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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Chemical bonding dictates drastic critical temperature difference in two seemingly identical superconductors

Though YB 6 and LaB 6 share the same crystal structure, atomic valence electron configuration, and phonon modes, they exhibit drastically different phonon-mediated superconductivity. YB 6 superconducts below 8.4 K, giving it the second-highest critical temperature of known borides, second only to MgB 2 . LaB 6 does not superconduct until near-absolute zero temperatures (below 0.45 K), however. Though previous studies have quantified the canonical superconductivity descriptors of YB 6 ’s greater Fermi-level (E f ) density of states and higher electron–phonon coupling (EPC), the root of this difference has not been assessed with full detail of the electronic structure. Through chemical bonding, we determine low-lying, unoccupied 4f atomic orbitals in lanthanum to be the key difference between these superconductors. These orbitals, which are not accessible in YB 6 , hybridize with π B–B bonds and bring this π-system lower in energy than the σ B–B bonds otherwise at E f . This inversion of bands is crucial: the optical phonon modes we show responsible for superconductivity cause the σ-orbitals of YB 6 to change drastically in overlap, but couple weakly to the π-orbitals of LaB 6 . These phonons in YB 6 even access a crossing of electronic states, indicating strong EPC. No such crossing in LaB 6 is observed. Finally, a supercell (the M k-point) is shown to undergo Peierls-like effects in YB 6 , introducing additional EPC from both softened acoustic phonons and the same electron-coupled optical modes as in the unit cell. Overall, we find that LaB 6 and YB 6 have fundamentally different mechanisms of superconductivity, despite their otherwise near-identity.

Science & Technology - Other Topics↗
NASA NTRS2019

Near Real-Time Sub/Seasonal Prediction of Aerosol at NASA Global Modeling and Assimilation Office

A new version of the coupled modeling and analysis system used to produce near real time subseasonal to seasonal forecasts was released over a year ago by the NASA/Goddard Global Modeling and Assimilation Office. The model runs at approximately 1/2 degree globally in the atmosphere and ocean, contains a realistic description of the cryosphere, and includes an interactive aerosol model. The data assimilation used to produce initial conditions is weakly coupled, in which the atmosphere-only assimilated state is coupled to an ocean data assimilation system using a Local Ensemble Transform Kalman Filter. Here will briefly describe the new system, and show results of aerosol-derived air quality from an extensive series of retrospective forecasts. The interactive aerosol is shown to improve seasonal time scale prediction skill during some "forecasts of oppurtunity". Plans for a future version of the system with predicted biomass burning from fires will also be discussed.

Molod, Andrea M.↗
NASA NTRS2019

Near Real-Time Sub/Seasonal Prediction of Aerosol and Air Quality at the NASA Global Modeling and Assimilation Office

Version 2 of the coupled modeling and analysis system used to produce near real time subseasonal to seasonal forecasts was released almost two years ago by the NASA/Goddard Global Modeling and Assimilation Office. The model runs at approximately 1/2 degree globally in the atmosphere and ocean, contains a realistic description of the cryosphere, and includes an interactive aerosol model. The data assimilation used to produce initial conditions is weakly coupled, in which the atmosphere-only assimilated state is coupled to an ocean data assimilation system using a Local Ensemble Transform Kalman Filter. Results of aerosol-derived air quality (Particulate Matter) from an extensive series of retrospective forecasts will be shown, with particular focus on the continental United States and eastern Asia. In addition, under some circumstances, the interactive aerosol is shown to improve seasonal time scale prediction skill. Plans for a future version of the system with predicted biomass burning from fires will also be discussed.

