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At least 19 records

Brown-York charges at null boundaries

The Brown-York stress tensor provides a means for defining quasilocal gravitational charges in subregions bounded by a timelike hypersurface. We consider the generalization of this stress tensor to null hypersurfaces. Such a stress tensor can be derived from the on-shell subregion action of general relativity associated with a Dirichlet variational principle, which fixes an induced Carroll structure on the null boundary. The formula for the mixed-index tensor T i j takes a remarkably simple form that is manifestly independent of the choice of auxiliary null vector at the null surface, and we compare this expression to previous proposals for null Brown-York stress tensors. The stress tensor we obtain satisfies a covariant conservation equation with respect to any connection induced from a rigging vector at the hypersurface, as a result of the null constraint equations. For transformations that act covariantly on the boundary structures, the Brown-York charges coincide with canonical charges constructed from a version of the Wald-Zoupas procedure. For anomalous transformations, the charges differ by an intrinsic functional of the boundary geometry, which we explicity verify for a set of symmetries associated with finite null hyper-surfaces. Applications of the null Brown-York stress tensor to symmetries of asymptotically flat spacetimes and celestial holography are discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

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↗

Anomalies of cosmic anisotropy from holographic universality of great-circle variance

We examine all-sky cosmic microwave background temperature maps on large angular scales to compare their consistency with two scenarios: the standard inflationary quantum picture, and a distribution constrained to have a universal variance of primordial curvature perturbations on great circles. The latter symmetry is not a property of standard quantum inflation, but may be a symmetry of holographic models with causal quantum coherence on null surfaces. Since the variation of great-circle variance is dominated by the largest angular scale modes, in the latter case the amplitude and direction of the unobserved intrinsic dipole (that is, the ℓ = 1 harmonics) can be estimated from measured ℓ = 2, 3 harmonics by minimizing the variance of great-circle variances including only ℓ = 1, 2, 3 modes. It is found that including the estimated intrinsic dipole leads to a nearly-null angular correlation function over a wide range of angles, in agreement with a null anti-hemispherical symmetry independently motivated by holographic causal arguments, but highly anomalous in standard cosmology. Simulations are used here to show that simultaneously imposing the constraints of universal great-circle variance and the vanishing of the angular correlation function over a wide range of angles tends to require patterns that are unusual in the standard picture, such as anomalously high sectorality of the ℓ = 3 components, and a close alignment of principal axes of ℓ = 2 and ℓ = 3 components, that have been previously noted on the actual sky. The precision of these results appears to be primarily limited by errors introduced by models of Galactic foregrounds.

79 ASTRONOMY AND ASTROPHYSICS↗

Mutual information superadditivity and unitarity bounds

We derive the property of strong superadditivity of mutual information arising from the Markov property of the vacuum state in a conformal field theory and strong subadditivity of entanglement entropy. We show this inequality encodes unitarity bounds for different types of fields. These unitarity bounds are precisely the ones that saturate for free fields. This has a natural explanation in terms of the possibility of localizing algebras on null surfaces. A particular continuity property of mutual information characterizes free fields from the entropic point of view. We derive a general formula for the leading long distance term of the mutual information for regions of arbitrary shape which involves the modular flow of these regions. We obtain the general form of this leading term for two spheres with arbitrary orientations in spacetime, and for primary fields of any tensor representation. For free fields we further obtain the explicit form of the leading term for arbitrary regions with boundaries on null cones.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Pattern of perturbations from a coherent quantum inflationary horizon

It is proposed that if quantum states of space-time are coherent on null surfaces, holographic Planck-scale fluctuations of inflationary horizons dominate the formation of primordial scalar curvature perturbations. It is shown that the reduction of quantum states on nearly-spherical emergent horizon surfaces around each observer creates a distinctive pattern whose correlations in the angular domain differ from the standard quantum theory of inflation. Causal constraints are used in a semiclassical model to formulate candidate directional symmetries. It is suggested that this hypothesis could provide a physical explanation for several well known anomalies measured in CMB anisotropy. New exact symmetries are predicted, such as a vanishing temperature correlation function at 90 degrees angular separation, that can be tested with current data.

