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Gauge transformations of third kind and operator gauge transformations of first and second kinds, relating electron and photon propagators to quantum electrodynamical vertex function
Recently, the authors presented preliminary results of an initial study of a dimensional reduction scheme for treating (near-)singular integrals (D. R. Wilton et al., “Dimensionality Reduction Approach for Treating Singular and Near-Singular Multidimensional Integrals of Electromagnetics,” 2022 URSI USNC National Radio Science Meeting, Boulder, CO, Jan. 2022). The approach reported there refined and extended several ideas appearing in a recent paper (R. R. Chang, Z. Wang, and Q. Xie, "Fast Convergent Quadrature Method for Evaluating the RWG- and SWG-Related Convolutional Integrals," IEEE Trans. Antennas Propagat., 69, Dec. 2021). That paper reported a curated collection of important, previously published results all leading to very efficient and accurate line integral methods for handling the most common (near-)singular integrals associated with triangles and tetrahedrons with RWG and SWG bases, respectively. Our contributions provided a simpler exposition as well as a more unified, systematic, and robust overall framework for deriving and applying the approach. This presentation further elucidates our extensions to the approach and broadens our initial study to examine the convergence behaviors of the various potential forms over a wider range of triangular source element shape and observation point parameters for various smoothing transformations; we also examine convergence, not just at the subtriangle level, but also overcomplete triangles. In addition, we investigate the application of the recently reported “vertex function” concept to develop faster converging test integrals (Rivero et al., “Acceleration of the Surface Test Integral Using Vertex Functions,” 2021 IEEE Int’l Symp. Ant. Propagat. and USNC-URSI Rad. Sci. Meeting,” Singapore, 4-10 Dec. 2021). Combining these separate schemes has the potential for yielding a near-optimal approach for accurately evaluating singular and near-singular integrals for moment methods.
Partially conserved axial vector currents and current algebra to obtain vertex functions at point having zero mass by extrapolations
With the need for ever faster codes, a limiting factor that must be dealt with is the accurate yet efficient evaluation of interaction integrals between the more problematic near-field elements. Several recent works have together shown that all evaluations of source potential integrals and their derivatives for the most common bases and elements can be reduced to the evaluation of boundary line integrals; these can be evaluated by Gauss-Legendre quadrature, though integrand-smoothing transforms are often needed to accelerate their computation. In this paper, we modify the reported approach to eliminate cancellation errors in the line integral integrand, reinterpret the integral as a vertex function, and study the scalar potential integral form under the sinh transform and static subtraction acceleration methods.
The theory of Taylor and Maccoll (Ref,1) gives the surface pressure on an infinite cone in supersonic flow as a function of the cone vertex angle and the free stream Mach number and static pressure for a gas of vanishing viscosity. When a slender conical probe is used together with an impact pressure probe to determine the static pressure and Mach number in a low density gas stream, it is desirable to have some theoretical estimate of the effect of viscous boundary layer on the probe readings. Theoretical and experimental results with respect to impact probes have been presented in Refs. 5 and 6. A simple approximation for a conical probe based on linearized supersonic flow and compressible boundary layer theory is presented here.
The potential development of large aperture ground?based "photon bucket" optical receivers for deep space communications has received considerable attention recently. One approach currently under investigation is to polish the aluminum reflector panels of 34?meter microwave antennas to high reflectance, and accept the relatively large spotsize generated by state of?the?art polished aluminum panels. Theoretical analyses of receiving antenna pointing, temporal synchronization and data detection have been addressed in previous papers. Here we describe the experimental effort currently underway at the Deep Space Network (DSN) Goldstone Communications Complex in California, to test and verify these concepts in a realistic operational environment. Two polished aluminum panels (a standard DSN panel polished to high reflectance, and a custom designed aluminum panel with much better surface quality) have been mounted on the 34 meter research antenna at Deep?Space Station 13 (DSS?13), and a remotely controlled CCD camera with a large CCD sensor in a weather?proof container has been installed next to the subreflector, pointed directly at the custom polished panel. The point?spread function (PSF) generated by the Vertex polished panel has been determined to be smaller than the sensor of the CCD camera, hence a detailed picture of the PSF can be obtained every few seconds, and the sensor array data processed to determine the center of the intensity distribution. In addition to estimating the center coordinates, expected communications performance can also been evaluated with the recorded data. The results of preliminary pointing experiments with the Vertex polished panel receiver using the planet Jupiter to simulate the PSF generated by a deep?space optical transmitter are presented and discussed in this paper.
