Rectangular Array Research Articles

Prospective Teachers’ Conceptions of Area

This study explored 10 prospective teachers’ (PTs’) understanding of the area of a rectangular region using square and non-square rectangular area-units. In an hour-long interview, each PT was first asked to explain how they would find the area of a given rectangular region in terms of a non-square notecard. For several PTs, this task prompted discussion of a square unit defined by the edge of the notecard. In a second task, PTs were presented with a rectangular array of squares and were asked to explain to a fictional child why multiplying length times width does not count the top left corner square twice. An analysis of transcripts of the interview suggested three conceptual components to understanding the area of a rectangular region—area-units, multiplication, and their connection to the length times width formula. Based on the PTs’ responses, we propose multi-tiered levels of reasoning. Each new level of understanding was built on the prior level in a hierarchical fashion. Juxtaposing tasks involving different area-units revealed PTs’ thinking about non-square and square area-units and how these related to the formula “L × W”.

Tunable bandpass frequency selective surface with wideband tuning and low insertion loss based on tunneling waveguide array

AbstractIn this paper, we present a tunable bandpass frequency‐selective surface (FSS) with wide tuning range. The FSS consists of a metallic rectangular waveguide array integrated into the double‐sided printed circuit board (DSPCB) and an array of embedded varactors with a bias network on the backside of the DSPCB. The waveguide array exhibits a frequency‐selective transmission peak due to the tunneling effect, and the transmission frequency can be adjusted by modifying the capacitance of varactors using different bias voltages. One benefit of this setup is that the varactors, along with the bias network, are situated on the same layer, resulting in a significant reduction in overall thickness to just 0.006λc (where λc represents the free‐space wavelength at the highest transmission frequency). Additionally, the insertion loss related to the parasitic resistance of varactors is notably reduced due to the innovative integrated design of biasing lines with varactors and the nearly full‐metal waveguide array. A prototype has been manufactured and tested, demonstrating that by varying the varactor capacitance from 0.12 to 1 pF, the passband showcases a frequency tuning range of 2.32:1, spanning from 5.8 to 2.5 GHz with an insertion loss ranging from 0.2 to 2.6 dB.

Multiple high-Q resonances from mirror-coupled dielectric arrays

This paper reports how high-Q resonances can be created at multiple designated wavelengths in a low-index-contrast dielectric nanoparticle array coupled with a metal mirror. A rectangular array of TiO2 nanoparticles over a silver film (separated by a SiO2 spacer layer) can support collective resonances of magnetic and electric dipoles with their wavelengths determined mainly by the lattice spacings of the rectangular lattice. These resonances can be modulated by the spacer layer thickness to form accidental bound states in the continuum. Furthermore, resonances related to the periodicity along the diagonal of the rectangular unit cell can be produced by perturbing the lattice through modifying the dimensions of adjacent nanoparticles in the unit cell. Our result expands the potential of lattice resonances in low-index-contrast dielectric lattices, making them promising for applications in compact multi-wavelength and unidirectional light-emitting devices.

Improved Sparrow Search Algorithm for Rectangular Planar Array Synthesis

To optimize sparse rectangular planar array antennas under multiple constraints, including array aperture, number of elements, and minimum element spacing, an improved sparrow search algorithm (ISSA) is proposed. Initially, a position distribution matrix is generated using the Blackman window weighting method. The sparrow search algorithm (SSA) is then enhanced by incorporating Kent mapping for population initialization, which improves the initial population’s diversity. Additionally, the strategy for updating the discoverer’s position integrates elements from the sine cosine algorithm (SCA), along with a nonlinear sine learning factor, thereby enhancing global search capability. Finally, a crossover strategy is embedded into the SSA to refine the optimization accuracy by improving the search methodology used by the vigilantes. To verify the efficacy of our approach, we carried out simulation experiments. The results demonstrate that this method significantly enhances the performance of the array antenna by reducing the peak sidelobe level and minimizing the zero-trap depth. These findings validate the reliability and effectiveness of the suggested method.