79 ASTRONOMY AND ASTROPHYSICS↗

Optical nulling apparatus and method for testing an optical surface

An optical nulling apparatus for testing an optical surface includes an aspheric mirror having a reflecting surface for imaging light near or onto the optical surface under test, where the aspheric mirror is configured to reduce spherical aberration of the optical surface under test. The apparatus includes a light source for emitting light toward the aspheric mirror, the light source longitudinally aligned with the aspheric mirror and the optical surface under test. The aspheric mirror is disposed between the light source and the optical surface under test, and the emitted light is reflected off the reflecting surface of the aspheric mirror and imaged near or onto the optical surface under test. An optical measuring device is disposed between the light source and the aspheric mirror, where light reflected from the optical surface under test enters the optical measuring device. An imaging mirror is disposed longitudinally between the light source and the aspheric mirror, and the imaging mirror is configured to again reflect light, which is first reflected from the reflecting surface of the aspheric mirror, onto the optical surface under test.

Olczak, Eugene↗

Simple, general, realistic, robust, analytic tokamak equilibria. Part 1. Limiter and divertor tokamaks

Tokamak equilibria have been derived that are analytic solutions to the Grad–Shafranov equation. Here in this paper, Part 1, describes a wide range of such equilibria including smooth limiter surfaces, double- and single-null divertor surfaces, arbitrary aspect ratio, elongation, triangularity and beta. Part 2 generalizes the analysis to include edge pedestals and toroidal flow.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Simple, general, realistic, robust, analytic tokamak equilibria. Part 2. Pedestals and flow

Part 1 described a wide range of analytic tokamak equilibria modelling smooth limiter surfaces, double- and single-null divertor surfaces, arbitrary aspect ratio, elongation, triangularity and beta. Part 2 generalizes the analysis to further include edge pedestals and toroidal flow. Specifically, edge pedestals are allowed in the pressure, pressure gradient and toroidal current density. Also, an edge-localized contribution to the bootstrap current is treated. In terms of flow, analytic solutions are obtained for two cases: a $\gamma = 2$ adiabatic and a $\gamma = \infty $ incompressible energy conservation relation.

Physics↗

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↗

Self-Nulling Eddy Current Probe for Surface and Subsurface Flaw Detection

An eddy current probe which provides a null-signal in the presence of unflawed material without the need for any balancing circuitry has been developed at NASA Langley Research Center. Such a unique capability of the probe reduces set-up time, eliminates tester configuration errors, and decreases instrumentation requirements. The probe is highly sensitive to surface breaking fatigue cracks, and shows excellent resolution for the measurement of material thickness, including material loss due to corrosion damage. The presence of flaws in the material under test causes an increase in the extremely stable and reproducible output voltage of the probe. The design of the probe and some examples illustrating its flaw detection capabilities are presented.

Wincheski, B.↗

Modeling Phase-Aligned Gamma-Ray and Radio Millisecond Pulsar Light Curves

Since the discovery of the first eight gamma-ray millisecond pulsars (MSPs) by the Fermi Large Area Telescope, this population has been steadily expanding. Four of the more recent detections, PSR J00340534, PSR J1939+2134 (B1937+21; the first MSP ever discovered), PSR J1959+2048 (B1957+20; the first discovery of a black widow system), and PSR J2214+3000, exhibit a phenomenon not present in the original discoveries: nearly phase-aligned radio and gamma-ray light curves (LCs). To account for the phase alignment, we explore models where both the radio and gamma-ray emission originate either in the outer magnetosphere near the light cylinder or near the polar caps. Using a Markov Chain Monte Carlo technique to search for best-fit model parameters, we obtain reasonable LC fits for the first three of these MSPs in the context of altitude-limited outer gap (alOG) and two-pole caustic (alTPC) geometries (for both gamma-ray and radio emission). These models differ from the standard outer gap (OG)/two-pole caustic (TPC) models in two respects: the radio emission originates in caustics at relatively high altitudes compared to the usual conal radio beams, and we allow both the minimum and maximum altitudes of the gamma-ray and radio emission regions to vary within a limited range (excluding the minimum gamma-ray altitude of the alTPC model, which is kept constant at the stellar radius, and that of the alOG model, which is set to the position-dependent null charge surface altitude). Alternatively, phase-aligned solutions also exist for emission originating near the stellar surface in a slot gap scenario (low-altitude slot gap (laSG) models). We find that the alTPC models provide slightly better LC fits than the alOG models, and both of these give better fits than the laSG models (for the limited range of parameters considered in the case of the laSG models). Thus, our fits imply that the phase-aligned LCs are likely of caustic origin, produced in the outer magnetosphere, and that the radio emission for these pulsars may come from close to the light cylinder. In addition, we were able to constrain the minimum and maximum emission altitudes with typical uncertainties of 30% of the light cylinder radius. Our results therefore describe a third gamma-ray MSP subclass, in addition to the two previously found by Venter et al.: those with LCs fit by standard OG/TPC models and those with LCs fit by pair-starved polar cap models.

