Tetrad formulation of junction conditions in general relativity.
Junction conditions across internal boundaries for Ricci rotation coefficients and Riemann tensor components in arbitrary reference tetrad frame
Estabrook, F. B.↗
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Surface stress tensor and junction conditions on a rotating null horizon
The general form of the surface stress tensor of an infinitesimally thin shell located on a rotating null horizon is derived, when different interior and exterior geometries are joined there. Even though the induced metric on the surface must be the same approached from either side, the first derivatives of the metric need not be. Such discontinuities lead to a Dirac δ-distribution in the Einstein tensor localized on the horizon. For a general stationary axisymmetric geometry the surface stress tensor can be expressed in terms of two geometric invariants that characterize the surface, namely the discontinuities [κ] and [J] of the surface gravity κ and angular momentum density J. The Komar energy and angular momentum are given in coordinates adapted to the Killing symmetries, and the surface contributions to each determined in terms of [κ] and [J] . Guided by these, a simple modification of the original Israel junction conditions is verified directly from the Einstein tensor density to give the correct finite result for the surface stress, when the normal n to the surface is allowed to tend continuously to a null vector. The relation to Israel’s original junction conditions, which fail on null surfaces, is given. The modified junction conditions are suitable to the matching of a rotating “black hole” exterior to any interior geometry joined at the Kerr null horizon surface, even when the surface normal is itself discontinuous and the Barrabès-Israel formalism is also inapplicable. This joining on a rotating null horizon is purely of the matter shell type and does not contain a propagating gravitational shock wave.
79 ASTRONOMY AND ASTROPHYSICS↗
Junction conditions in general relativity
Tetrad and dyadic formulations of junction conditions in general relativity obtained and used to solve Einstein field equations
RELATIVITY THEORY↗
Nonequilibrium effects on stability of hybrid stars with first-order phase transitions
The stability of hybrid stars with first-order phase transitions as determined by calculating fundamental radial oscillation modes is known to differ from the predictions of the widely used Bardeen-Thorne-Meltzer criterion. We consider the effects of out-of-chemical-equilibrium physics on the radial modes and hence stability of these objects. For a barotropic equation of state, this is done by allowing the adiabatic sound speed to differ from the equilibrium sound speed. We show that doing so extends the stable branches of stellar models, allowing stars with rapid phase transitions to support stable higher-order stellar multiplets similarly to stars with multiple slow phase transitions. We also derive a new junction condition to impose on the oscillation modes at the phase transition. Termed the reactive condition, it is physically motivated, consistent with the generalized junction conditions between two phases, and has the common rapid and slow conditions as limiting cases. Unlike the two common cases, it can only be applied to nonbarotropic stars. Here, we apply this junction condition to hybrid stellar models generated using a two-phase equation of state consisting of nuclear matter with unpaired quark matter at high densities joined by a first-order phase transition and show that, like in the slow limiting case, stars that are classically unstable are stabilized by a finite chemical reaction speed.
79 ASTRONOMY AND ASTROPHYSICS↗
Two first-order phase transitions in hybrid compact stars: Higher-order multiplet stars, reaction modes, and intermediate conversion speeds
We study compact stars with hybrid equations of state consisting of a nuclear outer region and two nested quark phases, each separated from the lower density phase by a strong first-order phase transition. The stability of these models is determined by calculating their radial oscillation modes with different conversion rates between adjacent phases and hence junction conditions for the modes at the phase separation interface between them. In the case when the timescale of transition is faster than the period of oscillations, we recover the traditional stability criterion implying that ∂M/∂ρ c > 0 on the stable branch(es), where M is the mass and ρ c is the central density. In the opposite limit of slow conversion, we find stable stellar multiplets beyond triplets consisting of stars that are stable by the usual criterion plus slow-conversion (denoted by s) hybrid stars with ∂M/∂ρ c < 0 that are stabilized due to an alternative junction condition on the fluid displacement field at the interface reflecting the slow rate of conversion. We also study the properties of the reaction mode, the radial mode that only exists for stars with rapid (abbreviated by r) phase transitions, in stars with either two rapid phase transitions or alternating rapid and slow phase transitions for the first time. Here, the implications of alternative junction conditions are also examined, with these conditions generally being found to provide stability properties similar to those for a slow conversion rate.
