Kinds Of Arrays Research Articles

A simpler proof of Sternfeld’s Theorem

In Sternfeld’s work on Kolmogorov’s Superposition Theorem appeared the combinatorial–geometric notion of a basic set and a certain kind of arrays. A subset [Formula: see text] is basic if any continuous function [Formula: see text] could be represented as the sum of compositions of continuous functions [Formula: see text] and projections to the coordinate axes. The definition of a Sternfeld array is presented in this paper. Sternfeld’s Arrays Theorem. If a closed bounded subset[Formula: see text] contains Sternfeld arrays of arbitrary large size then[Formula: see text] is not basic. The paper provides a simpler proof of this theorem.

Efficient Radiation Pattern Prediction of Array Antennas Based on Complex-Valued Graph Neural Networks

Antenna design with the traditional numerical methods is a highly computationally expensive task. In this letter, a complex-valued graph neural network (GNN) with residual connections is proposed to efficiently predict radiation pattern for antenna arrays with different geometric structures. The model uses GNN as a backbone, and the topological structure and excitation of the antenna array are encoded into a graph representation. Complex weights and residual connections are designed to improve the accuracy of the model. Experiments are conducted on five kinds of arrays under amplitude–phase control. The experimental results show that the average mean absolute percentage error and the average root-mean-square error of the model on five types of the antenna array are 1.86% and 0.032, respectively, while the time efficiency of the model is six orders of magnitude faster than that of the traditional full-wave simulation.

Equal Baseline Camera Array—Calibration, Testbed and Applications

This paper presents research on 3D scanning by taking advantage of a camera array consisting of up to five adjacent cameras. Such an array makes it possible to make a disparity map with a higher precision than a stereo camera, however it preserves the advantages of a stereo camera such as a possibility to operate in wide range of distances and in highly illuminated areas. In an outdoor environment, the array is a competitive alternative to other 3D imaging equipment such as Structured-light 3D scanners or Light Detection and Ranging (LIDAR). The considered kinds of arrays are called Equal Baseline Camera Array (EBCA). This paper presents a novel approach to calibrating the array based on the use of self-calibration methods. This paper also introduces a testbed which makes it possible to develop new algorithms for obtaining 3D data from images taken by the array. The testbed was released under open-source. Moreover, this paper shows new results of using these arrays with different stereo matching algorithms including an algorithm based on a convolutional neural network and deep learning technology.

Irregular Layout for a Satellite’s Interferometric Array

We address the optimization problem of antenna placement on satellite-mounted interferometric synthetic-aperture instruments. In classic designs, the antennas on satellites are aligned regularly on the satellite’s frame. Inspired by methods proposed for the placement of antennas in astronomical interferometers, such as ALMA or SKA, we explore irregular layouts and show that they are a valid alternative in terms of spatial resolution and reconstruction error. We formalize mathematically the optimization problem of irregularly placed antennas and we show that this kind of arrays can still be calibrated with the same methods used for regular arrays. Finally, this strategy is evaluated in the context of soil moisture and ocean salinity (SMOS) follow-up concepts, such as SMOS-HR (high resolution), for which the new optimized irregular configurations are compared to the regular ones.

Frequency Diversity Array for Near-Field Focusing

In this study, a numerical optimization method is proposed to achieve the near-field focusing of square arrays and circular arrays. This method introduced the frequency diversity array (FDA) approach to change the initial amplitude and working frequency. By adjusting the working state of each antenna, the field distribution on any plane can be artificially controlled. To analyze the FDA, a mathematical model for the FDA has been built and the model has been optimized by a numerical algorithm. The results of two different kinds of arrays are verified by numerical methods and full-wave simulation.

Systems Underlying Human and Old World Monkey Communication: One, Two, or Infinite.

Using artificially synthesized stimuli, previous research has shown that cotton-top tamarin monkeys easily learn simple AB grammar sequences, but not the more complex AnBn sequences that require hierarchical structure. Humans have no trouble learning AnBn combinations. A more recent study, using similar artificially created stimuli, showed that there is a neuroanatomical difference in the brain between these two kinds of arrays. While the simpler AB sequences recruit the frontal operculum, the AnBn array recruits the phylogenetically newer Broca’s area. We propose that on close inspection, reported vocal repertoires of Old World Monkeys show that these nonhuman primates are capable of calls that have two items in them, but never more than two. These are simple AB sequences, as predicted by previous research. In addition, we suggest the two-item call cannot be the result of a combinatorial operation that we see in human language, where the recursive operation of Merge allows for a potentially infinite array of structures. In our view, the two-item calls of nonhuman primates result from a dual-compartment frame into which each of the calls can fit without having to be combined by an operation such as Merge.

