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At least 181 records · Page 10

Polarimetric Geometric Modeling for mm-VLBI Observations of Black Holes

The Event Horizon Telescope (EHT) is a millimeter very long baseline interferometry (VLBI) array that has imaged the apparent shadows of the supermassive black holes M87* and Sagittarius A*. Polarimetric data from these observations contain a wealth of information on the black hole and accretion flow properties. In this work, we develop polarimetric geometric modeling methods for mm-VLBI data, focusing on approaches that fit data products with differing degrees of invariance to broad classes of calibration errors. We establish a fitting procedure using a polarimetric “m-ring” model to approximate the image structure near a black hole. By fitting this model to synthetic EHT data from general relativistic magnetohydrodynamic models, we show that the linear and circular polarization structure can be successfully approximated with relatively few model parameters. We then fit this model to EHT observations of M87* taken in 2017. In total intensity and linear polarization, the m-ring fits are consistent with previous results from imaging methods. In circular polarization, the m-ring fits indicate the presence of event-horizon-scale circular polarization structure, with a persistent dipolar asymmetry and orientation across several days. The same structure was recovered independently of observing band, used data products, and model assumptions. Despite this broad agreement, imaging methods do not produce similarly consistent results. Our circular polarization results, which imposed additional assumptions on the source structure, should thus be interpreted with some caution. Polarimetric geometric modeling provides a useful and powerful method to constrain the properties of horizon-scale polarized emission, particularly for sparse arrays like the EHT.

79 ASTRONOMY AND ASTROPHYSICS↗

On the hardness of learning ground state entanglement of geometrically local Hamiltonians

Characterizing the entanglement structure of ground states of local Hamiltonians is a fundamental problem in quantum information. In this work we study the computational complexity of this problem, given the Hamiltonian as input. Our main result is that to show it is cryptographically hard to determine if the ground state of a geometrically local, polynomially gapped Hamiltonian on qudits (d=O(1)) has near-area law vs near-volume law entanglement. This improves prior work of Bouland et al. (arXiv:2311.12017) showing this for non-geometrically local Hamiltonians. In particular we show this problem is roughly factoring-hard in 1D, and LWE-hard in 2D. Our proof works by constructing a novel form of public-key pseudo-entanglement which is highly space-efficient, and combining this with a modification of Gottesman and Irani's quantum Turing machine to Hamiltonian construction. Our work suggests that the problem of learning so-called "gapless" quantum phases of matter might be intractable.

Computational Complexity (cs.CC)↗

Digital correction of geometric and radiometric errors in ERTS data.

The sensor systems of the ERTS-A satellite are discussed and sources of geometric and radiometric errors in the received images are identified. Digital algorithms are presented for detection of reseau and ground control points, for rapid implementation of geometric corrections, and for radiometric correction of errors caused by shading, image motion, modulation transfer function, and quantum and systematic noise.

Bakis, R.↗

Geometrical geodesy techniques in Goddard earth models

The method for combining geometrical data with satellite dynamical and gravimetry data for the solution of geopotential and station location parameters is discussed. Geometrical tracking data (simultaneous events) from the global network of BC-4 stations are currently being processed in a solution that will greatly enhance of geodetic world system of stations. Previously the stations in Goddard earth models have been derived only from dynamical tracking data. A linear regression model is formulated from combining the data, based upon the statistical technique of weighted least squares. Reduced normal equations, independent of satellite and instrumental parameters, are derived for the solution of the geodetic parameters. Exterior standards for the evaluation of the solution and for the scale of the earth's figure are discussed.

Lerch, F. J.↗

A system to geometrically rectify and map airborne scanner imagery and to estimate ground area

A system of computer programs were developed which performs geometric rectification and line-by-line mapping of airborne multispectral scanner data to ground coordinates and estimates ground area. The system requires aircraft attitude and positional information furnished by ancillary aircraft equipment, as well as ground control points. The geometric correction and mapping procedure locates the scan lines, or the pixels on each line, in terms of map grid coordinates. The area estimation procedure gives ground area for each pixel or for a predesignated parcel specified in map grid coordinates. The results of exercising the system with simulated data showed the uncorrected video and corrected imagery and produced area estimates accurate to better than 99.7%.