79 ASTRONOMY AND ASTROPHYSICS↗
Phosphorus diffusion conditions for shallow junction solar cells
Phosphorus diffusion conditions for shallow junction solar cells
Kautz, H. E.↗
Slowly rotating gravastars
We solve Einstein’s equations for slowly rotating gravitational condensate stars (gravastars) up to second order in the rotation by expanding about the spherically symmetric gravastar with de Sitter interior and Schwarzschild exterior matched at their common horizon. Requiring that the perturbations are finite on the null surface reduces the exterior geometry to that of a Kerr black hole, implying that a slowly rotating gravastar cannot be distinguished from a Kerr black hole by any measurement or observation restricted to the macroscopic spacetime exterior to the horizon. Here we determine the interior solution, the surface stress tensor, and the Komar mass and angular momentum localized on the slowly rotating horizon surface. With the interior equation of state fixed at p = –ρ, finite junction conditions on the null horizon surface necessarily lead to an interior solution with a singular core, where the perturbative expansion breaks down. Comparison to other models and implications for more rapidly rotating gravastars are briefly discussed.
79 ASTRONOMY AND ASTROPHYSICS↗
Characteristics of a Josephson junction harmonic mixer with external pumping
Numerical calculations are carried out on harmonic mixing with an externally pumped Josephson junction. Bias conditions for optimum conversion efficiency are studied for a variety of junction parameters. The predicted noise temperature for harmonic mixing is compared with that for fundamental mixing at the same signal frequency.
Taur, Y.↗
In Situ Irradiation and Measurement of Triple Junction Solar Cells at Low Intensity, Low Temperature (LILT) Conditions
The performance of triple junction InGaP/(In)GaAs/Ge space solar cells was studied following high energy electron irradiation at low temperature. Cell characterization was carried out in situ at the irradiation temperature while using low intensity illumination, and, as such, these conditions reflect those found for deep space, solar powered missions that are far from the sun. Cell characterization consisted of I-V measurements and quantum efficiency measurements. The low temperature irradiations caused substantial degradation that differs in some ways from that seen after room temperature irradiations. The short circuit current degrades more at low temperature while the open circuit voltage degrades more at room temperature. A room temperature anneal after the low temperature irradiation produced a substantial recovery in the degradation. Following irradiation at both temperatures and an extended room temperature anneal, quantum efficiency measurement suggests that the bulk of the remaining damage is in the (In)GaAs sub-cell
Quantum Efficiency↗
Reflecting boundary conditions for graded p-n junctions
In a graded junction, the formalism for handling reflecting boundary conditions must be modified. Since a significant drift term is present, zero recombination velocity at the surface does not imply a zero excess carrier gradient but rather zero overall flux. A model for analyzing p-n junctions fabricated by implantation or diffusion is presented, assuming the dominant recombination mechanism in the graded region is Auger. The model enables optimization of diode design. By proper selection of parameters, mainly by reducing surface concentration or by increasing the steepness of the dopant profile, it is possible to drastically reduce the saturation current generated by the graded region.
Schacham, S. E.↗
The Effect of Grain Boundary Facet Junctions on Segregation and Embrittlement
Junctions are discontinuities in flat grain boundaries that arise in all polycrystalline materials and are thought to play important roles in the response of a grain boundary network to thermal and mechanical loads. A key open question concerns the mechanisms by which solute segregation to junctions impacts properties of the grain boundary. Here, in this work, we investigate the influence of grain boundary facet junctions on solute embrittlement, and we present an analytical model that uses the hydrostatic stress field contributed by dislocations at multiple junctions to describe these effects. Specifically, we study junctions between {112} facets of various lengths in Au $\langle111\rangle$ Σ3 tilt grain boundaries. Copper and silver solutes are employed to determine if the effect of junctions on solute segregation and embrittlement is dependent on size relative to the host. Combined, atomistic simulation data and the analytical model show that Cu and Ag have opposite segregation responses to junctions due to the sign of the hydrostatic stress field induced by junctions. However, a positive shift in the embrittling potency is computed near junctions regardless of solute type or the stress state of the segregation site. Hence, for the conditions studied, junctions consistently shift the energetic landscape towards embrittlement.