Improved Nested Arrays With Sum-Difference Coarray for DOA Estimation

In this paper, we propose two kinds of improved nested arrays for direction of arrival (DOA) estimation, which are obtained by rearranging physical sensors of the prototype nested array. Specifically, the sum-difference coarrays (SDCAs) of the proposed arrays are constructed by jointly using the temporal and spatial information of the received signal. By systematically analyzing the structures of the proposed two kinds of arrays, we derive the closed-form expressions about their physical sensor positions, SDCAs, consecutive degrees of freedom (DOFs), and maximum physical array apertures, respectively. Compared to the prototype nested array which only considers the difference coarray (DCA), the proposed arrays with SDCAs have a lot more consecutive DOFs. Moreover, all physical sensors of the proposed arrays, except the one at zero point, can be placed at the positions opposite to their original ones, which will not result in a change in the consecutive DOFs. This phenomenon means that the proposed arrays have flexible array configurations with different physical array apertures, which make them more beneficial for practical application. In the end, simulation results demonstrate the superiorities of the proposed arrays in terms of detection performance and estimation accuracy.

Diagnosis of Planar Arrays Through Phaseless Measurements and Sparsity Promotion

A new compressive-sensing-inspired approach is proposed to the detection of faulty radiators in planar antenna arrays from a reduced set of phaseless far-field measurements. In order to deal with whatever kind of arrays, the problem is cast as the recovery of the aperture-field distribution, and two new convex-programming solution procedures are introduced. The first one relies on the improvement of the Total Variation norm technique, while the second one exploits a new aperture field expansion, which allows drastically reducing the number of unknowns of the problem. A wide set of numerical experiments involving benchmark scenarios, as well as full-wave data relative to a realistic antenna, is provided in support of the given theory.

Determination of the Slip Constant in the Beavers-Joseph Experiment for Laminar Fluid Flow through Porous Media Using a Meshless Method

In the paper, a numerical simulation of the Beavers-Joseph experiment is presented. The simulation is based on a meshless method which is called the Trefftz method with the special purpose Trefftz functions. The porous medium is modeled as a regular array of fibers. Three kinds of arrays are taken under consideration: triangular, square, and hexagonal. Firstly, the permeability of the fibrous porous medium is determined by consideration of flow between an infinite array of fibers. In the next step the considered region is divided into two parts. The first half of the channel is a porous medium modeled by a regular array of fibers and the second part which is a free fluid flow region. In the paper, the slip constant existing in the Beavers-Joseph boundary condition is determined in terms of the volume fraction of fibers.

Switchable phase/intensity sensor made with ring-shaped and hexagonal ferroelectric domains.

We present a device, similar to a Shack-Hartmann sensor, that can detect both the intensity distribution and wavefront of an incident wave. Its operation is based on the use of an array of electrically controllable Fresnel zone plates made in a ferroelectric crystal, lithium niobate. This sensor, which requires only one camera, can be quickly switched between intensity- and phase-detecting modes. Two kinds of arrays are shown: Fresnel zone plates with a few ring-shaped ferroelectric domains and plates made with nested hexagonal domains. Both arrays are suitable for use in a Shack-Hartmann wavefront sensor. However, since in lithium niobate domains naturally tend to form hexagons, it is easier to make hexagonal, rather than ring-shaped, domains and, consequently, smaller zone plates can be produced. This allows an increase in the number of zone plates and a reduction in their focal length, which improves the fidelity of the reconstructed wavefront.

Ideal ramp schemes and related combinatorial objects

In 1996, Jackson and Martin (Jackson and Martin, 1996) proved that a strong ideal ramp scheme is equivalent to an orthogonal array. However, there was no good characterization of ideal ramp schemes that are not strong. Here we show the equivalence of ideal ramp schemes to a new variant of orthogonal arrays that we term augmented orthogonal arrays. We give some constructions for these new kinds of arrays, and, as a consequence, we also provide parameter situations where ideal ramp schemes exist but strong ideal ramp schemes do not exist.

Developing Josephson junction array chips for microvolt applications**Project supported by the National Key Technology Research and Development Program of the Ministry of Science and Technology of China (Grant No. 2011BAK15B00), the Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 61401418), and the Basic Research Foundation of National Institute of Metrology of China (Grant No. 20-AKY1415).

