Equivalent Source Research Articles

Conformal theory of central surface density for galactic dark halos

Numerous dark matter studies of galactic halo gravitation depend on models with core radius r0 and central density ρ0. Central surface density product ρ0r0 is found to be nearly a universal constant for a large range of galaxies. Standard variational field theory with Weyl conformal symmetry postulated for gravitation and the Higgs scalar field, without dark matter, implies nonclassical centripetal acceleration ∆a, for a = aN +∆a, where Newtonian acceleration aN is due to observable baryonic matter. Neglecting a halo cutoff at very large galactic radius, conformal ∆a is constant over the entire halo and a = aN + ∆a is a universal function, consistent with a recent study of galaxies, with independently measured mass, that constrains acceleration due to dark matter or to alternative theory. An equivalent dark matter source would be a pure cusp distribution with cutoff parameter determined by a halo boundary radius. This is shown to imply universal central surface density for any dark matter core model.

Modification in airfoil’s tonal noise using periodic suction-blowing excitation

This paper examines the modifications in the flow and sound fields due to the application of a periodic suction-blowing excitation strip on the top and bottom surfaces of a NACA0012 airfoil. The flow and sound fields have been directly computed (DNS approach) by solving unsteady, two-dimensional compressible Navier–Stokes equations using physical dispersion relation preserving schemes. The flow approaches the airfoil at a Reynolds number of 5000 and 5o angle of attack. In the no-excitation case, the sound is mainly created by the lift and drag dipole equivalent sources associated with vortex shedding. However, the application of suction-blowing excitation results in two additional sound sources: monopole-equivalent sound sources due to fluid movement in and out of the airfoil surface and the drag dipole-equivalent sound sources due to periodic change in the airfoil’s effective cross-sectional area. The combined effects of these sound sources result in significant mitigation of sound on the suction side of the airfoil. The excitation amplitude and forcing frequency effects on sound field modifications have been studied in depth. Beats of sound have been observed when the forcing frequency is close to the excitation frequency.

Analysis of antenna arrays using equivalent sources for increase in computational efficiency for 5G and beyond

AbstractThe use of equivalent sources for the analysis of antenna arrays for high computational efficiency has been proposed. A single antenna element has been designed, and the fields have been saved on an enclosed geometry. The surface equivalence principle has been utilized to calculate the far‐field patterns from the fields saved on the enclosed geometry which has been termed as Huygens' box (HB). The antenna element has been used to design , , , and array and the far‐fields have been calculated. For linear arrays of HBs far‐field patterns and computation time have been compared with that of the actual antenna array. As the number of elements increases from 4 to 16, the computation time has been found to reduce from to . Further, the computation time has been found to reduce by and for and configurations, respectively. The method is suitable for analysis of complex geometry of antennas used in 5G technology and beyond.

The torsion of stellar streams and the overall shape of galactic gravity's source

Flat rotation curves, $v(r)$, are naturally explained by elongated (prolate) dark matter (DM) distributions, and we have provided competitive fits to the SPARC database. To further probe the geometry of the halo, or the equivalent source of gravity in other formulations, one needs observables outside the galactic plane. Stellar streams, poetically analogous to airplane contrails, but caused by tidal dispersion of massive substructures such as satellite dwarf galaxies, would lie on their own plane (consistently with angular momentum conservation) should the DM-halo gravitational field be spherically symmetric. Tracks resembling entire orbits are seldom available because their periods are commensurable with Hubble time, with streams often presenting themselves as short segments. Therefore, we aim to establish stellar stream torsion, a local observable that measures the deviation from planarity in differential curve geometry, as a diagnostic providing sensitivity to aspherical DM distributions and ensuring the use of even relatively short streams. We performed small-scale simulations of tidally distorted star clusters to check that indeed a central force center produces negligible torsion, while distorted halos can generate it. Turning to observational data, we identified among the known streams those that are at the largest distance from the Galactic center, and that are likely not affected by the Magellanic clouds, as the most promising for the study, and by means of polynomial fits we extracted their differential torsion. We find that the torsion of the few known streams that should be sensitive to most of the Milky Way's DM halo is much larger than expected for a central spherical bulb alone. This is consistent with the nonsphericity of the halo. Future studies of stellar stream torsion with larger samples and further out of the galactic plane should be able to extract the ellipticity of the halo to see whether it is just a slight distortion of a spherical shape or whether it rather resembles a more elongated cigar.

