Journal articles: 'Array theory'

1

Kummer, W. H. "Basic array theory." Proceedings of the IEEE 80, no. 1 (1992): 127–40. http://dx.doi.org/10.1109/5.119572.

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Beard, Les P., and Alan C. Tripp. "Investigating the resolution of IP arrays using inverse theory." GEOPHYSICS 60, no. 5 (September 1995): 1326–41. http://dx.doi.org/10.1190/1.1443869.

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Using a fast 2-D inverse solution, we examined the resolution of different resistivity/IP arrays using noisy synthetic data subject to minimum structure inversion. We compared estimated models from inversions of data from the dipole‐dipole, pole‐dipole, and pole‐pole arrays over (1) a dipping, polarizable conductor, (2) two proximate conductive, polarizable bodies, (3) a polarizable conductor beneath conductive overburden, and (4) a thin, resistive, polarizable dike. The estimated resistivity and polarizability models obtained from inversion of the dipole‐dipole data were usually similar to the pole‐dipole estimated models. In the cases examined, the estimated models from the pole‐pole data were more poorly resolved than the models from the other arrays. If pole‐pole resistivity data contain even a fraction of a percent of Gaussian noise, the transformation of such data through superposition to equivalent data of other array types may be considerably distorted, and significant information can be lost using the pole‐pole array. Though the gradient array is reputed to be more sensitive to dip than other arrays, it evidently contains little information on dip that does not also appear in dipole‐dipole data, for joint inversion of dipole‐dipole and gradient array data yields models virtually identical to those obtained from inversion of dipole‐dipole data alone.

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Hanson, Jordan C. "Broadband RF Phased Array Design with MEEP: Comparisons to Array Theory in Two and Three Dimensions." Electronics 10, no. 4 (February 8, 2021): 415. http://dx.doi.org/10.3390/electronics10040415.

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Phased array radar systems have a wide variety of applications in engineering and physics research. Phased array design usually requires numerical modeling with expensive commercial computational packages. Using the open-source MIT Electrogmagnetic Equation Propagation (MEEP) package, a set of phased array designs is presented. Specifically, one and two-dimensional arrays of Yagi-Uda and horn antennas were modeled in the bandwidth [0.1–5] GHz, and compared to theoretical expectations in the far-field. Precise matches between MEEP simulation and radiation pattern predictions at different frequencies and beam angles are demonstrated. Given that the computations match the theory, the effect of embedding a phased array within a medium of varying index of refraction is then computed. Understanding the effect of varying index on phased arrays is critical for proposed ultra-high energy neutrino observatories which rely on phased array detectors embedded in natural ice. Future work will develop the phased array concepts with parallel MEEP, in order to increase the detail, complexity, and speed of the computations.

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Darwood, P., P. N. Fletcher, and G. S. Hilton. "Pattern synthesis in small phased arrays using adaptive array theory." Electronics Letters 33, no. 4 (1997): 254. http://dx.doi.org/10.1049/el:19970212.

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Lohmann, Adolf W. "Array illuminators and complexity theory." Optics Communications 89, no. 2-4 (May 1992): 167–72. http://dx.doi.org/10.1016/0030-4018(92)90153-i.

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Xu, Qian, and Haitao Wang. "Sound Field Modeling Method and Key Imaging Technology of an Ultrasonic Phased Array: A Review." Applied Sciences 12, no. 16 (August 9, 2022): 7962. http://dx.doi.org/10.3390/app12167962.

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An ultrasonic phased array consists of multiple ultrasonic probes arranged in a certain regular order, and the delay time of the excitation signal sent to each array element is controlled electronically. The testing system model based on ultrasonic propagation theory is established to obtain a controllable and focused sound field, which has theoretical and engineering guiding significance for the calculation and analysis of ultrasonic array sound fields. Perfecting array theory and exploring array imaging methods can obtain rich acoustic information, provide more intuitive and reliable research results, and further the development of ultrasonic phased-array systems. This paper reviews the progress of research on the application of ultrasound arrays for non-destructive testing (NDT) and brings together the most relevant published work on the application of simulation methods and popular imaging techniques for ultrasonic arrays. It mainly reviews the modeling approaches, including the angular spectrum method (ASM), multi-Gaussian beam method (MGB), ray tracing method, finite element method (FEM), finite difference method (FDM), and distributed point source method (DPSM), which have been used to assess the performance and inspection modality of a given array. In addition, the array of imaging approaches, including the total focusing method (TFM), compression sensing imaging (CSI), and acoustic nonlinearity imaging (ANI), are discussed. This paper is expected to provide strong technical support in related areas such as ultrasonic array testing theory and imaging methods.

