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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Excitation of toroidally localized harmonics of global Alfvén eigenmodes

Abstract The spherical tokamak NSTX and the upgraded, higher toroidal field, NSTX-U, routinely create plasmas with large un-thermalized populations of super-Alfvénic fast ions. This population of non-thermal energetic ions excites a broad spectrum of Alfvénic waves, from the lower frequency (≈30 kHz–≈200 kHz) toroidal Alfvén eigenmodes (Cheng and Chance 1986 Phys. Fluids 29 3695), to the higher frequency (400 kHz–3 MHz) global Alfvén eigenmodes (GAEs) and compressional Alfvén eigenmodes (Goedbloed 1975 Phys. Fluids 18 1258). In this paper we present evidence that the GAE non-linearly excite modes, presumably GAE, at frequencies consistent with non-linear or 3-wave coupling. The observation of the excitation of 2 nd harmonic GAE through the intrinsic non-linearity of Global Alfvén modes demonstrates that the non-linear terms can act as an exciter-antenna inside the plasma, broadcasting at harmonics of the mode frequency and with concomitantly shorter wavelengths. As with experiments using external antenna to excite otherwise weakly stable Alfvénic modes, this data can provide information about the stability of modes at harmonics of the GAE. It may also provide information on the nature of the non-linearities in the wave dispersion equation or a direct measure of the mode amplitude (Smith et al 2006 Phys. Plasmas 13 042504). We also report that the short wavelength 2 nd harmonic GAE can be strongly toroidally localized. The observation that the shorter wavelength ( n ≈ 20) 2 nd harmonic modes can be toroidally localized potentially has implications for the impact of fast-ion driven instabilities on fast-ion confinement in ITER and future fusion reactors (Gorelenkov et al 2014 Nucl. Fusion 54 125001).

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

End-To-End Decentralized Transmission Line Protection in IBR-Dominated Weak Grids Using Interpretable Data-Driven Methods

Traditional transmission line protection relies on predictable synchronous-based fault signatures, which frequently fail under the non-standard, current-limited fault characteristics of Inverter-Based Resources (IBRs). This study investigates how to achieve secure, communication-free fault isolation in IBR-dominated weak grids without relying on opaque, computationally heavy "black-box" machine learning algorithms. To address this, we propose a novel, standalone, and inherently interpretable data-driven protection framework. Unlike centralized methods requiring multi-terminal communication, this decentralized approach relies solely on local measurements using a hierarchical linear-kernel Support Vector Machine (SVM). The methodology decomposes the protection task into four sequential stages that mimic traditional protection elements: fault detection and fault direction identification, fault type classification, zone classification, and location estimation. This multi-stage architecture allows for specialized feature engineering at each stage, combining high computational efficiency with logic traceability. The framework's end-to-end performance was validated via C-code and PSCAD/EMTDC co-simulation, utilizing a real-world utility network and an OEM black-box IBR model. The proposed relay achieves 97.2% overall accuracy and provides a reliable trip decision within a 2.5-cycle window. The results confirm 100% accuracy in fundamental fault detection, reliable zone selectivity across low to moderate fault resistances, and robust security against non-fault transients, proving its immediate viability for integration into commercial numerical relays.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

Fractional Chern insulators in magic-angle twisted bilayer graphene

Fractional Chern insulators (FCIs) are lattice analogues of fractional quantum Hall states that may provide a new avenue towards manipulating non-Abelian excitations. Early theoretical studies have predicted their existence in systems with flat Chern bands and highlighted the critical role of a particular quantum geometry. However, FCI states have been observed only in Bernal-stacked bilayer graphene (BLG) aligned with hexagonal boron nitride (hBN), in which a very large magnetic field is responsible for the existence of the Chern bands, precluding the realization of FCIs at zero field. By contrast, magic-angle twisted BLG supports flat Chern bands at zero magnetic field and therefore offers a promising route towards stabilizing zero-field FCIs. Here we report the observation of eight FCI states at low magnetic field in magic-angle twisted BLG enabled by high-resolution local compressibility measurements. The first of these states emerge at 5 T, and their appearance is accompanied by the simultaneous disappearance of nearby topologically trivial charge density wave states. We demonstrate that, unlike the case of the BLG/hBN platform, the principal role of the weak magnetic field is merely to redistribute the Berry curvature of the native Chern bands and thereby realize a quantum geometry favourable for the emergence of FCIs. Our findings strongly suggest that FCIs may be realized at zero magnetic field and pave the way for the exploration and manipulation of anyonic excitations in flat moiré Chern bands.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Electronic band contraction induced low temperature methane activation on metal alloys