Molod, Andrea↗
DOE OSTI2022

A model of persistent breaking of continuous symmetry

We consider a UV-complete field-theoretic model in general dimensions, including d=2+1, which consists of two copies of the long-range vector models, with O(m) and O(N-m) global symmetry groups, perturbed by double-trace operators. Using conformal perturbation theory we find weakly-coupled IR fixed points for N\geq 6 N ≥ 6 that reveal a spontaneous breaking of global symmetry. Namely, at finite temperature the lower rank group is broken, with the pattern persisting at all temperatures due to scale-invariance. We provide evidence that the models in question are unitary and invariant under full conformal symmetry. Furthermore, we show that this model exhibits a continuous family of weakly interacting field theories at finite N.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Multichannel Topological Kondo Effect

A Coulomb blockaded M-Majorana island coupled to normal metal leads realizes a novel type of Kondo effect where the effective impurity “spin” transforms under the orthogonal group SO⁡(M). The impurity spin stems from the nonlocal topological ground state degeneracy of the island and thus the effect is known as the topological Kondo effect. We introduce a physically motivated N-channel generalization of the topological Kondo model. Starting from the simplest case N =2, we conjecture a stable intermediate coupling fixed point and evaluate the resulting low-temperature impurity entropy. The impurity entropy indicates that an emergent Fibonacci anyon can be realized in the N =2 model. We also map the case N =2, M =4 to the conventional four-channel Kondo model and find the conductance at the intermediate fixed point. By using the perturbative renormalization group, we also analyze the large-N limit, where the fixed point moves to weak coupling. In the isotropic limit, we find an intermediate stable fixed point, which is stable to “exchange” coupling anisotropies, but unstable to channel anisotropy. We evaluate the fixed point impurity entropy and conductance to obtain experimentally observable signatures of our results. Here, in the large-N limit, we evaluate the full crossover function describing the temperature-dependent conductance.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Strong-coupling anisotropic s-wave superconductivity in the type-II Weyl semimetal TaIrTe 4

TaIrTe 4 is a recently discovered type-II Weyl semimetal, hosting only four Weyl points. In this work, we study the cleaved TaIrTe 4 crystal using scanning tunneling microscopy/spectroscopy and find that it also hosts a superconducting state with a transition temperature of 3.9 K. From Dynes function fitting, the superconducting phase is consistent with anisotropic s-wave pairing, with a superconducting gap of 1.31 meV. This value leads to a value of 2Δ max /k B T C = 7.81 , much larger than the 3.53 predicted by Bardeen-Cooper-Schrieffer theory for weak-coupling superconductors. The critical field is found to be 0.7 T based on the analysis of tunneling conductance as a function of magnetic field. Two types of nonmagnetic defects on the TaIrTe 4 surface are observed, neither of which induce bound states inside the superconducting gap, further supporting conventional s-wave superconductivity in the TaIrTe 4 system.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Stripe and bubble ratchets on asymmetric substrates

We show that various nonmonotonic ratchet effects can arise when mesophase pattern-forming systems, which exhibit anisotropic crystal, stripe, and bubble regimes, are coupled to one-dimensional asymmetric substrates under ac driving. The patterns emerge in the absence of a substrate when the ratio of attraction to repulsion is varied for particles with competing short-range attraction and long-range repulsion potentials. In the presence of the substrate, we find that the ratchet efficiency varies nonmonotonically with increasing attraction, depending upon how well the mesophase morphology matches the substrate spacing and periodicity. For strong repulsion, there is a weak but finite ratchet effect, while at intermediate attraction, there is a robust ratchet effect in which the system forms stripes aligned with the substrate symmetry direction. For strong attraction, large bubbles appear that have weak or no ratchet effects when the bubble width exceeds the substrate lattice spacing, causing the bubble to be only weakly coupled to the substrate. For very strong attraction, small bubbles form and undergo a strong ratchet effect with an efficiency that oscillates as a function of ac drive amplitude. Although the small bubble regime is a strongly correlated regime in which each bubble contains many particles, the system behaves as if it is in a single-particle regime since the bubble width is much smaller than the substrate lattice spacing. We map out the different rectification phases as a function of the pattern morphology, substrate strength, and ac drive amplitude. The pronounced ratchet effects that we observe in some regimes can be exploited for pattern sorting in hard and soft matter systems. Published by the American Physical Society 2024

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1985

Coupled-mode analysis of gain and wavelength oscillation characteristics of diode laser phased arrays

The lasing wavelengths and gain characteristics of the modes of phase-locked arrays of channel-substrate-planar (CSP) lasers are presented. The gain values for the array modes are determined from complex coupling coefficients calculated using the fields of neighboring elements of the array. The computations show that, for index guided lasers which have nearly planar phase fronts, the highest order array mode will be preferred. The 'in-phase' or fundamental mode, which produces only one major lobe in the far-field radiation pattern, has the lowest modal gain of all array modes. The modal gain differential between the highest order and fundamental modes is less than 10/cm for weak coupling between the elements.