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Duren, Richard E. "A theory for marine source arrays." GEOPHYSICS 53, no. 5 (May 1988): 650–58. http://dx.doi.org/10.1190/1.1442499.

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General mathematical expressions for a marine source array’s (1) far‐field pulse spectrum, (2) radiated energy density, and (3) directivity are developed for both a source in an infinite homogeneous medium and a source operating near the ocean surface. These results, intended to assist the analysis and design of marine source arrays, apply to any marine source array when (1) individual elements radiate isotropically, (2) their individual waveforms are specified, and (3) the array geometry is specified. Arbitrary geometry and arbitrary isotropic waveforms are allowed. The theory assumes linear superposition of the individually specified waveforms, and is consistent with the “square law effect” for identical elements. For an array of small elements, expended energy agrees with the array’s radiated energy found using far‐field methods. Also, the energy radiated from an array with large element spacing is equal to the sum of the independently radiated energies. Two closely spaced identical elements radiate four times the energy contained in a single outgoing waveform over all space. The appropriate directivity definition for marine seismic sources is the ratio of the radiated energy density per unit solid angle in a particular direction to the average radiated energy density per unit solid angle. This definition allows directivity to be expressed explicitly in terms of the individual frequency spectra and geometry.

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Salihoglu, Hakan, Zhuo Li, and Sheng Shen. "Theory of thermal radiation from a nanoparticle array." Applied Physics Letters 121, no. 24 (December 12, 2022): 241701. http://dx.doi.org/10.1063/5.0117131.

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Thermal radiation has diffusive and broad emission characteristics. Controlling emission spectrum and direction is essential for various applications. Nanoparticle arrays, supporting collective lattice resonances, can be employed for controlling optical properties. However, thermal emission characteristics remain unexplored due to the lack of a theoretical model. Here, we develop an analytical model to predict thermal radiation from a nanoparticle array using fluctuation–dissipation theorem and lattice Green's functions. Our findings reveal that the periodicity and particle size of the particle array are main parameters to control both emission spectrum and direction. The derived simple expression for thermal emission enables insightful interpretation of physics. This model will lay a foundation for analytical derivation of thermal radiation from metasurfaces. Our study can be useful in engineering infrared thermal sources and radiative cooling applications.

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Cui, Wuwei. "Modern Electromagnetic Field Theory and Its Application in Future Wireless Communication." Journal of Physics: Conference Series 2386, no. 1 (December 1, 2022): 012044. http://dx.doi.org/10.1088/1742-6596/2386/1/012044.

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Abstract With the advent of the 5G era, more and more technologies in life are applied to the technological development and theory of antennas. Waveform constraints. These basic applications are obtained due to the natural seismic source and the continuous arrangement and combination of arrays. In this article, we first discuss the spherically symmetric electric field distribution of antenna elements in space, and then discuss the influence of a circular array on the electromagnetic intensity of the space radiated field. At the same time, the basic characteristics of waveform restraint, array radar and array telescope are discussed. Afterwards, from a theoretical point of view, the physical properties and radiation characteristics of the near-field induction field and radiation field of the factory around the vibrator were analyzed quantitatively and qualitatively. Later, I discussed the relationship between an annular array and the eddy current. Through theoretical derivation and excitation factors, we used the original radiation equation to derive the Bessel function, and used a computer to make a simulation to explore the factors that can affect the array radiation.

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10

Nwokah, O. D. I., R. E. Nordgren, and G. S. Grewal. "Inverse Nyquist array: a quantitative theory." IEE Proceedings - Control Theory and Applications 142, no. 1 (January 1, 1995): 23–30. http://dx.doi.org/10.1049/ip-cta:19951227.

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11

Stoffregen, Thomas A., and Benoît G. Bardy. "Theory testing and the global array." Behavioral and Brain Sciences 27, no. 6 (December 2004): 892–900. http://dx.doi.org/10.1017/s0140525x04270200.

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The new commentaries raise important issues about the target article (Stoffregen & Bardy 2001). The commentaries also highlight some assumptions, often implicit, that underlie traditional interpretations of perception. We argue that evaluation of the global array and its implications for perception requires both analytical research on specification in the global array and new empirical research on the use of information in the global array for the control of action.