The catalytic conversion of methane under mild conditions is an appealing approach to selectively produce value-added products from natural gas. Catalysts which can chemisorb methane can potentially overcome challenges associated with its high stability and achieve facile activation. Although transition metals can activate C–H bonds, chemisorption and low-temperature conversion remain elusive on these surfaces. The broad electronic bands of metals can only weakly interact with the methane orbitals, in contrast to specific transition metal oxide and supported metal cluster surfaces which are now recognized to form methane σ-complexes. Here, we report methane chemisorption can, remarkably, occur on metal surfaces via electronic band contraction and localization from metal alloying. From a broad screening including single atom and intermetallic alloys in various substrates, we find early transition metals as promising metal solutes for methane chemisorption and low-temperature activation. These findings demonstrate a combinatorial diversity of possible candidates in earth abundant metal alloys with this attractive catalytic behavior.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Linear vs. nonlinear acceleration in plasma turbulence. II. Hall–finite-Larmor-radius magnetohydrodynamics

The local k-space ratio of linear and nonlinear accelerations associated with a variety of initial conditions undergoing steady relaxation is investigated for the Hall–finite-Larmor-radius magnetohydrodynamics (MHD) system in the presence of a mean magnetic field. Building on a related study (Paper I) where it was shown that discrepancies exist between describing the global and local characterizations of the pure MHD system with mean magnetic field, we find regions of the Fourier space that are consistently dominated by linear acceleration and other regions that are consistently dominated by nonlinear acceleration, independent of the overall system's description as linear, weakly nonlinear, or turbulent. In general, dynamics within a certain angular range of the mean magnetic field direction are predominantly linear, while dynamics adjacent the Hall scales along the field-parallel direction and dynamics adjacent the finite Larmor radius scales in the field-perpendicular direction can become strongly nonlinear. The nonlinear influences are particularly significant as the plasma beta increases from unity to higher values.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

Supersymmetry: aspirations and prospects

The realization in the early 1980s that weak scale supersymmetry stabilizes the Higgs sector of the spectacularly successful Standard Model led several authors to explore whether low energy supersymmetry could play a role in particle physics. Among these were Richard Arnowitt, Ali Chamseddine and Pran Nath who constructed a viable {\em locally} supersymmetric Grand Unified Theory (GUT), laying down the foundation for supergravity GUT models of particle physics. Supergravity models continue to be explored as one of the most promising extensions of the Standard Model. After a quick overview of some of the issues and aspirations of early researchers working to bring supersymmetry into the mainstream of particle physics, here we re-evaluate early arguments that seemed to imply that superpartners would be revealed in experiments at LEP2 or at the Tevatron. Our purpose is to assess whether the absence of any superpartners in searches at LHC8 presents a crisis for supersymmetry. Toward this end, we re-evaluate fine-tuning arguments that lead to upper bounds on (some) superpartner masses. We conclude that phenomenologically viable superpartner spectra that could arise within a high scale model tuned no worse than a few percent are perfectly possible. While no viable underlying model of particle physics that leads to such spectra has yet emerged, we show that the (supergravity-based) Radiatively-driven Natural Supersymmetry (RNS) framework serves as a surrogate for a phenomenological analysis of an underlying theory with modest fine-tuning. We outline the phenomenological implications of this framework, with emphasis on those LHC and electron-positron collider signatures that might point to the underlying natural origin of gauge and Higgs boson masses. We conclude that the supergravity GUT paradigm laid down in 1982 by Arnowitt, Chamseddine and Nath, and others, remains a vibrant possibility

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Short-Term Energy and Meteorological Impacts on Thanksgiving CO2 in Salt Lake City