Butler, J. K.↗
DOE OSTI2021

Gravitational effective field theory islands, low-spin dominance, and the four-graviton amplitude

Abstract We analyze constraints from perturbative unitarity and crossing on the leading contributions of higher-dimension operators to the four-graviton amplitude in four spacetime dimensions, including constraints that follow from distinct helicity configurations. We focus on the leading-order effect due to exchange by massive degrees of freedom which makes the amplitudes of interest infrared finite. In particular, we place a bound on the coefficient of the R 3 operator that corrects the graviton three-point amplitude in terms of the R 4 coefficient. To test the constraints we obtain nontrivial effective field-theory data by computing and taking the large-mass expansion of the one-loop minimally-coupled four-graviton amplitude with massive particles up to spin 2 circulating in the loop. Remarkably, we observe that the leading EFT coefficients obtained from both string and one-loop field-theory amplitudes lie in small islands. The shape and location of the islands can be derived from the dispersive representation for the Wilson coefficients using crossing and assuming that the lowest-spin spectral densities are the largest. Our analysis suggests that the Wilson coefficients of weakly-coupled gravitational physical theories are much more constrained than indicated by bounds arising from dispersive considerations of 2 → 2 scattering. The one-loop four-graviton amplitudes used to obtain the EFT data are computed using modern amplitude methods, including generalized unitarity, supersymmetric decompositions and the double copy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Re-entrant unconventional superconductivity induced by rare-earth substitution in Nd 1-x Eu x NiO 2 thin films

High temperature superconductivity is typically associated with strong coupling and a large superconducting gap, yet these characteristics have not been demonstrated in the nickelates. Here, we provide experimental evidence that Eu substitution in the spacer layer of Nd 1-x Eu x NiO 2 (NENO) thin films enhances the superconducting gap, driving the system toward a strong-coupling regime. This is accompanied by a magnetic-exchange-driven magnetic-field-enhanced superconductivity. We investigate the upper critical magnetic field, H c2 , and the superconducting gap of superconducting NENO thin films with x = 0.2 to 0.35. Magnetoresistance measurements reveal magnetic-field-enhanced superconductivity in NENO films. We interpret this phenomenon as a result of an interaction between magnetic Eu ions and superconducting states in the Ni d x2-y2 orbital. The upper critical magnetic field strongly violates the weak-coupling Pauli limit. Infrared spectroscopy confirms a large gap-to-Tc ratio $2\Delta /{k}_{B}{T}_{{\rm{c}}}\simeq 5-6$, indicating a stronger coupling pairing mechanism in NENO relative to the Sr-doped NdNiO 2 . The substitution of Eu in the rare-earth layer causes pronounced modifications of the superconducting gap and magnetic interactions in Nd-based nickelates, opening new pathways to engineer high- T c superconductivity in infinite-layer nickelates.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Quantum Light Emission from Coupled Defect States in DNA-Functionalized Carbon Nanotubes

Solid-state single-photon sources are essential building blocks for quantum photonics and quantum information technologies. This study demonstrates promising single-photon emission from quantum defects generated in single-wall carbon nanotubes (SWCNTs) by covalent reaction with guanine nucleotides in their single-stranded DNA coatings. Low-temperature photoluminescence spectroscopy and photon-correlation measurements on individual guanine-functionalized SWCNTs (GF-SWCNTs) indicate that multiple, closely spaced guanine defect sites within a single ssDNA strand collectively form an exciton trapping potential that supports a localized quantum state capable of room-temperature single-photon emission. In addition, exciton traps from adjacent ssDNA strands are weakly coupled to give cross-correlations between their separate photon emissions. Theoretical modeling identifies coupling mechanism as a capture of band-edge excitons. Finally, because the spatial pattern of nanotube functionalization sites can be readily controlled by selecting ssDNA base sequences, GF-SWCNTs should become a versatile family of quantum light emitters with engineered properties.