High-resolution acoustic imaging method based on equivalent source method and reweighted l1 minimization

Sparse regularization has been successfully applied to equivalent source method (ESM) in order to improve the acoustic imaging resolution. However, the application is not always feasible, especially at low frequencies. To overcome the problem, this paper proposes a high-resolution acoustic imaging method. In this method, reweighted l1 minimization is introduced to ESM to deal with the ill-posed inverse problems. Then the obtained equivalent source strengths are used to locate the sound sources. Compared to the sparse regularization-based ESM, the proposed method can provide a low side lobe and higher spatial resolution of acoustic imaging. Meanwhile, by arranging equivalent sources in three-dimensional space, the proposed method can also realize the acoustic imaging in three-dimensional sound field with high resolution. The results of the simulation and experiment demonstrate the validations.

Far-Field Estimation Method of Antennas Above Conductive Plane Using a Partially Spherical Near-Field

For evaluating the practical performance of land mobile communication antennas via near-field measurement, it is essential to measure the electromagnetic field, including the housing in which the antennas are mounted. When measuring a heavy housing, scattered waves from the supporting turntable for the antenna under test (AUT) disturb the electromagnetic field. A technique for eliminating the influence of scattered waves is required to evaluate the abnormal AUT radiation performance. This paper proposes a method for estimating the far-field when the antenna exists above an infinite conductive plane, using partially spherical near-field measurements that include the turntable. The proposed method estimates the far-field by combining the equivalent source reconstruction and the far-field estimation with the reflection coefficient method. In the proposed method, the equivalent source distribution surrounding an AUT is reconstructed from a partially spherical near-field to remove the effects of the turntable. Through numerical calculations and experiments, this paper shows that the proposed method can estimate the far-field pattern above an infinite conductive plane, with arbitrary electric constants from a partially spherical near-field. The far-field estimation error is less than -20 dB when the upper hemispherical near-field can be obtained.

Prediction of Vibration Waveform and Division of Influenced Partitions under the Action of Blasting

To study the impact of cutting blasting on the surface, a vibration waveform prediction function was constructed, and a method of dividing the affected area was proposed. Based on the equivalent spherical charge theory, it is possible to establish a connection between the fitting coefficient and the engineering parameters in the equivalent source intensity function. Furthermore, a blasting vibration waveform function suitable for engineering can be constructed. Secondly, the reliability of the method introduced is verified through the data monitored on-site. Finally, the affected partitions of blasting vibration are divided based on the peak particle velocity and vibration displacement as standards. The results show that the vibration waveform prediction system introduced can restore the vibration waveform corresponding to cutting blasting. In addition, the zoning method can reasonably divide the scope of the affected area.

Acoustical Holography and Coherence-Based Noise Source Characterization of an Installed F404 Engine

Understanding the acoustic source characteristics of supersonic jets is vital to accurate noise field modeling and jet noise reduction strategies. This paper uses advanced, coherence-based partial field decomposition methods to characterize the acoustic sources in an installed, supersonic GE F404 engine. Partial field decomposition is accomplished using an equivalent source reconstruction via acoustical holography. Bandwidth is extended through the application of an array phase-unwrapping and interpolation scheme. The optimized-location virtual reference method is used. Apparent source distributions and source-related partial fields are shown as a function of frequency. Local maxima are observed in holography reconstructions at the nozzle lipline, distinct in frequency and space. The lowest-frequency local maximum may relate to noise generated by large-scale turbulence structures in the convectively subsonic region of the flow. Other local maxima are correlated primarily with Mach wave radiation originating from throughout the shear layer and into the fully mixed region downstream of the potential core tip. Source-elucidating decompositions show that the order and behavior of the decomposition lend to the local maxima being related to distinct subsources. Between the local maxima, however, there may be a combination of sources active, which is likely the cause of the spatiospectral lobes observed in other full-scale, supersonic jets.