36 MATERIALS SCIENCE↗
Graphite-Embedded High-Performance Insulated Metal Substrate for Wide-Bandgap Power Modules
Emerging wide-bandgap (WBG) semiconductor devices such as silicon carbide (SiC) metal–oxide semiconductor field-effect transistors (MOSFETs) and gallium nitride high-electron-mobility transistors can handle high power in reduced semiconductor areas better than conventional Si-based devices owing to superior material properties. With increased power loss density in a WBG-based converter and reduced die size in power modules, thermal management of power devices must be optimized for high performance. Here, we present a graphite-embedded insulated metal substrate (thermally-annealed-pyrolytic-graphite-embedded insulated metal substrate—IMSwTPG) designed for WBG power modules. Theoretical thermal performance analysis of graphite-embedded metal cores is presented, with design details for IMSwTPG with embedded graphite to replace a direct-bonded copper (DBC) substrate. The proposed IMSwTPG is compared with an aluminum nitride-based DBC substrate using finite-element thermal analysis for steady-state and transient thermal performance. The solutions’ thermal performances are compared under different coolant temperature and thermal loading conditions, and the proposed substrate's electrical performance is validated with static and dynamic characterization. Using graphite-embedded substrates, junction-to-case thermal resistance of SiC MOSFETs can be reduced up to 17%, and device current density can be increased by 10%, regardless of the thermal management strategy used to cool the substrate. Reduced transient thermal impedance of up to 40% of dies owing to increased heat capacity is validated in transient thermal simulations and experiments. The half-bridge power module's electrical performance is evaluated for on -state resistance, switching performance, and switching loss at three junction temperature conditions. The proposed substrate solution has minimal impact on conduction and switching performance of SiC MOSFETs.
42 ENGINEERING↗
A parametric study of three-dimensional separation at a wing/body junction for supersonic free-stream conditions
The problem of three-dimensional separation at a wing/body junction has been investigated numerically using a three-dimensional Navier-Stokes code which employs the MacCormack's time split finite volume technique. An algebraic grid generation technique is used for generating the grid at a wing/body junction. Specific computational results on velocity and pressure distribution in the separated flow region are compared with the experimental results. A parametric study of flow parameters such as Mach number and Reynolds number have been carried out to understand their effect in interaction flow field. The parametric study indicates a strong dependency of the number of vortices at the junction on Mach number and Reynolds number.
Lakshmanan, B.↗
Investigation of Off-Stoichiometry in Ternary Nitrides by EDS and HRTEM
We demonstrate an inverted metamorphic multijunction (IMM) photovoltaic cell comprising lattice-mismatched 1.2 eV AlGaInAs and 1.0 eV GaInAs junctions optimized for high-temperature thermophotovoltaic (TPV) applications. This device differs from traditional IMM solar cells because the mismatched junctions are grown at a single lattice constant. This architecture enables removal of the compositionally graded buffer which otherwise filters light from the junctions below and absorbs sub-bandgap light via free-carrier absorption. Sub-bandgap absorption dramatically reduces the efficiency of TPV systems using high reflectivity cells to enable bandedge spectrum filtering. Three components required development to enable this device: 1) a lattice-mismatched 1.2 eV AlGaInAs junction, 2) a metamorphic contact layer grown after the graded buffer, and 3) a transparent tunnel junction that sits in front of the 1.0 eV GaInAs junction. Growth conditions that minimize oxygen defect incorporation maximize AlGaInAs cell quality, enabling a 0.41 V bandgap open circuit voltage offset at 22 mA/cm2 under AM1.5D. A mismatched GaInAs:Se layer is developed as a low resistance contact. Lastly we develop a GaAsSb:C/GaInP:Se tunnel junction suitable for high-power densities with more transparency than the GaAsSb:C/GaInP:Se structure used in past IMM cells. We characterize the tandem device under a high-intensity spectrum that approximates the emission from a 2150 °C blackbody radiator and deduce a projected ideal TPV efficiency of 39.9% at ~30% of the blackbody irradiance, and 36% ideal TPV efficiency under the full 118 W/cm2 irradiance. Improvements to the back-surface reflectivity and series resistance are expected to increase the ideal TPV efficiency well above 40%.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Inverted Metamorphic AlGaInAs/GaInAs Tandem Thermophotovoltaic Cell Designed for Thermal Energy Grid Storage Application
We demonstrate an inverted metamorphic multijunction (IMM) photovoltaic cell comprising lattice-mismatched 1.2 eV AlGaInAs and 1.0 eV GaInAs junctions optimized for high-temperature thermophotovoltaic (TPV) applications. This device differs from traditional IMM solar cells because the mismatched junctions are grown at a single lattice constant. This architecture enables removal of the compositionally graded buffer that otherwise filters light from the junctions below and absorbs sub-bandgap light via free-carrier absorption. Sub-bandgap absorption dramatically reduces the efficiency of TPV systems using high reflectivity cells to enable band edge spectrum filtering. Three components required development to enable this device: (1) a lattice-mismatched 1.2 eV AlGaInAs junction, (2) a metamorphic contact layer grown after the graded buffer, and (3) a transparent tunnel junction that sits in front of the 1.0 eV GaInAs junction. Growth conditions that minimize oxygen defect incorporation maximize AlGaInAs cell quality, enabling a 0.41 V bandgap open circuit voltage offset at 22 mA/cm2 under AM1.5D. A mismatched GaInAs:Se layer is developed as a low resistance contact. Lastly, we develop a GaAsSb:C/GaInP:Se tunnel junction suitable for high-power densities with more transparency than the GaAsSb:C/GaInAs:Se structure used in past IMM cells. We characterize the tandem device under a high-intensity spectrum that approximates the emission from a 2150°C blackbody radiator and deduce a projected ideal TPV efficiency of 39.9% at ~30% of the blackbody irradiance and 36% ideal TPV efficiency under the full 118 W/cm2 irradiance. Improvements to the back-surface reflectivity and series resistance are expected to increase the ideal TPV efficiency well above 40%.