36 MATERIALS SCIENCE↗
NASA NTRS1985

On the relation between 'mixing length' and 'direct interaction approximation' theories of turbulence

The capabilities of direct interaction approximations (DIA) and weak-coupling approximations (WCA) in modeling turbulence in plasma physics studies are examined. DIA and WCA formalisms are reviewed and a DIA expression for homogeneous incompressible hydrodynamics is simplified to derive an energy spectrum in an arbitrary wavenumber space. A solution is defined for the expression when applied to long wavelength phenomena generated by an instability. The equation is further generalized to yield a transport equation for modeling the spectrum generated by homogeneous turbulence in a linearly unstable system undergoing nonlinear interaction. Finally, the technique is applied to two-dimensional turbulence in a low pressure, weakly ionized plasma embedded in a homogeneous magnetic field and experiencing instabilities caused by electron density and electric potential gradients, such as found in the ionospheric E region.

Sudan, R. N.↗
DOE OSTI2023

Recent progress in low energy neutrino scattering physics and its implications for the standard and beyond the standard model physics

Neutrinos continue to provide a testing ground for the structure of the standard model of particle physics as well as hints towards the physics beyond the standard model. Neutrinos of energies spanning over several orders of magnitude, originating in many terrestrial and astrophysical processes, have been detected via various decay and interaction mechanisms. At MeV scales, there has been one elusive process, until a few years ago, known as coherent elastic neutrino-nucleus scattering (CEvNS) that was theoretically predicted over five decades ago but was never observed experimentally. The recent experimental observation of the CEvNS process by the COHERENT collaboration at a stopped pion neutrino source has inspired physicists across many subfields. This has vital implications for nuclear physics, high-energy physics, astrophysics, and beyond. CEvNS, being a low-energy process, provides a natural window to study light, weakly-coupled, new physics in the neutrino sector. In this review, we intend to provide the current status of low energy neutrino scattering physics and its implications for the standard and beyond the standard model physics. We discuss the general formalism of calculating the tree-level CEvNS cross section and present estimated theoretical uncertainties on the CEvNS cross section stemming from different sources. We also discuss the inelastic scattering of tens of MeV neutrinos that have implications for supernova detection in future neutrino experiments. We discuss how the CEvNS experiments can be used as a testing ground for the Standard Model (SM) weak physics as well as in searching for the Beyond the Standard Model (BSM) physics signals. Any deviation from the SM predicted event rate either with a change in the total event rate or with a change in the shape of the recoil spectrum, could indicate new contributions to the interaction cross-section. The SM implications include the study of weak nuclear form factor and weak mixing angle. The BSM studies include non-standard interactions, neutrino electromagnetic properties, and sterile neutrino searches. In conclusion, stopped pion facilities are also a copious source of neutral and changed mesons that allow study of several dark sector physics scenarios such as vector portal models, leptophobic dark matter as well as axion-like particle searches.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Electronically-coupled redox centers in trimetallic cobalt complexes