SIMULATION OF MULTIPOINT CONTACT UNDER THERMOELECTRIC TESTING

The article presents the results of modeling a multipoint contact in the thermoelectric method of testing. Sources of thermoelectromotive force (thermoEMF) have shown different influences, according to their type, on the load characteristics of the equivalent source obtained by parallel connection of several thermocouples as shown in the explanatory figures. The presented model is implemented in the NI LabVIEW package, which is freely available. The model was verified on three types of thermocouples (copper-constantan, copper-nichrome, and chromel-alumel), which have been connected in parallel in different quantities. The calculated load characteristics of the equivalent sources differ from the experimental ones by no more than 6%. The results of modeling the load characteristics of the equivalent thermoEMF sources obtained by parallel connection of different quantities of two types of thermocouples are presented. It is shown that in order to obtain reliable data, it is necessary to provide an equivalent source load of at least 1 kOhm.

High-Resolution localization of broadband sound sources in a duct using out-duct array measurements

This paper investigates using an Iterated Bayesian Focusing Algorithm and out-duct array measurements to identify multiple broadband sources placed in a cylindrical duct. The problems of large main lobe and low resolution due to localization of sources using conventional methods are investigated in this paper. To solve these problems, an Iterated Bayesian Focusing (IBF) method is utilized to localize the broadband sources. To evaluate and confirm the efficacy of the method, simulation tests and experimental validation are performed. In our experiments, we used a 56-channel dobby spiral array for out-duct measurements and beamforming method, equivalent source method (ESM), deconvolution approach for the mapping of acoustic sources (DAMAS), and Iterated Bayesian Focusing (IBF) method to localize broadband sources inside the duct. Simulation and experimental results demonstrate that the Iterated Bayesian Focusing (IBF) method significantly reduces the main lobe width and minimizes the number of minor lobes. This leads to improved accuracy in localizing double sources.

Virtual source approach for maximizing resolution in high-penetration gamma-ray imaging

High-energy gamma-ray radiography has exceptional penetration ability and has become an indispensable nondestructive testing (NDT) tool in various fields. For high-energy photons, point projection radiography is almost the only feasible imaging method, and its spatial resolution is primarily constrained by the size of the gamma-ray source. In conventional industrial applications, gamma-ray sources are commonly based on electron beams driven by accelerators, utilizing the process of bremsstrahlung radiation. The size of the gamma-ray source is dependent on the dimensional characteristics of the electron beam. Extensive research has been conducted on various advanced accelerator technologies that have the potential to greatly improve spatial resolution in NDT. In our investigation of laser-driven gamma-ray sources, a spatial resolution of about 90 µm is achieved when the areal density of the penetrated object is 120 g/cm2. A virtual source approach is proposed to optimize the size of the gamma-ray source used for imaging, with the aim of maximizing spatial resolution. In this virtual source approach, the gamma ray can be considered as being emitted from a virtual source within the convertor, where the equivalent gamma-ray source size in imaging is much smaller than the actual emission area. On the basis of Monte Carlo simulations, we derive a set of evaluation formulas for virtual source scale and gamma-ray emission angle. Under optimal conditions, the virtual source size can be as small as 15 µm, which can significantly improve the spatial resolution of high-penetration imaging to less than 50 µm.

A new born‐approximation approach to compute the effects of motion on the solution of electromagnetic problems involving moving materials with stationary boundaries

AbstractThe non‐relativistic motion of media induces very weak effects on electromagnetic fields. For this reason, it is extremely difficult to compute such effects with traditional techniques. To overcome this difficulty, a novel approach is introduced in this work. It is based on the Born approximation of the solution of electromagnetic problems involving media in motion. The formulation of these problems makes use of equivalent field sources and is specifically tailored to find the effects of motion on the electromagnetic field. The new methodology exploits traditional simulators able to deal with media at rest. The motion of the materials has to be managed by specific programs performing simple algebraic calculations. The simplest of the methods proposed does not present any additional complexity with respect to more traditional approaches to the same problems. All methods deal with time‐harmonic electromagnetic fields and, for this reason, they can manage materials in motion with stationary boundaries. A complete set of simulations for cylinders moving in the axial direction show that the new methods outperform traditional numerical approaches and, in some significant cases, traditional approaches based on semi‐analytical techniques. The good features of the new methodology are shown to hold true for a range of velocity values spanning 11 decades; such a range covers most of the applications of practical interest.