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12

V. Ashikhmin, A. "Virtual Antenna Array Theory and Applications." American Journal of Electromagnetics and Applications 3, no. 1 (2015): 1. http://dx.doi.org/10.11648/j.ajea.20150301.11.

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13

Massa, A., M. Donelli, F. G. B. DeNatale, S. Caorsi, and A. Lommi. "Planar Antenna Array Control With Genetic Algorithms and Adaptive Array Theory." IEEE Transactions on Antennas and Propagation 52, no. 11 (November 2004): 2919–24. http://dx.doi.org/10.1109/tap.2004.837523.

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14

Manges, John B., John W. Silvestro, and Kezhong Zhao. "Finite-element analysis of infinite and finite arrays." International Journal of Microwave and Wireless Technologies 4, no. 3 (May 24, 2012): 357–64. http://dx.doi.org/10.1017/s1759078712000463.

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This paper considers and compares the numerical characterization of regular planar antenna arrays from two viewpoints. In the case where the array is sufficiently large, the well-known infinite array idealization applies and a very efficient simulation method is presented which combines array theory with a specialized form of the finite-element method called the transfinite element method (TFEM). Alternatively, a more direct approach is discussed in which the entire antenna array is simulated as a finite structure using recent advances in the domain decomposition method (DDM). Taken together, the two methods provide a comprehensive simulation method for regular arrays from small order to very large order.

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15

Doles, J. H., and F. D. Benedict. "Broad-band array design using the asymptotic theory of unequally spaced arrays." IEEE Transactions on Antennas and Propagation 36, no. 1 (1988): 27–33. http://dx.doi.org/10.1109/8.1071.

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16

Bender, Christopher M., and Shane W. Lani. "Theory of parametric receiving arrays processing utilizing sum and difference frequencies." Journal of the Acoustical Society of America 151, no. 4 (April 2022): A217. http://dx.doi.org/10.1121/10.0011099.

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The majority of highly directive receive arrays obtains their directivity from an often fully populated (lambda/2 spacing) array in one or more dimensions. Digital beamforming allows for steering of these densely populated arrays in multiple directions; however, if there is only one primary direction of interest, a similar highly directive receiver can be generated with just a few elements. Parametric receivers, such as parametric sources, can obtain enhanced directivity via a “virtual aperture” or a region in the medium where nonlinear mixing of a high intensity pump wave and a signal wave interact. For a parametric receiver, the pump element(s) with a frequency, F, and receiver element(s) are separated by a distance, L, and the signals of interest are the sum and difference frequency ( F + /− f) between the pump frequency and an incoming signal frequency, f. The directivity of these parametric receivers are comparable to the end fire response of a line array of similar length, L. This paper will review the highlights of parametric receivers as well as detail the analysis to extend this phenomenon to include the sum and difference frequencies for single element pairing and arrays of pumps and receivers.

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17

Bennetts, Luke G., Malte A. Peter, and Fabien Montiel. "Localisation of Rayleigh–Bloch waves and damping of resonant loads on arrays of vertical cylinders." Journal of Fluid Mechanics 813 (January 20, 2017): 508–27. http://dx.doi.org/10.1017/jfm.2016.855.

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Linear potential-flow theory is used to study loads imposed on finite line arrays of rigid, bottom-mounted, surface-piercing, vertical cylinders by surface water waves. Perturbations in the cylinder locations are shown to damp the resonant loads experienced by the unperturbed array. A relationship is established between the damping and the phenomenon of Anderson localisation. Specifically, the Rayleigh–Bloch waves responsible for the resonant loads are shown to attenuate along the array when perturbations are introduced, resulting in localisation when the attenuation rate is sufficiently large with respect to the array length. Further, an efficient solution method for line arrays is introduced that captures the Rayleigh–Bloch wave modes supported by unperturbed arrays from the scattering characteristics of an individual cylinder.

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18

Dufort, E. C. "Pattern synthesis based on adaptive array theory." IEEE Transactions on Antennas and Propagation 37, no. 8 (1989): 1011–18. http://dx.doi.org/10.1109/8.34138.

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19

Huang, Dehua. "Non‐uniform array synthesis concept and theory." Journal of the Acoustical Society of America 127, no. 3 (March 2010): 1981. http://dx.doi.org/10.1121/1.3385087.

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20

Smillie, K. W. "Array theory and the nial programming language." BIT 28, no. 3 (September 1988): 439–49. http://dx.doi.org/10.1007/bf01941127.