Design of A Rectangular Patch Microstrip Array Antenna with Proximity Coupled On ADS-B Receiver

One of the observation facilities available in Indonesia was Automatic Dependent Surveillance-Broadcast (ADS-B), a surveillance technology similar to Radio Detection and Ranging for monitoring air traffic. This system only received information transmissions from aircraft, broadcast on a frequency of 1090 MHz using a monopole antenna with large dimensions, ranging from 85 centimeters to 3,5 meters, and weighing between 1,5 kilograms to 26 kilograms. As an alternative, a microstrip antenna was chosen to reduce the large size and weight of the monopole antenna. This research aimed to design a 2x1 rectangular patch microstrip array antenna with a proximity coupled feeding method at a frequency of 1090 MHz. The antenna was designed using Antenna Design Software and fabricated using Epoxy substrate material with a copper ground plane. The simulation results showed a Return Loss of -28,87 decibels, VSWR 1,07, Bandwidth 28,87 MHz, Impedance 52,4 Ω, and Gain 8,49 decibels. The measurement results showed a Return Loss of -30,87 decibels, VSWR 1,07, Bandwidth 28 MHz, Impedance 48,91 Ω, and Gain 6,4 decibels. The test results demonstrated that the antenna successfully received signals from 32 aircraft, with the longest reception distance reaching 172,5 Nautical Miles (319.4 kilometer) at a maximum altitude of 36,950 feet.

Innovative enhancements in solar still performance: A comprehensive study on wick-absorber configurations

This study introduces a new thermo-fluid analysis of using wick-absorbers to enhance solar still performance. Three configurations of wick absorbers were tested in a conventional single-slope solar still: (i) Case I: individual wick balls, (ii) Case II: zig-zag wick pattern, and (iii) Case III: rectangular wick array (grid-like pattern). The study evaluates multiple parameters, including saline water temperature, daily water productivity, Nusselt number, Sherwood number, thermal and exergy efficiencies, water cost, and payback period. The addition of an absorbing plate with an insulation layer led to lower saline water temperatures and shifted peak values. Compared to a traditional still, wick utilization enhanced water productivity by 45.8 %, 84.5 %, and 86 % for Cases I, II, and III, respectively, due to increased evaporation rates. This resulted in a relative enhancement in daily thermal efficiency by 64 %, 76 %, and 97.5 %, respectively. Additionally, four correlations were developed to describe Nusselt and Sherwood numbers, with a maximum deviation of 25 %. Economic analysis demonstrated cost-effectiveness, significantly reducing water cost and the payback period by 37 %, 39 %, and 44 % for Cases I, II, and III, respectively, compared to the conventional system.

Parallelization of Curved Inertial Microfluidic Channels to Increase the Throughput of Simultaneous Microparticle Separation and Washing

The rising global need for clean water highlights the importance of efficient sample preparation methods to separate and wash various contaminants such as microparticles. Microfluidic methods for these purposes have emerged but they mostly deliver either separation or washing, with very low throughputs. Here, we investigate parallelization of a curved-channel particle separation and washing device in order to increase its throughput for sample preparation. A curved microchannel applies inertial forces to focus larger 10 µm microparticles at the inner wall of the channel and separate them from smaller 5 µm microparticles at the outer wall. At the same time, Dean flow recirculation is used to exchange the carrier solution of the large microparticles to a clean buffer (washing). We increased the number of curved channels in a stepwise manner from two to four to eight channels in two different arraying designs, i.e., rectangular and polar arrays. We examined efficient separation of target 10 µm particles from 5 µm particles, while transferring the larger microparticles into a clean buffer. Dean flow recirculation studies demonstrated that the rectangular arrayed device performs better, providing solution exchange efficiencies of more than 96% on average as compared to 89% for the polar array device. Our 8-curve rectangular array device provided a particle separation efficiency of 98.93 ± 0.91%, while maintaining a sample purity of 92.83 ± 1.47% at a high working flow rate of 12.8 mL/min. Moreover, the target particles were transferred into a clean buffer with a solution exchange efficiency of 96.81 ± 0.54% in our 8-curve device. Compared to the literature, our in-plane parallelization design of curved microchannels resulted in a 13-fold increase in the working flow rate of the setup while maintaining a very high performance in particle separation and washing. Our microfluidic device offers the potential to enhance the throughput and the separation and washing efficiencies in applications for biological and environmental samples.