Abstract Long-term, high-frequency atmospheric CO2 measurements at multiple sites in the Salt Lake City (SLC), Utah, reveal that annual and monthly CO2 variability aligns with a priori estimates of emissions from anthropogenic and biological sources. In this study, we investigate whether short-term fluctuations in anthropogenic emissions, as captured in the Vulcan3 dataset for the United States, can be detected in atmospheric CO2 observations. Specifically, we focus on Thanksgiving holidays, when traffic and energy usage patterns differ from the rest of November. Onroad CO2 emissions exhibit a double peak during weekday morning and evening rush hours but remain relatively low on weekends and Thanksgiving. Interestingly, CO2 mole fractions during Thanksgiving were higher than the rest of November at all SLC monitoring sites, particularly from 2008 to 2013. This increase is partially attributed to elevated energy-related emissions — especially residential sources — and meteorological factors such as weak wind speeds, cold temperature, and a low planetary boundary layer height (PBLH).

 While CO₂ emissions and mole fraction patterns align over time, notable spatial differences exist. For instance, the near-highway site in Murray shows the highest CO₂ mole fractions despite low local emissions, suggesting pollution transport via highways and wind advection. Random Forest model-based SHapley Additive exPlanations (SHAP) analysis reveals that onroad emissions dominate CO2 contributions on weekdays and weekends, while energy-related emissions play a larger role during Thanksgiving, alongside meteorological drivers such as wind speed and PBLH. Across six urban cities, CO2 emissions display a consistent pattern: residential and commercial (onroad) emissions peak during Thanksgiving (weekday) with substantial (minimal) year-to-year variability. These findings highlight that urban CO₂ variability is driven by the combined influence of emissions and meteorology, underscoring the need for integrated mitigation strategies. Additionally, multi-site measurements are essential for accurate source attribution and the development of effective policy interventions. 

Ryoo, Ju-Mee (ORCID:0000000234256296)↗
DOE OSTI2018

Weak ferromagnetism and glassy state in κ - ( BEDT - TTF ) 2 Hg ( SCN ) 2 Br

SInce the first observation of weak ferromagnetism in the charge-transfer salt kappa-(BEDT-TTF)(2)Cu[N(CN)(2)]Cl [U. Welp et al., Phys. Rev. Lett. 69, 840 (1992)], no further evidence of a ferromagnetic state in this class of organic materials has been reported. Here, static and dynamic spin susceptibility measurements on kappa-(BEDT-TTF)(2)Hg(SCN)(2)Br exhibit weak ferromagnetism below 20 K on the geometrically frustrated background. Our experimental results suggest that frustrated spins in the molecular dimers suppress long-range antiferromagnetic order, forming a spin-glass-type ground state of the triangular lattice in the insulating phase which locally contains ferromagnetic polarons. Moreover, specific-heat data reveal an excess peak located around 5 K, indicating the glassy nature of the electrons as well.

Hemmida, M.↗
DOE OSTI2026

Pb-Apatite Framework as a Generator of Novel Flat-Band CuO-Based Physics

Based upon density functional theory (DFT) calculations, we present the basic electronic structure of CuPb 9 (PO 4 ) 6 O (Cu-doped lead apatite, aka LK-99), in two scenarios: (1) where the structure is constrained to the P3 symmetry and (2) where no symmetry is imposed. At the DFT level, the former is predicted to be metallic while the latter is found to be a charge-transfer insulator. In both cases the filling of these states is nominally d 9 , consistent with the standard Cu 2+ valence state, and Cu with a local magnetic moment of order 0.7 μ B . In the metallic case we find these states to be unusually flat (∼0.2 eV dispersion), giving a very high density of electronic states (DOS) at the Fermi level that we argue can be a host for novel electronic physics. The flatness of the bands is the likely origin of symmetry-lowering gapping possibilities that would remove the spectral weight from E F . Motivated by some initial experimental observations of metallic or semiconducting behavior, we propose that disorder (likely structural) is responsible for closing the gap. Here, we consider a variety of possibilities that could possibly close the charge-transfer gap but limit consideration to kinds of disorder that preserve electron count. Of the possible kinds we considered (spin disorder, O populating vacancy sites, and Cu on less energetically favorable Pb sites), the local Cu moment, and consequently the charge-transfer gap, remains robust. We conclude that disorder responsible for metallic behavior entails some kind of doping where the electron count changes. Further, we claim that the emergence of the flat bands should be due to weak wave function overlap between the orbitals on Cu and O sites, owing to the directional character of the constituent orbitals. Therefore, finding an appropriate host structure for minimizing hybridization between Cu and O while allowing them to still weakly interact should be a promising route for generating flat bands at E F which can lead to interesting electronic phenomena, regardless of whether LK-99 is a superconductor.