Spencer, M. M.↗

Ultraviolet reflectivity and geometrical albedo of Titan

Titan's geometrical albedo of 0.094 plus or minus 0.012 was measured at 4255 A with a 50-A bandpass. From this and the spectral measurements, the geometrical albedo was derived as a function of wavelength. It is found that the wavelength dependences of Titan's UV spectrum and of the spectrum of Saturn's Rings are remarkably similar. No trace of any absorption bands is apparent. These results imply that UV gaseous absorption and Rayleigh scattering play a strongly subdued role in Titan's atmosphere. Any homogeneous atmospheric model implies that the absorber responsible for Titan's UV spectral albedo varies strongly with wavelength. On the other hand, it is found that the UV observations can be satisfied by an absorber having a relatively weak dependence upon wavelength if an inhomogeneous atmospheric model is employed. In particular, a fine dust, which absorbs as the reciprocal of the wavelength, can explain the UV observations, provided that it is preferentially distributed high up in Titan's atmosphere where the optical depth from Rayleigh scattering is low.

Barker, E. S.↗

Finite element analysis of geometrically nonlinear problems

Recent developments in geometrically nonlinear finite element analysis are reviewed. Following a discussion of the theoretical bases for the construction of finite element equations for geometrically nonlinear analysis, the algorithmic tools for solving the resulting nonlinear equations of the complete system are described. Separate consideration is given to preinstability nonlinear analysis, the calculation of limit points, bifurcation points, and to postbifurcation analysis.

Gallagher, R. H.↗

Geometric distortions of opticommercial panoramic television systems

One of the problems solvable by the spaceborne television system, topographical surveying, makes high demands on image quality, particularly on the geometric distortions introduced by the television camera. It is the geometric distortions which determine measurement accuracy and, consequently, the possibility of creating reliable planetary surface maps. Comparative analysis of the different television systems capable of solving the problem showed that the requirements on quality of the transmitted images are best satisfied by television cameras with opticomechanical scanning. The design of panoramic television systems and the process of image construction by the opticomechanical camera are discussed. Results indicate that panoramic television cameras have the necessary instrumental accuracy and permit determination of the direction to objects with an error practically equal to the resolution.

Govorov, V. M.↗

The geometric approach to sets of ordinary differential equations and Hamiltonian dynamics

The calculus of differential forms is used to discuss the local integration theory of a general set of autonomous first order ordinary differential equations. Geometrically, such a set is a vector field V in the space of dependent variables. Integration consists of seeking associated geometric structures invariant along V: scalar fields, forms, vectors, and integrals over subspaces. It is shown that to any field V can be associated a Hamiltonian structure of forms if, when dealing with an odd number of dependent variables, an arbitrary equation of constraint is also added. Families of integral invariants are an immediate consequence. Poisson brackets are isomorphic to Lie products of associated CT-generating vector fields. Hamilton's variational principle follows from the fact that the maximal regular integral manifolds of a closed set of forms must include the characteristics of the set.

Estabrook, F. B.↗

On the surface brightness and geometric albedo of some Martian areas

High-quality photographs of Mars (red, yellow, green, and blue) are used to analyze the surface, limb, and south-polar-cap brightness of Mars. The surface brightness can be fitted with the Lommel-Seeliger reflection law. For the limb and polar-cap brightness, the method suggested by Lumme (1974) has been used to correct for smearing effects. It is found that the brightness increases noticeably when approaching the limb, that the upper limit to optical thickness of the atmosphere in the blue is 0.16, and that the corresponding single-scattering albedo is 0.55, both with uncertainties of about 15%. Values for the geometric albedo and the phase function (at 37-deg phase angle) are also obtained for both the atmosphere and the ground for a central meridian of 0 deg. The south polar cap in September 1973 was nearly circular, with a radius of about 8 deg (heliocentric longitude of 0 deg) and geometric albedos of 0.68 (red), 0.68 (yellow), 0.60 (green), and 0.53 (blue).

Lumme, K.↗

Computer modeling of electromagnetic problems using the geometrical theory of diffraction

Some applications of the geometrical theory of diffraction (GTD), a high frequency ray optical solution to electromagnetic problems, are presented. GTD extends geometric optics, which does not take into account the diffractions occurring at edges, vertices, and various other discontinuities. Diffraction solutions, analysis of basic structures, construction of more complex structures, and coupling using GTD are discussed.

Burnside, W. D.↗

Geometrical meaning of the curl operation when A dot curl A does not equal 0

We examine the geometrical interpretation of the vector operation curl for vector fields A such that A dot curl A does not equal 0. It is not possible to construct even locally a surface normal to field lines of A at all points; an explicit geometrical demonstration of this fact is given. Such fields do not admit the construction of orthogonal curvilinear coordinates in which one set of coordinate curves lies along field lines of A.