Multi Environment Trials and Adaption of Advanced Bread Wheat (<i>Triticum aestivum </i>L.) Genotypes in Low Moisture Stress Areas of Ethiopia

To predict bread wheat genetic potential across environments and adaption in low moisture stress wheat growing areas of Ethiopia. Multi-location trials were conducted in Ethiopia from 2020 to 2021 in main seasons. A total of advanced genotypes including the checks were arranged in randomized complete block design in a rectangular (row x column) array of plots with two replications. The results showed that, under the linear mixed model, the spatial and factor analytic models were efficient methods of data analysis for this study. By ranking average best linear unbiased prediction (BLUPs) within clusters, the 13 bread wheat environments were clustered into three mega environments (C1, C2, and C3) for the trait grain yield. This method used as a selection indicator, assisting in the selection of superior and adaptable types. The predicted performance of genotypes based on BLUP values averaged across correlated settings of C1 and C2, eliminating C3 due to low genetic correlation with the other trials and low genetic variation. Based on these clusters, the genotypes with the highest potential EBW192350 and EBW192369 were selected for a subsequent verification study that might potentially use them as a released variety. For genetic variance, the estimates for variance component parameters ranged from 0.069 to 2.896 and error variance, they ranged from 0.175 to 1.002. Therefore, increasing the application of this efficient analysis method will improve the selection of superior bread wheat varieties. The two genotypes can be further verified using national performance trials/ or verified in farmers’ fields for registration and commercialization.

Domino Antimagic Squares and Rectangles

Abstract A domino antimagic square of order n is an n×n array formed from a subset of the standard set of 28 dominoes such that the sums of the rows, columns, and two main diagonals form a set of 2n + 2 distinct, consecutive integers while an m × n domino antimagic rectangle is an m × n rectangular array formed from a subset of the standard set of 28 dominoes such that the sums of the rows and columns form a set of m + n distinct, consecutive integers. This paper outlines what the possible dimensions are for m×n domino antimagic rectangles and provides many examples of both domino antimagic rectangles and squares. Many open questions are given at the end of the paper for future exploration.

Block-term tensor decomposition in array signal processing

The ability of tensor decomposition (TD)-based methods to recover latent information, including channel parameters and transmitted symbols in the array signal processing (ASP) context, in a deterministic manner and with little or no training overhead, fits well with the data efficiency needs of future-generation multi-user massive multiple-input multiple-output systems. However, such methods have mostly relied on a few classical TD models, notably the canonical polyadic decomposition (CPD), which can be quite restrictive in realistic scenarios. In this paper, a generalized CPD model, known as block-term decomposition (BTD), is re-visited in the context of ASP, and shown to be the natural choice in sensor arrays of increased dimensionality that also involve channel multipath. Semi-blind joint channel estimation/data detection (JCD) is addressed in this context via efficient algorithms that wed existing JCD schemes with BTD approximation. Robust to sensor failures and recursive versions are also developed. The special yet important case of the uniform rectangular array (URA) configuration is adopted to illustrate the ideas and results. The signal detection performance of the BTD-inspired semi-blind JCD schemes is evaluated under various conditions with the aid of simulations and seen to be favorably compared with that of the training-only-based solution.

Performance of surface structures in enhancing heat transfer rates of miniaturized pulsating heat pipe

Enhancement of the thermal performance by modifying the evaporator surface of a miniaturized pulsating heat pipe (PHP) is the primary target of the present work. Four PHPs having different evaporator surface types i.e., smooth, dimple cavity array, tunnel cavity, and rectangular cavity array were investigated numerically to compare the gas-liquid interfacial behavior and evaluate the role of bubble nucleation, slug-plug movement, and drop-film condensation on the thermal performance. Detailed modeling of evaporating and condensing interfaces shows that activation of nucleation sites at all defined discrete structures and undisturbed liquid flow path at the evaporator promote heat transfer rate. Through thermo fluidic analysis around different surface structures, evaporation dynamics is analyzed to understand the suitability of a structure type for enhancement of heat transfer. Associated slug-plug motion through the adiabatic zone and processes at the condenser have been also discussed to propose the characteristics of an ideal enhanced PHP. The capacity to transfer heat has been also characterized using thermal resistance for different structured PHPs which may be a guiding factor for the design of heat sinks for thermal applications.

Planar Rectangular Microstrip Patch Antenna Array with Corporate-Feed Network for Gain Enhancement

Abstract: The design and performance analysis of a inset-fed planar rectangular microstrip patch antenna array with corporatefeed network systems is presented in this paper. This design aims to increase the gain of the rectangular patch antenna through the use of a 16-element planar rectangular antenna array. Each element in this planar array is fed by T-junction power divider networks with quarter-wave transformer lines via the corporate-feed method. The antenna is designed over the operating frequency of 2.4 GHz using the substrate material FR-4, which has a dielectric constant of 4.4 and a loss tangent of 0.002. By the addition of radiating patches in the array design, the gain, directivity and bandwidth also has been improved significantly. The proposed antenna array provides a gain of 9.284 dB, a directivity of 16.2 dBi, and a bandwidth of 0.361 GHz. The designed antenna can be used for wireless applications.

