On a solution to the second-order phase-locked loop
Stationary phase error variance for second order phase locked loop for low signal to noise ratios
Holmes, J. K.↗
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Response of a Fabry-Perot cavity to phase modulated light
A solution to the lock-in detection method, which is valid for arbitrary values of the modulation frequency, is described. The theory for determining frequency modulation of a single frequency laser is presented. The theoretical predictions for the optimum modulation index are compared to experimental solutions for the quasi-static regime. Signal line shapes for first, second, and third harmonic generations are derived and examined. It is noted that there is good correlation between experimental and quasi-static theory data for the relation between small modulation frequency and resonance linewidth.
Hils, Dieter↗
Phase I SBIR Final report - Planar Magnetic Solution for Vehicle Chargers
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24 POWER TRANSMISSION AND DISTRIBUTION↗
Linking the Spin Transition of Ferric Iron in δ‐(Al,Fe)OOH to Water Storage in the Lower Mantle
As the most massive geochemical reservoir, the lower mantle affects the Earth's budget of volatile elements, including hydrogen or H 2 O. The properties of minerals in the lower mantle are further affected by changes in the electronic configurations of iron cations, that is, by spin transitions. The feedback between spin transitions and potential storage of H 2 O in solid hydrous phases in the lower mantle, however, remains unexplored. By combining high‐pressure nuclear resonant inelastic X‐ray scattering and high‐pressure high‐temperature X‐ray diffraction experiments, we constrained the thermal equation of state of δ‐(Al,Fe)OOH, a member of the phase H solid solution. Based on the derived thermal equation of state of δ‐(Al,Fe)OOH and the underlying thermodynamic model, we calculate the excess Gibbs free energy that arises from the spin transition of ferric iron in this compound and evaluate the effect on phase equilibria. The results of our analysis show that the spin transition of ferric iron in phase H may significantly reduce the thermodynamic activity and hence the concentration of H 2 O in a coexisting hydrous melt. As a consequence, nominally anhydrous minerals of the lower mantle may become dehydrated in the presence of phase H. Our analysis further suggests that, under certain conditions, the spin transition may expand the thermal stability of Fe 3+ ‐bearing phase H and create a geochemical link between the storage of H 2 O in phase H and ferric iron in the lower mantle.
Buchen, Johannes [Univ. of Bayreuth (Germany); Cal↗
Response of hot element flush wall gauges in oscillating laminar flow
The time dependent response characteristics of flush-mounted hot element gauges used as instruments to measure wall shear stress in unsteady periodic air flows were investigated. The study was initiated because anomalous results were obtained from the gauges in oscillating turbulent flows for the phase relation of the wall shear stress variation, indicating possible gauge response problems. Flat plate laminar oscillating turbulent flows characterized by a mean free stream velocity with a superposed sinusoidal variation were performed. Laminar rather than turbulent flows were studied, because a numerical solution for the phase angle between the free stream velocity and the wall shear stress variation that is known to be correct can be obtained. The focus is on comparing the phase angle indicated by the hot element gauges with corresponding numerical prediction for the phase angle, since agreement would indicate that the hot element gauges faithfully follow the true wall shear stress variation.
Giddings, T. A.↗
Quantum spatial propagation of squeezed light in a degenerate parametric amplifier
Differential equations which describe the steady state spatial evolution of nonclassical light are established using standard quantum field theoretic techniques. A Schroedinger equation for the state vector of the optical field is derived using the quantum analog of the slowly varying envelope approximation (SVEA). The steady state solutions are those that satisfy the time independent Schroedinger equation. The resulting eigenvalue problem then leads to the spatial propagation equations. For the degenerate parametric amplifier this method shows that the squeezing parameter obey nonlinear differential equations coupled by the amplifier gain and phase mismatch. The solution to these differential equations is equivalent to one obtained from the classical three wave mixing steady state solution to the parametric amplifier with a nondepleted pump.