25 ENERGY STORAGE↗
Analysis of a Transonic Alternating Flow Phenomenon Observed During Ares Crew Launch Vehicle Wind Tunnel Tests
A transonic wind tunnel test of the Ares I-X Rigid Buffet Model (RBM) identified a Mach number regime where unusually large buffet loads are present. A subsequent investigation identified the cause of these loads to be an alternating flow phenomenon at the Crew Module-Service Module junction. The conical design of the Ares I-X Crew Module and the cylindrical design of the Service Module exposes the vehicle to unsteady pressure loads due to the sudden transition from separated to attached flow about the cone-cylinder junction with increasing Mach number. For locally transonic conditions at this junction, the flow randomly fluctuates back and forth between a subsonic separated flow and a supersonic attached flow. These fluctuations produce a square-wave like pattern in the pressure time histories which, upon integration result in large amplitude, impulsive buffet loads. Subsequent testing of the Ares I RBM found much lower buffet loads since the evolved Ares I design includes an ogive fairing that covers the Crew Module-Service Module junction, thereby making the vehicle less susceptible to the onset of alternating flow. An analysis of the alternating flow separation and attachment phenomenon indicates that the phenomenon is most severe at low angles of attack and exacerbated by the presence of vehicle protuberances. A launch vehicle may experience either a single or, at most, a few impulsive loads since it is constantly accelerating during ascent rather than dwelling at constant flow conditions in a wind tunnel. A comparison of a wind-tunnel-test-data-derived impulsive load to flight-test-data-derived load indicates a significant over-prediction in the magnitude and duration of the buffet load
Sekula, Martin K.↗
Diffraction by a symmetric material junction simulated with generalized sheet transistion conditions
When diffraction by a material discontinuity in a thick dielectric/ferrite slab is treated for the dual integral equation approach (a variation of the Weiner-Hopf method), the resulting solution displays unknown constants, characteristic of the incompleteness associated with the generalized transition conditions employed in modeling a thick slab. The constants can be shown to depend on the geometry and properties of the discontinuity. Their explicit determination by enforcing field continuity across the slab junction is treated. The field internal to the slab is determined by first expressing the field as an expansion of discrete and continuous eigenmodes valid in the exterior and interior slab region. The expansion or mode coefficients are then identified by recasting the Weiner-Hopf solution in a suitable form, enabling the solution constants to be numerically computed by matching the field expansions to the left and right of the slab discontinuity at a discrete set of points.
Ricoy, Mark A.↗
Instrumentation System Diagnoses a Thermocouple
An improved self-validating thermocouple (SVT) instrumentation system not only acquires readings from a thermocouple but is also capable of detecting deterioration and a variety of discrete faults in the thermocouple and its lead wires. Prime examples of detectable discrete faults and deterioration include open- and short-circuit conditions and debonding of the thermocouple junction from the object, the temperature of which one seeks to measure. Debonding is the most common cause of errors in thermocouple measurements, but most prior SVT instrumentation systems have not been capable of detecting debonding. The improved SVT instrumentation system includes power circuitry, a cold-junction compensator, signal-conditioning circuitry, pulse-width-modulation (PWM) thermocouple-excitation circuitry, an analog-to-digital converter (ADC), a digital data processor, and a universal serial bus (USB) interface. The system can operate in any of the following three modes: temperature measurement, thermocouple validation, and bonding/debonding detection. The software running in the processor includes components that implement statistical algorithms to evaluate the state of the thermocouple and the instrumentation system. When the power is first turned on, the user can elect to start a diagnosis/ monitoring sequence, in which the PWM is used to estimate the characteristic times corresponding to the correct configuration. The user also has the option of using previous diagnostic values, which are stored in an electrically erasable, programmable read-only memory so that they are available every time the power is turned on.
Perotti, Jose↗