36 MATERIALS SCIENCE↗
DOE OSTI2020

The Stellar Velocity Distribution Function in the Milky Way Galaxy

The stellar velocity distribution function in the solar vicinity is reexamined using data from the Sloan Digital Sky Survey Apache Point Observatory Galactic Evolution Experiment (APOGEE) survey’s DR16 and Gaia DR2. By exploiting APOGEE’s ability to chemically discriminate with great reliability the thin-disk, thick-disk, and (accreted) halo populations, we can, for the first time, derive the three-dimensional velocity distribution functions (DFs) for these chemically separated populations. We employ this smaller but more data-rich APOGEE+Gaia sample to build a data-driven model of the local stellar population velocity DFs and use these as basis vectors for assessing the relative density proportions of these populations over the 5 < R < 12 kpc and −1.5 < z < 2.5 kpc range as derived from the larger, more complete (i.e., all-sky, magnitude-limited) Gaia database. We find that 81.9% ± 3.1% of the objects in the selected Gaia data set are thin-disk stars, 16.6% ± 3.2% are thick-disk stars, and 1.5% ± 0.1% belong to the Milky Way stellar halo. We also find the local thick-to-thin-disk density normalization to be ρ {sub T}(R {sub ⊙})/ρ {sub t}(R {sub ⊙}) = 2.1% ± 0.2%, a result consistent with, but determined in a completely different way from, typical star-count/density analyses. Using the same methodology, the local halo-to-disk-density normalization is found to be ρ {sub H}(R {sub ⊙})/(ρ {sub T}(R {sub ⊙}) + ρ {sub t}(R {sub ⊙})) = 1.2% ± 0.6%, a value that may be inflated due to the chemical overlap of halo and metal-weak thick-disk stars.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1993

Interstellar Mg II and C IV absorption toward Markarian 205 by NGC 4319 - An 'optically thick' QSO absorption system

We have used the Goddard High-Resolution Spectrograph aboard HST to detect interstellar Mg II and C IV absorption lines toward Mrk 205, a QSO whose sightline passes within 3/h kpc of the foreground galaxy NGC 4319. Absorption is detected from both local Milky Way gas and from NGC 4319, making this the first observation of an isolated, low-redshift galaxy causing an 'optically thick' QSO absorption system. We also observed for the first time Mg II absorption from two local High Velocity Clouds along this same sightline. The data support the premise that metal absorption lines seen at higher redshift in QSO spectra originate in gas associated with intervening galaxies. However, neither the strong absorption by (half) of our own Galaxy, nor the weak absorption by NGC 4319, may be typical of absorbers in general.

Bowen, David V.↗
NASA NTRS1997

Energy Transfer and Triadic Interactions in Compressible Turbulence

Using a two-point closure theory, the Eddy-Damped-Quasi-Normal-Markovian (EDQNM) approximation, we have investigated the energy transfer process and triadic interactions of compressible turbulence. In order to analyze the compressible mode directly, the Helmholtz decomposition is used. The following issues were addressed: (1) What is the mechanism of energy exchange between the solenoidal and compressible modes, and (2) Is there an energy cascade in the compressible energy transfer process? It is concluded that the compressible energy is transferred locally from the solenoidal part to the compressible part. It is also found that there is an energy cascade of the compressible mode for high turbulent Mach number (M(sub t) greater than or equal to 0.5). Since we assume that the compressibility is weak, the magnitude of the compressible (radiative or cascade) transfer is much smaller than that of solenoidal cascade. These results are further confirmed by studying the triadic energy transfer function, the most fundamental building block of the energy transfer.