The extended resonant modal theory and its applications

AbstractThe authors extend the resonant modal theory (RMT) developed previously for a metal object to an arbitrary source region consisting of metals, dielectrics, or a combination of both. The influences of dielectrics on the fields are replaced by equivalent volume sources through the use of the compensation theorem in electromagnetic theory. The resonant frequencies can be determined by finding the roots of the determinant of the matrix resulted from the discretisation of the real homogeneous volume–surface integral equation derived from the requirement that the difference of stored field energies in the source region vanishes. As applications of the extended RMT, three examples have been investigated. The first example is a dielectric resonator antenna and is designed by exciting the first resonant mode of the composite structure in which the dielectric cylinder is combined with a conformal metallic strip. The second example is a dual‐band dielectric‐coated metallic wire antenna. The third example studies the resonant modes of a rectangular patch antenna.

Multizone sound field reproduction using pressure matching with sparse equivalent source

Multizone sound field reproduction aims to create different acoustic environments in multiple spatial zones, allowing listeners to enjoy their individual sounds without being disturbed by sound from other zones. The conventional pressure matching method is used in practice to reproduce the desired sound field by minimizing the sound field error with a limited number of control points, whose reproduction performance decreases above the cutoff frequency. In this paper, a multizone sound field reproduction method based on a sparse equivalent source method is proposed to reproduce the sound field in the whole target region. The acoustic transfer function of each loudspeaker and the desired sound field are represented by the sparse equivalent sources. The whole target region is controlled by interpolating fine virtual control points within the region of the uncontrolled points, and the acoustic transfer functions between the virtual control points and the loudspeaker array are interpolated by the sparse equivalent sources. An optimization reproduction model with the objective of reproducing a desired sound field in the bright zone and constraining the acoustic energy in the dark zone is formulated to find the sparse loudspeaker weights. The simulation results and experimental results show that the proposed method achieves better performance than the conventional pressure matching method in free field and reverberant environments.

A Continental Model of Curie Point Depth for China and Surroundings Based on Equivalent Source Method

AbstractThe Curie Point Depth (CPD) marks a significant temperature boundary (∼580°C) within the Earth's lithosphere. However, there has been ongoing debate regarding its spatial distribution. In this research, we utilized the Equivalent Source Method (ESM) based on Gauss‐Legendre integration and data obtained from the EMM2017 model, along with a five‐layer susceptibility model, to generate a 0.5° × 0.5° grid of continental CPD distribution for China and surroundings. The average CPD in the study area is 30.4 km, which is slightly shallower than the average depth of global continental Moho (∼33 km). Notably, stable and cold cratonic basins, such as the Tarim Basin and the Sichuan Basin, exhibit deep CPD of ∼45 km. In contrast, the North China Craton, which has experienced significant tectono‐thermal activity since the Late Mesozoic, shows moderate CPD of ∼30 km and a gradual uplift from west to east. The Tuva‐Mongol orocline within the Central Asian Orogenic Belt, the Deccan Volcanic Province in the Indian subcontinent and the Eastern Yangtze Craton have shallow CPD of ∼20 km. We estimate the surface heat flow by CPD, and the result is consistent with measurements within a RMSE of 18.1 mW/m2. When comparing the CPD with Moho, we find that the CPD may lie below Moho in stable and cold cratonic areas. In comparison to two recent global CPD models, our regional model demonstrates better alignment with tectonic features.

Sound field separation based on dictionary learning and sparse sampling

Sound field separation techniques are an advancing tool for extracting a target sound field from a mixed sound field. However, the methods bear a high measurement cost due to the restriction of the sampling theorem. In this study, a sound field separation method based on sparse sampling is established. The method initially utilizes dictionary learning to generate a sparse basis of the sound field. Then, a mixed sound field can be precisely recovered from sparse sampling of sound pressure and the target sound field can be extracted based on the recovered sound field by means of the theory of equivalent source method. The method is validated by numerical simulations. Compared to sound field separation based on the equivalent source method, the proposed method has advantage in terms of both the accuracy and the stability for sparse sampling.

[formula omitted]piler: Compilers in search of compilations

Compilers pose significant challenges in their development as software products. Language developers face the complexities of ensuring efficiency, adhering to good design practices, and maintaining the overall codebase. These factors make it difficult to predict the unexpected impact of updates on existing software built on the current compiler stack. Furthermore, software created for a specific compiler often lacks reusability for other compiler environments. In this study, we propose a comprehensive framework for the uniform development of compilers that addresses these issues. Our approach involves developing compilers as a collection of small transpilation units, referred to as deltas. The transpilation infrastructure takes source code written in a particular source language and searches for a path of deltas to generate equivalent source code in the target language. By adopting this methodology, language developers can easily update their languages by introducing new deltas into the system. Existing code remains unaffected as old transpilation paths remain available. To support this framework, we have devised a metric space for efficient delta search. This metric space enables us to define a non-overestimating heuristic function, which proves valuable in solving the search problem. Leveraging the A* search algorithm, we can efficiently transpile programs from a source language to the target language. To evaluate the effectiveness of our approach, we conducted a benchmark comparison between the A* search algorithm and the simpler breadth-first search (BFS) algorithm. The benchmark consisted of over 100 transpilation searches, providing valuable insights into the performance and capabilities of this framework.