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21

Gan, Woon-Seng, Jun Yang, and Tamoo Kamakura. "Parametric acoustic array: Theory, advancement, and applications." Applied Acoustics 73, no. 12 (December 2012): 1209–10. http://dx.doi.org/10.1016/j.apacoust.2012.06.016.

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22

Vongchumyen, C., S. Mitatha, J. Ali, and P. P. Yupapin. "Dark soliton array generation: Theory and experiment." Microwave and Optical Technology Letters 52, no. 11 (August 17, 2010): 2397–400. http://dx.doi.org/10.1002/mop.25514.

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23

Abdalmalak, Kerlos Atia, Ayman Abdulhadi Althuwayb, Choon Sae Lee, Gabriel Santamaría Botello, Enderson Falcón-Gómez, Luis Emilio García-Castillo, and Luis Enrique García-Muñoz. "Standing-Wave Feeding for High-Gain Linear Dielectric Resonator Antenna (DRA) Array." Sensors 22, no. 8 (April 18, 2022): 3089. http://dx.doi.org/10.3390/s22083089.

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A novel feeding method for linear DRA arrays is presented, illuminating the use of the power divider, transitions, and launchers, and keeping uniform excitation to array elements. This results in a high-gain DRA array with low losses with a design that is simple, compact and inexpensive. The proposed feeding method is based on exciting standing waves using discrete metallic patches in a simple design procedure. Two arrays with two and four DRA elements are presented as a proof of concept, which provide high gains of 12 and 15dBi, respectively, which are close to the theoretical limit based on array theory. The radiation efficiency for both arrays is about 93%, which is equal to the array element efficiency, confirming that the feeding method does not add losses as in the case of standard methods. To facilitate the fabrication process, the entire array structure is 3D-printed, which significantly decreases the complexity of fabrication and alignment. Compared to state-of-the-art feeding techniques, the proposed method provides higher gain and higher efficiency with a smaller electrical size.

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24

Botez, D. "Array-mode far-field patterns for phase-locked diode-laser array: Coupled-mode theory versus simple diffraction theory." IEEE Journal of Quantum Electronics 21, no. 11 (November 1985): 1752–55. http://dx.doi.org/10.1109/jqe.1985.1072579.

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Zhang, Gexiang, G. Samdanielthompson, N. Gnanamalar David, Atulya K. Nagar, and K. G. Subramanian. "A Bio-Inspired Model of Picture Array Generating P System with Restricted Insertion Rules." Applied Sciences 10, no. 22 (November 23, 2020): 8306. http://dx.doi.org/10.3390/app10228306.

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In the bio-inspired area of membrane computing, a novel computing model with a generic name of P system was introduced around the year 2000. Among its several variants, string or array language generating P systems involving rewriting rules have been considered. A new picture array model of array generating P system with a restricted type of picture insertion rules and picture array objects in its regions, is introduced here. The generative power of such a system is investigated by comparing with the generative power of certain related picture array grammar models introduced and studied in two-dimensional picture language theory. It is shown that this new model of array P system can generate picture array languages which cannot be generated by many other array grammar models. The theoretical model developed is for handling the application problem of generation of patterns encoded as picture arrays over a finite set of symbols. As an application, certain floor-design patterns are generated using such an array P system.

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Lv, Qinyi, Yu-Hang Yang, Shi-Gang Zhou, Chan Shao, Deyun Zhou, and Chow-Yen-Desmond Sim. "Design of a Single-Layer ±45° Dual-Polarized Directional Array Antenna for Millimeter Wave Applications." Sensors 21, no. 13 (June 24, 2021): 4326. http://dx.doi.org/10.3390/s21134326.

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A single-layer ±45° dual-polarized directional array antenna for millimeter wave (mm-wave) applications is designed in this communication. Based on the theory of orthogonal circularly polarized (CP) wave multiplexing, two ports of a series-fed dual CP array are fed with equal amplitudes, and the array can radiate a linearly polarized wave with ±45° polarization orientations through the adjustment of the feeding phase difference. As the two ports of the series-fed array are simultaneously excited, the antenna can achieve directional radiation. In addition, the cross-polarization level of the array can be effectively suppressed by placing two series-fed arrays side by side. A prototype of the designed array antenna operating at 30 GHz is fabricated and measured; the working bandwidth of the proposed antenna is approximately 3.5%. Owing to its simple structure and directional radiation, the proposed antenna array is a competitive candidate for mm-wave applications.