Barnes, A.↗

Numerical procedure to determine geometric view factors for surfaces occluded by cylinders

A numerical procedure was developed to determine geometric view factors between connected infinite strips occluded by any number of infinite circular cylinders. The procedure requires a two-dimensional cross-sectional model of the configuration of interest. The two-dimensional model consists of a convex polygon enclosing any number of circles. Each side of the polygon represents one strip, and each circle represents a circular cylinder. A description and listing of a computer program based on this procedure are included in this report. The program calculates geometric view factors between individual strips and between individual strips and the collection of occluding cylinders.

Sawyer, P. L.↗

Analysis of simulated measurements of earth emitted radiation using geometric shape factors, and some results from analysis of ESSA 7 and Nimbus 6 data

In the reported study, simulated measurements of earth radiation with wide field-of-view (WFOV) radiometers are reduced to earth fluxes through geometric shape factors. Estimates of emitted flux for global and zonal scales and for regions smaller than the detector field-of-view are compared to fluxes derived directly from a model. Geometric shape factors are used to estimate global, zonal, and regional averages of earth-emitted flux from measurements with WFOV detectors on the ESSA 7 satellite and the Nimbus 6 satellite. Zonal and global averages of emitted flux for each of the 3-month periods of ESSA 7 data are shown in a graph. Another graph shows zonal and global averages of emitted flux for August 1975 obtained with the aid of Nimbus 6. The data are compared to values reported by Green and Smith (1977) who used a spherical harmonic solution.

Weaver, W. L.↗

Influence of optimized leading-edge deflection and geometric anhedral on the low-speed aerodynamic characteristics of a low-aspect-ratio highly swept arrow-wing configuration

An investigation conducted in the Langley 7 by 10 foot tunnel to determine the influence of an optimized leading-edge deflection on the low speed aerodynamic performance of a configuration with a low aspect ratio, highly swept wing. The sensitivity of the lateral stability derivative to geometric anhedral was also studied. The optimized leading edge deflection was developed by aligning the leading edge with the incoming flow along the entire span. Owing to spanwise variation of unwash, the resulting optimized leading edge was a smooth, continuously warped surface for which the deflection varied from 16 deg at the side of body to 50 deg at the wing tip. For the particular configuration studied, levels of leading-edge suction on the order of 90 percent were achieved. The results of tests conducted to determine the sensitivity of the lateral stability derivative to geometric anhedral indicate values which are in reasonable agreement with estimates provided by simple vortex-lattice theories.

Coe, P. L., Jr.↗

Geometric modeling and analysis of large latticed surfaces

The application of geometrical schemes, similar to geodesic domes, to large spherical antenna reflectors was investigated. The shape and size of flat segmented latticed surfaces which approximate general shells of revolution, and in particular spherical and paraboloidal reflective surfaces, were determined. The extensive mathematical and computational geometric analyses of the reflector resulted in the development of a general purpose computer program capable of generating the complete design parameters of the dish. The program also includes a graphical self contained subroutine for graphic display of the required design.

Nayfeh, A. H.↗

Simulation study of geometric shape factor approach to estimating earth emitted flux densities from wide field-of-view radiation measurements

A study was performed on the use of geometric shape factors to estimate earth-emitted flux densities from radiation measurements with wide field-of-view flat-plate radiometers on satellites. Sets of simulated irradiance measurements were computed for unrestricted and restricted field-of-view detectors. In these simulations, the earth radiation field was modeled using data from Nimbus 2 and 3. Geometric shape factors were derived and applied to these data to estimate flux densities on global and zonal scales. For measurements at a satellite altitude of 600 km, estimates of zonal flux density were in error 1.0 to 1.2%, and global flux density errors were less than 0.2%. Estimates with unrestricted field-of-view detectors were about the same for Lambertian and non-Lambertian radiation models, but were affected by satellite altitude. The opposite was found for the restricted field-of-view detectors.

Weaver, W. L.↗

Geometric methods in computational fluid dynamics

General methods for the construction of geometric computational fluid dynamic algorithms are presented which simulate a variety of flow fields in various nontrivial regions. Included are: basic developments with tensors; various forms for the equations of motion; generalized numerical methods and boundary conditions; and methods for mesh generation to meet the strong geometric constraints of turbomachines. Coordinate generation is shown generally to yield mesh descriptions from one or more transformations that are smoothly joined together to form a composite mesh.

Eiseman, P. R.↗