The laminar boundary-layer flow about a circular cone at large angles of attack to a supersonic stream has been analyzed in the plane of symmetry by a method applicable in general to the flow about conical bodies. At the bottom of the cone, velocity profiles were obtained showing the expected tendency of the boundary layer to become thinner on the under side of the cone as the angle of attack is increased. At the top of the cone, the analysis failed to yield unique solutions except for small angles of attack. Beyond a certain critical angle of attack, boundary-layer flow does not exist in the plane of symmetry, thus indicating separation. This critical angle is presented as a function of Mach number and cone vertex angle.
A method of calculating the fuzzy response of a system is presented. This method, called the Optimized Vertex Method (OVM), is based upon the vertex method but requires considerably fewer function evaluations. The method is demonstrated by calculating the response membership function of strain-energy release rate for a bonded joint with a crack. The possibility of failure of the bonded joint was determined over a range of loads. After completing the possibilistic analysis, the possibilistic (fuzzy) membership functions were transformed to probability density functions and the probability of failure of the bonded joint was calculated. This approach is called a possibility-based hybrid reliability assessment. The possibility and probability of failure are presented and compared to a Monte Carlo Simulation (MCS) of the bonded joint.
A mesh-vertex finite volume scheme for solving the Euler equations on triangular unstructured meshes is implemented on a multiple-instruction/multiple-data stream parallel computer. An explicit four-stage Runge-Kutta scheme is used to solve two-dimensional flow problems. A family of implicit schemes is also developed to solve these problems, where the linear system that arises at each time step is solved by a preconditioned GMRES algorithm. Two partitioning strategies are employed: one that partitions triangles and the other that partitions vertices. The choice of the preconditioner in a distributed memory setting is discussed. All of the methods are compared both in terms of elapsed times and convergence rates. It is shown that the implicit schemes offer adequate parallelism at the expense of minimal sequential overhead. The use of a global coarse grid to further minimize this overhead is also investigated. The schemes are implemented on a distributed memory parallel computer, the Intel iPSC/860.
This annual report summarizes the research activities that were performed from 26 Jun. 1993 to 28 Feb. 1994. We continued to investigate the Robust Stability of Systems where transfer functions or characteristic polynomials are affine multilinear functions of parameters. An approach that differs from 'Stability by Linear Process' and that reduces the computational burden of checking the robust stability of the system with multilinear uncertainty was found for low order, 2-order, and 3-order cases. We proved a crucial theorem, the so-called Face Theorem. Previously, we have proven Kharitonov's Vertex Theorem and the Edge Theorem by Bartlett. The detail of this proof is contained in the Appendix. This Theorem provides a tool to describe the boundary of the image of the affine multilinear function. For SPR design, we have developed some new results. The third objective for this period is to design a controller for IHM by the H-infinity optimization technique. The details are presented in the Appendix.
Methods to increase the amount of data that can be received from outer planet missions are described with emphasis on antenna arraying systems designed to increase the total effective aperture of the receiving system. One such method is virtual center arraying (VCA). In VCA, a combined carrier reference is derived at a point that is, conceptually, the geometric center of the array. This point need not coincide with any of the actual antennas of the array. A noise analysis of the VCA system is given along with formulas for the phase jitter as a function of loop bandwidths and the amount of loop damping. If the ratio of the loop bandwidths of the center loop to the vertex loops is greater than 100, then the jitter is very nearly equal to that expected for ideal combined carrier referencing.
The Large Deployable Reflector (LDR) concept is outlined. The LDR telescope is based on a 20-m diameter reflector. The primary mirror is a filled aperture made up of 84 hexagonal panels, each 2 m edge-to-edge. The panels are based on lightweight structural composite materials. The optical configuration is a four mirror two stage system. The primary mirror is passive. The active optical elements for figure control are at the quaternary mirror. The primary mirror panels are supported by a deployable PAC truss backup structure at the vertices of each hexagon. The four focal plane instruments covering the range of 30 to 1000 microns are located near the vertex of the primary mirror. Some instruments will be cooled with stored cryogens to liquid helium temperatures, others to liquid nitrogen temperatures. The spacecraft functions will be located in a resource module behind the primary mirror. The LDR will be transferred to orbit by the space transportation system and assembled and tested at the space station. It will then be boosted to an orbit of greater than or = 700 km as a free flyer.
