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Periodicity in Rectangular Arrays [article]

Guilhem Gamard, Gwenaël Richomme, Jeffrey Shallit, Taylor J. Smith
2016 arXiv   pre-print
Finally, we show that one can test primitivity and compute the primitive root of an array in linear time.  ...  We discuss several two-dimensional generalizations of the familiar Lyndon-Schutzenberger periodicity theorem for words.  ...  Acknowledgments Funded in part by a grant from NSERC. We are grateful to the referees for several suggestions.  ... 
arXiv:1602.06915v2 fatcat:dyma7uy5gfhetctk4dnymfoxj4

Two-Dimensional Periodicity in Rectangular Arrays

Amihood Amir, Gary Benson
1998 SIAM journal on computing (Print)  
In this paper, we de ne and analyze two-dimensional periodicity in rectangular arrays. One de nition of string periodicity is that a periodic string can self-overlap in a particular way.  ...  In addition, our algorithms nd a witness proving that the array does not self overlap in any other location.  ...  But, a rectangular array is not in nite and may cut a unit cell in many di erent ways at its edges.  ... 
doi:10.1137/s0097539795298321 fatcat:ndr4tnxivbbujlv55krbaovuwa

Tunable rectangular array illuminator in periodically poled LiNbO3 crystal

Qiuying Li Qiuying Li, Juan Huo Juan Huo, Xiaohui Zhao Xiaohui Zhao, Xianfeng Chen Xianfeng Chen
2014 Chinese Optics Letters (COL)  
An electro-optic tunable rectangular array illuminator in one-dimensional periodically poled LiNbO3 (PPLN) crystal is presented experimentally which result is in good agreement with results from simulation  ...  The intensity distribution of rectangular array could be precisely modulated.  ...  In this letter, we realized a rectangular array illuminator that was made by a phase grating which was a one-dimensional (1D) periodically poled LiNbO 3 (PPLN) with an external electric field.  ... 
doi:10.3788/col201412.050701 fatcat:wg6oksnwifb3hij3s2crb3jrw4

COMPUTATION OF EFFECTIVE PROPERTIES IN TWO-PHASE PIEZOCOMPOSITES WITH A RECTANGULAR PERIODIC ARRAY

Ransés Alfonso Rodríguez, Julián Bravo Castillero, Renald Brenner, David Guinovart Sanjuán, Raúl Guinovart Díaz, Reinaldo Rodríguez Ramos
2014 Visión electrónica  
The cross-sections of the fibers are circular and are centered in a periodic array of rectangular cells. The composite state is anti-plane shear piezoelectric.  ...  Based on the Asymptotic Homogenization Method, the electromechanical global behavior of a two-phase piezoelectric unidirectional periodic fibrous composite is investigated.  ...  The periodic distribution of the fibers follows a rectangular array, as observed in Figure 1 .  ... 
doaj:22a3e6f3c8b841c8b496eeb7e0f62802 fatcat:kxnrriwrkfenfdrcsbpxmxg5tu

Longitudinal Permeability of Spatially Periodic Rectangular Arrays of Circular Cylinders I. A Single Cylinder in the Unit Cell

V. Mityushev, P.M. Adler
2002 Zeitschrift für angewandte Mathematik und Mechanik  
We study the longitudinal permeability of a spatially periodic rectangular array of circular cylinders, when a Newtonian fluid is flowing at low Reynolds number along the cylinders.  ...  The major advantage of this technique is that the permeability of the array can be expressed analytically in terms of the radius of the cylinders and of the aspect ratio of the unit cell.  ...  Analytical and numerical results For rectangular array an analogous formula can be written, but it is too long.  ... 
doi:10.1002/1521-4001(200205)82:5<335::aid-zamm335>3.0.co;2-d fatcat:2bdxsktsavaszco3vzaq5prw6e

Asymptotic high-frequency Green's function for a large rectangular planar periodic phased array of dipoles with weakly tapered excitation in two dimensions

