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At least 793 records · Page 44
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Slow electron-phonon relaxation controls the dynamics of the superconducting resistive transition

Here, we investigate the temporal and spatial scales of resistance fluctuations (𝑅 fluctuations) at the superconducting resistive transition accessed through voltage fluctuation measurements in thin epitaxial TiN films. This material is characterized by slow electron-phonon relaxation, which puts it far beyond the applicability range of the textbook scenario of superconducting fluctuations. The measured Lorentzian spectrum of the 𝑅 fluctuations identifies their correlation time, which is nearly constant across the transition region and has no relation to the conventional Ginzburg-Landau timescale. Instead, the correlation time coincides with the energy relaxation time determined by a combination of the electron-phonon relaxation and the relaxation via diffusion into reservoirs. Our data are quantitatively consistent with the model of spontaneous temperature fluctuations and highlight the lack of understanding of the resistive transition in materials with slow electron-phonon relaxation.

critical phenomena↗
NASA NTRS2012

Validation of Atmosphere/Ionosphere Signals Associated with Major Earthquakes by Multi-Instrument Space-Borne and Ground Observations

The latest catastrophic earthquake in Japan (March 2011) has renewed interest in the important question of the existence of pre-earthquake anomalous signals related to strong earthquakes. Recent studies have shown that there were precursory atmospheric/ionospheric signals observed in space associated with major earthquakes. The critical question, still widely debated in the scientific community, is whether such ionospheric/atmospheric signals systematically precede large earthquakes. To address this problem we have started to investigate anomalous ionospheric / atmospheric signals occurring prior to large earthquakes. We are studying the Earth's atmospheric electromagnetic environment by developing a multisensor model for monitoring the signals related to active tectonic faulting and earthquake processes. The integrated satellite and terrestrial framework (ISTF) is our method for validation and is based on a joint analysis of several physical and environmental parameters (thermal infrared radiation, electron concentration in the ionosphere, lineament analysis, radon/ion activities, air temperature and seismicity) that were found to be associated with earthquakes. A physical link between these parameters and earthquake processes has been provided by the recent version of Lithosphere-Atmosphere-Ionosphere Coupling (LAIC) model. Our experimental measurements have supported the new theoretical estimates of LAIC hypothesis for an increase in the surface latent heat flux, integrated variability of outgoing long wave radiation (OLR) and anomalous variations of the total electron content (TEC) registered over the epicenters. Some of the major earthquakes are accompanied by an intensification of gas migration to the surface, thermodynamic and hydrodynamic processes of transformation of latent heat into thermal energy and with vertical transport of charged aerosols in the lower atmosphere. These processes lead to the generation of external electric currents in specific regions of the atmosphere and the modifications, by dc electric fields, in the ionosphere-atmosphere electric circuit. We retrospectively analyzed temporal and spatial variations of four different physical parameters (gas/radon counting rate, lineaments change, long-wave radiation transitions and ionospheric electron density/plasma variations) characterizing the state of the lithosphere/atmosphere coupling several days before the onset of the earthquakes. Validation processes consist in two phases: A. Case studies for seven recent major earthquakes: Japan (M9.0, 2011), China (M7.9, 2008), Italy (M6.3, 2009), Samoa (M7, 2009), Haiti (M7.0, 2010) and, Chile (M8.8, 2010) and B. A continuous retrospective analysis was preformed over two different regions with high seismicity- Taiwan and Japan for 2003-2009. Satellite, ground surface, and troposphere data were obtained from Terra/ASTER, Aqua/AIRS, POES and ionospheric variations from DEMETER and COSMIC-I data. Radon and GPS/TEC were obtaining from monitoring sites in Taiwan, Japan and Italy and from global ionosphere maps (GIM) respectively. Our analysis of ground and satellite data during the occurrence of 7 global earthquakes has shown the presence of anomalies in the atmosphere. Our results for Tohoku M9.0 earthquake show that on March 7th, 2011 (4 days before the main shock and 1 day before the M7.2 foreshock of March 8, 2011) a rapid increase of emitted infrared radiation was observed by the satellite data and an anomaly was developed near the epicenter. The GPS/TEC data indicate an increase and variation in electron density reaching a maximum value on March 8. From March 3 to 11 a large increase in electron concentration was recorded at all four Japanese ground-based ionosondes, which returned to normal after the main earthquake. Similar approach for analyzing atmospheric and ionospheric parameters has been applied for China (M7.9, 2008), Italy (M6.3, 2009), Samoa (M7, 2009), Haiti (M7.0, 2010) and Chile (M8.8, 2010) eahquakes. Results have revealed the presence of related variations of these parameters implying their connection with the earthquake process. The second phase (B) of this validation included 102 major earthquakes (M>5.9) in Taiwan and Japan. We have found anomalous behavior before all of these events with no false negatives. False alarm ratio for false positives is less then 10% and has been calculated for the same month of the earthquake occurrence for the entire period of analysis (2003-2009). The commonalities for detecting atmospheric/ionospheric anomalies are: i.) Regularly appearance over regions of maximum stress (i.e., along plate boundaries); ii.) Anomaly existence over land and sea; and iii) association with M>5.9 earthquakes not deeper than 100km. Due to their long duration over the same region these anomalies are not consistent with a meteorological origin. Our initial results from the ISTF validation of multi-instrument space-borne and ground observations show a systematic appearance of atmospheric anomalies near the epicentral area, one to seven (average) days prior to the largest earthquakes, and suggest that it could be explained by a coupling process between the observed physical parameters and the pre-earthquake preparation processes.