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27

Di, Jiaying, Wen Hu, Mengxia Li, and Hongtao Li. "An optimized 2D-Robust Adaptive Beamforming algorithm based on Matrix Completion in sparse array." MATEC Web of Conferences 208 (2018): 01003. http://dx.doi.org/10.1051/matecconf/201820801003.

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The sparse arrays can reduce the cost of beamforming, it greatly reduces the number of actual array elements. However, it also brings about the problem of information loss. A 2D-robust adaptive beamforming algorithm in sparse array based on Singular Value Thresholding algorithm is proposed. At first, a signal model of planar array is established based on Matrix Completion, which can be proved to meet Null Space Property. Then the Genetic Algorithm is used to optimize the sparse array, which is determined to reduce the Spectral Norm Error of Matrix Completion and make the array recovered closer to the full array. In the case of sparse array, the missing information is restored by using the theory of Singular Value Thresholding, and then the restored signal is used to design the digital beamformer weights. This algorithm significantly reduces the Spectral Norm Error and forms robust adaptive beam.

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Wei, Xue Ye, Bin Guo, De Yue Li, and Gzhong Yang. "A Modeling Method and I-V Characteristics for PV Array." Applied Mechanics and Materials 713-715 (January 2015): 1202–7. http://dx.doi.org/10.4028/www.scientific.net/amm.713-715.1202.

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The output characteristics of a PV array vary nonlinearly when the number of solar cells interconnected in series and parallel changes. The model and its parameters for a single solar cell are analyzed firstly. Then the models and there parameters for series, parallel circuits and series-parallel PV array are proposed respectively using circuit theory and observational method. Especial, the parameters of the equivalent circuits for PV arrays are characterized by a equation. A simulations are implemented to verify the three types of theoretical models and there parameters.Keywords: Solar cell; Model; PV array; I-V curve; Equivalent circuit

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29

Sun, Ya Jie, Yong Hong Zhang, Hui Qiang Tang, Cheng Shan Qian, and Shen Fang Yuan. "Research on Parallel PZT Phased Array Based Structural Health Monitoring in CFPR." Advanced Materials Research 753-755 (August 2013): 2343–46. http://dx.doi.org/10.4028/www.scientific.net/amr.753-755.2343.

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Phased array theroy can controll the Lamb wave beem steering in certain range by adding the time delay to the signals. Phased array theory is used to identify the damge in the structure. One dimensional PZT array is restricted in monitoring distance. Two parellel PZT sensors arrays are utilized to monitor the CFPR structure to extend the monitoring distance and to improve the precision of the damage locatilization. The experiment is done on the CFPR structure by using two parellel PZT arrays to detect the damage in the structure. The results of the experiment is shown on the mapped image. Gray-scale in the mapped image from dark to light corresponds to the signal amplitude from low to high. The highlight of the mapped image is the damage location in the structure. The monitoring results in the CFPR structure by two parellel PZT arrays is accurate and identical.

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30

Wilson, Ross. "Clare's Indistinct Array." Romanticism 17, no. 2 (July 2011): 148–59. http://dx.doi.org/10.3366/rom.2011.0020.

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31

Kristensen, Mads R. B., and James E. Avery. "Array streaming for array programming." International Journal of Computational Science and Engineering 17, no. 3 (2018): 263. http://dx.doi.org/10.1504/ijcse.2018.095848.

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32

Carey, William M., and Ronald A. Roy. "High‐frequency bubble scattering theory and array processing." Journal of the Acoustical Society of America 102, no. 5 (November 1997): 3211. http://dx.doi.org/10.1121/1.420972.

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33

Ghavami, M. "Wideband smart antenna theory using rectangular array structures." IEEE Transactions on Signal Processing 50, no. 9 (September 2002): 2143–51. http://dx.doi.org/10.1109/tsp.2002.801891.

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Li, Yong, Shuibao Qi, and M. Badreddine Assouar. "Theory of metascreen-based acoustic passive phased array." New Journal of Physics 18, no. 4 (April 18, 2016): 043024. http://dx.doi.org/10.1088/1367-2630/18/4/043024.

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35

Wilson Pearson, L. "Array theory via a Fourier-transform operational calculus." IEEE Antennas and Propagation Magazine 44, no. 4 (August 2002): 98–102. http://dx.doi.org/10.1109/map.2002.1043156.

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36

Sirignano, William A. "Advances in droplet array combustion theory and modeling." Progress in Energy and Combustion Science 42 (June 2014): 54–86. http://dx.doi.org/10.1016/j.pecs.2014.01.002.