Bataille, F.↗
NASA NTRS2004

IR Fine-Structure Line Signatures of Central Dust-Bounded Nebulae in Luminous Infrared Galaxies

To date, the only far-infrared spectroscopic observations of ultraluminous infrared galaxies have been obtained with the European Space Agency s Infrared Space Observatory Long Wavelength Spectrometer. The spectra of these galaxies are characterized by molecular absorption lines and weak emission lines from photodissociation regions (PDRs), but no far-infrared (greater than 40 microns) lines from ionized regions have been detected. ESA s Herschel Space Observatory, slated for launch in 2007, will likely be able to detect these lines in samples of local and moderate redshift ultra luminous galaxies and to enable measurement of the ionization parameters, the slope of the ionizing continuum, and densities present in the ionized regions of these galaxies. The higher spatial resolution of proposed observatories discussed in this workshop will enable isolation of the central regions of local galaxies and detection of these lines in high-redshift galaxies for study of the evolution of galaxies. Here we discuss evidence for the e.ects of absorption by dust within ionized regions and present the spectroscopic signatures predicted by photoionization modeling of dust-bounded regions.

Fischer, J.↗
DOE OSTI2018

Cyclic plastic deformation behaviour of a directionally solidified nickel base superalloy at 850 °C: Damage micromechanisms

Highlights: • Isothermal LCF life of CM 247 DS is reduced using R = 0 instead of R = −1. • Reduction in LCF life is significant at lower values of Δε/2. • Reduction in fatigue life is attributed to the development of sustained mean stress. • Sustained mean stress prevents the slip transfer from γ-channels to γ′-precipitates. • Sustained mean stress promotes dislocation network formation and looping. - Abstract: Dislocation based deformation micromechanisms during low cycle fatigue deformation of nickel base superalloy CM 247 DS LC at 850 °C was investigated by conducting fatigue tests employing constant strain amplitudes for strain ratio (R) values of 0, −1 and carrying out extensive SEM and TEM examinations. Cyclic life of the alloy reduces for all fatigue tests conducted employing R = 0 in comparison with R = −1 owing to sustained mean stress developed during fatigue at R = 0. TEM examinations confirmed that sustained mean stress developed during low strain amplitude fatigue test (Δε/2 = 0.5%) using R = 0 condition prevented slip transfer from γ-channels to γ′-precipitates and resulted in the formation of dislocation substructures such as networks, nodes etc. and also promoted dislocation looping around γ′-precipitates. Lower fatigue life at R = 0 is mainly attributed to the development of these types of substructures, which promotes strain localization in both intra as well intergranular regions. Whereas, in specimen fatigue tested (Δε/2 = 0.5%) using R = −1 condition, shearing of γ′-precipitates by APB coupled dislocation and formation of stacking faults were observed. The formation and nature of stacking faults were analysed using weak beam imaging technique. Stacking fault formed during fatigue tests using R = −1 condition matured to micro-twins when Δε/2 value was increased to 0.8%. The mechanism of formation of these microtwins is discussed in detail. SEM based microstructural and fractographic examinations revealed that mean stress induced creep effect resulted in intergranular crack initiation and grain boundary cavitation during fatigue tests under R = 0 condition and therefore verified the facts revealed in TEM studies.

36 MATERIALS SCIENCE↗
DOE OSTI2018

An intrinsic velocity–curvature–acceleration relationship for weakly unstable gaseous detonations

The shock motion of calculated weakly unstable cellular detonation was analyzed using concepts from velocity-curvature theory to develop new insight into the underlying physical mechanisms driving the cellular instability. The cellular cycle was shown to follow a surface in a three-dimensional coordinate system composed of the local shock velocity, curvature, and acceleration. Wavelets of the detonation shock were found to follow a velocity-curvature trajectory that was characteristic of an initially reactive wave that decays in time to a decoupled blast wave. Near the Mach stem, these trajectories were only modulated by the strength of the Mach stem at the time the wavelet was generated, indicating that the small reaction zone present in this region is the dominant factor driving the flow. Away from the Mach stem, all wavelet trajectories collapsed to a common curve in velocity-curvature space that was consistent with motion of a decaying blast wave. For the mixture studied, the apparent adherence of shock motion to a unique surface in velocity-curvature-acceleration space indicates the possible existence of an intrinsic mixture-specific relationship for cellular gaseous detonation. In conclusion, this relationship and analysis methodology also provides a mechanism for quantification of the shock velocity and shape fluctuations present in cellular detonation, which may provide utility for modeling detonation engineering applications such as rotating detonation engine design.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Shake-Down Spectroscopy as State- and Site-Specific Probe of Ultrafast Chemical Dynamics