Research on an Equivalent Heat Source Model of the AC Arc in the Short Gap of a Copper-Core Cable and a Fire Risk Assessment Method.

The magnetohydrodynamics (MHD) model of the alternating current (AC) arc is complex, so a simplified equivalent heat source (EHS) model can be used to replace the complex model in studying the AC arc's thermal characteristics and cable fire risk. A 2D axisymmetric AC arc MHD simulation model in the short gap of a copper-core cable is established in this paper. The AC arc voltage and current obtained by the model are consistent with experiments. The AC arc's heat source distribution obtained by the MHD model is fitted to obtain the heat source function Q of the AC arc. Q is divided into 16 independent segmented heat sources, and a correction matrix is constructed to optimize the segmented heat sources. A neural network and a genetic algorithm give the prediction model and the optimal correction matrix of the segmented heat source. The EHS model optimized by the optimal correction matrix can obtain a minimum temperature error of 5.8/4.4/4.2% with the MHD model in different AC arc peak currents 2/4/6 A. The probability of a cable fire is calculated by using AC arc's optimized EHS model when different numbers of AC arcs are generated randomly in AC half-waves. The EHS model can replace the complex MHD model to study the thermal characteristics of AC arcs and quickly calculate the probability of a cable fire caused by random AC arcs.

Noise Separation Technique for Enhancing Substation Noise Assessment Using the Phase Conjugation Method

The intrinsic noise of different transformers in the same substation belongs to the same type of noise, which is strongly coherent and difficult to separate, greatly increasing the cost of substation noise assessment and treatment. To solve the problem, the present paper proposes a noise separation technique using the phase conjugation method to separate the intrinsic noise signals of different transformers: firstly, the reconstruction of sound source information is realized by the phase conjugation method based on the measurement and emission of a line array; secondly, the intrinsic noise signals of the sound source are obtained by the equivalent point source method. The error of the separation technique is analyzed by point source simulation, and the optimal arrangement form of the microphone line array is studied. A validation experiment in a semi-anechoic chamber is also carried out, and the results prove that the error of separation technique is less than 2dBA, which is the error tolerance of engineering applications. Finally, a noise separation test of three transformers is performed in a substation using the proposed technique. The results show that the proposed technique is able to realize the intrinsic noise separation of each transformer in the substation, which is of positive significance for substation noise assessment and management.

Crustal Apparent Density Variations in the Middle Segment of the North Tianshan Mountains and Their Tectonic Significance

In this study, we collected mobile gravity observations in the middle segment of the North Tianshan Mountains from August 2016 to July 2022 and carried out classical adjustment calculations under the constraint of the absolute gravity datum to obtain the spatiotemporal variation pattern of the local gravity field. We used equivalent source inversion to obtain the spatiotemporal variation characteristics of crustal apparent density. We also extracted the coseismic deformation field from SAR data, using the 2016 Hutubi earthquake as an example, and constructed a model of the seismogenic fault. The gravity monitoring network in the study area performed well in resolving the earthquake source parameters. Both the time-varying gravity field and equivalent apparent density variation pattern show prominent zoning characteristics with a smoothly evolving spatial distribution over time. The variation trends of the gravity field and equivalent apparent density are in line with the orientation of tectonic structures, and their anomalous signals can be detected before and after an earthquake. The constructed seismogenic structure of the 2016 Hutubi earthquake indicates a typical thrust earthquake, probably occurring on a north-dipping blind fault beneath a region with intense crustal deformation. The subsurface tectonic system reflected by this earthquake can be informatively extended to the entire middle segment of the North Tianshan Mountains by subsurface configuration. Our findings can serve as a reference for analyzing the source characteristics of the time-varying gravity field and interpreting anomalous pre-seismic signals, and aid in understanding earthquake preparation zones and the mode of crustal tectonic movements.