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37

Lulec, Sevil Zeynep, Ulas Adiyan, Goksen G. Yaralioglu, Yusuf Leblebici, and Hakan Urey. "MEMS cantilever sensor array oscillators: Theory and experiments." Sensors and Actuators A: Physical 237 (January 2016): 147–54. http://dx.doi.org/10.1016/j.sna.2015.11.028.

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Rocca, P., F. Yang, L. Poli, and S. Yang. "Time-modulated array antennas – theory, techniques, and applications." Journal of Electromagnetic Waves and Applications 33, no. 12 (June 10, 2019): 1503–31. http://dx.doi.org/10.1080/09205071.2019.1627251.

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Zhou, Min, Fei He, Bow-Yaw Wang, Ming Gu, and Jiaguang Sun. "Array Theory of Bounded Elements and its Applications." Journal of Automated Reasoning 52, no. 4 (September 24, 2013): 379–405. http://dx.doi.org/10.1007/s10817-013-9293-6.

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40

Pan, Shi Bing, Cheng Jun Zhang, Hai Kun Wu, Lei Qian, Ming Xun Yu, and Run Hua Fan. "High Permeability of Z-Type Ferrite Sheets Directional Array." Materials Science Forum 898 (June 2017): 1645–48. http://dx.doi.org/10.4028/www.scientific.net/msf.898.1645.

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Z-type ferrite sheets were prepared by chemical precipitation method to investigate influences of directional arrays from the Z-type ferrite sheets on magnetic properties. The permeability of the ferrite directional arrays was obviously improved in the specific direction. Assuming that the intrinsic permeability of Z-type ferrite was existed, the magnetic permeability in array was calculated by the Maxwell-Garnett equation of effective media theory. The reason for the large difference between the theoretical calculation and measured value was also discussed.

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He, Zhengyao, Qiang Shi, and Shaoxuan Wu. "Investigation of Low-Sidelobe Beampattern Controlling Methods for Acoustic Transmitting Array of Underwater Vehicles." Polish Maritime Research 24, s2 (August 28, 2017): 103–10. http://dx.doi.org/10.1515/pomr-2017-0071.

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Abstract In underwater unmanned vehicles, complex acoustic transducer arrays are always used to transmitting sound waves to detect and position underwater targets. Two methods of obtaining low-sidelobe transmitting beampatterns for acoustic transmitting arrays of underwater vehicles are investigated. The first method is the boundary element model optimization method which used the boundary element theory together with the optimization method to calculate the driving voltage weighting vector of the array. The second method is the measured receiving array manifold vector optimization method which used the measured receiving array manifold vectors and optimization method to calculate the weighting vector. Both methods can take into account the baffle effect and mutual interactions among elements of complex acoustic arrays. Computer simulation together with experiments are carried out for typical complex arrays. The results agree well and show that the two methods are both able to obtain a lower sidelobe transmitting beampattern than the conventional beamforming method, and the source level for each transmitting beam is maximized in constraint of the maximum driving voltage of array elements being constant. The effect of the second method performs even better than that of the first method, which is more suitable for practical application. The methods are very useful for the improvement of detecting and positioning capability of underwater unmanned vehicles.

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Alhazov, Artiom, Rudolf Freund, Sergiu Ivanov, and Marion Oswald. "Relations between Control Mechanisms for Sequential Grammars1." Fundamenta Informaticae 181, no. 2-3 (August 4, 2021): 239–71. http://dx.doi.org/10.3233/fi-2021-2058.

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We extend and refine previous results within the general framework for regulated rewriting based on the applicability of rules in sequential grammars [3]. Besides the well-known control mechanisms as control graphs, matrices, permitting and forbidden rules, partial order on rules, and priority relations on rules we also consider the new variant of activation and blocking of rules as investigated in [1, 2, 4]. Moreover, we exhibit special results for strings and multisets as well as for arrays in the general variant defined on Cayley grids of finitely presented groups. Especially we prove that array grammars defined on Cayley grids of finitely presented groups using #-context-free array productions together with control mechanisms as control graphs, matrices, permitting and forbidden rules, partial order on rules, priority relations on rules, or activation and blocking of rules have the same computational power as such array grammars using arbitrary array productions.

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Marn, Jure, and Ivan Catton. "Analysis of Flow Induced Vibration Using the Vorticity Transport Equation." Journal of Fluids Engineering 115, no. 3 (September 1, 1993): 485–92. http://dx.doi.org/10.1115/1.2910164.