Deutsch, Ivan H.↗
Precipitation of Carbides and Dissolution of Widmanstätten Structure for Enhanced Hardness in Ti{sub 2}AlNb-Based Alloys
Carbide-reinforced Ti{sub 2}AlNb matrix composites were spark plasma sintered at 1100 °C by incorporating CNTs into single-B2-phase Ti-22Al-25Nb powders. The as-SPSed alloys were solution treated and then aged in different phase regions. By kinetics analysis and energy-dispersive spectroscopy, it is found carbon will stabilize α{sub 2} phase during solution treatment, and the formation of carbide results in the Nb-depleted regions, which further induces the formation of curly B2 + O Widmanstätten structure during quenching. Different from the general Widmanstätten structure in the aged Ti{sub 2}AlNb alloy, the remained α{sub 2} will consume the B2 within the Widmanstätten structure, when the carbon-added alloy is aged in B2 + O phase region. Compared to the alloy without CNTs, the Vickers hardness of the aged carbon-added Ti{sub 2}AlNb alloy is increased significantly, which is related to the uniform and abundant columnar carbides within the O-phase matrix.
36 MATERIALS SCIENCE↗
Influence of the secondary phase on micro galvanic corrosion of low carbon bainitic steel in NaCl solution
Highlights: • Micro galvanic couple forms between steel matrix and secondary phase for LCB steel. • Micro galvanic couple causes non-uniform corrosion on micro area surface of steel. • The ω secondary phase acts as the micro anode in lath bainitic steel. • The M secondary phase acts as the micro cathode in granular bainitic steel. • Galvanic accelerated corrosion is obvious initially and weakened for long term. - Abstract: The corrosion behavior of lath bainitic and granular bainitic steels in 0.01 mol/L NaCl solution was studied by SEM and TEM observation, electrochemical monitoring and weight loss test. The results indicate that the micro galvanic couple forms between the steel matrix and the secondary phase, which causes non-uniform micro corrosion on surfaces of two steels. In lath bainitic steel, the secondary phase ω acts as the micro anode. While in granular bainitic steel, the secondary phase M acts as the micro cathode. Moreover, the corrosion acceleration caused by micro galvanic couple is obvious in the initial immersion stage, and then it becomes weak during the long term corrosion.
36 MATERIALS SCIENCE↗
Cell partition in two phase polymer systems
Aqueous phase-separated polymer solutions can be used as support media for the partition of biological macromolecules, organelles and cells. Cell separations using the technique have proven to be extremely sensitive to cell surface properties but application of the systems are limited to cells or aggregates which do not significantly while the phases are settling. Partition in zero g in principle removes this limitation but an external driving force must be applied to induce the phases to separate since their density difference disappears. We have recently shown that an applied electric field can supply the necessary driving force. We are proposing to utilize the NASA FES to study field-driven phase separation and cell partition on the ground and in zero g to help define the separation/partition process, with the ultimate goal being to develop partition as a zero g cell separation technique.
Brooks, D. E.↗
Atomic structural mechanism for ferroelectric-antiferroelectric transformation in perovskite NaNbO 3
Sodium niobate (NaNbO 3 or NN) is described as “the most complex perovskite system,” which exhibits transitions between, as well as coexistence of, several ferroelectrics (FE) and antiferroelectric (AFE) phases at different temperatures. Recently, solid solutions of NN with stabilized AFE phases(s) have gained attention for energy-related applications, such as high-density energy storage and electrocaloric cooling. A better understanding of the atomic mechanisms responsible for AFE/FE phase transitions in NaNbO 3 can enable a more rational design of its solid-solution systems with tunable functional properties. In this work, we have investigated changes in the average and local atomic structure of NN using a combination of x-ray/neutron diffraction and neutron pair-distribution function (PDF) analyses. The Rietveld refinement of the x-ray/neutron-diffraction patterns indicates a coexistence of the FE Q (P2 1 ma) and AFE P (Pbma) phases in the temperature range of 300 K ≤ T ≤ 615K, while PDF analysis indicated that the local structure (r < 8Å) is better described by a P2 1 ma symmetry. Above 615 K, the average structure transitions to an AFE R phase (Pmmn or Pnma), while PDF analysis shows an increased disordering of the octahedral distortions and Na displacements at the local scale. These results indicate that the average P/Q/R phase transitions in NN can be described as a result of complex ordering of distorted octahedral tilts at the nanoscale and off-centered displacements of the Na atoms.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Process Engineering to Increase the Layered Phase Concentration in the Immediate Products of Flame Spray Pyrolysis