Venter, C.↗

Alignment of optical system components using an ADM beam through a null assembly

A system for testing an optical surface includes a rangefinder configured to emit a light beam and a null assembly located between the rangefinder and the optical surface. The null assembly is configured to receive and to reflect the emitted light beam toward the optical surface. The light beam reflected from the null assembly is further reflected back from the optical surface toward the null assembly as a return light beam. The rangefinder is configured to measure a distance to the optical surface using the return light beam.

Hayden, Joseph E.↗

An Overview of the Null-Field Method. I. Formulation and Basic Results

In this paper we revisit the fundamentals of the null-field method with discrete sources. We prove the unique solvability of the null-field equations for the total field inside the particle and the internal field outside the particle, at all wavenumbers. For this purpose, we use the equivalence between the null-field and surface integral equations methods. Furthermore, we discuss the completeness property of different systems of discrete sources for a surface field approximation, and derive an infinite set of integral equations for the surface fields in a variety of discrete sources. Finally, we formulate the null-field scheme as an approach aiming to construct an approximate solution to the scattering problem. The way in which we introduce the matrix of a particle is different from the standard approach relying on the assumption that the system of regular vector spherical wave functions for the interior problem is a basis.

Null-field method↗

Simulations of the churning mode: Toroidally symmetric plasma convection and turbulence around the X-points in a snowflake divertor

Using a reduced MHD model, extended to include field-aligned thermal conduction, we present numerical simulations of the churning mode (CM): a toroidally symmetric, non-linear plasma vortex in the vicinity of the null points in a snowflake (SF) divertor [D. D. Ryutov et al., Phys. Scr. 89, 088002 (2014)]. Simulations are carried out across a range of inter-null separations, d xx ⁠, and inter-null orientations, θ⁠, primarily in conditions relevant to the MAST-U tokamak. We find that, when d xx is small, the CM induces additional transport across the X-points when β pm ≳8%, where β pm is the ratio of the plasma pressure in the null region to poloidal magnetic pressure at the midplane. This transport also increases approximately linearly as d xx is reduced. A diffusive model of this transport is shown to predict the total transport across the null points, where diffusion coefficients of up to ∼ 10 2 m 2 s −1 centered on a small region around the X-points are used. However, the CM also results in significant changes to the flux surfaces in the null region, which is not captured by this diffusive model. The changes in magnetic geometry mean the fractional exhaust power delivered to each divertor leg is highly sensitive to β pm ⁠, d xx ⁠, and θ⁠. For small values of θ⁠, the CM can induce a change in topology, redirecting exhaust power from a secondary divertor leg on the high field side to one on the low field side. Similar behavior is found in the fraction of exhaust power going to the inner and outer divertor. Such changes in the flux surfaces may not be captured by Grad–Shafranov solvers and so may be a source of error in the magnetic reconstruction of SF experiments. We consistently find that the fractional exhaust power going to a secondary divertor leg on the high field side is small, consistent with SF experiments.