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Crossflow induced vibrations are the subject of this work. The analysis is two dimensional. The governing equations for fluid motion are solved using linearized perturbation theory and coupled with the equations of motion for cylinders to yield the threshold of dynamic instability for an array of cylinders. Parametric analysis is performed to determine the lowest instability threshold for a rotated square array and correlations are developed relating the dominant parameters. The results are compared with theoretical and experimental data for similar arrays and the discrepancies are discussed.

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Yang, Lijie, Ruirui Dang, Min Li, Kailong Zhao, Chunyi Song, and Zhiwei Xu. "A Fast Calibration Method for Phased Arrays by Using the Graph Coloring Theory." Sensors 18, no. 12 (December 7, 2018): 4315. http://dx.doi.org/10.3390/s18124315.

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Phased array radars are able to provide highly accurate airplane surveillance and tracking performance if they are properly calibrated. However, the ambient temperature variation and device aging could greatly deteriorate their performance. Currently, performing a calibration over a large-scale phased array with thousands of antennas is time-consuming. To facilitate the process, we propose a fast calibration method for phased arrays with omnidirectional radiation patterns based on the graph coloring theory. This method transforms the calibration problem into a coloring problem that aims at minimizing the number of used colors. By reusing the calibration time slots spatially, more than one omnidirectional antenna can perform calibration simultaneously. The simulation proves this method can prominently reduce total calibration time and recover the radiation pattern from amplitude and phase errors and noise. It is worth noting that the total calibration time consumed by the proposed method remains constant and is negligible compared with other calibration methods.

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Sakov, Pavel, and Peter R. Oke. "Objective Array Design: Application to the Tropical Indian Ocean." Journal of Atmospheric and Oceanic Technology 25, no. 5 (May 1, 2008): 794–807. http://dx.doi.org/10.1175/2007jtecho553.1.

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Abstract A simple, versatile, computationally efficient ensemble-based method for objectively designing an observation array is described. The method seeks to compute the observation array that minimizes the analysis error variance, according to Kalman filter theory. While most elements of the method have been described elsewhere, this paper attempts to present a simple, yet comprehensive, recipe for array design based on an ensemble of anomalies that represents the background error covariance. The versatility of the method is demonstrated through a series of applications to the tropical Indian Ocean (TIO). The first application uses model-generated fields of high-pass-filtered mixed layer depth to design an array to monitor intraseasonal variability. The second uses gridded observations of sea level anomaly to design an array to monitor intraseasonal-to-interannual variability. For both applications, the objectively designed arrays are compared to an array that will soon be implemented under the auspices of the Climate Variability and Predictability–Global Ocean Observing System (CLIVAR–GOOS) Indian Ocean Panel (CG-IOP). The authors conclude that the CG-IOP array produces results that compare well to the objectively designed arrays for intraseasonal variability, and observations to the east and northeast of the TIO and south of India are most important for resolving intraseasonal variability. The authors also find that observations near 9°S, where seasonal Rossby waves dominate, are important for observing seasonal-to-interannual variability. The described method for objective array design can be applied to a wide range of geophysical applications where time series of gridded modeled or observed fields are available.

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Peng, Ke-Ou, and Marcel R. de la Fonteijne. "Quasi-Paraxial Acoustic Field Approximation for Phased Arrays." Ultrasonic Imaging 11, no. 4 (October 1989): 260–72. http://dx.doi.org/10.1177/016173468901100404.

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The quasi-paraxial theory for phased arrays presented here can be used to estimate and analyze the acoustic field in the focal plane for a large scanning angle. The transient acoustic field is considered as the product of two terms that describe the time characteristics of the acoustic vibration over the array and the geometrical characteristics of the array, respectively. This method requires little computation time. The influence of special element shapes and functions that modulate the amplitude of the element vibration on the field distribution is also investigated.

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Rodr�guez, J. A., L. Landesa, J. L. Rodr�guez, F. Obelleiro, F. Ares, and A. Garc�a-Pino. "Pattern synthesis of array antennas with arbitrary elements by simulated annealing and adaptive array theory." Microwave and Optical Technology Letters 20, no. 1 (January 5, 1999): 48–50. http://dx.doi.org/10.1002/(sici)1098-2760(19990105)20:1<48::aid-mop13>3.0.co;2-p.

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Zhang, Quan, Guo-an Cheng, and Rui-ting Zheng. "The Internal Buckling Behavior Induced by Growth Self-restriction in Vertical Multi-walled Carbon Nanotube Arrays." MRS Advances 3, no. 45-46 (2018): 2815–23. http://dx.doi.org/10.1557/adv.2018.429.