Flame-spray-pyrolysis (FSP) is a robust and scalable process to synthesize particles at the commodity-scale. FSP has been used to produce the precursor powders which were converted to the layered structure $(R\bar{3m} \text { phase})$ by a postannealing step in making nickel-rich cathode materials (NCMs). Theoretically, the high flame temperature (normally >1500 K) in FSP can provide adequate energy for the phase conversion from rock-salt to layered structures and potentially enables one-step synthesis. However, the high flame temperature is a critical issue to cause lithium loss and structural degradation, preventing the formation of the layered phase. Here, guided by the gaseous nucleation theory, we implemented several FSP processes with different solution recipes. The layered phase concentration in the as-burned products can be increased with the solution enthalpies. By adding a rapid quench step to suppress the lithium loss and phase degradation, the layered phase can be further increased. This work contributes new ideas to innovating process regarding the process efficiency and throughput of manufacturing cathode materials at a large scale.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Lightcurves and phase relation of asteroid 324 Bamberga
Results of a worldwide photometric investigation of the asteroid 324 Bamberga conducted from September to November 1978 are presented. The full-cycle light curve obtained from observations at Torino, Graz, Catania and Table Mountain observatories shows two maxima and two minima with a maximum amplitude of 0.075 magnitudes from which rotation period of 29.42 plus or minus 0.01 hours is derived. Linear least squares solution of the phase relation results in a phase coefficient of 0.034 plus or minus 0.001 mag/deg, a mean V magnitude of 7.20 and a zero-phase absolute V magnitude of 7.17 plus or minus 0.01. The color indices obtained (0.69 for B-V and 0.36 for U-B) are in agreement with the C taxonomic type assigned to the asteroid. The unusual length of the period of 324 Bamberga relative to that of other asteroids of diameter greater than 200 km is pointed out.
Scaltriti, F.↗
Phase shift of TE and TM modes in an optical fiber due to axial strain (exact solution)
Axial strain may be determined by monitoring the phase shift of modes of a variety of optical fiber sensors. In this paper, the exact solution of a circular optical fiber is used to calculate the phase shift of the TE and TM modes. Whenever an optical fiber is stressed, the optical path length, the index of refraction, and the propagation constants of each fiber mode change. In consequence, the modal phase term, beta(ln)z, of the fields is shifted by an amount Delta phi. In certain cases, it is desirable to control the phase shift term in order to make the fiber either more or less sensitive to certain kinds of strain. It is shown that it can be accomplished by choosing appropriate fiber parameters.
Egalon, Claudio O.↗
An interaction algorithm for prediction of mean and fluctuating velocities in two-dimensional aerodynamic wake flows
A theoretical analysis is presented yielding sets of partial differential equations for determination of turbulent aerodynamic flowfields in the vicinity of an airfoil trailing edge. A four phase interaction algorithm is derived to complete the analysis. Following input, the first computational phase is an elementary viscous corrected two dimensional potential flow solution yielding an estimate of the inviscid-flow induced pressure distribution. Phase C involves solution of the turbulent two dimensional boundary layer equations over the trailing edge, with transition to a two dimensional parabolic Navier-Stokes equation system describing the near-wake merging of the upper and lower surface boundary layers. An iteration provides refinement of the potential flow induced pressure coupling to the viscous flow solutions. The final phase is a complete two dimensional Navier-Stokes analysis of the wake flow in the vicinity of a blunt-bases airfoil. A finite element numerical algorithm is presented which is applicable to solution of all partial differential equation sets of inviscid-viscous aerodynamic interaction algorithm. Numerical results are discussed.
