the CPS-based classifications are good enough to be useful for many purposes, there is almost certainly room for improvement – in the representation of the storms in reanalyses, in our objective metrics of ET, and in our scientific understanding of the ET process.

Melanie Bieli↗

DOE OSTI2024

High Performance Metal-Supported SOFC System for Range Extension of Commercial Aviation

The DOE ARPA-E REEACH program [1] has enabled this Phase 1 study that conceptualizes a commercial 154 passenger electric aircraft using renewable aviation fuel for range extension while meeting similar mission performance levels as current commercial aircraft. Commercial aviation accounts for about 2.5% of global CO2 emissions, and close to 5% of overall anthropogenic climate change due to the added accounting of contrail’s effects [2]. The sector has adopted a goal of carbon neutrality by 2050 [3]. 110 nations, and recently the new US administration, have embarked on work to address this important challenge. The US DOE has released a roadmap to enable the further development of sustainable aviation fuel (SAF) in the hopes that it could meet all of aviation’s fuel needs by 2050 [4]. However, SAF fuel price and sufficient future feedstock availability remains a concern [5]. Considering the first commercial biofuel flight demonstration 14 years ago [6] and that SAF still only comprises less than 0.1% of jet fuel use, the question arises as how it can ramp up to 100% use in the next 27 years. One option that has the potential to substantially reduce the need for SAF is to implement light-weight Solid Oxide Fuel Cells (SOFCs) that can efficiently utilize SAF or other sulfur-free hydrocarbon fuels. As opposed to lower temperature PEM (Proton Exchange Membrane) fuel cells that can use high-purity hydrogen, SOFC’s fuels are very flexible, ranging from low cost liquefied natural gas (LNG), renewable liquefied natural gas (RLNG), to SAF, to generate clean electrical power for use in aviation propulsion and auxiliary power units [7] [8]. Research progress is needed to enable SOFCs to achieve 3.0 kW/kg power density, making them viable for aviation [9]. The DOE’s Advanced Research Projects Agency – Energy (ARPA-E) has therefore initiated an aviation SOFC R&D program that is anticipated to dramatically reduce aircraft fuel use though the implementation of “Range Extenders for Electric Aviation with low Carbon and High efficiency” (REEACH) [1] for medium range commercial aircraft. This report summarizes the progress during phase 1 of the REEACH program.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2017

Two-dimensional lithium diffusion behavior and probable hybrid phase transformation kinetics in olivine lithium iron phosphate

Olivine lithium iron phosphate is a technologically important electrode material for lithium-ion batteries and a model system for studying electrochemically driven phase transformations. Despite extensive studies, many aspects of the phase transformation and lithium transport in this material are still not well understood. Here we combine operando hard X-ray spectroscopic imaging and phase-field modeling to elucidate the delithiation dynamics of single-crystal lithium iron phosphate microrods with long-axis along the [010] direction. Lithium diffusivity is found to be two-dimensional in microsized particles containing ~3%lithium-iron anti-site defects. Our study provides direct evidence for the previously predicted surface reaction-limited phase-boundary migration mechanism and the potential operation of a hybrid mode of phase growth, in which phase-boundary movement is controlled by surface reaction or lithium diffusion in different crystallographic directions. These findings uncover the rich phase-transformation behaviors in lithium iron phosphate and intercalation com-pounds in general and can help guide the design of better electrodes.

25 ENERGY STORAGE↗

DOE OSTI2018

Morphology of phase-separated VO2 films deposited on TiO2-(001) substrate

Highlights: • Phase separation in VO{sub 2} films at room temperature was studied by TEM. • Tetragonal phase with a zig-zag interface was observed in the neighborhood of the VO{sub 2}/TiO{sub 2} boundary. • The peculiar interface could be explained by the crystallographic relationship between the monoclinic and tetragonal phases. - Abstract: The basic morphology of phase-separated VO{sub 2} films, in which the tetragonal (metallic) phase coexists with the monoclinic (insulating) phase, was studied using transmission electron microscopy. While the phase transformation temperature in an unstrained crystal is approximately 340 K, it was observed that at 298 K, elastic strain (caused by lattice mismatch with the TiO{sub 2}-(001) substrate) stabilized the tetragonal phase near the VO{sub 2}/TiO{sub 2} boundary. The observed zig-zag-shaped interface of the tetragonal phase was explained by the crystallographic orientation relationship between the tetragonal and monoclinic phases. The observations provide valuable information for future applications of VO{sub 2} films.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS1974

A study of the effects of solid phase reactions on the thermal degradation and ballistic properties of solid propellants

The thermal stability of perchlorate composite propellants was studied at 135 and 170 C. The experimental efforts were concentrated on determining the importance of heterogeneous oxidizer-fuel reactions in the thermal degradation process. The experimental approach used to elucidate the mechanisms by which the oxidizer fuel composites thermally degrade was divided into two parts: (1) keeping the fuel constant and varying the nature of the oxidizers, and (2) holding the oxidizer constant and varying the fuel components. The fuel component primarily utilized in the first phase was polyethylene. Oxidizers included KClO4, KClO3, NH4ClO4 and NH4ClO4 doped with materials such as chlorate, phosphate and arsenate. In the second phase the oxidizer used was primarily NH4ClO4 while the fuels included saturated and unsaturated polybutadiene prepolymers and a series of bonding agents. Techniques employed in the current study include thermogravimetric measurements, differential thermal analysis, infrared, mass spectrometry, electron microscopy, and appropriate wet chemical analysis.