Synthesis and isolation of molecular building blocks of metal–organic frameworks (MOFs) can provide unique opportunities for characterization that would otherwise be inaccessible due to the heterogeneous nature of MOFs. Herein, we report a series of trinuclear cobalt complexes incorporating dithiolene ligands, triphenylene-2,3,6,7,10,11-hexathiolate (THT) (1 3+ ), and benzene hexathiolate (BHT) (2 3+ ), with 1,1,1,-tris(diphenylphosphinomethyl)ethane (triphos) employed as the capping ligand. Single crystal X-ray analyses of 1 3+ and 2 3+ display three five-coordinate cobalt centers bound to the triphos and dithiolene ligands in a distorted square pyramidal geometry. Cyclic voltammetry studies of 1 3+ and 2 3+ reveal three redox features associated with the formation of mixed valence states due to the sequential reduction of the redox-active metal centers (Co III/II ). Using this electrochemical data, the comproportionality values were determined for 1 and 2 (log K c = 1.4 and 1.5 for 1, and 4.7 and 5.8 for 2), suggesting strong resonance-stabilized coupling of the metal centers, with stronger electronic coupling observed for complex 2 compared to that for complex 1. Cyclic voltammetry studies were also performed in solvents of varying polarity, whereupon the difference in the standard potentials (ΔE 1/2 ) for 1 and 2 was found to shift as a function of the polarity of the solvent, indicating a negative correlation between the dielectric constant of the electrochemical medium and the stability of the mixed valence species. Spectroelectrochemical studies of in situ generated multi-valent (MV) states of complexes 1 and 2 display characteristic NIR intervalence charge transfer (IVCT) bands, and analysis of the IVCT transitions for complex 2 suggests a weakly coupled class II multi-valent species and relatively large electronic coupling factors (1700 cm –1 for the first multi-valent state of 2 2+ , and 1400 and 4000 cm –1 for the second multi-valent state of 2 + ). Here, density functional theory (DFT) calculations indicate a significant deviation in relative energies of the frontier orbitals of complexes 1 3+ , 2 3+ , and 3 + that contrasts those calculated for the analogous trinuclear cobalt dithiolene complexes employing pentamethylcyclopentadienyl (Cp*) as the capping ligand (Co 3 Cp* 3 THT and Co 3 Cp* 3 BHT, respectively), and may be a result of the cationic nature of complexes 1 3+ , 2 3+ , and 3 + .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Luther-Emery liquid and dominant singlet superconductivity in the hole-doped Haldane spin-1 chain

We investigate the pairing tendencies in the hole-doped Haldane spin-1 chain. To allow for doping, we extend the original spin chain Hamiltonian into a fermionic model involving a two-orbital Hubbard chain at intermediate or strong repulsive interaction strengths U and for degenerate orbitals. At half filling and large U, the ferromagnetic Hund's coupling, J H , generates effective spin-1 moments, with antiferromagnetic correlations between sites. Using large-scale density matrix renormalization group calculations, we accurately study the system's behavior under light hole-doping. For U = 1.6 in units of the noninteracting bandwidth and for J H /U ≳ 0.275, we find that singlet pairing dominates the long-distance physics, establishing this system as a promising platform for repulsively mediated superconductivity. We provide concrete examples of materials that could realize the physics described here. We also provide evidence that the system approaches a Luther-Emery liquid state at large system sizes, reminiscent of the behavior of doped one-orbital two-leg ladders at weak coupling, which also have superconducting tendencies. The numerically calculated central charge approaches one in the thermodynamic limit, indicating a single gapless mode as is expected for the Luther-Emery state. Exponents characterizing the power-law decays of singlet pair-pair and charge density-density correlations are determined, and found to approximately satisfy the Luther-Emery identity.

1-dimensional systems↗
NASA NTRS1986

Group-kinetic theory of turbulence

The two phases are governed by two coupled systems of Navier-Stokes equations. The couplings are nonlinear. These equations describe the microdynamical state of turbulence, and are transformed into a master equation. By scaling, a kinetic hierarchy is generated in the form of groups, representing the spectral evolution, the diffusivity and the relaxation. The loss of memory in formulating the relaxation yields the closure. The network of sub-distributions that participates in the relaxation is simulated by a self-consistent porous medium, so that the average effect on the diffusivity is to make it approach equilibrium. The kinetic equation of turbulence is derived. The method of moments reverts it to the continuum. The equation of spectral evolution is obtained and the transport properties are calculated. In inertia turbulence, the Kolmogoroff law for weak coupling and the spectrum for the strong coupling are found. As the fluid analog, the nonlinear Schrodinger equation has a driving force in the form of emission of solitons by velocity fluctuations, and is used to describe the microdynamical state of turbulence. In order for the emission together with the modulation to participate in the transport processes, the non-homogeneous Schrodinger equation is transformed into a homogeneous master equation. By group-scaling, the master equation is decomposed into a system of transport equations, replacing the Bogoliubov system of equations of many-particle distributions. It is in the relaxation that the memory is lost when the ensemble of higher-order distributions is simulated by an effective porous medium. The closure is thus found. The kinetic equation is derived and transformed into the equation of spectral flow.