Ouzounov, Dimitar↗
NASA NTRS1978

Ionization equilibrium and radiative energy loss rates for C, N, and O ions in low-density plasmas

The results of calculations of the ionization equilibrium and radiative energy loss rates for C, N and O ions in low-density plasmas are presented for electron temperatures in the range 10,000-10,000,000 K. The ionization structure is determined by using the steady-state corona model, in which electron impact ionization from the ground states is balanced by direct radiative and dielectronic recombination. With an improved theory, detailed calculations are carried out for the dielectronic recombination rates in which account is taken of all radiative and autoionization processes involving a single-electron electric-dipole transition of the recombining ion. The radiative energy loss processes considered are electron-impact excitation of resonance line emission, direct radiative recombination, dielectronic recombination, and electron-ion bremsstrahlung. For all three elements, resonance line emission resulting from 2s-2p transitions produces a broad maximum in the energy loss rate near 100,000 K.

Jacobs, V. L.↗
NASA NTRS2001

Deep UV Native Fluorescence Imaging of Antarctic Cryptoendolithic Communities

An interdisciplinary team at the Jet Propulsion Laboratory Center for Life Detection has embarked on a project to provide in situ chemical and morphological characterization of Antarctic cryptoendolithic microbial communities. We present here in situ deep ultraviolet (UV) native fluorescence and environmental scanning electron microscopy images transiting 8.5 mm into a sandstone sample from the Antarctic Dry Valleys. The deep ultraviolet imaging system employs 224.3, 248.6, and 325 nm lasers to elicit differential fluorescence and resonance Raman responses from biomolecules and minerals. The 224.3 and 248.6 nm lasers elicit a fluorescence response from the aromatic amino and nucleic acids. Excitation at 325 nm may elicit activity from a variety of biomolecules, but is more likely to elicit mineral fluorescence. The resultant fluorescence images provide in situ chemical and morphological maps of microorganisms and the associated organic matrix. Visible broadband reflectance images provide orientation against the mineral background. Environmental scanning electron micrographs provided detailed morphological information. The technique has made possible the construction of detailed fluorescent maps extending from the surface of an Antarctic sandstone sample to a depth of 8.5 mm. The images detect no evidence of microbial life in the superficial 0.2 mm crustal layer. The black lichen component between 0.3 and 0.5 mm deep absorbs all wavelengths of both laser and broadband illumination. Filamentous deep ultraviolet native fluorescent activity dominates in the white layer between 0.6 mm and 5.0 mm from the surface. These filamentous forms are fungi that continue into the red (iron-rich) region of the sample extending from 5.0 to 8.5 mm. Using differential image subtraction techniques it is possible to identify fungal nuclei. The ultraviolet response is markedly attenuated in this region, apparently from the absorption of ultraviolet light by iron-rich particles coating the filaments. Below 8.5 mm the filamentous morphology of the upper layers gives way to punctate 1-2 micron particles evidencing fluorescent activity following excitation at both deep ultraviolet wavelengths.