A method and system for data modeling that incorporates the advantages of both traditional response surface methodology (RSM) and neural networks is disclosed. The invention partitions the parameters into a first set of s simple parameters, where observable data are expressible as low order polynomials, and c complex parameters that reflect more complicated variation of the observed data. Variation of the data with the simple parameters is modeled using polynomials; and variation of the data with the complex parameters at each vertex is analyzed using a neural network. Variations with the simple parameters and with the complex parameters are expressed using a first sequence of shape functions and a second sequence of neural network functions. The first and second sequences are multiplicatively combined to form a composite response surface, dependent upon the parameter values, that can be used to identify an accurate mode
The time dependent thermal equations of two types of conical radiation detectors are discussed and solved for a step function application of radiation parallel to the axis of the cases. The first type has a heat sink at the base and the second has the vertex buried in a heat sink to a variable proportion of its total height. It is found that the first case has the lower sensitivity and better time response. The time response of the second case is improved by more deeply burying the vertex, but to the detriment of sensitivity. At no value of this inclusion can both a superior sensitivity and time response be achieved for the second case.
A multidimensional kinetic fluctuation-splitting scheme has been developed for the Euler equations. The scheme is based on an N-scheme discretization of the Boltzmann equation at the kinetic level for triangulated Cartesian meshes with a diagonal-adaptive strategy. The resulting Euler scheme is a cell-vertex fluctuation-splitting scheme where fluctuations in the conserved-variable vector Q are obtained as moments of the fluctuation in the Maxwellian velocity distribution function at the kinetic level. Encouraging preliminary results have been obtained for perfect gases on Cartesian meshes with first-order spatial accuracy. The present approach represents an improvement to the well-established dimensionally-split upwind schemes.
The effects of uncertainties on the predicted strength of a single lap shear joint are examined. Probabilistic and possibilistic methods are used to account for uncertainties. A total of ten variables are assumed to be random, with normal distributions. Both Monte Carlo Simulation and the First Order Reliability Method are used to determine the probability of failure. Triangular membership functions with upper and lower bounds located at plus or minus three standard deviations are used to model uncertainty in the possibilistic analysis. The alpha cut (or vertex) method is used to evaluate the possibility of failure. Linear and geometrically nonlinear finite element analyses are used calculate the response of the joint; fracture in the adhesive and material strength failure in the strap are used to evaluate its strength. Although probabilistic and possibilistic analyses provide significantly more information than do conventional deterministic analyses, they are computationally expensive. A novel scaling approach is developed and used to substantially reduce the computational cost of the probabilistic and possibilistic analyses. The possibilistic approach for treating uncertainties appears to be viable during the conceptual and preliminary design stages when limited data are available and high accuracies are not needed. However, this viability is mixed with several cautions that are discussed herein.
The Space Interferometer Mission (SIM), scheduled for launch in 2009, is a space-born visible light stellar interferometer capable of micro-arcsecond-level astrometry. The Micro-Arcsecond Metrology testbed (MAM) is the ground-based testbed that incorporates all the functionalities of SIM minus the telescope, for mission-enabling technology development and verification. MAM employs a laser heterodyne metrology system using the Sub-Aperture Vertex-to-Vertex (SAVV) concept. In this paper, we describe the development and modification of the SAVV metrology launchers and the metrology instrument electronics, precision alignments and pointing control, locating cyclic error sources in the MAM testbed and methods to mitigate the cyclic errors, as well as the performance under the MAM performance metrics.
Formal solutions of the static equilibrium equations for the form of the outer surface of a pendent liquid drop are studied. An approach is adopted in which only the one-parameter family determined by vertex height (u sub 0) need be described. Attention is restricted to rotationally symmetric configurations, and all symmetric solutions are characterized for the case where the Lagrange parameter lambda is equal to zero. It is shown that for any u sub 0 the function u(r; u sub 0) can be extended as a parametric solution of a system of equations for all arc lengths, yielding a curve without limit sets or double points, and that the resulting capillary rotation surface spreads out indefinitely away from the axis r = 0. The asymptotic form of the surface in the case of large absolute values of u sub 0 is characterized quantitatively, along with the global structure of all such surfaces.