Tchen, C. M.↗
DOE OSTI2025

Studying Open Quantum Systems Relevant to Chemistry on a Trapped-Ion Quantum Simulator (Final Technical Report)

This project advances the trapped-ion quantum simulator as a versatile platform for studying open quantum system phenomena. We aim to contribute to the emerging quantum simulation toolkits and enable simulation of nanoscale energy processes. Trapped-ion platforms offer unique capabilities: their vibrational motion can be precisely manipulated, measured, and coherently coupled to auxiliary qubits. The vibrational mode can function both as a highly sensitive quantum sensor and a programmable environment bath. Using this platform, we achieved three major outcomes. First, we demonstrated using the vibrational mode as an ultrasensitive probe for testing fundamental physics, including possible nonlinear quantum mechanics effects. Second, we established that these modes can act as controllable baths in which tunable noise and loss can enhance or modify energy-transfer dynamics, providing the experimental preparation toward studying mechanisms relevant to chemical reactions and light-harvesting systems. Third, by introducing controllable nonlinear gain and loss, we showed theoretically how simulations using trapped ions can model vibrationally-assisted energy transport in a non‐Hermitian quantum system comprising a chromophore dimer weakly coupled to a vibrational mode. Exploring the non‐Hermitian dynamics of the whole system including vibrations, we found that energy transfer accompanied by absorption of phonons from a vibrational mode can be significantly enhanced near an exceptional point. This theoretical work on simulation of energy transfer processes in driven non‐Hermitian quantum systems revealed an interesting novel path to study open quantum systems dynamics under conditions of gain and loss. We then further explored the benefits of controllable gain and loss with an experimental realization of quantum analogs of nonlinear oscillators, namely, the van der Pol oscillator. Here we observed mutual synchronization mediated by collective dissipation between two oscillators. In parallel, we explored related quantum networking protocols using the same trapped-ion platform, developing fast, high-fidelity schemes for distributing entanglement. Together, these achievements show that trapped-ion vibrational modes provide a highly programmable and high-fidelity platform for investigating complex dissipative quantum behavior, while enabling new approaches to remote quantum sensing, energy science, and nonlinear quantum dynamics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1993

An Agile Beam Transmit Array Using Coupled Oscillator Phase Control

A few years ago York and colleagues suggested that injection locking of voltage controlled oscillators could be used to implement beam steering in a phased array [I]. The scheme makes use of the fact that when an oscillator is injection locked to an external signal, the phase difference between the output of the oscillator and the injection signal is governed by the difference between the injection frequency and the free running frequency of the oscillator (the frequency to which the oscillator is tuned). Thus, if voltage controlled oscillators (VCOs) are used, this phase difference is controlled by an applied voltage. Now, if a set of such oscillators are coupled to nearest neighbors, they can be made to mutually injection lock and oscillate as an ensemble. If they are all tuned to the same frequency, they will all oscillate in phase. Thus, if the outputs are connected to radiating elements forming a linear array, the antenna will radiate normal to the line of elements. Scanning is accomplished by antisymmetrically detuning the end oscillators in the array by application of a pair of appropriate voltages to their tuning ports. This results in a linear phase progression across the array which is just the phasing required to scan the beam. The scan angle is determined by the degree of detuning. We have constructed a seven element one dimensional agile beam array at S-band based on the above principle. Although, a few such arrays have been built in the past, this array possesses two unique features. First, the VCO MMICs have buffer amplifiers which isolate the output from the tuning circuit, and second, the oscillators are weakly coupled to each other at their resonant circuits rather than their outputs. This results in a convenient isolation between the oscillator array design and the radiating aperture design. An important parameter in the design is the so called coupling phase which determines the phase shift of the signals passing from one oscillator to its neighbors. Using this array, we have been able to verify the theoretical predictions concerning the effect of this phase on both the locking range and ensemble frequency of the array. However, the scan range achieved fell somewhat short of the theoretical value because of the amplitude variation of the oscillator outputs with tuning.

Pogorzelski, Ronald S.↗