Tracking the multifarious ultrafast electronic and structural changes occurring in a molecule during a photochemical transformation is a challenging endeavor that benefits from recent experimental and computational progress in time-resolved techniques. Measurements of valence electronic states, which provide a global picture of the bonding structure of the molecule, and core electronic states, which provide insight into the local environment, traditionally require different approaches and are often studied separately. Here, we demonstrate that X-ray pulses from a seeded free-electron laser (FEL) enable the measurement of high-resolution, time-resolved X-ray photoelectron spectra (XPS) that capture weak satellite states resulting from shake-down processes in a valence-excited molecule. This approach effectively combines the advantages of both valence- and core-state investigations. We applied this method to investigate photoexcited CS2 molecules, where the role of internal conversion (IC) and intersystem crossing (ISC) in determining the predissociation dynamics is controversial. We present XPS spectra from photoexcited CS2, obtained at the FERMI FEL. High-resolution measurements, compared to the corresponding spectra obtained from accurate multireference quantum chemical calculations, reveal that shake-down satellite channels are highly sensitive to both valence electronic and geometric changes. Previous studies of the predissociation dynamics have led to uncertain assignments of the branching between singlet and triplet excited states. We derive a propensity rule that demonstrates the spin-selectivity of the shake-downs. This selectivity allows us to unequivocally assign contributions from the bright and dark singlet excited states, with populations tracked along the predissociation dynamic pathway.

Thompson, Henry J. [Univ. of Southampton (United K↗
DOE OSTI2014

Magnetism of zigzag edge phosphorene nanoribbons

We have investigated, by means of ab initio calculations, the electronic and magnetic structures of zigzag edge phosphorene nanoribbons (ZPNRs) with various widths. The stable magnetic state was found in pristine ZPNRs by allowing the systems to be spin-polarized. The ground state of pristine ZPNRs prefers ferromagnetic order in the same edge but antiferromagnetic order between two opposite edges. The magnetism arises from the dangling bond states as well as edge localized π-orbital states. The presence of a dangling bond is crucial to the formation of the magnetism of ZPNRs. The hydrogenated ZPNRs get nonmagnetic semiconductors with a direct band gap. While, the O-saturated ZPNRs show magnetic ground states due to the weak P-O bond in the ribbon plane between the p{sub z}-orbitals of the edge O and P atoms.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2026

Interplay of Kondo physics with incommensurate charge density waves in CeTe 3

CeTe 3 is a 2-dimensional (2D) Van der Waals (VdW) material with incommensurate charge density waves (CDW), extremely high transition temperature (T CDW ), and a large momentum-dependent CDW gap that leaves a significant portion of the Fermi surface intact. It is also considered to be a weak Kondo system, a property unexpected for a material with incommensurate CDW, where each atomic site is slightly different. Here, we study the properties of the CDW state in several RTe3 (R is rare earth) materials and examine the hybridization of itinerant states with the localized Ce 4f multiplet in CeTe 3 by using angle resolved photoemission spectroscopy. We find that the renormalization of the itinerant states originating from the hybridization with the deeper localized 4f states at −260 meV is k−dependent and extends to the Fermi level. As these localized states are far from the Fermi level, the observed hybridization affects the effective masses only marginally and does not lead to heavy fermions. However, since the same renormalizing mechanism normally leads to the heavy fermion physics when the localized 4f states are near the Fermi level, our observation of its strong k−dependence suggests that this could be the reason for discrepancy between the heavy masses in specific heat and light ones in Shubnikov de Haas oscillations, often observed in heavy fermions.

36 MATERIALS SCIENCE↗