Transverse size effect of relaxor ferroelectric Pb(In1/2Nb1/2)O3-Pb(Mg1/3Nb2/3)O3-PbTiO3 film for one- and two-dimensional integrated sensors by simulation

In this work, the transverse size effect of the new-generation relaxor ferroelectric Pb(In1/2Nb1/2)O3-Pb(Mg1/3Nb2/3)O3-PbTiO3 (PIMNT) thin film was studied by finite element method, aiming to revealing the lateral size and shape dependence of the piezoelectric, dielectric, and pyroelectric behavior for guiding one- and two-dimensional integrated array sensor applications. The results indicated that as the aspect ratio (width to thickness ratio) decreased from 100 to 0.01, for both one-dimensional rectangular and two-dimensional square PIMNT array elements, a sharp increase in piezoelectric and dielectric constants could be observed for the PIMNT with <001> direction while a slight increase could be found for those along <111> orientation, exhibiting a strong orientation dependence. In comparison, the PIMNT with <110> direction exhibited strong shape dependence. The piezoelectric and dielectric constants of <110>-oriented square element increased more remarkably than those of the rectangular one. The pyroelectric coefficients of PIMNT exhibited weak shape dependence, decreasing from 8.5 × 10−4 C/(m2·K) to about 8.0 × 10−4 C/(m2·K) for both element shapes with transverse size decreasing. These findings give insight into the transverse size and shape effect on the new-generation PIMNT thin film and provide a guide for its design in one- and two-dimensional piezoelectric and pyroelectric array sensor applications.

Millimeter Wave Massive MIMO systems using Hybrid Beamforming

The goal of next-generation wireless systems is to support many users by achieving higher data rates and reduced latency. Multiple input and multiple output systems (MIMO) are utilized in order to achieve high data rates. Multiple antennas are employed by Massive MIMO systems in both the transmitter along with the receiver. A signal processing method known as beamforming is used on several transmitting and receiving stations in order to deliver and receive multiple messages at once. To increase spectral efficiency, hybrid beamforming using a uniform rectangular antenna array is used in this research work. The results of hybrid beamforming using different numbers of antennas are compared with those of fully digital beamforming. A comparison between signal-to-noise (SNR) and bit error rate (BER) is performed. Comparing hybrid beamforming to fully digital beamforming, simulation findings show that hybrid beamforming reduces computing complexity due to reduced number of RF links. Also observed that the spectral efficiency rises with an increase in the quantity of transmitting antennas.

Synthesis of sparse rectangular planar arrays with weight function and improved grey wolf optimization algorithm

AbstractThe present article proposes a novel hybrid approach for addressing the synthesis problem of rectangular planar arrays under multiple constraints, through joint optimization of the weight function and the improved grey wolf optimization (IGWO) algorithm. Firstly, the grey wolf optimization (GWO) algorithm is improved by using tent chaotic mapping, nonlinear convergence factor, dominant wolf dynamic belief strategy, and opposition‐based learning strategy to increase the population diversity and the ability to jump out of the local optimum. Secondly, the array elements are weighted using the weight function to generate the position distribution matrix, which reduces the thinned matrix optimization time and improves the optimization efficiency. Finally, the position distribution matrix is used to generate the thinned array, and the IGWO algorithm is applied to perform the sparse optimization with multiple constraints. The effectiveness of the method is verified through numerical simulation and full‐wave simulation experiments, demonstrating its capability to enhance array antenna performance and reduce peak sidelobe level (PSLL). These experimental results hold significant engineering implications and provide valuable references for addressing the array distribution problem under multiple constraints.

A top-mounted, chain-driven, bidirectional point absorber type wave energy convertor

The aims of this paper are to introduce the structure of a point absorber type wave energy convertor (WEC) mounted above sea level, to analyze the motion characteristics and power absorptions of such a WEC and to describe the numerous advantages of installing it in the nearshore. The motion equation is solved by representing the excitation force with the dynamic wave pressure and obtaining an approximate system transfer function. The possibility of the buoy becoming airborne or submerged is considered and the power absorption is increased optimally by reshaping the frequency response using a flywheel. The time, phase and spectral averages of power absorptions are presented for offshore waves, nearshore waves and for concentrated nearshore waves using standard wave spectrums and compared. Approximate gains possible with linear and rectangular arrays are also presented. Considering different phase distributions, it is shown that downgrading WECs based on short term power absorptions is not justifiable. With a buoy of radius 2 m, the power absorption of this kind of a WEC is estimated to be about 114 kW in the deep sea and 117 kW in the nearshore, when the energy flux is about 31 kW/m. By concentrating just 13.6 kW/m nearshore waves, it could be increased to 186 kW. If a 3-element longshore in-line array is placed inside the wave concentrator, the total power absorption could be about 556 kW. A 9-element rectangular array would be capable of absorbing about 1 MW by making use of the remaining energy of the down wave.