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ABSTRACTThe internal buckling is a common phenomenon in the as-grown carbon nanotube arrays. It makes the physical properties of carbon nanotube array in experiment lower than that in theory. In this work, we analyzed the formation and evolution mechanism of the internal buckling based on quasi-static compression model, which is different from collective effect of the van der Waals interactions. The self-restriction effect and the different growth rate of carbon nanotubes verify the possibility of the quasi-static compression model to explain the morphology evolution of vertical carbon nanotube arrays, especially the phenomenon of the quasi-straight and bent carbon nanotubes coexisted in the array. We generalized the Euler beam to wave-like beam and explained the mechanism of high-mode buckling combined with the van der Waals interaction. The calculated result about the link between compressive stress and strain confirms with the stage of collective buckling in the quasi-static compression test of carbon nanotube array. Preparation of well-organized carbon nanotube arrays was strong evidence verified the effect of self-restriction in experiment.

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Li, Longjun, and Buhong Wang. "Design of Wideband Multifunction Antenna Array Based on Multiple Interleaved Subarrays." International Journal of Antennas and Propagation 2016 (2016): 1–7. http://dx.doi.org/10.1155/2016/1320726.

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A new Modified Iterative Fourier Technique (MIFT) is proposed for the design of interleaved linear antenna arrays which operate at different frequencies with no grating lobes, low-sidelobe levels, and wide bandwidths. In view of the Fourier transform mapping between the element excitations and array factor of uniform linear antenna array, the spectrum of the array factor is first acquired with FFT and its energy distributions are investigated thoroughly. The relationship between the carrier frequency and the element excitation is obtained by the density-weighting theory. In the following steps, the element excitations of interleaved subarrays are carefully selected in an alternate manner, which ensures that similar patterns can be achieved for interleaved subarrays. The Peak Sidelobe Levels (PSLs) of the interleaved subarrays are further reduced by the iterative Fourier transform algorithm. Numerical simulation results show that favorable design of the interleaved linear antenna arrays with different carrier frequencies can be obtained by the proposed method with favorable pattern similarity, low PSL, and wide bandwidths.

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Hall, Philip. "Vortex–wave interaction arrays: a sustaining mechanism for the log layer?" Journal of Fluid Mechanics 850 (July 2, 2018): 46–82. http://dx.doi.org/10.1017/jfm.2018.425.

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Vortex–wave interaction theory is used to describe new kinds of localised and distributed exact coherent structures. Starting with a localised vortex–wave interaction state driven by a single inviscid wave, regular arrays of interacting vortex–wave states are investigated. In the first instance the arrays described are operational in an infinite uniform shear flow; we refer to them as ‘uniform shear vortex–wave arrays’. The basic form of the interaction remains identical to the canonical one found by Hall & Smith (J. Fluid Mech., vol. 227, 1991, pp. 641–666) and subsequently used to describe exact coherent structures by Hall & Sherwin (J. Fluid Mech., vol. 661, 2010, pp. 178–205). Thus in each cell of a vortex–wave array a roll stress jump is induced across the critical layer of an inviscid wave riding on the streak part of the flow. The theory is extended to arbitrary shear flows using a nonlinear Wentzel–Kramers–Brillouin–Jeffreys or ray theory approach with the wave–roll–streak field operating on a shorter length scale than the mean flow. The evolution equation governing the slow dynamics of the interaction turns out to be a modified form of the well-known mean equation for a turbulent flow, and its particular form can be interpreted as a ‘closure’ between the small and large scales of the flow. If the array structure is taken to be universal, in the sense that it applies to arbitrary shear flows, then the array takes on a form which supports a logarithmic mean velocity profile trapped between what can be identified with the ‘wake region’ and a ‘buffer layer’ well known in the context of wall-bounded turbulent flows. The many similarities between the distributed structures described and wall-bounded turbulence suggest that vortex–wave arrays might be involved in the self-sustaining process supporting the log layer. The modification of the mean profile within each cell of the array leads to ‘staircase’-like streamwise velocity profiles similar to those observed experimentally in turbulent flows. The wave field supporting the ‘staircase’ is concentrated in critical layers which can be associated with the shear layer structures that have been attributed by experimentalists to be the mechanism supporting the uniform-momentum zones of the staircase.

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Journal articles on the topic 'Array theory'

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