Baker, A. J.↗
Phase Discovery and Selected Synthesis of Subvalent Niobium Tellurides Using a Polytelluride Flux Strategy
Transition metal subchalcogenides involve electron-rich metals and can facilitate an in-depth understanding of the relationships among quantum properties such as superconductivity, charge density wave, and topological band structures. However, effective experimental routes toward synthesizing transition metal subchalcogenides are still lacking, hindering the development of new quantum materials. Herein, we propose a eutectic polytelluride flux strategy as an excellent solution to address phase discovery and crystal growth in transition metal subtelluride systems. We report new phases easily and selectively synthesized using a eutectic “K 3 Te 4 ” polytelluride flux upon adjusting the ratio of Nb metal to flux in the starting materials (K/Nb/Te = 3:x:4). Using a high Nb content in the solvent (x = 2 and 1), crystals of KNb 3 Te 3 O 0.38 and K 0.9 Nb 3 Te 4 are obtained. Both subtellurides exhibit diverse Nb clusters, including face-sharing and edge-sharing Nb 6 octahedral columns and zig-zag Nb chains. Reducing the Nb content to x = 0.33 leads to the formation of a layered compound, K 1.06 NbTe 2 . This compound comprises a NbTe 6 trigonal prism with K intercalated between the layers. Single crystals of known binary Nb tellurides can also be grown using another eutectic flux “KTe 3 . 2 ”, and the obtained NbTe 2 exhibits a new polymorphism with extra trimerization along the b-axis in the Nb–Nb bonded double zig-zag cluster. Finally, precise control over the structural dimensionality and oxidation state, combined with the facile crystal growth process, makes our synthetic strategy an efficient route to explore quantum materials in transition metal subchalcogenides.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
KMT-2021-BLG-0171Lb and KMT-2021-BLG-1689Lb: Two Microlensing Planets in the KMTNet High-Cadence Fields With Followup Observations
Follow-up observations of high-magnification gravitational microlensing events can fully exploit their intrinsic sensitivity to detect extrasolar planets, especially those with small mass ratios. To make followup observations more uniform and efficient, we develop a system, HighMagFinder, to automatically alert possible ongoing high-magnification events based on the real-time data from the Korea Microlensing Telescope Network (KMTNet). We started a new phase of follow-up observations with the help of HighMagFinder in 2021. Here we report the discovery of two planets in high-magnification microlensing events, KMT- 2021-BLG-0171 and KMT-2021-BLG-1689, which were identified by the HighMagFinder. We find that both events suffer the ‘central-resonant’ caustic degeneracy. The planet-host mass-ratio is q ∼4.7 × 10 −5 or q ∼2.2 × 10 −5 for KMT-2021-BLG-0171, and q ∼2.5 × 10 −4 or q ∼1.8 × 10 −4 for KMT-2021-BLG-1689. Together with two other events, four cases that suffer such degeneracy have been discovered in the 2021 season alone, indicating that the de generate solutions may have been missed in some previous studies. We also propose a quantitative factor to weight the probability of each solution from the phase space. The resonant interpretations for the two events are disfavoured under this consideration. This factor can be included in future statistical studies to weight degenerate solutions.
Micro gravitational lensing↗
The growth of metastable peritectic compounds
The influence of gravitationally driven convection on the directional solidification of peritectic alloys was evaluated. The Pb-Bi peritectic was studied as a model solidification system. Analyses of directionally solidified Pb-Bi peritectic samples indicate that appreciable macrosegregation occurs due to thermosolutal convection and/or Soret diffusion. The macrosegregation results in sequantial change of phase and morphology as solidification progresses down the length of the sample. Banding was eliminated when furnace conditions were selected which resulted in a planar solidification interface. The directional solidification that occurs in the vicinity of the Pb-Bi peritectic isothermal was found to be isocompositional and to consist solely of the equilibrium terminal solid solution and peritectic phases on an extremely fine scale. Evidence was found to support the peritectic supercooling mechanism, but not the proposed peritectic superheat mechanism.
Larson, D. J., Jr.↗
Primal and dual formulations of sequential gradient-restoration algorithms for trajectory optimization problems
One of the most effective first-order algorithms for solving trajectory optimization problems is the sequential gradient-restoration algorithm (SGRA). Originally developed in the primal formulation, this algorithm is extended to incorporate a dual formulation. Both the primal formulation and the dual formulation involve a sequence of two-phase cycles, each cycle including a gradient phase and a restoration phase. In turn, each iteration of the gradient phase and the restoration phase requires the solution of an auxiliary minimization problem (AMP). In the primal formulation, the AMP is solved with respect to the variations of the state, the control, and the parameter. In the dual formulation, the AMP is solved with respect to the Lagrange multipliers. A characteristic of the dual formulation is that the AMPs associated with the gradient phase and the restoration phase of SGRA can be reduced to mathematical programming problems involving a finite number of parameters as unknowns. A comparison of the primal formulation and the dual formulation is presented. The comparison is done in terms of several trajectory optimization problems having current aerospace interest.
Miele, A.↗