Storrie-Lombardi, M. C.↗
DOE OSTI2026

Quantum calculations of the cavity shift in electron magnetic moment measurements

The measurement of the anomalous electron magnetic moment g – 2 through quantum transitions of a single trapped electron is the most stringent test of quantum field theory. These experiments are now so precise that they must account for the effects of the cavity containing the electron. Classical calculations of this “cavity shift” must subtract the electron’s divergent self-field, and thus require knowledge of the exact Green’s function for the cavity’s electromagnetic field. We perform the first fully quantum calculation of the cavity shift in a closed cavity, which instead involves subtracting linearly divergent cavity mode sums and integrals. Using contour integration methods, we find perfect agreement with existing classical results for both spherical and cylindrical cavities, justifying their current use. Moreover, our mode-based results can be naturally generalized to account for systematic effects, necessary to push future measurements to the next order of magnitude in precision.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Crystal and magnetic structure of polar oxide HoCrWO 6

In this study, polar magnetic oxide HoCrWO 6 is synthesized and its crystal structure, magnetic structure, and thermodynamic properties are investigated. HoCrWO 6 forms the polar crystal structure (space group Pna 2 1 (#33)) due to the cation ordering of W 6+ and Cr 3+ . There is an antiferromagnetic transition at T N = 24.5 K along with the magnetic entropy change (~5 J.Kg. –1 K –1 at 70 kOe). Neutron diffraction measurement indicates that both Cr and Ho sublattices are ordered with the moment of 2.32(5)μ B and 8.7(4)μ B at 2 K, respectively. While Cr forms A-type collinear antiferromagnetic (AFM) structure with magnetic moment along the b axis, Ho sublattice orders in a non-coplanar AFM arrangement. A comparison with isostructural DyFeWO 6 and DyCrWO 6 indicates that the magnetic structure of this family of compounds is controlled by the presence or absence of e g electrons in the transition metal sublattice.

42 ENGINEERING↗
DOE OSTI2021

Particle charge distributions in the effluent of a flow-through atmospheric pressure low temperature plasma

Atmospheric pressure low-temperature plasmas are often utilized to perform particle synthesis, treatment, and removal. It is well-known that dust particles are highly negatively charged in these plasmas; however, little is known about dust particle charging behavior as particles leave the plasma volume and pass through the spatial afterglow region. In this work, monodisperse particles of various sizes and work functions were introduced into an atmospheric pressure radiofrequency capacitively coupled flow-through plasma. Dust particle electrical mobility distributions downstream of the flow-through plasma were measured utilizing a differential mobility analyzer in conjunction with a condensation particle counter at various gas flow velocities. Charge distributions were determined from the measured electrical mobility distributions. Experiments confirm that particles become less negatively charged, and even net-positively charged after leaving the plasma volume, with a distribution that follows a shifted Boltzmann charge distribution. Additionally, particle charge in the effluent of the flow-through plasma is negligibly dependent on work function but highly size and flow velocity dependent. Larger particles were shown to have a higher magnitude of charge under all studied conditions; however, particle polarity was switchable by varying gas flow velocity. The charging dynamics were simulated utilizing a constant number Monte Carlo model that accounts for electron temperature decay and the transition from ambipolar to free diffusion of electrons and ions in the spatial afterglow. Simulation results also suggest that, at the same flow velocity, larger particles obtain a greater magnitude of charge, negative or positive. Furthermore, the decrease in electron mobility and the difference between ion and electron convective loss rates create an ion-rich region in the plasma effluent that promotes ion–particle collisions and drives particle charge removal and even reversal of polarity. Larger particles more favorably collide with energetic species in these environments, which results in higher charge states.