F. Mariottini, F. Capolino, S. Maci, L.B. Felsen
2005 IEEE Transactions on Antennas and Propagation  
and scattering from weakly amplitude-tapered rectangular periodic structures.  ...  This paper deals with the derivation and physical interpretation of a uniform high-frequency representation of the Green's function for a large planar rectangular phased array of dipoles with weakly varying  ...  STATEMENT OF THE PROBLEM Consider a large rectangular periodic array of linearly phased dipoles located in the plane (Fig. 1) .  ... 
doi:10.1109/tap.2004.841321 fatcat:plfepiwrynaipj26holbz6kjmi

Numerical Analysis of Turbulent Flow in a Rectangular Duct with Periodic Arrays of Blocks
三次元ブロックを有する矩形断面管路内の乱流解析

Hitoshi SUGIYAMA, Shota TAKESHIMA
2004 TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series B  
Numerical analysis has been performed for three-dimensional developing turbulent flow in a rectangular cross sectioned duct with periodic arrays of blocks by using an algebraic Reynolds stress model.  ...  Upper and bottom wall of straight duct with rectangular cross section are composed of many blocks, which are periodically located along the flow direction.  ...  成 され て い る.両 計 算 結 果 も,零 等 値 線 を 予測 し て い るが,管 路 中 央 部 近 傍 に形 成 さ れ る零 等 値 線 は, 下 流 に発 達 す る に従 い 消滅 す る傾 向 を示 して い る.こ れ は,せ ん断 応 力u1u2が 主流 方 向速 度 の 水 平 方 向 の 速 度 こう配値 に よ り大 き く左 右 Fig. 1 1 Fig. 1 Rectangular  ... 
doi:10.1299/kikaib.70.1132 fatcat:bqt2ozxiu5ewroikk36kurpy4i

Effect of Wood's anomalies on the profile of extraordinary transmission spectra through metal periodic arrays of rectangular subwavelength holes with different aspect ratio

Yu-Wei Jiang, Lawrence D. Tzuang, Yi-Han Ye, Yi-Ting Wu, Ming-Wei Tsai, Chia-Yi Chen, Si-Chen Lee
2009 Optics Express  
By designing the rectangular hole arrays in a rectangular lattice, the Wood's anomaly can be shifted far apart from the transmission peak, the real localized resonance peak wavelength was identified and  ...  The extraordinary transmission through silver film perforated with rectangular hole array with different aspect ratio was investigated.  ...  the rectangular hole array with aspect ratio of 9, i.e., the length is 12.7 µm and the width is 1.4 µm , in a rectangular lattice with the fixed period of 15 µm along x axis and the different periods from  ... 
doi:10.1364/oe.17.002631 pmid:19219166 fatcat:n4rgdbsyzbeofniof7rurw6ufm

Temperature dependence and mechanisms of vortex pinning by periodic arrays of Ni dots in Nb films

J. I. Martín, M. Vélez, A. Hoffmann, Ivan K. Schuller, J. L. Vicent
2000 Physical Review B (Condensed Matter)  
This same temperature dependence is found for the critical current at the first matching field with a rectangular array of dots.  ...  Moreover, for the rectangular dot array, the temperature dependence of the crossover between the low field regime with a rectangular vortex lattice to the high field regime with a square configuration  ...  and the temperature dependence of periodic pinning in samples with rectangular arrays is discussed and the conclusions are presented in section V.  ... 
doi:10.1103/physrevb.62.9110 fatcat:pnh7ohfm3jbi3hd3wfvkdrtq5a

Observation of vortex matching phenomena in antidot arrays of NbN thin films

A.D. Thakur, S. Ooi, S.P. Chockalingham, John Jesudasan, P. Raychaudhuri, K. Hirata
2010 Physica. C, Superconductivity  
We report vortex matching phenomenon in rectangular antidot array fabricated on epitaxial NbN thin film. The antidot array was fabricated using Focussed Ion Beam milling technique.  ...  The magneto-transport measurements points to a period doubling transition at higher magnetic field for rectangular lattices.  ...  SUMMARY We observe the vortex matching effect phenomena in rectangular antidot array sample fabricated on NbN thin film.  ... 
doi:10.1016/j.physc.2010.02.008 fatcat:ktslelohufa7rdksg6np3wreku