Schmidt, W. G.↗

DOE OSTI2020

Evaluating Building Energy Code Compliance and Savings Potential through Large-Scale Simulation with Models Inferred by Field Data

Building energy code compliance is the crucial link between the actual energy savings and the efficiency prescribed in energy codes. A research project aiming to identify opportunities to reduce energy consumption in new single-family residential construction by increasing compliance with the building energy code was conducted in several states of the United States. The study was comprised of three phases: (1) a baseline study to document typical practice and identify opportunities for improvement based on empirical data gathered from the field; (2) an education and training phase targeting the opportunities identified; and (3) a post-study to assess whether a reduction in average state-wide energy use could be achieved following the education and training phase. We proposed a novel methodology based on large-scale building energy simulation inferred by limited field data to assess the performance of a large population of homes. This paper presents the methodology, findings, and results of this study. The state-wide average energy consumption decreased at Phase III from Phase I for five of the seven states involved in the analysis. The measure-level savings potential analysis shows an overall reduction. Overall, the training and education phase plays a recognizable role in improving compliance with building energy codes.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2017

Crystallization kinetics of poly(ethylene oxide) confined in semicrystalline poly(vinylidene) fluoride

ABSTRACT Polymer blends based on poly(vinylidene fluoride) (PVDF) and poly(ethylene oxide) (PEO) have been prepared to analyze the crystallization kinetics of poly(ethylene oxide) confined in semicrystalline PVDF with different ratios of both polymers. Both blend components were dissolved in a common solvent, dimethyl formamide. Blend films were obtained by casting from the solution at 70 °C. Thus, PVDF crystals are formed by crystallization from the solution while PEO (which is in the liquid state during the whole process) is confined between PVDF crystallites. The kinetics of crystallization of the confined PEO phase was studied by isothermal and nonisothermal experiments. Fitting of Avrami model to the experimental DSC traces allows a quantitative comparison of the influence of the PVDF/PEO ratio in the blend on the crystallization behavior. The effect of melting and further recrystallization of the PVDF matrix on PEO confinement is also studied. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56 , 588–597

Tamaño‐Machiavello, Maria Noel↗

DOE OSTI2023

Tailoring the γ-γ'-γ" dual superlattice microstructure of INCONEL® 725 by high temperature aging and Nb/Ta additions for superior creep properties

Next-generation energy systems require superior resistance to creep deformation due to the considerably prolonged exposure times at operating stress and temperature. To improve the elevated temperature properties of INCONEL® 725 (IN725), a corrosion resistant alloy, several variants with different Ti/Al ratio and judicious amounts of Nb and Ta were made. Furthermore, a high temperature aging (HTA) heat treatment, designed to promote favorable precipitate phase formation, was explored. These adjustments allowed to tailor the amount and type of precipitate strengthening which led to significant increases in time to failure. The Ti/Al ratio was used to favor the formation of γ' or γ" precipitates. Compact morphology precipitates, consisting of γ' precipitates surrounded by a γ" shell, were formed in alloys with a low Ti/Al ratio. The HTA increased the creep life of various alloy formulations up to a maximum improvement of 371% as compared to the standard aging heat treatment. The Nb and Ta additions had a similar effect on increasing creep life by promoting and stabilizing γ" precipitation. The positive effect of the additions was even more pronounced when coupled with the HTA. A phase stability study with up to 10,000 h exposure at 700°C revealed that the compact morphology helped in slightly reducing coarsening of the γ' precipitates, although the effect on creep was not significant. The findings of this study enable design of dual superlattice alloys through microstructural engineering that yields superior performance and can be applied to a wide range of alloys in the IN718 and derivatives family.

Antonov, Stoichko↗

DOE OSTI2023

Four-fermion deformations of the massless Schwinger model and confinement

We consider the massless charge-N Schwinger model and its deformation with two four-fermion operators. Without the deformations, this model exhibits chiral symmetry breaking without confinement. It is usually asserted that the massless Schwinger model is always deconfined and a string tension emerges only when a mass for the fermion field is turned on. We show that in the presence of these four-fermion operators, the massless theory can in fact confine. One of the four-fermion deformations is chirally neutral, and is a marginal deformation. The other operator can be relevant or irrelevant, and respects a Z 2 subgroup of chiral symmetry for even N, hence forbidding a mass term. When it is relevant, even the exactly massless theory exhibits both confinement and spontaneous chiral symmetry breaking. The construction is analogous to QCD(adj) in 2d. While the theory without four-fermion deformations is deconfined, the theory with these deformations is generically in a confining phase. We study the model on R 2 using bosonization, and also analyze the mechanism of confinement on R × S 1 , where we find that confinement is driven by fractional instantons.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