atmospheric pressure low temperature plasma↗
NASA NTRS2006

An Ultrasensitive Hot-Electron Bolometer for Low-Background SMM Applications

We are developing a hot-electron superconducting transition-edge sensor (TES) that is capable of counting THz photons and operates at T = 0.3K. The main driver for this work is moderate resolution spectroscopy (R approx. 1000) on the future space telescopes with cryogenically cooled (approx. 4 K) mirrors. The detectors for these telescopes must be background-limited with a noise equivalent power (NEP) approx. 10(exp -19)-10(exp -20) W/Hz(sup 1/2) over the range v = 0.3-10 THz. Above about 1 THz, the background photon arrival rate is expected to be approx. 10-100/s), and photon counting detectors may be preferable to an integrating type. We fabricated superconducting Ti nanosensors with a volume of approx. 3x10(exp -3) cubic microns on planar substrate and have measured the thermal conductance G to the thermal bath. A very low G = 4x10(exp -14) W/K, measured at 0.3 K, is due to the weak electron-phonon coupling in the material and the thermal isolation provided by superconducting Nb contacts. This low G corresponds to NEP(0.3K) = 3x10(exp -19) W/Hz(sup 1/2). This Hot-Electron Direct Detector (HEDD) is expected to have a sufficient energy resolution for detecting individual photons with v > 0.3 THz at 0.3 K. With the sensor time constant of a few microseconds, the dynamic range is approx. 50 dB.

bolometers↗
DOE OSTI2021

Rotaxane rings promote oblique packing and extended lifetimes in DNA-templated molecular dye aggregates

Abstract Molecular excitons play a central role in natural and artificial light harvesting, organic electronics, and nanoscale computing. The structure and dynamics of molecular excitons, critical to each application, are sensitively governed by molecular packing. Deoxyribonucleic acid (DNA) templating is a powerful approach that enables controlled aggregation via sub-nanometer positioning of molecular dyes. However, finer sub-Angstrom control of dye packing is needed to tailor excitonic properties for specific applications. Here, we show that adding rotaxane rings to squaraine dyes templated with DNA promotes an elusive oblique packing arrangement with highly desirable optical properties. Specifically, dimers of these squaraine:rotaxanes exhibit an absorption spectrum with near-equal intensity excitonically split absorption bands. Theoretical analysis indicates that the transitions are mostly electronic in nature and only have similar intensities over a narrow range of packing angles. Compared with squaraine dimers, squaraine:rotaxane dimers also exhibit extended excited-state lifetimes and less structural heterogeneity. The approach proposed here may be generally useful for optimizing excitonic materials for a variety of applications ranging from solar energy conversion to quantum information science.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Nematic transition and nanoscale suppression of superconductivity in Fe(Te,Se)

The interplay of different electronic phases underlies the physics of unconventional superconductors. One of the most intriguing examples is a high-temperature superconductor, FeTe 1 – x Se x . This superconductor undergoes both a topological transition, linked to the electronic band inversion, and an electronic nematic phase transition, associated with rotation symmetry breaking, around the same Se composition where the superconducting transition temperature peaks. In this regime, nematic fluctuations and symmetry-breaking strain could be important, but this is yet to be fully explored. Using spectroscopic-imaging scanning tunnelling microscopy, we study the electronic nematic transition in FeTe 1 – x Se x as a function of composition. Near the critical Se composition, we find electronic nematicity in nanoscale regions. The superconducting coherence peaks are suppressed in areas where static nematic order is the strongest. By analysing atomic displacement in scanning tunnelling microscopy topographs, we find that small anisotropic strain can give rise to these strongly nematic localized regions. Furthermore, our experiments reveal a tendency of FeTe 1 – x Se x , near x ≈ 0.45, to form puddles hosting static nematic order, suggestive of nematic fluctuations pinned by structural inhomogeneity, and demonstrate the effect of anisotropic strain on superconductivity in this regime.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Continuous pressure-induced valence and magnetic transitions in EuMnSb 2