Josephson junction array chips for microvolt applications have been designed and fabricated. A voltage step as small as 1 μV has been observed for a single junction in the array when it is driven by 483.59 MHz microwave. By selecting different parts of the array, it can output a voltage from 1 μV to 256 μV. The flat region of the voltage steps is over 200 μA. This kind of array is useful for potential microvolt applications.

Connecting Time

Past research suggests that scene organization affects duration judgments (Varakin, Klemes, & Porter, 2013, QJEP). The current experiments investigated whether organization affects duration judgments for arrays of abstract geometric shapes, using the gestalt cue of “connectedness” as a test case. In experiment 1, participants (n = 26) performed a temporal bisection task, judging on each trial whether an object array’s duration was closer to a pre-learned short (400ms) or long (1600ms) standard. On each trial, one of two kinds of arrays was presented: unorganized or organized. The 6 elements of unorganized arrays (two lines and four shapes) were presented at random, non-overlapping positions. In organized arrays, each line connected two shapes, thus creating two groupings. Bisection points (BP), calculated separately for each array type for each participant, were used to evaluate duration judgment biases. A BP is the duration at which 50% of the responses are predicted to be long, thus, smaller BPs indicate longer subjective duration. Unlike past work using real scenes, BPs for unorganized arrays (M = 981ms, SD = 109ms) were lower than BPs for organized scenes (M = 1011ms, SD = 115ms), (p< .05). To ensure participants attended to connectedness, in experiment 2 participants (n = 24) classified scenes as either organized or unorganized on half the trials, and performed temporal bisection on the rest. Participants did not know which task was to be performed until the end of a trial. In contrast to experiment 1, but consistent with past work using realistic scenes, BPs for organized scenes (M = 952 ms, SD = 155 ms) were smaller than BPs for unorganized scenes (M = 1030 ms, SD = 180 ms), (p< .05). Together, these results suggest that connectedness affects duration judgments, but the direction of the effect may depend on how participants process the display. Meeting abstract presented at VSS 2015

Three-Dimensional Induced Polarization Parallel Inversion Using Nonlinear Conjugate Gradients Method

Four kinds of array of induced polarization (IP) methods (surface, borehole-surface, surface-borehole, and borehole-borehole) are widely used in resource exploration. However, due to the presence of large amounts of the sources, it will take much time to complete the inversion. In the paper, a new parallel algorithm is described which uses message passing interface (MPI) and graphics processing unit (GPU) to accelerate 3D inversion of these four methods. The forward finite differential equation is solved by ILU0 preconditioner and the conjugate gradient (CG) solver. The inverse problem is solved by nonlinear conjugate gradients (NLCG) iteration which is used to calculate one forward and two “pseudo-forward” modelings and update the direction, space, and model in turn. Because each source is independent in forward and “pseudo-forward” modelings, multiprocess modes are opened by calling MPI library. The iterative matrix solver within CULA is called in each process. Some tables and synthetic data examples illustrate that this parallel inversion algorithm is effective. Furthermore, we demonstrate that the joint inversion of surface and borehole data produces resistivity and chargeability results are superior to those obtained from inversions of individual surface data.

2D and 3D ordered arrays of Co magnetic nanowires

Cobalt nanowire arrays spatially distributed in 2D and 3D arrangements have been performed by pulsed electrodeposition into the pores of planar and cylindrical nanoporous anodic alumina membranes, respectively. Morphological characterization points out the good filling factor reached by electroplated Co nanowires in both kinds of alumina membranes exhibiting hexagonally self-ordered porous structures. Co nanowires grown in both kinds of alumina templates exhibit the same crystalline phases. DC magnetometry and First Order Reversal Curve (FORC) analysis were carried out in order to determine the overall magnetic behavior for both nanowire array geometries. It is found that when the Co nanowires of two kinds of arrays are perpendicularly magnetized, both hysteresis loops are identical, suggesting that neither the intrinsic magnetic behavior of the nanowires nor the collective one depend on the arrays geometry. FORC analysis performed along the radial direction of the Co nanowire arrays embedded in the cylindrical alumina template reveals that the contribution of each nanowire to the magnetization reversal process involves its specific orientation with respect to the applied field direction. Furthermore, the comparison between the magnetic properties for both kinds of Co nanowire arrays allows discussing about the effect of the cylindrical geometry of the template on the magnetostatic interaction among nanowires.