Computer simulation↗

Measurement Via Optical Near-Nulling and Subaperture Stitching

A subaperture stitching interferometer system provides near-nulling of a subaperture wavefront reflected from an object of interest over a portion of a surface of the object. A variable optical element located in the radiation path adjustably provides near-nulling to facilitate stitching of subaperture interferograms, creating an interferogram representative of the entire surface of interest. This enables testing of aspheric surfaces without null optics customized for each surface prescription. The surface shapes of objects such as lenses and other precision components are often measured with interferometry. However, interferometers have a limited capture range, and thus the test wavefront cannot be too different from the reference or the interference cannot be analyzed. Furthermore, the performance of the interferometer is usually best when the test and reference wavefronts are nearly identical (referred to as a null condition). Thus, it is necessary when performing such measurements to correct for known variations in shape to ensure that unintended variations are within the capture range of the interferometer and accurately measured. This invention is a system for nearnulling within a subaperture stitching interferometer, although in principle, the concept can be employed by wavefront measuring gauges other than interferometers. The system employs a light source for providing coherent radiation of a subaperture extent. An object of interest is placed to modify the radiation (e.g., to reflect or pass the radiation), and a variable optical element is located to interact with, and nearly null, the affected radiation. A detector or imaging device is situated to obtain interference patterns in the modified radiation. Multiple subaperture interferograms are taken and are stitched, or joined, to provide an interferogram representative of the entire surface of the object of interest. The primary aspect of the invention is the use of adjustable corrective optics in the context of subaperture stitching near-nulling interferometry, wherein a complex surface is analyzed via multiple, separate, overlapping interferograms. For complex surfaces, the problem of managing the identification and placement of corrective optics becomes even more pronounced, to the extent that in most cases the null corrector optics are specific to the particular asphere prescription and no others (i.e. another asphere requires completely different null correction optics). In principle, the near-nulling technique does not require subaperture stitching at all. Building a near-null system that is practically useful relies on two key features: simplicity and universality. If the system is too complex, it will be difficult to calibrate and model its manufacturing errors, rendering it useless as a precision metrology tool and/or prohibitively expensive. If the system is not applicable to a wide range of test parts, then it does not provide significant value over conventional null-correction technology. Subaperture stitching enables simpler and more universal near-null systems to be effective, because a fraction of a surface is necessarily less complex than the whole surface (excepting the extreme case of a fractal surface description). The technique of near-nulling can significantly enhance aspheric subaperture stitching capability by allowing the interferometer to capture a wider range of aspheres. More over, subaperture stitching is essential to a truly effective near-nulling system, since looking at a fraction of the surface keeps the wavefront complexity within the capability of a relatively simple nearnull apparatus. Furthermore, by reducing the subaperture size, the complexity of the measured wavefront can be reduced until it is within the capability of the near-null design.

Forbes, Greg↗

Thermal performance of a customized multilayer insulation (MLI)

The thermal performance of a LH2 tank on a shroudless vehicle was investigated. The 1.52 m (60 in) tank was insulated with 2 MLI blankets consisting of 18 double aluminized Mylar radiation shields and 19 silk net spacers. The temperature of outer space was simulated by using a cryoshroud which was maintained at near liquid hydrogen temperature. The heating effects of a payload were simulated by utilizing a thermal payload simulator (TPS) viewing the tank. The test program consisted of three major test categories: (1) null testing, (2) thermal performance testing of the tank installed MLI system, and (3) thermal testing of a customized MLI configuration. TPS surface temperatures during the null test were maintained at near hydrogen temperature and during test categories 2 and 3 at 289 K (520R). The heat flow rate through the tank installed MLI at a tank/TPS spacing of 0.457 m was 1.204 watts with no MLI on the TPS and 0.059 watts through the customized MLI with three blankets on the TPS. Reducing the tank/TPS spacing from 0.457 m to 0.152 m the heat flow through the customized MLI increased by 10 percent.

Leonhard, K. E.↗

Effects of a rough boundary surface on polarization of the scattered field from an inhomogeneous medium

A combination of the standard Kirchhoff method for rough surface scattering with the Rayleigh phase function radiative transfer method for volume scattering is employed in the present study of the effect of surface roughness on the polarization of the scattered field. It is found that for pure surface scattering, the polarization ratio between zero and 20 deg incidence angles is sensitive to surface roughness change. When both surface and volume scattering are present, however, copolarization nulls by colatitude or degree of polarization at zero to 15 deg incidence angle, and copolarization or crosspolarization nulls by longitude at large incidence angles, are better indicators of surface roughness changes. It is noted that degree of polarization and copolarization nulls by colatitude vary monotonously with incidence angle, while in combined surface and volume scattering these have, respectively, a minimum and a maximum. This characteristic allows the separation of combined surface and volume scattering from pure surface or volume scattering.

Fung, A. K.↗