EuMnSb 2 is a unique and promising compound with complex magnetism (Eu and Mn sublattices) to realize magnetic control of topological quasiparticles. By applying pressure (P) to this system, we have observed a continuous pressure-induced valence change from Eu 2+ to Eu 3+ . Remarkably, despite the significant valence change in Eu ions, an extremely large increase in the magnetic ordering temperature (T N,Eu ) from 21 K at ambient pressure to 180 K at 28.4 GPa is detected.The substantial enhancement in T N,Eu is likely the consequence of the reduced distance between neighboring Eu ions and the enhanced indirect exchange interaction through increased 4f -5d mixing under pressure. Furthermore, T N,Eu (P) shows a discontinuous change above 8 GPa, although the orthorhombic crystal structure remains stable. Our experimental data indicate the record high value in the magnetic hyperfine field of 151 Eu, reaching 74.1 T at 28.4 GPa and 26 K. In conclusion, these unusual electronic and magnetic transitions revealed by pressure highlight that EuMnSb 2 is a rich magnetic topological semimetal candidate for investigating a multitude of strong correlations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Dynamics of HCN, HNC, and HNCO Formation in the 193 nm Photodissociation of Formamide

Formamide (NH 2 CHO) is the simplest molecule containing a peptide linkage [-NH-C($=$O)-], and it plays an essential role in the study of prebiotic chemistry. Exposure to UV irradiation allows formamide to decompose and act as a prebiotic feedstock in the formation of nucleobases and other necessary starting materials. The photodissociation mechanism of gaseous formamide at 193 nm is studied using (a) chirped-pulse Fourier transform millimeter-wave spectroscopy in the 260-290 GHz spectral region in a room-temperature flow-tube reactor at 1 mu bar pressure, (b) a combination of electronic structure theory, transition state theory, and quasiclassical trajectories, and (c) the Active Thermochemical Tables. The HCN and HNC photoproducts of hydrogenated (NH 2 CHO) and deuterated (NH 2 CDO and ND 2 CHO) formamide precursors are examined to gain insight into the photodissociation mechanism. Here, the theoretical investigation has characterized the main pathway leading to each of the HCN/HNC isomers from the precursor isotopologues. The theoretical branching ratio [HNC]/[HCN] = 2.1 for nascent photofragments agrees with the experiment. The effect of the postphotolysis HNC ↔ HCN isomerization on the [HNC]/[HCN] ratio is predicted. We report the experimental branching ratio [HNCO]: ([HNC] + [HCN]) = 12 ± 3 and propose that most of HNCO originates from dissociation on the S-1 electronic state of formamide.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2003

Computation of Free-Free Transitions in Atomic Physics: Foundations

The amplitude T for "free-free" processes, such as bremsstrahlung or photo- absorption by an electron in the continuum in the presence of an external field, is usually written as the matrix element of the radiation operator taken between two continuum states. However, unlike the case when at least one of the states is bound, as in radiative transitions, electron capture, or the photo-effect, this expression contains an unphysical term, proportional to a delta-function and is not really the physical amplitude Tphys. This continues to be true for both the velocity and length form of the dipole approximation to the amplitude T. We first give an a priori definition of Tphys in terms of the scattering parts of the continuum functions, which has an obvious interpretation in terms of time-ordered diagrams. We then show that when the formal amplitude is modified by a long- distance cutoff, the modified form approaches Tphys as the cutoff is removed. The modified form then serves as a basis for the definition of a physical velocity dipole amplitude and this in turn leads to an equivalent length form of the dipole amplitude. This exercise provides a clear theoretical basis for many extant calculations in which cutoff factors are introduces somewhat ad hoc, as needed.

Bhatia, A. K.↗
NASA NTRS2006

Computational Spectroscopy of Polycyclic Aromatic Hydrocarbons In Support of Laboratory Astrophysics

Polycyclic aromatic hydrocarbons (PAHs) are strong candidates for the molecular carriers of the unidentified infrared bands (UIR) and the diffuse interstellar bands (DIBs). In order to test the PAH hypothesis, we have systematically measured the vibronic spectra of a number of jet-cooled neutral and ionized PAHs in the near ultraviolet (UV) to visible spectral ranges using the cavity ring-down spectroscopy. To support this experimental effort, we have carried out theoretical studies of the spectra obtained in our measurements. Ab initio and (time-dependent) density.functiona1 theory calculations are performed to obtain the geometries, energetics, vibrational frequencies, transition dipole moments, and normal coordinates of these PAH molecules. Franck-Condon (FC) calculations and/or vibronic calculations are then performed using the calculated normal coordinates and vibrational frequencies to simulate the vibronic spectra. It is found that vibronic interactions in these conjugated pi electron systems are often strong enough to cause significant deviations from the Born-Oppenheimer (BO) approximation. For vibronic transitions that are well described by the BO approximation, the vibronic band profiles are simulated by calculating the rotational structure of the vibronic transitions. Vibronic oscillator strength factors are calculated in the frame of the FC approximation from the electronic transition dipole moments and the FC factors. This computational effort together with our experimental measurements provides, for the first time, powerful tools for comparison with space-based data and, hence, a powerful approach to understand the spectroscopy of interstellar PAH analogs and the nature of the UIR and DIBs.