Enhancement of synchronized vortex lattice motion in hybrid magnetic/amorphous superconducting nanostructures

D. Perez de Lara, A. A. Alija, E. M. Gonzalez, J. I. Martin, M. Velez, J. M. Colino, J. V. Anguita, J. L. Vicent
2009 Applied Physics Letters  
The interplay between the random intrinsic pinning of the superconducting films and the periodic pinning of the array govern the vortex lattice configurations.  ...  Different vortex lattice configurations are obtained with the same array unit cell. These different vortex lattices occur at matching conditions between the vortex lattice and the array unit cell.  ...  vortices in comparison with the until now known, most favorable matching condition for this rectangular array, i.e., rectangular vortex lattice 600ϫ 400 nm 2 .  ... 
doi:10.1063/1.3103560 fatcat:yx2qohciuza7vdc66by7trawfy

Comparative Analysis of Measured and Simulated Performance of Printed Excited Rectangular Log Periodic Array Patch

O. Olabisi, A.O. Adeniran, O.S. Ajao, S.O. Areo
2019 Zenodo  
A gain of 3.47dB gain of 2.8dB for rectangular, directivity of 7.06 dB efficiency of 1.038% and resonant frequency of 3.35GHz respectively.  ...  This paper described the design, simulation, construction using iron on glossy method and comparative analysis of simulated and measured parameters of inset feed seven elements log periodic microstrip  ...  Fig. 4 : 4 The Input and Output Return Loss for Rectangular Log Periodic Array Microstrip Antenna. Fig. 5 : 5 Smith Chart for the Input Impedance.  ... 
doi:10.5281/zenodo.3589656 fatcat:ao57lzbnanf3fkxmy2fvweic6q

Extraordinary transmission and left-handed propagation in miniaturized stacks of doubly periodic subwavelength hole arrays

Miguel Beruete, Mario Sorolla, Miguel Navarro-Cía, Francisco Falcone, Igor Campillo, Vitaliy Lomakin
2007 Optics Express  
to the areas required in the case of free standing rectangular hole arrays.  ...  Metallic plates embedded between dielectric slabs and perforated by rectangular arrays of subwavelength holes with a dense periodicity in one of the directions support extraordinary transmission (ET) phenomena  ...  LHP through a stack of rectangular hole arrays A bulk PhC is constructed by periodically stacking the rectangular hole arrays (Fig. 1(d) ).  ... 
doi:10.1364/oe.15.001107 pmid:19532338 fatcat:6jn5xsp4gzgjlmllnoe4tq5oz4

Taper array in silica glass for beam splitting

Zehua Xia, Yan Li, Yanhua Han, Meng Ge, Jingfu Ye, Duo Deng, Benyang Wang, Jianmin Gao, Shiliang Qu
2016 Optical materials (Amsterdam)  
The experimental results show that the taper periodic microstructures in silica glass are uniform and smooth, and the tapers can divide the incident light into beam array.  ...  Then the heat treatment should be used to reshape the rectangular cylinders into taper array.  ...  Finally, the rectangular cylinders array could be reshaped and the taper array was realized in silica glass.  ... 
doi:10.1016/j.optmat.2016.01.001 fatcat:umgcda7yavgf3gyeiw4fxrslba

Enhanced terahertz transmission through a periodic array of tapered rectangular apertures [article]

Koijam Monika Devi, Amarendra K. Sarma, Gagan Kumar
2016 arXiv   pre-print
We numerically analyse extraordinary terahertz transmission properties of an array of rectangular shaped apertures perforated periodically on a thin metal film.  ...  We compare results of transmission with the rectangular shaped apertures of same parameters and observe a significant increase in the transmission for the tapered case.  ...  Acknowledgement The authors would like to thank the Board of Research in Nuclear Sciences (BRNS), Project no: PHY1P1GK102 for their financial assistance.  ... 
arXiv:1602.08601v1 fatcat:tczsymrkdrakdcidnplua37zje
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