Pattern Synthesis of Sub-Arrayed Monopulse Planar Arrays

Synthesis of sum and difference patterns of a planar array is introduced in this article by means of a clustering algorithm. The whole array aperture is divided into several sub-arrays, which will reduce the cost and complexity of manufacturing the array antenna. The sub-array configurations and the corresponding sub-array weights are defined to minimize the maximum level of the side-lobes of the corresponding sum and difference patterns. Two kinds of arrays are considered here: in the first, the whole aperture is divided into several sub-arrays to get sum and difference patterns; in the other, the compromise difference pattern is obtained. Some numerical experiments are given to assess the feasibility and effectiveness of the proposed method.

Direction-of-Arrival Estimation in Subarrays-Based Linear Sparse Arrays with Gain/Phase Uncertainties

Sparse arrays are of great interest in practical applications owing to their enlarged array apertures, which enable us to achieve better performance in direction finding. A kind of linear sparse arrays (LSpAs) composed of multiple uniform linear subarrays (ULSAs) with gain/phase uncertainties is considered. The problem of direction-of-arrival (DOA) estimation using such kinds of arrays is addressed. In particular two different cases are studied. In the first case all ULSAs are well calibrated, whereas there are unknown gains/phases among them. Using a new ESPRIT-like method, we show that the DOAs can be estimated in closed form. Interestingly, it is found that the unknown gains/phases can also be estimated in closed form by taking advantage of the subspace principle. In the second case we consider a more general situation where some of the ULSAs themselves are suffering from unknown sensor gain/phase responses. Again, we exploit the ESPRIT algorithm and propose a new approach to DOA and gain/phase estimation using this class of arrays. In our proposed methods the unknown parameters (i.e., DOAs and gains/phases) are estimated in closed form without performing spectral search. Representative numerical results are demonstrated to assess the effectiveness of the methods.

Design of Antipodal Vivaldi Antenna Array

Firstly in this paper,an antipodal Vivaldi antenna is designed.The bandwidth is from 6GHz to 18GHz. The simulated results show good electric performance and the voltage standing wave ratio is less than 2 in the whole bandwidth.Secondly depending on this unit,this paper designs two kinds of arrays and estimates their radiation characteristics,respectively.The one array is a 1×8 array and the another array is a X-cross structure array with four elements.

Electrical resistivity characterization and defect detection on a geosynthetic clay liner (GCL) on an experimental site

In this paper we analyze the onsite characterization of a geosynthetic clay liner (GCL) that serves to ensure the impermeability of a landfill cap by DC electrical methods. The imaging of the GCL geoelectrical properties is a challenging problem because it is a very thin (between 4 and 7 mm thick) and resistive layer (from 100,000 to 2,000,000 Ω·m) depending on meteorological conditions and aging. We compare results obtained using electrical resistivity tomography (ERT) using two different kinds of arrays (dipole–dipole DD and Wenner–Schlumberger) on an experimental site with engineered defects. To confirm these results and to find the real onsite GCL resistivity we have performed sampling of the posterior distribution of this parameter using vertical electrical sounding (VES) inversions. Different VES methods were extracted from ERT with DD array and converted into a Schlumberger array.

Editorial - Special Issue on Low-Power Arrays

The papers contributed to this Special Issue were inspired by the papers presented at the 2008 IEEE International Symposium on Circuits and Systems (ISCAS) and the 2009 IEEE Sensors conference. In both of these international events, we have initiated special sessions regarding low-power imager arrays and low-power memory arrays. The growing field of sensors triggered our attention to the fact that it has been a while since such a special Issue was provided on this subject, especially with emphasis on low power. The incentive was the recent results, showing that advanced concepts utilized in one niche implemented for large arrays, can be actually beneficial for the other. Moreover, there are systems on-chip where both kind of arrays are implemented, and leverage can be sought. This gives analog and digital designers another boost for developing creative circuit solutions for low-power array based systems. Also, technology and engineering progress have enabled Active Pixel Sensors (APS) in CMOS to compete with Charge Coupled Devices (CCDs) in imaging quality and to surpass them in focal-plane image processing applications, especially for low-power systems such as the cellphone. All these developments seem to show that the field of low-power sensor and memory arrays will be exciting and growing in the future. The papers in this Special Issue cover a broad range of topics, such as smart sensory arrays, new concepts for memory design, and integrated systems. The papers also come from four different continents. We have gathered the Special Issue papers in three groups. The first is image sensor array papers, the second is newmemory array design papers, and the last is other integrated arrays.