Numerical investigation of natural convection from a horizontal heat sink with an array of rectangular fins

This research focuses on the numerical analysis of a rectangular fin array with a horizontal heat sink to examine its performance in natural convection heat transfer. The study uses air as the primary working medium. Steady-state 3D modeling is carried out using the finite volume method (FVM), allowing velocity and temperature distributions to be evaluated by solving equations relating to mass conservation, fluid dynamics, turbulence, and heat transfer. This research details temperature and velocity variations as well as fluid trajectories. It also explores how the intensification of heat flow, varying from 361 W/m2 to 2527 W/m2, influences the cooling efficiency of the fins. It is observed that the increase in heat flux reduces the formation of vortices and intensifies natural convection by rising the temperature gradient between the radiator and the surrounding. The temperature increases at all parts of the heat sink fin array as heat flux increases. Besides, it is noticed that the maximum temperature is generated at the mid-region of the base plate heat sink and gradually dissipates to the surroundings through the bodies of the fins. Moreover, the study indicates that the average convection heat transfer coefficient (hav) and the average Nusselt number (Nus) increase by 86 % and 84 %, respectively, when the heat flux is increased from 361 W/m2 to 2527 W/m2. These observations are corroborated by a comparison with existing experimental data, showing an agreement of less than 9 %. The digital model is validated by comparing pre-existing data on radiators with horizontal rectangular louvers, revealing minimal deviations of less than 2 %.

Chiral metasurface device in near-infrared region designed by rectangular arrays

Chiral metasurface device in near-infrared region designed by rectangular arrays

Collimated beam formation in 3D acoustic sonic crystals

We demonstrate strongly collimated beam formation, at audible frequencies, in a three-dimensional acoustic phononic crystal where the wavelength is commensurate with the crystal elements; the crystal is a seemingly simple rectangular cuboid constructed from closely-spaced spheres, and yet demonstrates rich wave phenomena acting as a canonical three-dimensional metamaterial. We employ theory, numerical simulation and experiments to design and interpret this collimated beam phenomenon and use a crystal consisting of a finite rectangular cuboid array of 4×10×10 polymer spheres 1.38 cm in diameter in air, arranged in a primitive cubic cell with the centre-to-centre spacing of the spheres, i.e. the pitch, as 1.5 cm. Collimation effects are observed in the time domain for chirps with central frequencies at 14.2 kHz and 18 kHz, and we deployed a laser feedback interferometer or Self-Mixing Interferometer – a recently proposed technique to observe complex acoustic fields—that enables experimental visualisation of the pressure field both within the crystal and outside of the crystal. Numerical exploration using a higher-order multi-scale finite element method designed for the rapid and detailed simulation of 3D wave physics further confirms these collimation effects and cross-validates with the experiments. Interpretation follows using High Frequency Homogenization and Bloch analysis whereby the different origin of the collimation at these two frequencies is revealed by markedly different isofrequency surfaces of the sonic crystal.

Fast Low-Sidelobe Pattern Synthesis Using the Symmetry of Array Geometry.

Array pattern synthesis with low sidelobe levels is widely used in practice. An effective way to incorporate sensor patterns in the design procedure is to use numerical optimization methods. However, the dimension of the optimization variables is very high for large-scale arrays, leading to high computational complexity. Fortunately, sensor arrays used in practice usually have symmetric structures that can be utilized to accelerate the optimization algorithms. This paper studies a fast pattern synthesis method by using the symmetry of array geometry. In this method, the problem of amplitude weighting is formulated as a second-order cone programming (SOCP) problem, in which the dynamic range of the weighting coefficients can also be taken into account. Then, by utilizing the symmetric property of array geometry, the dimension of the optimization problem as well as the number of constraints can be reduced significantly. As a consequence, the computational efficiency is greatly improved. Numerical experiments show that, for a uniform rectangular array (URA) with 1024 sensors, the computational efficiency is improved by a factor of 158, while for a uniform hexagonal array (UHA) with 1261 sensors, the improvement factor is 284.