Tan, Xiaofeng↗
DOE OSTI2022

Spin-triplet superconductivity from excitonic effect in doped insulators

Despite being of fundamental importance and potential interest for topological quantum computing, spin-triplet superconductors remain rare in solid state materials after decades of research. In this work, we present a three-particle mechanism for spin-triplet superconductivity in multiband systems, where an effective attraction between doped electrons is produced from the Coulomb repulsion via a virtual interband transition involving a third electron [V. Crépel, L. Fu, Sci. Adv. 7, eabh2233 (2021)]. Our theory is analytically controlled by an interband hybridization parameter and explicitly demonstrated in doped band insulators with the example of an extended Hubbard model. Our theory of exciton-mediated pairing reveals how, as a matter of principle, a two-particle bound state can arise from the strong electron repulsion upon doping, opening a viable path to Bose–Einstein condensate (BEC)–Bardeen–Cooper–Schrieffer (BCS) physics in solid state systems. In light of this theory, we propose that recently discovered dilute superconductors such as ZrNCl, WTe 2 , and moiré materials can be spin-triplet and compare the expected consequences of our theory with experimental data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1986

Strong electron bidirectional anisotropies in the distant tail - ISEE 3 observations of polar rain

A detailed observational treatment of bidirectional electrons (about 50 to 500 eV) in the distant magnetotail (r not below 100 earth radii) is presented. It is found that electrons in this energy range commonly exhibit strong, field-aligned anisotropies in the tail lobes. Because of large tail motions, the ISEE 3 data provide extensive sampling of both the north and south lobes in rapid succession. These data directly demonstrate the strong asymmetries that exist between the north and south lobes at any one time. The bidirectional fluxes are found to occur predominantly in the lobe directly connected to the sunward interplanetary magnetic field in the open magnetosphere model (north lobe for away sectors and south lobe for toward sectors). Electron anisotropy and magnetic field data are presented which show the transition from unidirectional (sheath) electron populations to bidirectional (lobe) populations. The open nature of the distant magnetopause is demonstrated and it is shown that the source of the higher-energy, bidirectional lobe electrons is the tailward directed electron heat flux population in the distant magnetosheath. Taken together, the present evidence suggests that the bidirectional electrons that were observed in the distant tail are closely related to the polar rain electrons observed previously at lower altitudes. Furthermore, these data provide strong evidence that the distant tail is composed largely of open magnetic field lines in contradistinction to some recently advanced models.

Baker, D. N.↗
NASA NTRS1987

Bidirectional electron anisotropies in the distant tail - ISEE 3 observations of polar rain

A detailed observational treatment of bidirectional electrons (50 approx. 500 eV) in the distant magnetotail (or greater than or equal to 100 R sub E) is presented. It is found that electrons in this energy range commonly exhibit strong, field aligned anisotropies in the tail lobes. Because of large tail motions, the ISEE-3 data provide extensive sampling of both the north and south lobes in rapid succession, demonstrating directly the strong asymetries that exist between the north and south lobes at any one time. The bidirectional fluxes are found to occur predominantly in the lobe directy connected to the sunward IMF in the open magnetosphere model (north lobe for away sectors and south lobe for toward sectors). Electron anisotropy and magnetic field data are presented which show the transition from unidirectional (sheath) electron populations to bidirectional (lobe) populations. Taken together, the present evidence suggests that the bidirectional electrons that we observe in the distant tail are closely related to the Polar rain electrons observed previously at lower altitudes. Furthermore, these data provide strong evidence that the distant tail is comprised largely of open magnetic field lines in contra distinction to some recently advanced models.

Baker, D. N.↗